Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions: Towards Non-invasive Glucose Sensing (Springer Theses) 3030761789, 9783030761783

Table of contents :
Supervisors’ Foreword
Foreword
Parts of this thesis have been published in the following articles.
Journals
Conferences
Funding
Acknowledgements
Contents
Acronyms
Glossary of Symbols
1 Introduction
1.1 Introduction
1.2 Motivation
1.3 Objectives and Contributions
1.4 Thesis Structure
1.5 Framework of the Thesis
1.6 Publications
References
2 State of the Art
2.1 Dielectric Dispersion Characterization
2.1.1 Dielectric Relaxations and Resonances
2.1.2 Dielectric Characterization Methods
2.2 Microwave Resonators: Fundamentals
2.3 Application to Diabetes
2.3.1 Diabetes Mellitus and Its Complications
2.3.2 Glycemia Measurement Systems
2.3.3 Continuous Glycemia Measurement
2.3.4 Approaches to Non-invasive Glycemia Measurements
2.3.5 Microwave Sensors for Non-invasive Glycemia Measurement
References
3 Dielectric Characterization of Water–Glucose Solutions
3.1 Introduction
3.2 Materials and Methods
3.3 Measurements
3.4 Results
3.5 Discussion
3.6 Conclusions
References
4 Glucose Concentration Detection in Aqueous Solutions with Microwave Sensors
4.1 Introduction
4.2 Materials and Methods
4.3 Measurements
4.4 Results
4.5 Discussion
4.6 Conclusions
References
5 Glucose Concentration Detection in Biological Solutions with Microwave Sensors
5.1 Introduction
5.2 Materials and Methods
5.3 Measurements
5.4 Results
5.5 Discussion
5.6 Conclusions
References
6 Microwave Resonator for NIBGM: Proof of Concept
6.1 Introduction
6.2 Materials and Methods
6.3 Measurements
6.4 Results
6.5 Discussion
6.6 Conclusions
References
7 Microwave Sensors for Glucose Detection: Open Lines
7.1 Introduction
7.2 Simplification of the Electronic System
7.3 Sensitivity
7.4 Selectivity
7.5 Discussion
7.6 Conclusions
References
8 Conclusions
8.1 Summary and Conclusions
8.2 Future Scope
References
Appendix A Fitting the Measured Raw Data to a Quadratic Function to Obtain fr, S21max and BW
Appendix B Calculation of the Instrumental Error in the Unloaded Quality Factor
About the Author

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Carlos G. Juan

Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions Towards Non-invasive Glucose Sensing

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses may be nominated for publication in this series by heads of department at internationally leading universities or institutes and should fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder (a maximum 30% of the thesis should be a verbatim reproduction from the author’s previous publications). • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to new PhD students and scientists not expert in the relevant field. Indexed by zbMATH.

More information about this series at http://www.springer.com/series/8790

Carlos G. Juan

Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions Towards Non-invasive Glucose Sensing Doctoral Thesis accepted by Miguel Hernández University of Elche, Spain

Author Dr. Carlos G. Juan Department of Systems Engineering and Automation Miguel Hernández University of Elche Elche, Spain

Supervisors Prof. José María Sabater-Navarro Department of Systems Engineering and Automation Miguel Hernández University of Elche Elche, Spain Assoc. Prof. Enrique Bronchalo Department of Communications Engineering Miguel Hernández University of Elche Elche, Spain

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-76178-3 ISBN 978-3-030-76179-0 (eBook) https://doi.org/10.1007/978-3-030-76179-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Andrea, who constantly provided me with the required support and encouragement to get up one hour earlier every day for writing this thesis.

Supervisors’ Foreword

We are greatly honored to introduce the doctoral thesis by Dr. Carlos G. Juan, accepted for publication within Springer Theses book series and awarded with a prize for outstanding original research. Dr. Juan started collaborating with our research group at Miguel Hernández University of Elche, Elche, Spain, during the last years of his M.Sc. in telecommunication engineering. After successfully defending his master’s thesis, obtaining the highest qualification, he joined our group in 2014 as Ph.D. student within the Doctoral Program in Industrial and Telecommunication Technologies. In the very early stages of his Ph.D., he gained his own funds in the framework of the FPU program, a competitive 4-year predoctoral grant from the Spanish Government, through the project Glucose Concentration Detection in Aqueous and Biological Solutions with Microwave Sensors. In addition, during his Ph.D. he also actively participated in the following bioengineering research projects: Supervising and Surgery Field Cooperative Control Interface for Hand-assisted Laparoscopic Surgery (funded by the Ministry of Economy and Competitiveness, Spain), CRANEEAL—System for Brain-shift Prediction Based upon Non-invasive Distance Measurements (funded by Spanish Research State Agency and European Research Development fund), and Development and Validation of a Non-invasive Glucose Measurement System (funded by FISABIO—Foundation for the Promotion of Health and Biomedical Research of Valencia Region). Furthermore, he also kept close collaboration with Lab-STICC group at Université de Bretagne Occidentale, Brest, France, where he conducted research stays in 2016 and 2018, and he finally joined the group as a postdoctoral fellow in 2020. He successfully defended his doctoral thesis on November 2019 and received the highest qualification (cum laude). Dr. Juan’s thesis gathers the results of all this above-mentioned work, and it thereby includes significant original scientific contributions which represent remarkable advancement in the field of the development of glucose content sensors with microwave techniques. This research and the results thereof have been published in highly ranked international journals and conferences. This book shows a comprehensive documentation of Dr. Juan’s work covering the full research cycle. After

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Supervisors’ Foreword

introducing the interest, motivation, and framework of the work, the theoretical foundations are deeply discussed and the topic is placed from the scientific point of view. Then, the main research works are presented in a gradually progressing approach, from the physical phenomena characterization to the design guidelines of the sensors and their development and assessment in simple and later more complex biological environments, including real clinical contexts. The discussion, conclusions, and open lines are also deeply addressed in the final chapters. Specifically, this book offers a painstaking discussion upon the application of microwave sensors for the glucose concentration detection in aqueous and biological solutions. During the last years, some attempts have been made in the pursue of a non-invasive blood glucose level measuring device. Among the studied principles, microwave technology has been shown to present convenient penetration depths for non-invasive measurements in the human skin and other biological tissues. With a proper configuration, these devices can achieve electrical responses sensitive to the glucose content of the medium being measured. Dr. Juan’s thesis shows a thorough assessment of the feasibility of such approach, deepening on the sensor designs based on open-loop resonators, with the novelty of analyzing the unloaded quality factor as the main measurement parameter. Also, special emphasis is placed on its use in real application contexts and on the open lines to be faced in the near future. Elche, Spain December 2020

Prof. José María Sabater-Navarro Assoc. Prof. Enrique Bronchalo

Foreword

Bioengineering research is focused on carrying out research activities that pursue the generation of new knowledge and the development of technological solutions aimed at understanding and controlling human biological systems and their relationship with the environment. As a result, the analysis and evaluation of bodily functions and structures are contemplated, as well as the compensation of certain deficits, dependencies, and pathologies. This work includes the capture of signals and their processing, the subsequent analysis of the data derived from them, as well as any other type of biological data present and the modeling of biosystems. In different phases of this process, knowledge from various sources can be integrated to guide the analysis of the data more accurately or complement the knowledge resulting from it. The monograph written by Dr. Carlos G. Juan is a contribution in the area of bioengineering, which has been receiving a growing deal of attention by the research community in the latest few years. The contents are focused on the study of the appropriate measurement techniques to monitor, in a non-invasive way, glucose concentration in aqueous and biological solutions. It thus works toward a solution that facilitates the full and harmonious functioning of human organisms affected by diabetes. Special emphasis is placed on the validation of the proposed technologies in real application contexts. Remarkably, the monograph is based on the first author’s doctoral thesis, awarded for best Ph.D. thesis in bioengineering during the fourth edition of the award call organized by the Bioengineering group of the Comit´e Espa˜nol de Autom´atica (CEA), the Spanish Committee of Automatic Control, in 2020. This annual award is aimed at recognizing the outstanding Ph.D. research in the bioengineering field. Participation requires at least one of the theses’ supervisors to be a partner of CEA and a member of the Bioengineering group. The jury is composed of three well-known doctors in the field: Two of them are partners of CEA, and the third one is a foreign professor. A total number of 4 Ph.D. theses, examined in 2019, were submitted to this fourth edition in 2020. Notably, their authors show altogether a scientific production of about 40 publications in international indexed journals, with more than 20 works published in the top-quartile journals of their categories. ix

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Foreword

Carlos G. Juan’s Ph.D. thesis was selected by the Bioengineering group of CEA as the best among other excellent candidates. His outstanding Ph.D. work clearly deserves the label “the best of the best,” which is also the Springer Theses motto. Through this publication, we hope that Carlos’ work reaches a large international audience and becomes a valuable source of information and inspiration for other students working in the bioengineering field. On behalf of CEA, we wish Carlos to continue his outstanding career and to keep his genuine enthusiasm for science. Madrid, Spain

Assoc. Prof. Eduardo Rocon Coordinator of the Bioengineering Group of CEA Best Thesis Award

Parts of this thesis have been published in the following articles. Journals C.G. Juan, E. Bronchalo, B. Potelon, C. Quendo, E. Ávila-Navarro, and J.M. SabaterNavarro. (2019). Concentration measurement of microliter-volume water– glucose solutions using Q factor of microwave sensors. IEEE Transactions on Instrumentation and Measurement, 68(7), 2621–2634. C.G. Juan, E. Bronchalo, B. Potelon, C. Quendo, and J.M. Sabater-Navarro. (2019). Glucose concentration measurement in human blood plasma solutions with microwave sensors. Sensors, 19(17), 3779. C.G. Juan, H. García, E. Ávila-Navarro, E. Bronchalo, V. Galiano, Ó. Moreno, D. Orozco, and J.M. Sabater-Navarro. (2019). Feasibility study of portable microwave microstrip open-loop resonator for non-invasive blood glucose level sensing: proof of concept. Medical & Biological Engineering & Computing, 57(11), 2389–2405. C.G. Juan, E. Bronchalo, G. Torregrosa, E. Ávila, N. García, and J.M. SabaterNavarro. (2017). Dielectric characterization of water glucose solutions using a transmission/reflection line method. Biomedical Signal Processing and Control, 31(1), 139–147. C.G. Juan, E. Bronchalo, G. Torregrosa, A. Garcia, and J.M. Sabater-Navarro. (2015). Microwave microstrip resonator for developing a non-invasive glucose sensor. International Journal of Computer Assisted Radiology and Surgery, 10(S1), 172–173. Conferences C.G. Juan, B. Potelon, C. Quendo, E. Bronchalo, and J.M. Sabater-Navarro (2019). Highly-sensitive glucose concentration sensor exploiting inter-resonators couplings. In Proceedings of the 49th European Microwave Conference (EuMC), Paris, France (pp 662–665). H. García, C.G. Juan, E. Ávila-Navarro, E. Bronchalo, and J.M. Sabater-Navarro (2019). Portable device based on microwave resonator for noninvasive blood glucose monitoring. In Proceedings of the IEEE 41st International Engineering in Medicine and Biology Conference (EMBC), Berlin, Germany (pp 1115–1118). Funding The work by Carlos G. Juan throughout the development of this doctoral thesis has been supported by the Spanish Ministry of Education, Culture and Sport (MECD) through the Ph.D. and University Lecturers Training Program FPU, with grant number FPU14/00401 (2015–2019).

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Parts of this thesis have been published in the following articles.

In addition, the mobility actions and international stays made by the author during this period were funded with the following grants: • Mobility of International Doctoral Students in Brittany, Incoming Mobility Grants, by Université de Bretagne Occidentale, Brest, France, with grant number EIO-Spring2018-1 (2018). • Mobility Funds for Short Stays and Temporary Transfers for Ph.D. and University Lecturers Training Program Grant Holders, by the Spanish Ministry of Education, Culture and Sport (MECD), with grant number EST17/00205 (2018). • Miguel Hernández University of Elche International Mobility Funds, by Miguel Hernández University of Elche, Elche, Spain, with grant number UMH0707/16 (2016).

Acknowledgements

I wish to thank my thesis supervisors, José María and Enrique, for all the help and support placed on me. Not only did they show me to do research, but also to love research. During these years, they have provided me with valuable advice for my academic, professional, and personal life. Thank you very much for all your time, all your effort, all your guidance, and, mainly, all your patience. I would also like to convey my deep gratitude to my colleagues in the Neuroengineering Biomedical Research group for spending so many hours working together, sharing suggestions, points of view, collaborations, and precious mutual help. I am also grateful to all the members in the Department of Systems Engineering and Automation, Department of Communications Engineering, and Department of Materials Science, Optics and Electronic Technology, and all the people in the Miguel Hernández University of Elche who have helped me, supported me, or collaborated with me during this period. I wish to especially thank Dr. Benjamin Potelon and all my colleagues in the University of Brest for welcoming me in such a warm manner during my stays there, periods that I recall so fondly. Thank you for sharing with me invaluable knowledge and tools that have remarkably helped me evolving as a researcher and which have played a fundamental role in this thesis. I would like to thank my family, Carlos, Mari Carmen, and Javier, as well as Puri and Miguel for supporting me so warmly during all this time and, most importantly, for believing in me. I wish also to thank the rest of my family and my friends for all the encouragement and affection placed on me. Finally, I wish to sincerely thank you, Andrea, because it is you, always you, and only you. Thank you very much for putting up with me during all these years, for becoming my strength in the moments of weakness, for being my role model, and for showing me what happiness really is. And, of course, I could not finish these lines without thanking those four-legged friends with the lovely power of instantly brightening a dark day.

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Acknowledgements

The work carried out during the development of this thesis has been funded by the Spanish Ministry of Education, Culture and Sport (MECD) through the grant FPU14/00401. In addition, some parts of the work were funded by MECD, Université de Bretagne Occidentale, and Miguel Hernández University of Elche by means of grants EST17/00205, EIO-Spring2018-1, and UMH0707/16, respectively.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Framework of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 4 6 8 9 12

2 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Dielectric Dispersion Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Dielectric Relaxations and Resonances . . . . . . . . . . . . . . . . . . 2.1.2 Dielectric Characterization Methods . . . . . . . . . . . . . . . . . . . . 2.2 Microwave Resonators: Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Application to Diabetes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Diabetes Mellitus and Its Complications . . . . . . . . . . . . . . . . . 2.3.2 Glycemia Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Continuous Glycemia Measurement . . . . . . . . . . . . . . . . . . . . 2.3.4 Approaches to Non-invasive Glycemia Measurements . . . . . 2.3.5 Microwave Sensors for Non-invasive Glycemia Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 17 17 28 33 43 44 46 47 49

3 Dielectric Characterization of Water–Glucose Solutions . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69 69 71 78 79 82 86 87

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Contents

4 Glucose Concentration Detection in Aqueous Solutions with Microwave Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91 91 99 109 118 122 125 126

5 Glucose Concentration Detection in Biological Solutions with Microwave Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

133 133 135 136 137 143 149 151

6 Microwave Resonator for NIBGM: Proof of Concept . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

155 155 159 171 174 177 181 183

7 Microwave Sensors for Glucose Detection: Open Lines . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Simplification of the Electronic System . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

189 189 190 204 211 220 222 223

8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

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Appendix A: Fitting the Measured Raw Data to a Quadratic Function to Obtain f r , S21max and BW . . . . . . . . . . . . . . . . . . . 233 Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

Acronyms

AA AC ADS BDS BGL BW CC CD CGM DC DS DUT HFSS HN I/O IDF IEEE ISF JCR LA MCU MUT NIBGM NRW OGTT PLA PTFE RF SMA

Ascorbic acid Alternating current Advanced design system Broadband dielectric spectroscopy Blood glucose level Bandwidth Cole–Cole Cole–Davidson Continuous glucose monitoring Direct current Dielectric spectroscopy Dielectric under test High-frequency structure simulator Havriliak–Negami Input/output International Diabetes Federation Institute of Electrical and Electronics Engineers Interstitial fluid Journal Citation Reports Lactic acid Microcontroller unit Material under test Non-invasive blood glucose monitoring Nicolson–Ross–Weir Oral glucose tolerance test Polylactic acid Polytetrafluoroethylene Radio frequency Surface-mount assembly

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T/R TDS VCO VNA

Acronyms

Transmission/reflection Time-domain dielectric spectroscopy Voltage-controlled oscillator Vector network analyzer

Glossary of Symbols

α β γ   in (ω) δ δ(p) δ(ω) E E0 Eeff Er Es E∞ E*(ω) Er *(ω) λ λ0 λr μ μ0 σ σ*(ω) τ τ meas τ theor φ(t) (t) χ ω

Attenuation constant Phase constant Propagation constant Reflection coefficient Input reflection coefficient Frequency-dependent reflection coefficient Penetration depth Fractional bandwidth at the power fraction p Phase difference for the angular frequency ω Dielectric permittivity Dielectric permittivity of vacuum Effective relative dielectric permittivity Relative dielectric permittivity Low-frequency limit of the relative dielectric permittivity High-frequency limit of the relative dielectric permittivity Complex, frequency-dependent dielectric permittivity Complex, frequency-dependent relative dielectric permittivity Wavelength Free space wavelength Wavelength at the resonant frequency Magnetic permeability Magnetic permeability of vacuum Conductivity Complex, frequency-dependent conductivity Characteristic relaxation time Measured group delay Theoretical group delay Relaxation function of the dielectric polarization Dielectric response function Electric susceptibility Angular frequency xxi

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ωr [S] B c C C*(ω)  D D0 D*(t) D*(ω) E E0 E*(t) E*(ω) f fr G I I*(ω) j k L P P Q Qe QL Qu R SQ SS1 SS2 Sk t T T(ω) tan δ U UE UM v V vp V*(ω)

Glossary of Symbols

Resonant angular frequency Scattering matrix Susceptance Speed of light in vacuum Capacitance Complex, frequency–dielectric capacitance Electric displacement vector Electric displacement amplitude Strength of the complex, time-varying electric displacement Strength of the complex, frequency-dependent electric displacement Electric field Electric field amplitude Strength of the complex, time-varying electric field Strength of the complex, frequency-dependent electric field Frequency Resonant frequency Conductance Current Phasor sinusoidal current Electric current density Coupling factor Inductance Power Polarization Quality factor External quality factor Loaded quality factor Unloaded quality factor Resistance Sensitivity for the unloaded quality factor Sensitivity for the minimum of S11 Sensitivity for the maximum of S22 Sensitivity for the coupling factor Time Transmission coefficient Frequency-dependent transmission coefficient Loss tangent Energy stored Average electric energy Average magnetic energy Propagation speed Voltage Phase velocity Phasor sinusoidal voltage

Glossary of Symbols

Y Y0 Y in Z Z(ω) Z0 Zin

Admittance Characteristic admittance Input admittance Impedance Frequency-dependent impedance Characteristic impedance Input impedance

xxiii

Chapter 1

Introduction

If we knew what it was we were doing, it would not be called research, would it? Albert Einstein

1.1 Introduction Sensors based upon microwave techniques constitute an intense research field which has shown considerable activity during the last decades. The progresses achieved have been successfully used to provide for many different applications. These sensors exploit the phenomena derived from the interaction between the electromagnetic waves and the media. Thus, the propagation of the waves through a medium provokes reorientation of the molecules and ions of the medium, accounting for changes in its polarization. These changes actually depend on the dielectric permittivity of the medium, which is a frequency-dependent parameter intrinsic to every material. The propagation of the electromagnetic waves will therefore depend on the permittivity of the medium. Consequently, a sensor able to characterize the propagation will allow to characterize the permittivity as well, identifying the medium and its properties. In this sense, microwave technology is widely used due to its dependence on the permittivity of the surrounding media, among other features. This technology has been applied to many contexts. An interesting one is the field of biosensors. The electromagnetic waves show the advantage of being able to travel through the tissues in order to react with elements inside the body. This can be done without the need of inserting anything inside the body, in a non-invasive way, and without any undesired after-effect, provided that the suitable wave propagation is achieved [1, 2]. The differences found between the permittivities of many biological tissues, and even between samples of the same tissue with different characteristics (e.g. healthy versus cancerous tissue), suggest the use of microwave sensors for tissue identification, characterization and screening. A widely studied application field is microwave imaging systems, aimed to the detection and localization of cancerous tissue [3–8], due to the increment of permittivity in tumorous tissues (up to tenfold © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_1

1

2

1 Introduction

compared to healthy tissue [9]). Some other popular applications are the detection of concentration of particles or specific cells for screening of unhealthy ranges [10, 11], microfluidic biological liquids characterization [12, 13], or immunosensing [14]. Due to the variety of applications, different technologies have been investigated in the scientific literature, like wideband antennas [8], coaxial line methods [15], capacitor techniques [10], interferometry [16], frequency synthesizer methods [17] or CMOS microwave sensors [18, 19]. However, one of the most employed techniques is based on the use of microwave resonators in different configurations [20–22]. Effectively, microwave sensors based on resonator techniques are capable of measuring the permittivity of the materials [23], and they find an interesting application in characterizing lossy organic liquids [24]. This dissertation offers an in-depth study and discussion on the development of microwave sensors based upon resonator techniques for glucose concentration detection in aqueous and biological solutions. The fundamental principle is found in the changes of the permittivity of lossy solutions due to variations in their glucose concentration, which will be studied in the following chapters. Hence, microwave resonator sensor techniques will be analyzed and applied to track those permittivity variations and relate them to the actual glucose concentration of the solution. This thesis is therefore closely related to the diabetes management context. As it will be discussed later, people with diabetes need to constantly self-monitor their blood glucose level (BGL). Since the current methods are invasive and uncomfortable, research is actively being conducted considering different techniques to measure BGL in a more convenient way, aiming at non-invasive and continuous measuring. In this sense, microwave sensors provide a convenient tool due to several reasons, like their dependence on the permittivity of the surrounding media or their penetration depth. Thus, their thorough study for this field of application is interesting and advisable. This document shows the work carried out with the aim of contributing towards reliable non-invasive BGL sensing. The underlying theory and state of the art will be explained firstly to approach the topic. Then, the development of dielectric characterization techniques will be reviewed, so that the dielectric behavior of the targeted solutions can be studied. After that, the sensor design guidelines will be comprehensively studied, and several sensor proposals will be discussed. The developed sensors will be assessed as glucose concentration trackers with aqueous and biological solutions, analyzing and discussing their performance and their possible improvements. A large study with one of the sensors in a real clinical scenario will also be shown, to analyze its results obtained in a real patient-oriented application and identify future enhancement aspects. Finally, the remaining open lines will be addressed and the future scope will be discussed.

1.2 Motivation

3

1.2 Motivation The presence of diabetes within the world population increases every day, showing a worrying growing tendency, as shown in Fig. 1.1. According to the International Diabetes Federation (IDF), approximately 425 million adults (aged 20–79) were living with diabetes in 2017, a figure which is estimated to rise to 629 million in 2045 [25], although other studies point to almost 700 million for the same year [26], which will be roughly 8–10% of the global population. A striking piece of data is that, in 2017, 1 in 2 people with diabetes (~212 million) were undiagnosed. It is also important to note that diabetes incidence is not uniformly distributed throughout the globe, since three quarters of people with diabetes live in low- and middle-income countries [25]. The growth estimations for the disease by IDF can be clearly seen in this picture. Other remarkable data from IDF’s last report are that, during 2017, diabetes was the direct cause of 4 million deaths worldwide (5 million deaths if the age range is widened [26]), more than 1,100,000 children were living with diabetes, and more than 21 million live births (i.e. 1 in 7 births) were affected by diabetes during pregnancy. All these data raise a clear motivation to conduct any kind of research aimed to achieve benefits for dealing with diabetes. In this sense, since diabetes has no known cure, the most helpful contributions are expected to be related to improvements of the management and treatment of the disease. Self-monitoring of BGL is part and parcel of this treatment, which means that the effectiveness of the treatment is directly linked to the efficiency of the BGL measuring systems. These systems also account for the

Fig. 1.1 Global diabetes incidence in 2017, and estimation for 2045, from [25]

4

1 Introduction

detection and screening of the disease, which is another aspect showing considerable room for improvement. All these reasons become a fundamental motivation for carrying out research aimed to enhance the treatment and, from a technological point of view, the devices used to measure and monitor the BGL. Currently, the common BGL meters are invasive, requiring the user to prick their skin and squeeze it to let a drop of blood out. This sample is collected in a disposable test strip which, inserted into the meter, shows the measured BGL. As a result of this uncomfortable process, the number of measurements per day in diagnosed people is often reduced, and the checks in undiagnosed people are well-nigh null. In addition, the measurements are intrinsically intermittent, not able to track the significant events between consecutive measurements (periods that may last for several hours). Also, this management requires considerable investments: USD 850 billion worldwide in 2017 (being the share of low- and middle-income countries noticeable lower), representing 6–16% of the total healthcare budgets [26]. Due to all these reasons, research on novel BGL measuring systems is advised. Specifically, non-invasive blood glucose monitoring (NIBGM) is highly desirable. A system able to measure the user’s BGL in a non-invasive way could notably reduce the above-mentioned discomfort. With a proper configuration and setup, NIBGM could even lead to continuous BGL monitoring, tracking all the significant events and allowing to perform the required actuations at the moment. This would doubtlessly yield a considerable better management of the disease. Also, producing such a system in an optimized, affordable way, not requiring disposable stuff, could contribute to expand its use worldwide, thus helping to reduce the remarkable differences between geographic regions (see Fig. 1.1). These two aspects (comfortable measurement process and affordable device) could also encourage healthy people to have regular checks, a highly desirable fact considering the undiagnosed people rate. Therefore, the benefits NIBGM technology could bring are evident, and they constitute the main motivation in the development of all the work presented in this dissertation. As the Hungarian-born American theoretical physicist Edward Teller pointed, “the science of today is the technology of tomorrow”.

1.3 Objectives and Contributions As main objective, this doctoral thesis aims to study in a comprehensive manner the design and application of microwave sensors for glucose concentration detection, with a special focus on glucose concentration tracking in watery and biological solutions. To achieve it, the following goals were pursued: • Studying the dielectric behavior of glucose solved in aqueous solutions. The fundamental working principle of the sensors proposed in this document is the variations of the dielectric permittivity of the material to be sensed. Therefore, the dielectric behavior of the targeted materials needs to be comprehensively studied and characterized. In this regard, water–glucose solutions at different

1.3 Objectives and Contributions

•

•

•

•

•

5

concentrations are chosen as a convenient medium with the objective of analyzing the contribution of glucose to the changes in the overall dielectric permittivity of the solution. Chapter 3 shows a thorough study in this regard. Designing suitable sensors for glucose concentration detection. This goal is essential for the fulfilment of the main objective. The microstrip resonator is singled out in this approach due to the dependence of its electrical response to the dielectric permittivity of the media upon it. This objective intends to thoroughly study and discuss the design guidelines for this element, in order to provide for optimized designs concerning sensing purposes. Such work will be shown in Chap. 4. Assessing the proposed sensors with aqueous and biological solutions. Comprehensive experimentation needs to be carried out both in vitro and in silico to test the performance of the proposed sensors as glucose concentration trackers with different kinds of solutions, comprising watery and biological ones. This objective places a special emphasis on assessing the sensitivity of the sensors to the glucose concentration for the different cases considered, as well as the interference of the variations of other components. The results and discussion in this regard can be found in Chaps. 4 and 5. Evaluating the feasibility of the sensors for real NIBGM. To approach the application in diabetes context, a NIBGM device must be developed with the proposed sensors. Testing this device in real application conditions, in a clinical context and with a large number of individuals, seems mandatory for identifying the most relevant performance aspects and reach valuable conclusions for further developments. This study will be shown in Chap. 6. Identifying the potential improvement aspects of the sensors and addressing them. The continuous study and progress is essential for reaching the really successful NIBGM application. The results of all the work carried out must be critically analyzed and the possible enhancement points should be detected. From the conclusions reached so far, this objective intends to highlight the compulsory improvements required and propose how they can be addressed. This objective is met in some sections of Chaps. 5 and 6, and specially in Chap. 7. Discussing the remaining open lines and the future work to be done in the pursue of reliable NIBGM. In addition to the specific improvements of the sensors straightforwardly detected from the experimentation, this objective wills to foresee the general future aspects for effective comprehensive NIBGM systems that the scientific community should face. Besides the suitable sensing system, the rest of elements required for a reliable non-invasive BGL monitoring system must be discussed. Chapters 7 and 8 develop such discussion.

In fulfilling each one of these objectives, many contributions to the topic have been made. Most of them can currently be found in the scientific literature through different publications, as it will be shown in Sect. 1.5. The following list gathers and summarizes the main ones: • The dielectric dispersion of glucose-containing solutions at physiological concentrations has been described.

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1 Introduction

• Guidelines for efficient microwave sensors design for glucose concentration detection have been given. • Glucose concentration detection in aqueous and biological solutions with microwave sensors has been achieved, even for micro-liter volumes. • The main contribution of glucose to the dielectric behavior of the solution has been shown to be in the form of losses. The convenience of using the unloaded quality factor as sensing parameter has been consequently shown. • A large study of NIBGM with microwave technology in real application conditions has been offered, identifying the required improvement aspects. • Recommendations about how to address some remaining open lines have been given, like simplification of the system or increase of the sensitivity. Also, important aspects that should be put forward for consideration in pursuing successful NIBGM have been discussed.

1.4 Thesis Structure This dissertation has been divided into eight chapters according to the previously defined objectives. It should be noted that some of the objectives are developed and met throughout more than one chapter, given the close relationship between all the goals, pointing to the main objective. Also, an introductory chapter and another one explaining the state of the art are included, as well as a final chapter gathering the main conclusions. The next paragraphs describe the organization and structure of this document. This chapter constitutes the present introduction to this doctoral thesis and to the framework of the work carried out. It gives a brief approach to the contents of this document, and it also describes the main motivation to conduct this research. The objectives and contributions are summarized, and the structure of this document is outlined. Finally, the framework of this doctoral thesis is described, and the publications supporting this dissertation are shown. Chapter 2 provides an in-depth introduction to the topics covered throughout this dissertation. The underlying theory is reviewed to provide the reader with the required background for a better understanding of the following chapters. In this sense, a retrospective literature review is offered and the state of the art is comprehensively explained to show the evolution of these topics up to the present date. Specifically, the theory of dielectric dispersion is reviewed, as well as the dielectric characterization methods and the fundamentals of microwave resonators. Also, the context of diabetes and the different ways for measuring the BGL are commented, focusing on NIBGM approaches. Chapter 3 studies the development of a transmission/reflection line method for the dielectric characterization of liquids. Water–glucose solutions at several physiological concentrations are measured and characterized with the proposed method. The dielectric dispersion of these solutions is described from the measurements, and

1.4 Thesis Structure

7

the parameters of the Debye model for each solution are given, as well as their Cole– Cole plots. These results are discussed and conclusions are offered, oriented to the development of sensors aimed to track the observed behaviors. Chapter 4 presents three microwave sensors for glucose concentration detection. The sensors are based on open-loop microstrip resonators at several frequencies, equipped with special sample holders. A comprehensive discussion on the design guidelines is offered, focused on maximizing the sensitivity of the sensors to the changes in the permittivity of the samples. The optimization of the proposed sensors is demonstrated with electromagnetic simulations. Experimental measurement of water–glucose solutions at different concentrations with the sensors is shown. The results are analyzed, chiefly in terms of the sensitivities, and a thorough discussion is given, highlighting the best measurement technique. Chapter 5 shows the previously proposed sensors detecting the glucose concentration in biological solutions. Blood plasma solutions are measured at several glucose concentrations, in addition to different ascorbic acid and lactic acid concentrations. The resulting sensitivities and the interference of the variations of other components different from glucose are discussed. The conclusions identify some future aspects to be dealt with. Chapter 6 introduces a thorough proof of concept of the developed technology for real NIBGM. A portable version of one of the proposed sensors is implemented for evaluating its performance as NIBGM device in real application conditions. A large study with a considerable number of individuals in a multicenter clinical scenario is presented. As a result, experimental evidence of the potential of this technology is given. Also, its limitations and required improvement aspects are identified. Chapter 7 discusses the remaining open lines towards the achievement of completely successful NIBGM devices. Three main points are considered, namely simplification of the system, sensitivity and selectivity. New sensor designs and approaches resulting from the conclusions reached in prior chapters are presented, showing promise for the first two aspects. Regarding the selectivity, a successful attempt is still to be found, maybe involving more than one technology. In this regard, guidelines and suggestions for an effective future tackling of this issue are deeply discussed. Chapter 8 offers the main general conclusions of this dissertation. The contribution of glucose to the dielectric losses of the medium is highlighted. Also, the feasibility of microwave resonators for the pursued purpose is reviewed, and the convenience of using the unloaded quality factor as sensing parameter is asserted. The interference of other components and parameters in the response of the sensors is pointed as well, and the possible enhancements easily attainable in the near future are remarked. Finally, the future scope foreseen is depicted, mainly focused upon improving the sensors, tracking broader information, developing realistic computational models, considering multi-technology approaches and involving machine learning techniques. Besides, two appendices can be found at the end of the book. Appendix A explains a fitting method to fit the raw measured data into a quadratic function in order to

8

1 Introduction

obtain the desired parameters in a more precise manner, in reference to the measurement technique described in Chap. 4. Appendix B shows a theoretical description of the calculation of possible instrumental errors affecting the measured quality factor according to the techniques described in Chap. 4.

1.5 Framework of the Thesis The present doctoral thesis has been developed in the Department of Systems Engineering and Automation at Miguel Hernández University of Elche, Elche, Spain. During this period, the author has been an active member of the Neuroengineering Biomedical (nBio) research group. This work has been entirely made under the supervision of Prof. Dr. José María Sabater Navarro and Dr. Enrique Bronchalo. The work carried out by the author to develop this thesis has been funded with the following grant: – PhD and University Lecturers Training Program FPU, grant number FPU14/00401, funded by Spanish Ministry of Education, Culture and Sport (MECD). These funds applied for 4 years, from September 2015 to September 2019. In addition, during the development of this thesis the author spent two periods of approximately one month (from November 2016 to December 2016) and three months (from May 2018 to July 2018) collaborating with the Laboratoire des Sciences et Techniques de l’Information, de la Communication et de la Connaissance (LabSTICC), at Université de Bretagne Occidentale, Brest, France. During these research stays, both under the supervision of Dr. Benjamin Potelon, the author gained valuable expertise on several aspects such as electromagnetic simulation techniques, microwave engineering, resonators design and filter design. As a consequence, several joint works were published, which constitute the basis of Chap. 4 and Sect. 7.3. These research stays were funded with the following grants: – Mobility of International Doctoral Students in Brittany, Incoming Mobility Grants, grant number EIO-Spring2018-1, funded by Université de Bretagne Occidentale, Brest, France (2018). – Mobility Funds for Short Stays and Temporary Transfers for PhD and University Lecturers Training Program Grant Holders, grant number EST17/00205, funded by the Spanish Ministry of Education, Culture and Sport (MECD) (2018). – International Mobility Funds Miguel Herández University of Elche, grant number UMH0707/16, funded by Miguel Hernández University of Elche, Elche, Spain (2016).

1.6 Publications

9

1.6 Publications During the development of this doctoral thesis, either as a direct result of the research conducted or resulting from research collaborations, 5 papers were published in journals indexed in JCR Science Edition, as well as 8 international conference papers and 5 national conference papers. The metadata of the journal papers, which support the main contributions of this dissertation, are provided below. J1.

J2.

J3.

J4.

Concentration measurement of microliter-volume water–glucose solutions using Q factor of microwave sensors [27] C. G. Juan, E. Bronchalo, B. Potelon, C. Quendo, E. Ávila-Navarro, and J. M. Sabater-Navarro IEEE Transactions on Instrumentation and Measurement, vol. 68, no. 7, pp. 2621–2634, 2019. ISSN: 0018-9456 (print); 1557-9662 (electronic). Publisher: IEEE. JCR-SCI Impact Factor: 3.067, Quartile Q1 (Instruments & Instrumentation) Web: https://ieeexplore.ieee.org/document/8462783 DOI: https://doi.org/10.1109/TIM.2018.2866743 Glucose concentration measurement in human blood plasma solutions with microwave sensors [28] C. G. Juan, E. Bronchalo, B. Potelon, C. Quendo, and J. M. Sabater-Navarro Sensors, vol. 19, no. 17, p. 3779, 2019. ISSN: 1424-8220 (electronic). Publisher: MDPI. JCR-SCI Impact Factor: 3.031, Quartile Q1 (Instruments & Instrumentation) Web: https://www.mdpi.com/1424-8220/19/17/3779 DOI: https://doi.org/10.3390/s19173779 Feasibility study of portable microwave microstrip open-loop resonator for non-invasive blood glucose level sensing: proof of concept [29] C. G. Juan, H. García, E. Ávila-Navarro, E. Bronchalo, V. Galiano, O. Moreno, D. Orozco, and J. M. Sabater-Navarro Medical & Biological Engineering & Computing, vol. 57, no. 11, pp. 2389– 2405, 2019. ISSN: 0140-0118 (print); 1741-0444 (electronic). Publisher: Springer. JCR-SCI Impact Factor: 2.039, Quartile Q2 (Mathematical & Computational Biology) Web: https://link.springer.com/article/10.1007/s11517-019-02030-w https://rdcu.be/bP1T6 DOI: https://doi.org/10.1007/s11517-019-02030-w Dielectric characterization of water glucose solutions using a transmission/reflection line method [30] C. G. Juan, E. Bronchalo, G. Torregrosa, E. Ávila, N. García, and J. M. SabaterNavarro Biomedical Signal Processing and Control, vol. 31, no. 1, pp. 139–147, 2017. ISSN: 1746-8094 (print); 1746-8108 (electronic). Publisher: Elsevier.

10

J5.

1 Introduction

JCR-SCI Impact Factor: 2.783, Quartile Q2 (Engineering, Biomedical) Web: https://www.sciencedirect.com/science/article/pii/S174680941630091X DOI: https://doi.org/10.1016/J.BSPC.2016.07.011 Microwave microstrip resonator for developing a non-invasive glucose sensor [31] C. G. Juan, E. Bronchalo, G. Torregrosa, A. Garcia, and J. M. Sabater-Navarro International Journal of Computer Assisted Radiology and Surgery, vol. 10, no. S1, pp. 172–173, 2015. ISSN: 1861-6410 (print); 1861-6429 (electronic). Publisher: Springer. JCR-SCI Impact Factor: 1.827, Quartile Q2 (Engineering, Biomedical) Web: https://link.springer.com/article/10.1007/s11548-015-1213-2 DOI: https://doi.org/10.1007/s11548-015-1213-2

The first article offers extensive discussion on the design guidelines for developing glucose concentration sensors with microwave resonators. The microstrip open-loop resonator is selected due to several reasons, being the highly capacitive area created between the open ends an essential one. The sensors are provided with ad hoc sample holders to make possible the measurements with liquids. Optimization of the design to maximize the sensitivity to the permittivity variations of the sample is discussed. Simulations and measurement with watery solutions at different glucose concentrations are shown. The experimental sensitivities obtained compare well with the data found in the scientific literature concerning other measuring methods. The use of the unloaded quality factor as sensing parameter is advised. The second article provides the results of the previous sensors when measuring human blood plasma solutions. The promising results for glucose concentration detection when simple media are concerned (i.e. watery solutions), contrast with the lack of good results when real biological media are involved. In this sense, this article assesses the proposed sensors when real biological solutions are regarded, as an intermediate step towards measuring in real conditions. Specifically, human blood plasma solutions with different concentrations of glucose, ascorbic acid and lactic acid are measured, and the results are discussed. The conclusions reached allow to identify the performance issues that must be addressed and to envision the desirable attempts towards successful NIBGM. The third article shows a large proof of concept of this kind of sensors in a real application context. A portable NIBGM device is presented, which makes use of a sensor similar to the ones proposed in the first article. The device is tested in vivo in a multicenter clinical environment with more than 350 users, making a total amount of more than 1200 measurements. Comprehensive discussion of the performance of the device is offered. Experimental proof of the potential of this approach is given. Limitations and improvement aspects are identified and discussed. The fourth article presents a dielectric characterization method for liquids based upon transmission/reflection line techniques. The method consists in the use of a coaxial line with no dielectric inside. The scattering parameters of the line are measured after filling it with the solution to be studied. Several water–glucose solutions at physiological concentrations are analyzed. Two different types of coaxial

1.6 Publications

11

lines are employed to provide for wider frequency analysis. Several methods for obtaining the permittivity of the liquids under test are discussed and applied, both theoretical and computational. The dielectric dispersion of the solutions is described, and their Debye parameters and Cole–Cole diagrams are given. The fifth article demonstrates the feasibility of the use of microwave microstrip resonators for measuring the dielectric permittivity changes in the media upon them. A square patch resonator is presented and an in silico study varying the relative permittivity of the upper space is shown. The variations of the simulated electrical response are clearly seen, accounting for the tracking of the permittivity variations of the materials under test. The international conference papers are listed below. The first two papers correspond to remarkable contributions of this thesis. IC1.

IC2.

IC3.

IC4.

IC5.

IC6.

IC7.

C. G. Juan, B. Potelon, C. Quendo, E. Bronchalo, and J. M. Sabater-Navarro, “Highly-sensitive glucose concentration sensor exploiting inter-resonators couplings,” in Proceedings of the 49th European Microwave Conference (EuMC), Paris, France, October 2019, pp. 662–665 [32]. H. García, C. G. Juan, E. Ávila-Navarro, E. Bronchalo, and J. M. SabaterNavarro, “Portable device based on microwave resonator for noninvasive blood glucose monitoring,” in Proceedings of the IEEE 41st International Engineering in Medicine and Biology Conference (EMBC), Berlin, Germany, July 2019, pp. 1115–1118 [33]. C. G. Juan, C. Blanco-Angulo, N. Bermejo, N. García, J. M. Vicente-Samper, E. Ávila, and J. M. Sabater-Navarro, “Concept of a system for real-time measurement and visualization of brain-shift,” in Proceedings of the IEEE 41st International Engineering in Medicine and Biology Conference (EMBC), Berlin, Germany, July 2019 [34]. J. M. Vicente, E. Ávila-Navarro, C. G. Juan, N. García, and J. M. SabaterNavarro, “Design of wearable bio patch for monitoring patient’s temperature,” in Proceedings of the IEEE 38th International Engineering in Medicine and Biology Conference (EMBC), Orlando, FL, USA, August 2016, pp. 4792– 4795 [35]. A. Garcia-Martinez, R. Mora, C. G. Juan, A. F. Compañ, N. Garcia, and J. M. Sabater-Navarro, “Toward an enhanced modular operation room,” in Proceedings of the IEEE RAS/EMBS 6th International Conference on Biomedical Robotics and Biomechatronics (BioRob), Singapore, Singapore, June 2016, pp. 413–417 [36]. J. A. Díez, F. J. Badesa, S. Ezquerro, J. M. Sabater, Á. Bernabeu, C. G. Juan, and N. Garcia-Aracil, “HELPER: Collaborative project to develop a rehabilitation robotic device,” in Proceedings of the ROBOT’2015: Second Iberian Robotics Conference, Lisbon, Portugal, November 2015 [37]. C. G. Juan, E. Bronchalo, G. Torregrosa, A. García, and J. M. SabaterNavarro, “Microwave microstrip resonator for developing a non-invasive glucose sensor,” in Proceedings of the Computer Assisted Radiology and

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IC8.

Surgery 29th International Congress and Exhibition (CARS), Barcelona, Spain, June 2015, pp. 172–173 [38]. Á. García-Martínez, C. G. Juan, N. M. García, and J. M. Sabater-Navarro, “Automatic detection of surgical gauzes using computer vision,” in Proceedings of the 23rd Mediterranean Conference on Control and Automation (MED), Torremolinos, Spain, June 2015, pp. 747–751 [39].

Finally, the list of national conference papers is the following: NC1.

NC2.

NC3.

NC4.

NC5.

C. G. Juan, C. Blanco-Angulo, N. Bermejo, H. García, J. M. Vicente-Samper, E. Ávila, and J. M. Sabater-Navarro, “Sistema no invasivo para la medida y visualización de desplazamientos de tejidos en neurocirugía,” in Actas del 11º Simposio de Bioingeniería del Comité Español de Automática, Valencia, Spain, July 2019 [40]. C. G. Juan, Á. García, J. M. Vicente, and J. M. Sabater-Navarro, “Plataforma basada en la integración de Matlab® y ROS para la docencia de robótica de servicio,” in Actas de las XXXVIII Jornadas de Automática, Gijón, Spain, September 2017, pp. 766–771 [41]. C. G. Juan, J. M. Vicente, N. Bermejo, Á. García, and J. M. Sabater-Navarro, “Diseño de un dispositivo háptico multigestual para simulación quirúrgica,” in Libro de Actas de las Jornadas Nacionales de Robótica 2017, Valencia, Spain, June 2017, p. 21 [42]. A. García, J. M. Vicente, C. G. Juan, and J. M. Sabater-Navarro, “Algoritmo para la detección automática de sangrados quirúrgicos utilizando visión por computador,” in Actas de las XXXVII Jornadas de Automática, Madrid, Spain, September 2016, pp. 835–839 [43]. J. M. Vicente, E. Ávila-Navarro, C. G. Juan, and J. M. Sabater-Navarro, “Diseño de un bio-patch NFC para la monitorización de la temperatura corporal,” in Resúmenes del XXIII Seminario Annual de Automática, Electrónica Industrial e Instrumentación (SAAEI), Elche, Spain, July 2016, p. INS13 [44].

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5. Wang X, Bauer DR, Witte R, Xin H (2012) Microwave-induced thermoacoustic imaging model for potential breast cancer detection. IEEE Trans Biomed Eng 59(10):2782–2791 6. Bucci OM, Crocco L, Scapaticci R (2015) On the optimal measurement configuration for magnetic nanoparticles enhanced breast cancer microwave imaging. IEEE Trans Biomed Eng 62(2):407–414 7. Kwon S, Lee S (2016) Recent advances in microwave imaging for breast cancer detection. Int J Biomed Imaging 2016:5054912 8. Mahmud MZ, Islam MT, Misran N, Almutairi AF, Cho M (2018) Ultra-wideband (UWB) antenna sensor based microwave breast imaging: a review. Sensors 18(9):2951 9. Fear EC, Hagness SC, Meaney PM, Okoniewski M, Stuchly MA (2002) Enhancing breast tumor detection with near-field imaging. IEEE Microwave Mag 3(1):48–56 10. Grenier K, Dubuc D, Chen T, Artis F, Chretiennot T, Poupot M, Fournié J-J (2013) Recent advances in microwave-based dielectric spectroscopy at the cellular level for cancer investigations. IEEE Trans Microw Theory Tech 61(5):2023–2030 11. Chen T, Dubuc D, Poupot M, Fournié J-J, Grenier K (2013) Broadband discrimination of living and dead lymphoma cells with a microwave interdigitated capacitor. In: Proceedings of the 2013 IEEE topical conference on biomedical wireless technologies, networks, and sensing systems (BioWireleSS), Austin, TX, pp 64–66 12. Gubin AI, Barannik AA, Cherpak NT, Vitusevich S, Offenhaeusser A, Klein N (2011) Whispering-gallery mode resonator technique for characterization of small volumes of biochemical liquids in microfluidic channel. In: Proceedings of the 41st European microwave conference (EuMC), Manchester, pp 615–618 13. Shaforost EN, Klein N, Vitusevich SA, Barannik AA, Cherpak NT (2009) High sensitivity microwave characterization of organic molecule solutions of nanoliter volume. Appl Phys Lett 94(11):112901 14. Guha S, Warsinke A, Tientcheu CM, Schmalz K, Meliani C, Wenger C (2015) Label free sensing of creatinine using a 6 GHz CMOS near-field dielectric immunosensor. Analyst 140(9):3019– 3027 15. Rowe DJ, Porch A, Barrow DA, Allender CJ (2012) Microfluidic device for compositional analysis of solvent systems at microwave frequencies. Sens Actuators B Chem 169:213–221 16. Nikolic-Jaric M, Romanuik SF, Ferrier GA, Bridges GE, Butler M, Sunley K, Thomson DJ, Freeman MR (2009) Microwave frequency sensor for detection of biological cells in microfluidic channels. Biomicrofluidics 3(3):034103 17. Entesari K, Helmy AA, Sekar V (2013) A review of frequency synthesizer-based microwave chemical sensors for dielectric detection of organic liquids. In: Proceedings of the 2013 IEEE annual conference on wireless and microwave technology (WAMICON), Orlando, FL 18. Chien J-C, Anwar M, Yeh E-C, Lee LP, Niknejad AM (2014) A 6.5/17.5-GHz dual-channel interferometer-based capacitive sensor in 65-nm CMOS for high-speed flow cytometry. In: Proceedings of the 2014 IEEE MTT-S international microwave symposium (IMS), Tampa, FL 19. Guha S, Jamal FI, Wenger C (2017) A review on passive and integrated near-field microwave biosensors. Biosensors 7(4):42 20. Mata-Contreras J, Su L, Martín F (2017) Microwave sensors based on symmetry properties and metamaterial concepts: a review of some recent developments (invited paper). In: Proceedings of the IEEE 18th wireless and microwave technology conference (WAMICON), Cocoa Beach, FL 21. Naqui J, Martín F (2015) Microwave sensors based on symmetry properties of resonator-loaded transmission lines. J Sens 2015:741853 22. Su L, Mata-Contreras J, Vélez P, Martín F (2017) A review of sensing strategies for microwave sensors based on metamaterial-inspired resonators: dielectric characterization, displacement, and angular velocity measurements for health diagnosis, telecommunication, and space applications. Int J Antennas Propag 2017:5619728 23. Bahar AAM, Zakaria Z, Isa AAM, Ruslan E, Alahnomi RA (2015) A review of characterization techniques for materials’ properties measurement using microwave resonant sensor. J Telecommun Electron Comput Eng 7(2):1–6

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24. Sekar V, Torke WJ, Palermo S, Entesari K (2012) A self-sustained microwave system for dielectric-constant measurement of lossy organic liquids. IEEE Trans Microw Theory Tech 60(5):1444–1455 25. International Diabetes Federation (2017) IDF diabetes atlas, 8th edn. International Diabetes Federation, Brussels 26. Cho NH, Shaw JE, Karuranga S, Huang Y, da Rocha Fernandes JD, Ohlrogge AW, Malanda B (2018) IDF diabetes atlas: global estimates of diabetes prevalence for 2017 and projections for 2045. Diabetes Res Clin Pract 138:271–281 27. Juan CG, Bronchalo E, Potelon B, Quendo C, Ávila-Navarro E, Sabater-Navarro JM (2019) Concentration measurement of microliter-volume water–glucose solutions using Q factor of microwave sensors. IEEE Trans Instrum Meas 68(7):2621–2634 28. Juan CG, Bronchalo E, Potelon B, Quendo C, Sabater-Navarro JM (2019) Glucose concentration measurement in human blood plasma solutions with microwave sensors. Sensors 19(17):3779 29. Juan CG, García H, Ávila-Navarro E, Bronchalo E, Galiano V, Moreno O, Orozco D, SabaterNavarro JM (2019) Feasibility study of portable microwave microstrip open-loop resonator for noninvasive blood glucose level sensing: proof of concept. Med Biol Eng Comput 57(11):2389– 2405. [Online]. Available: https://rdcu.be/bP1T6. Accessed 1 Sept 2019 30. Juan CG, Bronchalo E, Torregrosa G, Ávila E, García N, Sabater-Navarro JM (2017) Dielectric characterization of water glucose solutions using a transmission/reflection line method. Biomed Signal Process Control 31(1):139–147 31. Juan CG, Bronchalo E, Torregrosa G, Garcia A, Sabater-Navarro JM (2015) Microwave microstrip resonator for developing a non-invasive glucose sensor. Int J Comput Assist Radiol Surg 10(S1):172–173 32. Juan CG, Potelon B, Quendo C, Bronchalo E, Sabater-Navarro JM (2019) Highly-sensitive glucose concentration sensor exploiting inter-resonators couplings. In: Proceedings of the 49th European microwave conference (EuMC), Paris, pp 662–665 33. García H, Juan CG, Ávila-Navarro E, Bronchalo E, Sabater-Navarro JM (2019) Portable device based on microwave resonator for noninvasive blood glucose monitoring. In: Proceedings of the 41st annual international conference of the IEEE engineering in medicine and biology society (EMBC), Berlin, pp 1115–1118 34. Juan CG, Blanco-Angulo C, Bermejo N, García H, Vicente-Samper JM, Ávila E, SabaterNavarro JM (2019) Concept of a system for real-time measurement and visualization of brainshift. In: Proceedings of the 41st annual international conference of the IEEE engineering in medicine and biology society (EMBC), Berlin 35. Vicente JM, Ávila-Navarro E, Juan CG, García N, Sabater-Navarro JM (2016) Design of wearable bio patch for monitoring patient’s temperature. In: Proceedings of the 38th annual international conference of the IEEE engineering in medicine and biology society (EMBC), Orlando, FL, pp 4792–4795 36. Garcia-Martinez A, Mora R, Juan CG, Compañ AF, Garcia N, Sabater-Navarro JM (2016) Toward an enhanced modular operation room. In: Proceedings of the IEEE RAS/EMBS 6th international conference on biomedical robotics and biomechatronics (BioRob), Singapore, pp 413–417 37. Díez JA, Badesa FJ, Ezquerro S, Sabater JM, Bernabeu Á, Juan CG, Garcia-Aracil N (2015) HELPER: collaborative project to develop a rehabilitation robotic device. In: Proceedings of the ROBOT’2015: second Iberian robotics conference, Lisbon 38. Juan CG, Bronchalo E, Torregrosa G, García A, Sabater-Navarro JM (2015) Microwave microstrip resonator for developing a non-invasive glucose sensor. In: Proceedings of the computer assisted radiology and surgery 29th international congress and exhibition (CARS), Barcelona, pp 172–173 39. García-Martínez Á, Juan CG, García N, Sabater-Navarro JM (2015) Automatic detection of surgical gauzes using computer vision. In: Proceedings of the 23rd Mediterranean conference on control and automation (MED), Torremolinos, pp 747–751

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15

40. Juan CG, Blanco-Angulo C, Bermejo N, García H, Vicente JM, Avila E, Sabater-Navarro JM (2019) Sistema no invasivo para la medida y visualización de desplazamientos de tejidos en neurocirugía. In: Actas del 11º Simposio de Bioingeniería del Comité Español de Automática, Valencia 41. Juan CG, García Á, Vicente JM, Sabater-Navarro JM (2017) Plataforma basada en la integración de Matlab® y ROS para la docencia de robótica de servicio. In: Actas de las XXXVIII Jornadas de Automática, Gijón, pp 766–771 42. Juan CG, Vicente JM, Bermejo N, García Á, Sabater-Navarro JM (2017) Diseño de un dispositivo háptico multigestual para simulación quirúrgica. In: Libro de Actas de las Jornadas Nacionales de Robótica 2017, Valencia, p 21 43. García A, Vicente JM, Juan CG, Sabater-Navarro JM (2016) Algoritmo para la detección automática de sangrados quirúrgicos utilizando visión por computador. In: Actas de las XXXVII Jornadas de Automática, Madrid, pp 835–839 44. Vicente JM, Ávila-Navarro E, Juan CG, Sabater-Navarro JM (2016) Diseño de un bio-patch NFC para la monitorización de la temperatura corporal. In: Resúmenes del XXIII Seminario Annual de Automática, Electrónica Industrial e Instrumentación (SAAEI), Elche, p INS13

Chapter 2

State of the Art

The good thing about science is that it’s true whether or not you believe in it. Neil deGrasse Tyson

2.1 Dielectric Dispersion Characterization In this section, the fundamentals of the dielectric relaxations will be reviewed, and the methods to measure and characterize them will be discussed. The theory of the dielectric dispersion will be outlined in the next paragraphs (Sect. 2.1.1), as well as the physical processes involved, the different ways to define them and their interest for sensing purposes. Section 2.1.2 will show the basic methods for dielectric characterization and their field of application, to be studied in Chap. 3, leading to the use of microwave resonators, a device on which this document puts a special focus. To finish, in Sect. 2.2 the theory fundamentals of microwave resonators will be discussed, which will be relevant for further Chaps. 4–7, and the application to diabetes context will be studied in Sect. 2.3.

2.1.1 Dielectric Relaxations and Resonances If a static electric field is applied to matter, charge displacements may occur depending on material properties. The characteristics of these displacements are different for free and bound charges. For free charges, the result is a movement of positive charges towards the direction of the field and negative charges opposite to the direction of the field. However, if the charges are bound, they will form dipoles under the action of the field or spontaneously. In this case, the effect of the field is to make the dipoles rotate until they are aligned parallel to the field. The materials able to form dipoles under the action of an electric field are called dielectric materials.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_2

17

18

2 State of the Art

In the former case, the final result is a constant electric current. As to the latter case, the electronic conduction appears as a displacement current, a transient effect only lasting until the dipoles are aligned to the field and reach their equilibrium orientation. It should be noted that real dielectrics may present both dipoles and free charges, and therefore a combination of these effects takes part. The orientation of the dipoles as the field is applied changes the value of the macroscopic dipole moment of the material, and hence the material gets polarized due to the field. In the linear approximation, this macroscopic polarization (or dipole density) of the material is proportional to the strength of the dielectric field to which it is subjected [1]. If, in addition, the dielectric is isotropic and uniform, the polarization − → P is given by: − → − → P = ε0 χ E

(2.1)

− → where E is the electric field, E0 = 8.854 × 10–12 F/m is the dielectric permittivity of vacuum, and χ is the electric susceptibility (the degree of polarization of the material in response to an electric field). The electric field inside a material is due to both free charges and polarization effects. Thus, the electric field only due to free charges is given by the electric − → displacement vector D , which is defined as: − → − → − → D = ε0 E + P

(2.2)

Combining (2.1) and (2.2) for a uniform isotropic dielectric medium: − → − → − → D = ε0 (1 + χ ) E = ε0 εr E

(2.3)

being Er = 1 + χ the relative dielectric permittivity, an intrinsic property of the material. The overall dielectric permittivity is therefore defined as E = E0 Er . Equations (2.1–2.3) show the importance of the polarization processes in the interactions of matter with electric fields. There are several kinds of polarization that can be produced (Fig. 2.1), briefly discussed below: • Orientation polarization (Fig. 2.1a): When a dielectric contains permanent dipoles (like pure water), the application of an electric field aligns them parallel to the field. In the absence of field, the thermal motions make the dipoles orientations random. Thus, this process is temperature-dependent. • Deformation polarization (Fig. 2.1b), also called electronic polarization: There are molecules or atoms in which, albeit lacking of permanent dipolar moment, the electric field can modify their natural distribution of charges by altering their shape and separating positive and negative charges. • Ionic polarization (Fig. 2.1c): In materials with ionic structure, the positive and negative ions may get slightly separated from their equilibrium positions by

2.1 Dielectric Dispersion Characterization

19

Fig. 2.1 Polarization types: a orientation, b deformation, c ionic, d interfacial

the electric field. This process is equivalent to the induction of a macroscopic polarization since the center of charges for the positive and negative ions do not coincide. • Interfacial or Maxwell–Wagner polarization [2, 3]: it appears due to the accumulation of opposite charges at dielectric boundaries separated by distances significantly greater than the typical intermolecular distance (Fig. 2.1d). For instance,

20

2 State of the Art

a cell in a solution with ionic or dipolar molecules can behave as a dipole under the action of an external electric field. If the molecules in the dielectric present a permanent dipolar moment (although in the absence of field the macroscopic polarization is null due to the random orientation of the dipoles because of thermal motion), it is called a polar dielectric. Otherwise, when the molecules do not have any dipolar moment in the absence of external electric field, it is called a non-polar dielectric. Thus, it has been shown how the interaction between the matter and electric fields depends on the permittivity, which at the same time is dependent on the chemical composition. Their study and characterization are therefore desirable when applications based upon chemical composition identification are considered, aimed to the development of sensors. So far, the electric polarization has been studied for static electric fields. In this case, regardless the type, the polarization finally achieves an equilibrium with the field. Conversely, for dynamic electric fields, such an equilibrium can be reached or not, depending on the situation. If the variations in the electric field strength are slower than the motion of the microscopic particles and charges required to reach the proper value of macroscopic polarization, equilibrium can be reached since there is enough time for the polarization to follow the variations of the field. Thus, Eqs. (2.1)–(2.3) remain valid by considering the time dependence of the electric field strength and polarization: − → − → P (t) = ε0 χ E (t)

(2.4)

− → − → D (t) = ε0 εr E (t)

(2.5)

It is easier to study the dynamic electric field case considering harmonic timevarying fields, for which the field strength E * (t) is defined next: E ∗ (t) = E 0 e jωt

(2.6)

where E 0 is the field amplitude, ω = 2πf is the angular frequency and f is the frequency. If the variations of the field are too fast for the microscopic dipoles to follow them, the polarization and electric displacement will no longer have enough time to reach an equilibrium with the field. Therefore, a phase difference will be produced between these magnitudes and the field. The electric displacement strength D* (t) is now given by: D ∗ (t) = D0 e j(ωt−δ(ω))

(2.7)

being δ(ω) the phase difference for the angular frequency ω. Hence, in order to obtain a relationship between E * (t) and D* (t) as it was given by Eq. (2.3) in the static case, Eqs. (2.6) and (2.7) suggest that the dielectric permittivity

2.1 Dielectric Dispersion Characterization

21

must be redefined as a complex, frequency-dependent parameter, to account for the new frequency-dependent phase difference. The relative dielectric permittivity is thereby defined as: εr ∗ (ω) =

D0 − jδ(ω) e ε0 E 0

(2.8)

being the overall dielectric permittivity E* (ω) = E0 Er * (ω). It is usual that the electric fields applied to the dielectric materials are expressed as linear combinations of harmonic fields at different frequencies. In this case, the amplitudes of the electric field E 0 and electric displacement D0 also vary with the frequency, and hence Eq. (2.5) turns into: D ∗ (ω) = ε0 εr ∗ (ω)E ∗ (ω)

(2.9)

which, considering Eq. (2.8) and applying Euler’s formula to have the complex exponential expressed in terms of sine and cosine, yields the common definition of the complex frequency-dependent dielectric permittivity: εr∗ (ω) = εr (ω) − jεr (ω)

(2.10)

with: εr (ω) =

D0 (ω) cos(δ(ω)) ε0 E 0 (ω)

(2.11)

εr (ω) =

D0 (ω) sin(δ(ω)) ε0 E 0 (ω)

(2.12)

and the loss tangent is given by: tan δ(ω) =

εr (ω) εr (ω)

(2.13)

It should be noted that, for the static case, Eq. (2.9) effectively turns into Eq. (2.3). It is also important to notice that this discussion is only valid for ideal nonconductive dielectrics. Real dielectrics, however, frequently show a certain conduc− → tivity σ. As a result, an electric current density j appears, in phase with the electric field, due to Ohm’s law, given by: − → j (ω) = σ E(ω)

(2.14)

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2 State of the Art

Following a similar discussion, this electric current density can be defined for the linear combination of harmonic fields as: − →∗ j (ω) = σ ∗ (ω)E ∗ (ω)

(2.15)

σ ∗ (ω) = σ  (ω) + jσ  (ω)

(2.16)

being:

This conductivity usually has a noticeable effect at low frequencies, and it is related to losses in the dielectric. This way, it is easy to understand that, when the electric field applied to the material is suddenly switched on, the polarization in the dielectric needs a specific time to achieve the new equilibrium. The same way, when the electric field is suddenly − → − → switched off, the polarization P (t) takes a certain time to relax from P (0) to the non-polarized state [4], the so-called characteristic relaxation time. To define this process, the relaxation function of the dielectric polarization φ(t) can be expressed as follows: − → P (t) φ(t) = − → P (0)

(2.17)

Hence, the dielectric displacement for time-dependent fields can be redefined as [1, 5, 6]: ⎡ − → − → D (t) = ε0 ⎣ε∞ E (t) +

t

⎤ − → ˙ (u) E (t − u)du ⎦

(2.18)

−∞

where the dielectric response function is denoted by (t) and it is defined as: (t) = (εs − ε∞ )[1 − φ(t)]

(2.19)

being E∞ the high-frequency limit of the relative permittivity, as well as Es is the respective low-frequency limit. It is known that the relaxation function φ(t) is related to the relative dielectric permittivity by means of the Laplace transform [1, 6] as shown below:   d εr ∗ (ω) − ε∞ = L − φ(t) εs − ε∞ dt

(2.20)

This means that the dielectric relaxation may be studied both in time and frequency domain, obtaining the same information. Hence, from the experimental point of view,

2.1 Dielectric Dispersion Characterization

23

the dielectric characterization of any sample may be achieved by collecting data related to the complex frequency-dependent dielectric permittivity Er * (ω) or to the time-dependent relaxation function φ(t). For instance, consider a relaxation function given as a simple exponential function: −t

φ(t) = e τ

(2.21)

being τ the characteristic relaxation time. Substituting Eq. (2.21) into Eq. (2.20) leads to the well-known Debye’s formula for representing the complex frequencydependent dielectric permittivity [7]: εr ∗ (ω) − ε∞ 1 = εs − ε∞ 1 + jωτ

(2.22)

In the case of real dielectrics, the DC conductivity should also be considered, leading to the next expression, modified from Debye’s formula: εr ∗ (ω) = ε∞ +

σs εs − ε∞ + 1 + jωτ jε0 ω

(2.23)

The real and imaginary parts of the relative permittivity are thereby given by: εr (ω) = ε∞ + εr (ω) =

εs − ε∞ 1 + (ωτ )2

ωτ (εs − ε∞ ) σs + ε0 ω 1 + (ωτ )2

(2.24) (2.25)

The evolution of Er  (ω) and Er  (ω) is plotted in Fig. 2.2 against log(ωτ ) to illustrate the relaxation process (without considering the effect of DC conductivity). It can be seen how the real part of the permittivity evolves from Es to E∞ , as logical, having a decrease during the relaxation (when ω tends to 1/τ ). On the other hand, the imaginary part of the permittivity, related to the losses in the dielectric, shows low values at Fig. 2.2 Permittivity evolution throughout a single dielectric relaxation

24

2 State of the Art

frequencies far from the relaxation frequency. At frequencies close to the relaxation, however, it grows to greater values since the polarization of the dielectric requires faster rotation of the dipoles, thus dissipating more energy and having more losses. Thus, it is easy to see how the dielectric evolves from highly polarized (i.e., it has high real permittivity values) to relaxed or weakly polarized (i.e., it has low real permittivity values). This is because the dipoles orient themselves parallel to the field at low frequencies as they rotate fast enough to follow the variations of the field. In this point they start to dissipate more energy due to the friction with the environment, and the values of the imaginary part increase. Notwithstanding, they can no longer follow the changes in the field when the frequency increases over a certain value. At this point, the inertia and interactions with the environment are large enough to hinder the rotations of the dipoles, and they decouple from the field. As a consequence, they orient randomly again due to thermal motion and hence dissipate less energy as the friction with the environment is remarkably reduced (and the imaginary part of the permittivity decreases). Therefore, Debye’s formula has been widely used when studying the physics of dielectrics, since it allows to understand the processes of dielectric dispersion in an easy manner. However, when it comes to real applications, more complex expressions are often required to perform as accurate models for the experimental data, since they do not always follow exponential relaxation functions. This is mainly because there are usually several relaxation processes in the same dielectric at different frequencies, linked to different relaxation times. In consequence, expressions concerning several relaxation times and weighting them properly according to the specific cases and frequency ranges have been studied and applied. The main types of dielectric dispersion processes depending on the frequency of the applied field can be seen in Fig. 2.3. It is important not to confuse the polarization processes depicted in Fig. 2.1 with the dielectric dispersion processes shown in Fig. 2.3. The former depend chiefly on the chemical composition and properties of the dielectric, whereas the latter depend mostly on the frequency of the field applied to the dielectric. Actually, the dielectric dispersion processes are a consequence of the frequency dependence of the polarization. In-depth discussion in this regard can be found in [6]. These processes are briefly described next: • Ionic relaxation: At very low frequencies (or DC), up to a few kilohertz, ionic diffusion processes can be found for very small sample cells [8]. Under the effect of the field, ions (or ionic molecules, such as OH− ) diffuse and accumulate in the cell borders according to the field. This effect is highly dependent on the sample cell size and on environmental factors [9], and it is believed to be linked to counterion movements in electrolyte solutions [10], although some controversy persists in this regard [11]. • Dipolar relaxation: If an AC electric field with enough frequency is applied, mostly in the microwave region, there is a continuous rotation of the dipoles to orient parallel to the field (Fig. 2.3b). In this situation it is important to take into account the viscosity of the medium, since the molecules are not isolated and they therefore interact with other molecules nearby. For high enough frequencies,

2.1 Dielectric Dispersion Characterization

25

Electric field

Electric field

H

- - +

-

O

+ +

- - + - -- - + - +

+

+ + +

-

- - -

+

H

+ + + +

Electric field H

+ + + + + +

O H

(a)

(b) No field

Electric field

-

H

+

O

H

Electric field

Electric field

H

-

O

+

H

(c)

(d)

Fig. 2.3 Types of dielectric dispersion processes: a ionic relaxation, b dipolar relaxation, c atomic resonance, d electronic resonance

the viscosity effects will no longer allow the molecules to rotate fast enough to follow the variations of the field. At this point the molecules will cease to rotate and will reach a new equilibrium, regardless the variations of the field. The viscosity actually depends on the density, as well as the intermolecular forces. The temperature is another factor to consider since the higher temperature the higher space between molecules and hence the lower viscosity. If other dipolar molecules are present in the medium (like glucose, C6 H12 O6 , solved in water, for instance), the molecular interactions augment and the space between molecules reduces. Thereby, the viscosity increases and the effect of this relaxation is altered. • Atomic resonances: At frequencies close to the natural vibration frequencies of atoms inside molecules (typically in the far- and mid-infrared regions), the electric field can induce atomic vibrations by a resonance mechanism (see Fig. 2.3c). In

26

2 State of the Art

Fig. 2.4 Permittivity evolution throughout the different dielectric dispersion processes

this situation, the dielectric permittivity will anew increase due to these atomic vibrations. Again, there will be a high frequency for which the atoms will not be able to continue oscillating. • Electronic resonances: At frequency values comparable to the oscillation frequencies of the electron in each atom, chiefly in the near-infrared, visible and ultraviolet regions. The electron orbit is altered, as it can be seen in Fig. 2.3d, due to the effect of the electric field. This means that, the electron density distribution in the atom is modified, which will provoke another raise of the dielectric permittivity. This will happen until the frequency grows too high for the electron to alter its orbit according to the field. In Fig. 2.4 the evolution of the generic dielectric dispersion processes is plotted throughout a wide enough frequency range. As shown, there are many relaxation and resonance processes throughout the frequency spectrum. Since the frequencies of main interest in this document are associated only to relaxation processes, these will be studied in a more comprehensive way in the next paragraphs. Due to this variety of relaxations of different nature, for practical applications the Debye’s formula was adapted to the so-called Havriliak–Negami (HN) dispersion function [12]: εr ∗ (ω) = ε∞ +

εs − ε∞ (1 + ( jωτ )α )β

(2.26)

where 0 ≤ α and β ≤ 1 are exponents to account for each specific case. This expression does not consider the conductivity since its effects are considerable only at very low frequencies. The reader can note that the case α = 1, β = 1 yields the previously discussed Debye’s formula. Although many dispersion functions have been proposed for different fields of application (see [13], for instance), two famous cases are α = 1, β = 1, the so-called Cole–Cole (CC) dispersion function [14], or α = 1, β = 1, the so-called Cole–Davidson (CD) function [15]. These functions will be discussed deeply further in this document (Chap. 3).

2.1 Dielectric Dispersion Characterization

27

Finally, Debye and HN generic dielectric model, as well as the numerous variations (CC, CD…) are widely used to describe the dielectric dispersion of many experimental cases. However, they are valid only when simple materials are concerned, with only one single dielectric permittivity E* (ω) taking place. In the cases of dielectric mixtures, where several materials with different permittivities play remarkable roles, there are some options to model the experimental data. This may be the case of layered materials made out of different components, but also of solutions and mixtures of different components. One simple solution consists in considering an effective relative complex permittivity Eeff describing the aggregate dielectric dispersion for the whole material. This effective relative permittivity can be obtained by means of the Maxwell–Garnett formula [16, 17] or Bruggeman’s formula [18, 19] when the volume fraction of one material with respect to the other is very small. Maxwell–Garnett formula reads:   ε2 − ε1 (2.27) εe f f = ε1 1 + 3ν ε2 + 2ε1 − ν(ε2 − ε1 ) where E1 is the relative complex permittivity of the solution medium in which particles of complex relative permittivity E2 are solved at a volume fraction ν  1. Bruggeman’s formula reads: εe f f =

b±



b2 + 8ε2 ε1 4

b = (2 − 3ν)ε1 − (1 − 3ν)ε2

(2.28)

where the sign before the square root can be chosen to correct for the experimental values of the imaginary part of the permittivity. Discussion on the use of these formulas may be found in [20]. These formulas, yet, are not valid when the volume fraction of the solute grows larger, or when solid materials are involved. In these cases, mostly for layered compound materials, other formulas can be applied to more precisely describe the experimental data. Three common formulas for fitting the aggregate measured relative dielectric permittivity Er of solid mixtures are Kraszewski’s equation [21]: εr =



νn εn 1/2

2 (2.29)

Landau, Lifshitz, and Looyenga’s equation [22]: εr =



and Lichtenecker’s equation [23, 24]:

νn εn 1/3

3 (2.30)

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2 State of the Art

εr =

(εn )νn

(2.31)

being νn and En the volume fraction and dielectric permittivity of the nth constituent, respectively. Comparison between these three formulas is offered in [25], and some application examples can be seen in [26–28]. Derivation of Lichtenecker’s equation from the Maxwell’s equations is shown in [29]. The study of the aggregate dielectric permittivity for solid mixtures with different geometric and chemical configurations can be found in [30, 31]. In the next section (Sect. 2.1.2) several experimental procedures to measure the dielectric permittivity will be discussed.

2.1.2 Dielectric Characterization Methods In this section, several experimental procedures for measuring the dielectric permittivity of a material under test (MUT) will be discussed. The group of experimental techniques to measure the dielectric properties of the materials as a function of time or frequency is called dielectric spectroscopy (DS). After a long period of development [32, 33], DS has achieved successful and accurate results that have helped to make noticeable contributions in many other fields. As a first approach, DS techniques are generally divided into time-domain dielectric spectroscopy (TDS) [34–38] and broadband dielectric spectroscopy (BDS) [39–42], since equivalent information can be obtained from time-domain and frequency measurements [as stated in Eq. (2.20)]. Some narrowband techniques have also been developed, like cavity perturbation [43–46]. In this thesis, DS is applied for glucose concentration measurement in aqueous and biological solutions with microwave sensors, and hence only DS techniques in the frequency domain will be concerned. For in-depth TDS discussion, the reader is kindly referred to [33] or [37]. Despite the last advances and modern sophisticated systems, no single technique is able to fully characterize the complex dielectric permittivity over all the frequencies and satisfy all the requirements. Thus, different techniques are needed, each one being suitable for specific frequency ranges and application situations [47]. The most common ones will be discussed next. Firstly, the early stages of DS development will be outlined. Secondly, the well-known openended coaxial probe will be described. Thirdly, transmission/reflection line methods will be commented. Finally, microwave resonator techniques will be introduced. Starting at RF frequencies, the most common methods to measure the complex dielectric permittivity of a MUT consist in inserting it (or a MUT sample) into a capacitor, waveguide or cavity, hereinafter denoted as measuring element. This element is a sensible part of a bigger circuit or system, whose overall response is highly dependent on the measuring element. Thus, the circuit is usually fed with an alternating voltage (or other functions, like step function), and the global response is measured. Then, calculations and estimations are performed to isolate the contribution of the measuring element in terms of impedance or admittance, and the required

2.1 Dielectric Dispersion Characterization

29

permittivity to get such a response in the element is computed. These methods are normally called impedance spectroscopy. It should be noted that in these methods the wavelength of the signal is quite larger than the MUT sample size. For example, when a capacitor is used to hold the MUT sample, the complex capacitance C * (ω) is retrieved from the overall circuit response measured. Then, the specific relative dielectric permittivity of the MUT is computed as: εr ∗ (ω) =

C ∗ (ω) C0

(2.32)

having C 0 as the capacitance value in the measuring element without sample. If a sinusoidal electric voltage, expressed in its phasor form V* (ω) = V0 ejωt is directly applied to the capacitor, the relative dielectric permittivity can be easily obtained from the impedance Z(ω) of the measuring element as follows: εr ∗ (ω) =

1 jωε0 Z (ω)C 0

(2.33)

where Z(ω) = V * (ω)/I * (ω), being I * (ω) = I 0 ejωt the measured current [42]. A couple of applications making use of these techniques are described in [48, 49]. The main sources of error are, on the one hand, non-idealities in the components of the circuit and, on the other, the erroneous association of effects due to the measuring circuitry to the MUT or the measuring element. In addition, for frequencies above a few tens of MHz, lumped element circuit analysis becomes unrealistic since the wires cannot be deemed as free of inductance or capacitance. In this case, when distributed element techniques provide for more accurate description of the systems, more specific measuring techniques are used to obtain the complex dielectric permittivity. These techniques rely on the effects that the MUT can have in the electromagnetic waves propagation, and therefore they are usually referred to as wave propagation methods, ranging from microwaves to millimeter waves frequencies [50]. The measurements in these methods are frequently expressed with the scattering parameters (denoted S-parameters, as it will be seen in Chap. 3), which give the reflection and transmission coefficients of the circuit with reference to a certain characteristic impedance Z 0 (generally 50 ) [51]. At microwave frequencies, the size of the MUT or the measuring element may be comparable to the wavelength, and the measuring techniques must be adapted in consequence. The microwave region, approximately including the frequency range from 100 MHz to 1 THz, provides for research of dielectric relaxations with characteristic relaxation times between roughly 2 ns and 0.2 ps. This is a very interesting range since it covers a great deal of relevant relaxation processes in biological systems, including the main dielectric relaxation of pure water (∼5 to 15 ps according to two popular reference works by Kaatze [52] and Ellison [53] for several temperatures). Therefore, in words by Kaatze et al., “microwave techniques open up the

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Fig. 2.5 Characteristic dielectric relaxation time of water as a function of temperature, according to [55]

possibility to investigate the effects of dissolved species on such relaxations” [42], and hence become a valuable opportunity to develop applications aimed to identify the components in biological solutions. It should be noted that the characteristic dielectric relaxation time actually depends on the temperature, as it can be seen in Fig. 2.5. At the beginning of microwave engineering, an accurate method to make measurements was the use of a slotted line. The method consisted in measuring the voltage amplitude and phase at the position of a moving impedance (the measuring element containing the MUT) at a fixed frequency as a function of the position on the line. In spite of its accuracy, this method is limited to one single frequency, and making a broadband study requires a great deal of cumbersome adjustments. However, thanks to transmission line properties it is known that the propagation term results from the product of the propagation constant and the position on the line. In other words, measuring at a fixed frequency as a function of the position on the line leads to equivalent results than measuring at a fixed point on the line as a function of frequency [54], which provides quite wieldy methods nowadays. In consequence, the majority of current methods are based upon broadband (multifrequency) measurements placing the MUT in a specified point. It is important to note that the calibration of such devices is of the utmost relevance for the success of the measuring process. A proper calibration allows to identify the effects of all the components of the system up to the measuring point, thus compensating for undesired losses, non-idealities and mismatches. This calibration is possible by means of using as MUT some trustable components with previously known properties, like short circuit loads, open circuit loads, transmission lines and specific impedance loads. A modern common measurement system for broadband dielectric characterization is based on an open-ended coaxial probe, firstly introduced by Roberts and von Hippel [56]. These probes are usually made of a coaxial line terminated in an open end. Their

2.1 Dielectric Dispersion Characterization

31

Fig. 2.6 Commercial coaxial probe: Agilent 85070E dielectric probe kit

popularity is due to their ease at handling, as well as the fact that they are widely sold commercially (one of them can be seen in Fig. 2.6). The use of these devices is simple: the MUT has to be attached to their open end, and then the overall reflection coefficient is measured as a function of frequency. Thus, the device is fed with a frequency-swept electromagnetic signal, and the fringing field at the end of the coaxial line interacts with the MUT (as depicted in Fig. 2.7). Usually, the measurement of the reflection coefficient is carried out with the help of a VNA. Once it is recorded for all the frequencies, an integral equation [57–59] derived from full-wave analysis of the aperture field at the end of the line [60–62] (which is out of the scope of this document) is numerically computed. This way, the measured reflection coefficient can be related to the dielectric complex permittivity of the sample, and the E* (ω) values are thereby obtained for each frequency in the sweep. Fig. 2.7 Diagram of an open-ended coaxial probe

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These systems work better with sufficiently large MUTs, especially when there is a good mechanical match at the interface between the MUT and the sensor. For this reason, as well as the capability to work in a broad frequency range, they are widely employed for the dielectric characterization of liquids [39, 63–68]. To mention some drawbacks, they require relatively large samples, they need direct contact with the sample (or at least direct handling of the sample), and they have size constraints which, in addition to the need of a VNA, often make them unable to be developed as portable devices. Another popular technique for measuring the complex dielectric permittivity of the MUT is based on transmission/reflection (T/R) line methods. It is a similar method in which the whole transmission line is considered (it is not terminated in an open end) to provide for reflected and transmitted signal measurement. The working principle in this case is similar to the open-ended coaxial probe, i.e., a sample of the MUT is placed inside a certain section of a coaxial line or waveguide, and the S-parameters are measured with a VNA. Then, the scattering equations of the whole system relate the experimental S-parameters to the dielectric permittivity of the MUT, and a numerical solution can be computed by several well-known methods, many of them being based upon the so-called Nicolson–Ross–Weir (NRW) method [69–73]. Since transmission and reflection information is available, there is more information to feed the computation algorithms, which have grown more sophisticated in the last years [74]. This is why this technique provides for more accurate measurements, at the expense of a more complex system compared to open-ended coaxial probes (two measuring ports instead of one). For the same above-mentioned reasons, these methods are widely used to characterize the dielectric behavior of liquids, and different configurations and applications have been proposed [75–80]. They also present similar drawbacks, namely the lack of portability, the need for direct contact or handling of the sample, and the sample size requirements (although some progresses have been made in this regard [81]). These techniques will be deeply discussed in Chap. 3, and an application for dielectric characterization of water–glucose solutions [75] (a work included in this dissertation) will be studied. There are situations in which only small amounts of the sample are available, or the sample cannot be moved and handled easily and hence a portable device would be desirable. Some examples are biological tissues characterization for physiological parameters tracking in medical applications or chemical composition control in specific industry processes (since it has been shown that measuring the dielectric permittivity could be helpful for chemical composition identification). In these cases, the sample is not easily accessible, the production process cannot be stopped, or it is desired to waste the smallest amount of sample during the checks. In this sense, mainly in biological applications, capability for non-invasive measuring is highly desirable. Under these circumstances, the methods discussed so far may present significant drawbacks, and other techniques arise as more suitable. These techniques are often based upon microwave coplanar systems (for example [82–85]), and they provide broadband characterization of very small samples (up to several nanoliters) but they still require direct handling of the samples due to their close configuration. To avoid

2.1 Dielectric Dispersion Characterization

33

this last drawback, the use of microwave resonator open structures has been studied and applied to many fields (see, for example, [86–90]). Paying the cost of lacking for broadband characterization (due to its narrowband nature), the electrical response of a microwave resonator has been shown to be quite sensitive to the dielectric permittivity of a MUT nearby at a given frequency, if a proper configuration is chosen. Placing the MUT in the right place, it can alter the electromagnetic boundaries of the resonator, and the changes in the electrical response can be analyzed to thereby deduce the properties of the MUT. As a microwave device, its size can be very reduced in comparison with the sizes required in the above-mentioned methods, and the needed driving electronics can be simplified and implemented avoiding large costs [91, 92], thus providing for portable capabilities. In addition, the sample amount required can be drastically reduced with proper techniques without significant sensitivity decreases [86]. This dissertation will put a special focus on the use of the microwave resonators for dielectric characterization and chemical composition sensing. For this reason, its theory fundamentals will be outlined in the next section.

2.2 Microwave Resonators: Fundamentals Resonators are widely used elements in many applications in microwave engineering. They are an essential part of bigger systems such as filters, oscillators, tuned amplifiers, frequency meters and so on. Basically, a resonator is a circuit able to store electromagnetic energy at a well-defined narrowband frequency range, regardless the broadband energy fed. In other words, it is a circuit able to accurately tune a certain frequency, and this is why lots of applications take benefit of it. This document has a special emphasis on them, and their use as permittivity and concentration sensors in aqueous solutions is studied. In this section the microwave resonator fundamentals will be reviewed. The concept of resonance can be easily approached by considering the analysis of an RLC lumped-element circuit. This analysis is worthy since, near the resonant frequency f r , a microwave resonator can usually be regarded as either a series or a parallel RLC circuit. For example, consider the series RLC circuit shown in Fig. 2.8. Adding the impedance of the three series elements in the circuit gives: Z in = R + jωL − j

1 ωC

(2.34)

The resonance occurs when the input impedance is purely real, that is, Z in = R. The resonant angular frequency ωr = 2π f r at which this condition is fulfilled is: ωr = √

1 LC

(2.35)

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Fig. 2.8 Series RLC lumped-element circuit

Considering an alternate current through the circuit in its phasor form I = I 0 ejωt , the average magnetic energy stored in the inductor U M is: UM =

1 2 I0 L 4

(2.36)

whereas the average electric energy stored in the capacitor U E is: UE =

1 1 2 1 VC C = I0 2 2 4 4 ω C

(2.37)

being V C the voltage across the capacitor. It can be seen that, at resonance, the average magnetic energy stored in the inductor equals the average electric energy stored in the capacitor. In this situation, the source can feed maximum power to the resonator, and therefore the power transmission from the resonator to a possible load is maximum at resonance. Therefore, at resonance U M (ωr ) = U E (ωr ). The power dissipated by the resistor PR is given by: PR =

1 2 I0 R 2

(2.38)

The input impedance magnitude of the resonator as a function of the angular frequency is plotted in Fig. 2.9, where BW stands for bandwidth, a characteristic frequency range delimited by the frequencies at which the power √ dissipated halves (it is reduced 3 dB from its maximum amplitude), i.e., |Z in | = 2R. An essential parameter of any resonant circuit is the quality factor Q, which compares the energy stored with the energy dissipated in one cycle. From an energetic standpoint, Q is defined as: Q = ωr

total average energy stored UM + UE = ωr power dissipated per second PR

At resonance, considering Eqs. (2.35)–(2.38) into Eq. (2.39) yields:

(2.39)

2.2 Microwave Resonators: Fundamentals

35

Fig. 2.9 Series RLC input impedance magnitude against angular frequency

Q = ωr

1 2UM 2U E ωr L = = ωr = PR PR R ωr RC

(2.40)

where L or C give the contribution of the reactive impedance (energy storage) and R gives the contribution of the resistive impedance (power dissipation). It should also be noted that, according to Eq. (2.40), Q is inversely proportional to R. It is interesting to study the behavior of the input impedance around the resonant frequency. To do it, ω ≡ ω − ωr is defined as a relatively small frequency deviation from the resonant frequency. The expression for the input impedance (Eq. 2.34) can be rearranged to read:  Z in = R + jωL 1 −

1 2 ω LC

 (2.41)

For ω  ωr , Eq. (2.41) can be approximated, using Eqs. (2.35) and (2.40), as:   Qω Z in ∼ R 1 + 2 j = ωr

(2.42)

As explained before, the resonator bandwidth BW is computed considering the √ frequencies at which |Z in | = 2R. From Eq. (2.42), this implies: 2Q

ωr ω = 1 ⇒ 2ω = ωr Q

(2.43)

Due to the symmetry of |Z in | around ωr , BW = 2ω. Then, the quality factor can be finally expressed as: Q=

fr BW

(2.44)

This relation shows that the resonant relative bandwidth increases with the losses in the resonator.

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Fig. 2.10 Parallel RLC lumped-element circuit

Regarding the parallel RLC lumped-element resonator, shown in Fig. 2.10, it can be analyzed in a similar way. In this case it is easier to consider the input admittance Y in = 1/Z in , given by: Yin = G + jωC − j

1 ωL

(2.45)

where G = 1/R is the conductance in the resistor. Again, the condition for the resonance is that the admittance must be purely real, thus yielding the same definition for ωr as shown in Eq. (2.35). Considering an alternate voltage supplied to the circuit in its phasor form V = V 0 ejωt , the average magnetic energy stored in the inductor is now: UM =

1 2 1 V0 2 4 ω L

(2.46)

and the average electric energy stored in the capacitor: UE =

1 2 V0 C 4

(2.47)

The new power dissipated by the resistor is given by: PR =

1 2 V0 G 2

(2.48)

It can be easily shown that at resonance (Eq. 2.35) both average energies are equal. The input admittance magnitude of the resonator as a function of the angular frequency is plotted in Fig. 2.11,√where the bandwidth is analogously defined by the frequencies that satisfy |Yin | = 2G. Concerning the Q factor, at resonance it is satisfied: Q = ωr

R 2UM 2U E ωr C = = ωr = PR PR G ωr L

(2.49)

Applying a similar analysis that for the series case, near the resonance the input admittance can be expressed as:

2.2 Microwave Resonators: Fundamentals

37

Fig. 2.11 Parallel RLC input admittance magnitude against angular frequency



1 Yin = G + jωC 1 − 2 ω LC

 (2.50)

Substituting Eq. (2.35) into Eq. (2.50) gives:  Yin = G + jωC

ω2 − ωr 2 ω2

 (2.51)

Considering the previously defined ω and the approximation ω2 −ωr 2 ∼ = 2ωω and applying it to Eq. (2.51) leads to: Yin ∼ = G + 2 jCω

(2.52)

  Qω G 1 + 2 j Yin ∼ = ωr

(2.53)

Applying Eq. (2.49) yields:

Then, considering the definition of√ the bandwidth as the frequency range delimited by the frequencies at which |Yin | = 2G, the same definition for the Q factor that the one discussed in Eqs. (2.43) and (2.44) is obtained. The ideal lumped elements considered in the series and parallel RLC circuits discussed so far are usually unattainable for microwave applications. These microwave circuits are made by printing the designed circuit as transmission line sections with a conductor material (usually copper) on a dielectric substrate. When the resonance concept is applied to microwave printed circuits with different technologies, such as microstrip or coplanar, analogous analysis can be done by considering the equivalent distributed-element models along a section of the transmission line, as shown in Fig. 2.12 for a transmission line of length dx. In the figure, R, G, C and L (namely the resistance, conductance, capacitance and inductance) are the distributed elements per unit length, dx is the section length, and I and V are the position-dependent current and voltage signals expressed as phasors. In this model, the power dissipated by the conductor is given by:

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Fig. 2.12 Lumped-element equivalent circuit for a transmission line section of length dx

d P cond =

1 Rd x I 2 2

(2.54)

whereas the power dissipated by the dielectric is: d P diel =

1 Gd x V 2 2

(2.55)

On the other hand, the average magnetic energy stored can be expressed as: dU M =

1 Ld x I 2 2

(2.56)

1 Cd x V 2 2

(2.57)

and the average electric energy stored: dU E =

To illustrate this, an open-circuited line will be considered, as shown in Fig. 2.13. This is a resonator implementation used quite often in microstrip circuits, and it will be deeply studied and applied in Chap. 4. In the figure, Z 0 is the characteristic impedance of the line, α is the attenuation constant, and β is the phase constant. This resonator consists of an open-circuited transmission line designed to have a length l that satisfies l = λ/2, being λ the wavelength at the resonant frequency (λ = vp /f , where vp is the phase velocity in the transmission line). From transmission line theory (see [93]), given a section of a lossy transmission line of length l, it is known that: Fig. 2.13 Open-circuited transmission line of length l

2.2 Microwave Resonators: Fundamentals

Z in = Z 0

39

Z L + Z 0 tanhγ l Z 0 + Z L tanhγ l

(2.58)

√ being Z L the load impedance and γ = α + jβ = (R + jωL)(G + jωC) is the complex propagation constant. In this case, since the transmission line ends in an open circuit, Z L = ∞, and hence Eq. (2.58) gives: Z in = Z 0 cot h(α + jβ)l

(2.59)

Now, using the next hyperbolic tangent identities: tan h(θ ± ϕ) =

tan hθ ± tan hϕ 1 ± tan hθ tan hϕ

tan h jθ = j tan hθ

(2.60) (2.61)

Equation (2.59) can be rewritten as: Z in = Z 0

1 + j tan βl tanh αl tanh αl + j tan βl

(2.62)

Although the considered transmission line is lossy, i.e., α = 0, the losses in the vast majority of transmission lines are small enough to assume αl  1, which implies tanh αl ∼ = αl. Hence, defining ω = ωr + ω being ω  ωr , as before, and considering a TEM line [93]: βl =

ωr l ωl ωl = + vp vp vp

(2.63)

At the resonant frequency f r = ωr /2π, due to the design of the line: l=

vp vp λ = =π 2 2 fr ωr

(2.64)

Then, substituting Eq. (2.64) into Eq. (2.63) yields: βl = π +

ωπ ωr

(2.65)

Thus:     ωπ ∼ ωπ ωπ = tan tanβl = tan π + = ωr ωr ωr

(2.66)

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Applying Eq. (2.66) in Eq. (2.62) and considering the low-loss approximation (the most common case), leads to: Z in ∼ = Z0

1 αl + j ωπ ωr

(2.67)

which can be written as admittance to get a wieldier expression:   ωπ 1 αl + j Yin ∼ = Z0 ωr

(2.68)

This expression is analogous to the input admittance for the parallel RLC lumpedelement circuit obtained in Eq. (2.52): Y in ∼ = G + 2jCω. By comparison, and bearing in mind that R = 1/G, the resistance of the short-circuited half-wave line equivalent circuit can be shown to be: Z0 αl

(2.69)

π 2ωr Z 0

(2.70)

R= whereas the capacitance is: C=

The inductance can be obtained applying the capacitance expressed in Eq. (2.70) into Eq. (2.35): L=

1 ωr

2C

=

2Z 0 ωr π

(2.71)

Therefore, this transmission line section acts as a resonator when the input admittance is purely real, i.e., Y in = G = 1/R = αl/Z 0 . By looking at Eq. (2.68) it can be seen that, effectively, this condition occurs when ω = 0, which happens at ω = ωr , the angular resonant frequency, if the design condition l = λ/2 is met. However, it is important to note that the discussion in Eqs. (2.64)–(2.67) remains true for l = nλ/2, n = 1, 2, 3, … due to the periodic condition of the tangent function. This means that infinite resonances will occur at integer multiples of the resonant frequency or wavelength (nλ), called harmonic resonances. For instance, the voltage distributions for the first (n = 1) and second (n = 2) resonant modes along the line are plotted in Fig. 2.14. Finally, the Q factor can be easily obtained substituting Eqs. (2.69)–(2.71) into Eq. (2.49), and considering that βl = π for the first resonant mode [as it can be deduced from Eq. (2.65)]: Q=

π β R ωr C = ωr RC = = = G ωr L 2αl 2α

(2.72)

2.2 Microwave Resonators: Fundamentals

41

Fig. 2.14 Voltage distributions for the first and second resonant modes in an open-circuited transmission line of length l = λ/2

This result points out that the quality factor decreases when the attenuation of the line (the losses αl) increases. Another widely used configuration is the short-circuited quarter-wave line, as shown in Fig. 2.15. This design also acts as a parallel resonator, and it will be studied and used in Sect. 7.2. It is a transmission line of length l, this time designed to satisfy l = λ/4, terminated with a short circuit. According to the transmission line theory, the input impedance for this resonator is given by: Z in = Z 0 tanh(α + jβ)l

(2.73)

Considering the hyperbolic tangent identities (2.60) and (2.61) yields: Z in = Z 0

1 − j tanh αl cot βl tanh αl − j cot βl

(2.74)

Applying a similar analysis assuming l = λ/4 at resonance, for a TEM line it is satisfied: βl = Therefore: Fig. 2.15 Short-circuited transmission line of length l

ωr l ωπ ωl π + = + vp vp 2 2ωr

(2.75)

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cotβl = −tan

ωπ ∼ ωπ =− 2ωr 2ωr

(2.76)

Applying Eq. (2.76) into Eq. (2.74) and considering the low-loss approximation, as before, the input impedance is: Z in = Z 0

1 + jαl ωπ 2ωr αl + j

ωπ 2ωr

∼ =

Z0 αl + j ωπ 2ωr

(2.77)

Again, Z in can be written as admittance:   1 ωπ ∼ Yin = αl + j Z0 2ωr

(2.78)

Following a similar analysis, this expression can be compared to the input admittance for the parallel RLC lumped-element circuit (Eq. 2.52): Y in ∼ = G + 2jCω. Then, the resistance of the short-circuited quarter-wave line equivalent circuit is: Z0 αl

(2.79)

π 4ωr Z 0

(2.80)

4Z 0 1 = ωr 2 C ωr π

(2.81)

R= the capacitance is expressed as: C= and the inductance is given as: L=

The resonance will occur when the input admittance is purely real, i.e., Y in = G = αl/Z 0 . Equation (2.78) shows that this condition happens at the resonant frequency, as expected. In this case, there will also be infinite resonant modes, as it always happens with distributed-element resonators. The voltage distributions for the first and second ones are plotted in Fig. 2.16. Regarding the Q factor, from Eq. (2.49) and Eqs. (2.79)–(2.81) and considering βl = π /2 for the first resonant mode it can be defined as: Q=

π β R ωr C = ωr RC = = = G ωr L 4αl 2α

(2.82)

Again, the quality factor is lower for higher attenuations of the line. Basing upon the preceding theoretical principles, many sorts of resonators can be achieved by choosing the proper configuration for each application. With these design

2.2 Microwave Resonators: Fundamentals

43

Fig. 2.16 Voltage distributions for the first and second resonant modes in a short-circuited transmission line of length l = λ/4

guidelines, and bearing in mind the concept of infinite harmonic resonances, a vast range of frequencies can be tuned for any application. A more detailed explanation of microwave resonators theory can be found in [94]. This document will consider the use of microwave resonators as permittivity and solvent concentration sensors in further chapters. Finally, it is important to notice that the quality factor discussed so far for any resonator is an intrinsic characteristic of the circuit, without considering the possible effects that any external load could have in its global behavior. For this reason, it is commonly denoted unloaded quality factor Qu , as it will be referred to hereinafter. However, a resonator does not have much utility as an isolated system, and it will be always loaded with further circuitry, depending on the application, either to take benefit of the tuned frequencies or to measure and characterize them. The consequence of these new components will be always a decrease in the overall quality factor of the resonator. In this case, the measured quality factor is called the loaded quality factor QL , and it represents the quality factor of the resonator when it is interacting with the load. Denoting as external quality factor Qe the quality factor associated to the elements that do not strictly belong to the resonator, the relationship between the different types of quality factor can be expressed as shown below: 1 1 1 = + QL Qe Qu

(2.83)

The unloaded quality factor will have a special importance in this document when using microwave resonators for sensing purposes, and it will be discussed more deeply later.

2.3 Application to Diabetes Given the dependence of the relaxation processes on the chemical composition of the materials, which can trigger the specific types of polarization and relaxations, it seems

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a good idea to have permittivity sensors to track the glucose concentration. A candidate manner to develop these sensors is by means of microwave resonators. These circuits have a well-defined, easy-to-track electrical response (as shown in Sect. 2.2), which can be quite sensitive to the permittivity changes of the surrounding medium if proper configurations are chosen. A possible field of application is diabetes management, which requires frequent measurement of blood glucose level (BGL, called glycemia). Thus, there has been an intense worldwide scientific activity to relate the changes in the permittivity of blood to the actual BGL, and measure these changes with microwave techniques. In the next sections, the complications of diabetes and the need for blood glucose measurements, as well as the existing procedures to do it and the research that is currently being carried out to make needed enhancements to them are reviewed.

2.3.1 Diabetes Mellitus and Its Complications The term diabetes mellitus is used for referring to a compilation of diverse disorders with a common characteristic: unhealthy blood glucose levels. In a basic approach, it consists in the wrong regulation of the hormone insulin by the body. This hormone is produced by the pancreas and secreted into the bloodstream in response to rising levels of glucose in the blood. Insulin interacts with cells to create transmembrane channels that allow glucose to enter the cells. Then, cells decompose glucose in a process called glycolysis, and use it as a power source by the body. Due to this reason, keeping the BGL within a healthy range (∼70 to 140 mg/dL) is vital. The most common symptoms of the presence of diabetes are poor blood circulation, blurred vision, loss of energy and slow-healing wounds, as well as issuing a volume of urine higher than expected (polyuria) and a strong need of drinking large amounts of water (polydipsia) in order to get rid of the excess of glucose [95]. Diabetes afflicts millions of people worldwide. According to the last reports [96], in the year 2014 the global prevalence of diabetes was estimated to be 9% among the adult population (more than 18 years old), meanwhile in 2012 the data showed that 1.5 million deaths were directly caused by it. Diabetes has a remarkable, fastgrowing presence, since it was estimated that in 2014 there were 422 million adults with diabetes worldwide (equivalent to roughly 1.3 times the population of the USA, or 9 times the population of Spain), a figure that has grown almost fourfold since 1980. The same estimations predict that this disease will be the seventh leading cause of death in 2030. What is more, some studies [97] have pointed out an increase of 55% in the number of diabetic adults for the year 2035, which will be greater in areas like Africa (109.1%) or South-East Asia (70.6%), and lower in other parts like North America and Caribbean (37.3%) or Europe (22.4%), thus confirming the more rapid increasing trend of diabetes prevalence in middle- and low-income countries predicted by [96]. ´ The word ‘diabetes’ comes from the Greek term διαβητης (in Latin diab¯e´t¯es). It is a substantive derived from the verb διαβα´ινω (diabaín¯o), formed from the prefix

2.3 Application to Diabetes

45

δια (diá), which means ‘through’, and the verb βα´ινω (baín¯o), which means ‘go’ [98, 99]. Thus, since the prefix that makes a substantive from the mentioned verb is της (t¯es), meaning ‘tool’, the primal meaning of the word ‘diabetes’ is “a tool to make something—generally liquids—go through some medium”, regarding the need of drinking lots of water to get the excess glucose out of the body. A large majority of people with diabetes are classified as having either insulindependent or non-insulin-dependent diabetes [100]. Commonly, the former are referred to as type 1 diabetes, whilst the latter are referred to as type 2 diabetes. In type 1 diabetes the pancreas losses the capability to generate the required amounts of insulin, whereas in type 2 diabetes there is a misfunction in the glucose receptors on the cells, so that they cannot make an effective use of insulin. Usually, type 1 diabetes appears at early stages of life, while type 2 diabetes develops over time. The classical screening symptoms leading to diagnose of diabetes are fasting plasma glucose ≥ 126 mg/dL or Oral Glucose Tolerance Test (OGTT) venous plasma glucose ≥ 200 mg/dL at 2 h after 75 g oral glucose intake [100]. Since diabetes has no known cure, the treatment consists in measuring the blood glucose level and making the needed correction to keep it within the healthy range. When the pancreas does not produce enough insulin, or the glucose receptors are not working well, the cells cannot take the glucose from blood and break it down, and thereby the BGL rises too high (hyperglycemia). When this occurs, cells cannot power up sufficiently by this mechanism, and other metabolic procedures take place to feed them, mostly by burning fatty acids (ketosis). As a consequence, organic compounds called ketones are generated and secreted into the bloodstream (developing ketoacidosis). Since ketones are acidic, some organs may be damaged after prolonged exposures to them [95]. Frequent side effects of this process are kidney failure or heart disease. If glycemia conversely falls too low (hypoglycemia), often as a result of a wrong regulation of the previous process, a similar situation happens since cells are again not able to power up from glucose. This is a more dangerous situation since this time the auxiliary powering processes are seldom sufficient to compensate for the lack of energy, and cells often start not to work properly. This situation is strongly menacing to the body because the brain and nervous system need considerable amounts of glucose to function, and therefore a severe hypoglycemia could finally lead to a hazardous coma [95]. Both situations can be dealt with either by using suitable insulin injections or by having a proper glucose intake. In case of hyperglycemia, an insulin injection can compensate the lack of insulin in the bloodstream for type 1 diabetes, or an excess of insulin in type 2 diabetes can help the damaged glucose receptors to interact properly with glucose. In case of hypoglycemia, a suitable glucose intake can rise BGL to a healthy value. Consequently, monitoring of BGL is essential for diabetes treatment and care [101], in order to carry out the right actuations as soon as anomalies are detected. In this sense, to have a normal life, self-measurement of BGL plays a crucial role in the life of a person with diabetes. In the next section, the most common BGL measuring systems will be reviewed.

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2.3.2 Glycemia Measurement Systems Several BGL measurements are needed in the daily life of a person with diabetes. Depending on the severity of the disease and associated disorders, the number of required measurements per day may vary from 2–3 to 6–8 in normal conditions [102, 103]. The usual way to monitor BGL is with a glucometer, a device commercially available which is capable to measure the BGL from a drop of blood within a certain accuracy range. Most of them are able to measure BGL ranging 0–600 mg/dL with approximately 15% accuracy [104], meeting ISO 15197 standard. These devices have been used for dealing with diabetes for more than five decades, since Clark and Lyons set in 1962 the basic working principles [105, 106]. Their paper is one of the most cited works in history of life sciences (over 1900 citations), and therefore Clark is commonly considered as the father of biosensors, at least as far as glucose sensing is concerned. The impact of their work can be understood by considering that the working principles they described remain almost unaltered in the current implementations of many glucometers [107]. The wide use of these devices has led to a noticeable evolution [108] which has allowed them to benefit from intense scientific research activity [109]. The general measuring method with a glucometer consists in the user pricking their skin, usually on the fingertip, with an ad hoc lancet. Then, the punctured area is squeezed until a sufficient drop of blood is obtained. The drop is collected on a test strip plugged into the glucometer, and the BGL of the blood sample is obtained by applying different principles, normally electrochemical procedures or photometry. A picture of this process with a conventional glucometer can be seen in Fig. 2.17. Regardless of the applied principle, all glucometers make use of glucose oxidase. This is an enzymatic reagent that, when mixed with glucose, induces a chemical reaction which produces a color change and an electron current, both related to the amount of glucose in the sample. This way, the working principle of glucometers based upon photometry consist in illuminating the collected blood drop after the Fig. 2.17 BGL measuring with a conventional glucometer

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chemical reaction is finished, and measuring the wavelength of the reflected light to identify the resultant color and hence the BGL. On the other hand, glucometers based on electrochemical procedures make measurements of the flow of electrons as a result of the chemical reaction, in order to determine the amount of glucose reacting and therefore the BGL. Despite their use worldwide, these devices have two important drawbacks. On the one hand, only intermittent measurements are possible, which give information about the individual’s BGL at certain moments. This implies that many significant events may become unnoticed, worsening the treatment. On the other hand, the measurement procedure is invasive, painful and uncomfortable, especially for young and aged users [110]. Consequently, the number of daily measurements performed is often lower than the desirable amount, and this can lead to additional complications. For these reasons, the scientific activity of the last decade has put a special emphasis on the pursue of non-invasive blood glucose monitoring (NIBGM) technology [111–113], in which there should be no need for direct contact with blood, as the glycemia would be retrieved by other means. Such a technology would avoid these problems and hence lead to a remarkable enhancement in diabetes treatment. Proper NIBGM technology could therefore increment the number of measurements per day without disturbing the user, and thus provide for quicker detection of undesired events. In addition, NIBGM could even lead to continuous glucose monitoring (CGM), making it possible to detect almost instantaneously any glycemia change, thanks to the possibility of making periodic measurements with relatively short measuring periods, once the painfulness is removed. This would yield to the solution for the first drawback, and for the general problem as well. For these reasons, research on CGM and NIBGM can contribute to provide better treatment and management for diabetes, and therefore be conducive to stop this burden which is threatening the global population. In the next sections current attempts for CGM (Sect. 2.3.3) and NIBGM (Sects. 2.3.4 and 2.3.5) will be reviewed.

2.3.3 Continuous Glycemia Measurement The problem of the intermittent BGL measurements has been approached from several points. Automatic diabetes management systems have been pursued for more than 30 years [114]. For example, autoregressive models and complex algorithms for prediction of future glycemia levels and their evolution have been widely investigated (for instance [115–124]). The main aim is to reduce the required amount of BGL measurements and predict the glycemia values between measurements, ideally avoiding the blind periods. However, none of them has hitherto been fully successful for use by the general population due to the need of sophisticated models for realistic patient-oriented conditions [125]. Despite that, the considerable amount of recent references in this regard, most of them based upon machine learning techniques, points out the intense activity of this field of study and its potential.

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These techniques require large experimental measurements to feed the algorithms, and thus the development of reliable sensors must be constantly faced. Thus, the pursue of a reliable CGM has been also an active field of research [126–129]. Such a system would be able to continuously track glycemia and detect immediately all the significant events (hyper and hypoglycemia). This information would allow the individual or other devices to carry out the right actuation at the moment, remarkably improving the treatment of diabetes [130]. Indirect approaches have been made for CGM. For example, a commercial multisensor technology (SenseWear® Pro Armband™) capable to measure several parameters, such as skin and ambient temperature, skin conductivity, heat flux or body motion, has been proposed for several health and sport applications [131–133]. Among these applications, it was proposed for non-invasive CGM, applying mathematical algorithms to try to indirectly obtain the user’s BGL from the available information of the sensors [134]. The results were not fully convincing, but the potential of CGM technology was highlighted. Electrochemical CGM sensors, although remaining invasive, have been studied during the last decade [135–138]. Some of them have even been commercialized and are being used by the population nowadays, like Dexcom G6® [139], Abbot FreeStyle Libre [140], Senseonics™ Eversense® Long-Term [141] or Medtronic Guardian™ Sensor3 [142]. However, they are not yet deemed as the definitive CGM solution as they present significant drawbacks. The sensors and receivers needed are often costly, and the need for constant disposable stuff replacement frequently makes them unsuitable for long-term use. Some of them require an incision at the physician’s office for insertion and removal of the sensor (for example [141]). The need for frequent calibrations, up to twice a day in some cases [141, 142], still involves the daily use of invasive intermittent measurements. Some of them can be seen in Fig. 2.18. Therefore, despite their commercial availability, research in this regard goes on because there are still many issues to be faced in order to provide for fully trustable CGM [143–145]. These systems remain invasive, and the measurements are made by placing a wearable sensor on the user’s skin. Since these systems require smaller sample volumes than the conventional ones, they can be placed in other areas such as forearm or abdomen, when the nerves are not as close together as in the fingertip, and the pain and discomfort is reduced. Their sensor makes a constant pricking in the skin and measures the BGL in the interstitial fluid, not directly in blood [146]. As a consequence, there is a variable time delay between interstitial glucose and blood glucose that must be dealt with [147]. In addition, they keep presenting significant measurement errors, chiefly due to the inherent inflammation of the skin in the surroundings of the sensor placing [148]. For these reasons, although the commercial availability brings optimism to the topic, current CGM has not fully met the expectations of diabetes community, especially concerning hypoglycemia [149, 150]. Moreover, recent researches have shown that current BGL monitoring systems have a clear economic impact for health institutions, which is related to their measurement inaccuracy and the outcoming complications [151]. With regard to this, health costs have been proven to be drastically lower

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Fig. 2.18 Commercial CGM systems

when involving CGM [152]. Therefore, the necessity of a reliable NIBGM technology that can provide for accurate and stable CGM is evident, and the scientific community is thoroughly working towards it. In the next section some approaches to NIBGM will be reviewed.

2.3.4 Approaches to Non-invasive Glycemia Measurements NIBGM technology has been approached from different points during the last decades [153, 154]. For instance, a contribution for hypoglycemia detection was made by trying to identify this event from electroencephalogram signal [155]. However, the main approach has been focused upon the development of specific sensors for BGL measurement basing on different principles. One of these principles relied on the measurement of salivary glucose as an indicator of blood glucose. Salivary glucose sensors were made of layer-by-layer assemblies of single-walled carbon nanotubes, chitosan, gold nanoparticles and glucose oxidase onto a screen-printed platinum electrode, so that salivary glucose could be detected by electrochemical means [156–158], as shown in Sect. 2.3.2. A non-invasive on-chip disposable sensor was developed for glycemia measurement [159], although significant delays between salivary glucose and blood glucose were obtained. This was an interesting approach, although this technology was not intended to replace common BGL meters, as the authors stated. Other methods have been studied, like glycemia measurement from breath, which raised some optimism a few years ago [160]. Breath acetone in expired air was shown to be correlated with ketones and blood acetone levels [161, 162]. Hence,

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breath acetone sensors based upon cavity ringdown spectroscopy techniques [163] or multisensor assemblies [164, 165] were developed to measure breath acetones and try to find their correlation with BGL [166]. Ultrasound techniques for glucose monitoring were also investigated [167]. Other attempts to indirectly measure glycemia from other biomarkers can be found in the literature, like the use of suction on the skin surface [168], or NIBGM from the individual’s gingival crevicular fluid [169, 170], tear fluid [171–173], or blood flow occlusion [174], none of them reaching conclusive results. A popular NIBGM device that has been intermittently commercialized since early 2000s is GlucoWatch® G2™ Biographer (Cygnus, Inc., Redwood City, CA, USA), shown in Fig. 2.19. It was a wrist-watch like glycemia monitoring system that applied a low electrical current through the skin under it. This current drew interstitial fluid from the skin by a process known as reverse iontophoresis [175]. Then, the device computed BGL from the interstitial fluid. It took measurements every 20 min for up to 12 uninterrupted hours, and rang an alarm when hyper or hypoglycemia was detected. The development and commercialization of Glucowatch® yielded to intense research about its reliability and convenience (for example [176–178]). Notwithstanding, it was not finally accepted by diabetes community [179] due to important shortcomings that were not solved, like the cumbersome calibration process (with invasive measurements), irritation after hours of use, inaccuracy, false alarms [180] or the delay between BGL and interstitial glycemia. Another field of active research is the development of sensors by optical means. Techniques involving reflective fiber optics measuring the refractive index of solutions by multimode interference in order to characterize the solutions are currently being investigated [181], and their use for estimating the glucose content of the solutions is under study [182]. More advanced are the attempts aiming to interstitial glucose measurement by means of optical or photoacoustic sensors based on red [183], mid- [184, 185] and near-infrared [186–190] spectroscopy techniques. Fig. 2.19 GlucoWatch® G2™ Biographer NIBGM device

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Despite the new contributions and advancements in optical sensors, some shortcomings must be addressed before real application, like background absorption by water, poor signal-to-noise ratio due to interference, calibration drawbacks, baseline drift or thermal noise, among others [191]. Notwithstanding all these approaches, when non-invasiveness is required for sensing purposes, sensors based upon microwave technology are often involved, mainly due to their penetration capabilities and sensitivity to the dielectric properties of the environment (see [42, 192, 193]). Indeed, this is one of the approaches that have raised the most attention in the pursue of NIBGM technology. This document is focused on these techniques for the development and assessment of these sensors, and they will be deeply discussed in Chaps. 4–7. In the following section their fundamentals and existing attempts will be reviewed.

2.3.5 Microwave Sensors for Non-invasive Glycemia Measurement In 2003 Hayashi et al. used time domain dielectric spectroscopy to study the properties of spherical erythrocytes suspended in diluted phosphate saline buffers (PBS) at varying glucose concentrations [194]. Their findings were of the utmost relevance, and it soon became a reference work in this field. Specifically, they reported how the interaction of glucose with the erythrocytes changes the measured cell membrane capacitance of the erythrocytes due to the polarization processes discussed in Sect. 2.1.1, mostly Maxwell–Wagner polarization. That work showed how these capacitance changes led to variations in the complex frequency-dependent permittivity, although in a non-monotonic manner. This was only seen for d-glucose (natural glucose), whereas its synthetical isomer l-glucose (found at comparatively smaller amounts) scarcely showed permittivity variations. Later, the same group quantified this change in the cell membrane capacitance and associated it to a change in the cell shape when interacting with glucose [195]. Other works soon supported this phenomenon, relating the change in the permittivity to erythrocytes aggregation and rouleaux formation processes [196, 197], which are known to be closely related to glucose intake in the erythrocytes [198–200]. However, not only the changes in the permittivity due to the interaction of erythrocytes with glucose were reported, but the presence of glucose itself in an aqueous solution was shown to change the overall permittivity, as reported by Park et al. [201] also in 2003 in another reference work in this field. They applied broadband dielectric spectroscopy techniques (as outlined in Sect. 2.1.2) to measure E* (ω) of glucosecontaining aqueous solutions at different glucose concentrations up to 1 GHz, and a correlation between the permittivity and the glucose level was seen, noticeably greater for E (ω). Other authors also gave support to this by reporting changes in the impedance parameters of aqueous solutions due to the variations in the glucose level, measured

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by impedance spectroscopy [202, 203], and related them to changes in E* (ω) [204]. Recent works have identified and characterized the permittivity changes in aqueous solutions at upper frequencies by means of dielectric spectroscopy techniques [75, 205]. This means that there are more fields of application of these techniques different to BGL measurement, as the dielectric changes are not only due to the interaction of glucose with erythrocytes. Therefore, having demonstrated how glucose alters the dielectric characteristics of the medium in which it is solved, due to several physical principles, it seems a good idea to develop permittivity sensors for glucose content measurement, as it was discussed in Sect. 2.1.1. This could be helpful in finding a good solution for BGL measurement. Indeed, the use of dielectric properties for biological markers monitoring has been successfully applied to several fields [206–208] (some recent ones are [209, 210], for example). Under this belief, some works have tried to characterize the dielectric properties of glucose solutions with dielectric spectroscopy techniques, like for instance waveguide systems [211], although the most used technique has been open-ended coaxial probe (as shown in Sect. 2.1.2). With these probes, the permittivity and conductivity of human skin were characterized [212]. The blood permittivity was obtained and shown to have an inverse relationship with frequency [213], at least up to a few GHz. Other works approximated and fitted the blood permittivity and conductivity to a single-pole [214] and a two-pole [215] Cole–Cole model including the glucose concentration dependence. The dielectric characteristics of blood were shown to vary when the BGL changes [68]. In addition, the dielectric properties of most biological tissues were comprehensively characterized for a wide range of frequencies in the painstaking works by Gabriel et al. [216–218], another remarkable contribution to the topic. Hence, given the sensitivity of microwave devices to the permittivity of the medium [219], some microwave techniques have been utilized with glucose sensing purposes. Techniques like transmission between two matched antennas [220, 221] have been studied, as well as transmission line techniques [222]. Also, waveguides were employed for dielectric characterization of biological liquids [223], glucose level estimation in aqueous solutions [224–226] and even in vivo BGL retrieval [227], without reporting conclusive results. In addition, these sensors are often bulky and not convenient for integration into more sophisticated electronic systems. To avoid these drawbacks, the use of microwave resonators is often considered in this regard, given its sensitivity to permittivity changes. As a matter of fact, it is well known that the propagation properties of a microstrip line change when the permittivity of the material in its upper space varies. Many works have explained this and highlighted the variations of some properties of the line such as characteristic impedance, phase velocity, attenuation and Q factor [228, 229] (as discussed in Sect. 2.2). Some other works have proven the potential of microstrip resonators for measuring the permittivity of any material placed upon them [230–232]. For a review on determination of complex permittivity with Q factor using microstrip resonators the reader is kindly referred to [233].

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Following these principles, Caduff et al. made in 2003 one of the first attempts to employ resonant circuits (in this case with an impedance meter configuration) to try to measure the BGL in humans [234] (further studied in [235, 236]). Significant changes in the user’s skin impedance as the glycemia varied were reported up to 200 MHz, which is consistent with the initial hypothesis by Hayashi et al. [194]. However, these variations were not clearly observed in pure water solutions, although Park et al. [201] and other authors did identify them, as explained before. Anyway, these works opened a new research line aimed to develop microwave sensors, for BGL estimation, and especially NIBGM. Almost fifteen years later, studies of the dielectric behavior of blood keep on pointing out the convenience of utilizing non-invasive microwave glucose sensors [237], and more specifically methods based on resonators [238]. Since the publication of those primal articles, the application of different techniques based on microwave resonators has been put forward, given their high sensitivity to the permittivity of the surrounding media. Works based upon electromagnetic simulations have shown the convenience of microwave resonators for such a purpose, giving models for biological tissue simulation. In [239] a wideband monopole antenna was designed and simulated using a layered model of tissues mimicking human skin and blood, with good results (mainly for hypoglycemia detection), although some noise was found in the implementation [240]. Also, preliminary simulation works with new models for the tissues were published, concerning patch [241] and spiral resonators [242]. Folded ring microstrip resonators in different configurations have also been studied and simulated with water–glucose solutions [243–246], as well as split-ring resonators with complex solutions [247] and microfluidic setups [248–250]. Microstrip line resonators have also been investigated with aqueous solutions [251]. The properties of the fingertip as measuring area have been studied and models for accurate electromagnetic simulation have been provided [252, 253]. An accurate Cole–Cole model for simulation of blood permittivity including the glucose contribution was reported in [237]. Some sensors have been implemented and tested in vitro, with different configurations. Works aimed to measure the glucose level in aqueous solutions have shown the real potential of these technology. To name a few, a spiral-shaped transmission line was used with a coaxial probe [254], or an ad hoc open-ended coaxial probe was proposed [255]. Glucose content of aqueous solutions was measured with microstrip ring resonators [256] and with half-wave resonators in microfluidic networks [257]. An open-loop resonator configuration for water–glucose solutions characterization in microliter-volume samples using Q factors was presented in [86] (a work included in this dissertation), reporting an increase in the sensitivity with regard to the existing literature. This work will be deeply discussed in Chap. 4. Some enhancements of this system leading to better sensitivities have been recently reported in [258] (another work included in this dissertation), and they will be seen in Chap. 7. In vitro studies concerning biological tissues have also been carried out. The effective dielectric constant of lossy phantoms mimicking biological tissues was measured with spiral resonators [88]. Glycemia in pig blood was measured with spiral resonators [259], although not much sensitivity was obtained. The glucose concentration of human blood plasma samples when other components content varies

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(lactic and ascorbic acid, in addition to glucose) has been recently measured with the open-loop resonators discussed in [86], obtaining different sensitivities according to the concentrations of the rest of components in the sample [260] (a work included in this dissertation). An in-depth review of this study will be given in Chap. 5. Finally, some attempts have been made to develop and assess this kind of sensors when applied to in vivo environments. The group by Jean et al. was one of the first to study spiral resonators to measure BGL in human volunteers, obtaining promising results [87], although no further works have been hitherto published in this line. A new approach based upon a double split-ring resonator was proposed in [90], aimed to compensate for temperature effects. Experiments for BGL measurements were performed both in vitro and in vivo, showing promising results in some cases. A recent comprehensive study of the use of open-loop resonator for NIBGM in real clinical scenarios is offered in [91, 92] (two works included in this dissertation), which will be analyzed in Chap. 6. For recent thorough reviews of these techniques applied to NIBGM see [154, 261, 262]. As shown, the constant activity of this field of research indicates that the scientific community has identified the potential of this technology for the future of NIBGM technology. In general, so far there are some works that have achieved promising results for in vitro trials, albeit not a fully convincing in vivo performing has been reported to date. This means that these sensors have shown good behavior as glucose sensors for simple media, conversely not meeting the expectations of diabetes community when real biological media are concerned. This is mainly due to the complexity and the big number of variables taking place, often requiring sophisticated algorithms to analyze great deals of data to make the measurements converge and retrieve the glucose level [263]. Therefore, there is still further research to be carried out for real implementation. It is an interesting topic not only for NIBGM, but also for many industrial processes in which the control of sugar level is required, like the production of sugared drinks. The existing open lines in this regard on how they can be faced will be discussed in Chap. 7.

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201. Park J-H, Kim C-S, Choi B-C, Ham K-Y (2003) The correlation of the complex dielectric constant and blood glucose at low frequency. Biosens Bioelectron 19(4):321–324 202. Tura A, Sbrignadello S, Barison S, Conti C, Pacini G (2007) Impedance spectroscopy of solutions at physiological glucose concentrations. Biophys Chem 129(2–3):235–241 203. Olarte O, Barbé K, Van Moer W, Van Ingelgem Y, Hubin A (2014) Measurement and characterization of glucose in NaCl aqueous solutions by electrochemical impedance spectroscopy. Biomed Signal Process Control 14:9–18 204. Yoon G (2011) Dielectric properties of glucose in bulk aqueous solutions: influence of electrode polarization and modeling. Biosens Bioelectron 26(5):2347–2353 205. Lin T, Gu S, Lasri T (2017) Highly sensitive characterization of glucose aqueous solution with low concentration: Application to broadband dielectric spectroscopy. Sens Actuators, A 267:318–326 206. Mohammed BJ, Abbosh AM, Mustafa S, Ireland D (2014) Microwave system for head imaging. IEEE Trans Instrum Meas 63(1):117–123 207. Bahrami H, Mirbozorgi SA, Rusch LA, Gosselin B (2015) Biological channel modeling and implantable UWB antenna design for neural recording systems. IEEE Trans Biomed Eng 62(1):88–98 208. Bashri MSR, Arslan T, Zhou W, Haridas N (2016) Wearable device for microwave head imaging. In: Proceedings of the 46th European microwave conference (EuMC), London, UK, pp 671–674 209. Greene J, Abdullah B, Cullen J, Korostynska O, Louis J, Mason A (2019) Non-invasive monitoring of glycogen in real-time using an electromagnetic sensor. In: Mukhopadhyay SC, Jayasundera KP, Postolache OA (eds) Modern sensing technologies. Smart sensors, measurement and instrumentation, vol 29. Springer, Berlin, pp 1–15 210. Amin B, Elahi MA, Shahzad A, Porter E, McDermott B, O’Halloran M (2019) Dielectric properties of bones for the monitoring of osteoporosis. Med Biol Eng Comput 57(1):1–13 211. Alison JM, Sheppard RJ (1993) Dielectric properties of human blood at microwave frequencies. Phys Med Biol 38(7):971–978 212. Grant JP, Clarke RN, Symm GT, Spyrou NM (1988) In vivo dielectric properties of human skin from 50 MHz to 2.0 GHz. Phys Med Biol 33(5):607–612 213. Jaspard F, Nadi M (2001) Open ended coaxial line for electrical characterization of human blood. In: Proceedings of the 23rd annual international conference of the IEEE engineering in medicine and biology society (EMBC), Istanbul, Turkey 214. Topsakal E, Karacolak T, Moreland EC (2011) Glucose-dependent dielectric properties of blood plasma. In: Proceedings of the XXXth URSI general assembly and scientific symposium, Istanbul, Turkey 215. Karacolak T, Moreland EC, Topsakal E (2013) Cole-Cole model for glucose-dependent dielectric properties of blood plasma for continuous glucose monitoring. Microw Opt Technol Lett 55(5):1160–1164 216. Gabriel C, Gabriel S, Corthout E (1996) The dielectric properties of biological tissues: I. Literature survey. Phys Med Biol 41(11):2231–2249 217. Gabriel S, Lau RW, Gabriel C (1996) The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 41(11):2251–2269 218. Gabriel S, Lau RW, Gabriel C (1996) The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41(11):2271–2293 219. Krupka J (2006) Frequency domain complex permittivity measurements at microwave frequencies. Meas Sci Technol 17(6):R55–R70 220. Hofmann M, Fersch T, Weigel R, Fischer G, Kissinger K (2011) A novel approach to noninvasive blood glucose measurement based on RF transmission. In: Proceedings of the 2011 IEEE international symposium on medical measurements and applications, Bari, Italy 221. Saha S, Cano-Garcia H, Sotiriou I, Lipscombe O, Gouzouasis I, Koutsoupidou M, Palikaras G, Mackenzie R, Reeve T, Kosmas P, Kallos E (2017) A glucose sensing system based on transmission measurements at millimetre waves using micro strip patch antennas. Sci Rep 7(1):6855

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240. Venkataraman J, Freer B (2011) Feasibility of non-invasive blood glucose monitoring: invitro measurements and phantom models. In: Proceeedings of the 2011 IEEE international symposium on antennas and propagation (APSURSI), Spokane, WA, USA 241. Yilmaz T, Hao Y (2011) Compact resonators for permittivity reconstruction of biological tissues. In: Proceedings of the XXXth URSI general assembly and scientific symposium, Istanbul, Turkey 242. Pimentel S, Agüero PD, Uriz AJ, Bonadero JC, Liberatori M, Castiñeira Moreira J (2013) Simulation of a non-invasive glucometer based on a microwave resonator sensor. J Phys: Conf Ser 477(1):012020 243. Deshmukh VV, Ghongade RB (2016) Measurement of dielectric properties of aqueous glucose using planar ring resonator. In: Proceedings of the 2016 international conference on microelectronics, computing and communications (MicroCom), Durgapur, India 244. Jagtap AS, Sawarkar SD (2017) Microstrip folded ring resonator for glucose measurement. In: Proceedings of the 2017 international conference on energy, communication, data analytics and soft computing (ICECDS), Chennai, India 245. Marattukalam F, Sawant D (2017) Efficient microstrip ring resonator antennas for glucose measurement. In: Proceedings of the 2017 international conference on wireless communications, signal processing and networking (WiSPNET), Chennai, India 246. Odabashyan L, Babajanyan A, Baghdasaryan Z, Friedman B, Lee K (2018) Glucose aqueous solution sensing by modified hilbert shaped microwave sensor. Armen J Phys 11(4):214–222 247. Camli B, Kusakci E, Lafci B, Salman S, Torun H, Yalcinkaya AD (2017) Cost-effective, microstrip antenna driven ring resonator microwave biosensor for biospecific detection of glucose. IEEE J Sel Top Quantum Electron 23(2):6900706 248. Abduljabar AA, Rowe DJ, Porch A, Barrow DA (2014) Novel microwave microfluidic sensor using a microstrip split-ring resonator. IEEE Trans Microw Theory Tech 62(3):679–688 249. Rowe DJ, al-Malki S, Abduljabar AA, Porch A, Barrow DA, Allender CJ (2014) Improved split-ring resonator for microfluidic sensing. IEEE Trans Microw Theory Tech 62(3):689–699 250. Vélez P, Mata-Contreras J, Dubuc D, Grenier K, Martín F (2018) Solute concentration measurements in diluted solutions by means of split ring resonators. In: Proceedings of the 48th European microwave conference (EuMC), Madrid, Spain, pp 231–234 251. Huang SY, Omkar, Yoshida Y, Garcia A, Chia X, Mu WC, Meng YS, Yu W (2019) Microstrip line-based glucose sensor for noninvasive continuous monitoring using the main field for sensing and multivariable crosschecking. IEEE Sens J 19(2):535–547 252. Turgul V, Kale I (2017) Simulating the effects of skin thickness and fingerprints to highlight problems with non-invasive RF blood glucose sensing from fingertips. IEEE Sens J 17(22):7553–7560 253. Turgul V, Kale I (2018) Sensitivity of non-invasive RF/microwave glucose sensors and fundamental factors and challenges affecting measurement accuracy. In: Proceedings of the 2018 IEEE international instrumentation and measurement technology conference (I2 MTC), Houston, TX, USA 254. Yilmaz T, Hao Y (2011) Electrical property characterization of blood glucose for on– body sensors. In: Proceedings of the 5th European conference on antennas and propagation (EuCAP), Rome, Italy 255. Turgul V, Kale I (2016) Characterization of the complex permittivity of glucose/water solutions for noninvasive RF/microwave blood glucose sensing. In: Proceedings of the 2016 IEEE international instrumentation and measurement technology conference (I2 MTC), Taipei, Taiwan 256. Schwerthoeffer U, Weigel R, Kissinger D (2013) A highly sensitive glucose biosensor based on a microstrip ring resonator. In: Proceedings of the 2013 IEEE MTT-S international microwave workshop series on RF and wireless technologies for biomedical and healthcare applications (IMWS-BIO), Singapore, Singapore 257. Schwerthoeffer U, Warter C, Weigel R, Kissinger D (2014) A microstrip resonant biosensor for aqueous glucose detection in microfluidic medical applications. In: Proceedings of the 2014 IEEE topical conference on biomedical wireless technologies, networks, and sensing systems (BioWireleSS), Newport Beach, CA, USA

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Chapter 3

Dielectric Characterization of Water–Glucose Solutions

Nature composes some of her loveliest poems for the microscope and the telescope. Theodore Roszak

3.1 Introduction This chapter presents an experimental study on the dielectric properties of water– glucose solutions at different concentrations [1]. This study is partly motivated by the findings by Park et al. [2], as they pointed out that glucose has a direct impact by itself in the permittivity of biological solutions, besides other possible biochemical effects related to the cell membrane. This aspect raises considerable interest as it broadens the field of actuation of sensors aiming at glucose concentration retrieval. Thus, they can also find applications out of the diabetes world, for example in sugared drinks production processes. For these reasons, whether it is for diabetes or industry context, the dielectric characterization of water–glucose solutions is worthwhile. As discussed in Sect. 2.1.1, there are several known physical principles that contribute to the polarization of dielectric media. These phenomena have been fully studied and it has been shown that for biological tissues and solutions at frequencies ranging 108 –1011 Hz the most relevant ones are orientation and Maxwell–Wagner (interfacial) polarization [3] (see Fig. 2.1). The orientation polarization is especially present in polar dielectrics, like water, and hence plays an essential role in the dielectric properties of aqueous solutions [4]. During the orientation polarization, the presence of cells and macromolecules might hinder the rotation of the dipoles and thereby affect the movement of the charges. As to interfacial polarization, it is especially important for biological fluids containing cells or other particles of similar spatial scale that can accumulate charge at their boundaries [5]. The biochemical processes associated to glucose can provoke shape changes in the mitochondria and therefore in the cell [6, 7]. These shape changes indeed affect the relaxation processes of the cell suspension [8]. The macroscopic dipolar moment associated to this effect is due to accumulation of charges © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_3

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in different molecular boundaries, depending on the geometry. In this sense, relationships between the solution permittivity and the permittivities of the particles (cells, macromolecules) in the medium can be obtained [9, 10]. These combined effects allow to expect noticeable variations in the permittivity of glucose-containing biological solutions with a high content of water, like it happens in blood. Basing on these principles, and also prompted by the discussion on the permittivity alterations due to the effect of glucose in erythrocytes by Hayashi et al. [11, 12], some works have used open-ended coaxial probes for measuring the dielectric properties of blood samples at several glucose levels. At low frequencies, the blood permittivity was shown to decrease with frequency [13]. The permittivity and conductivity were measured up to 20 GHz and data were fitted to a single- [14] and two-pole [15] Cole–Cole model, assuming some approximations. Blood–glucose permittivity characterization was later extended to overdosed samples [16]. Other techniques have also been put in practice, like waveguide transmission methods used to perform a dielectric characterization of biological liquids, leading to too noisy results for blood [17]. However, a universal consensus has not been reached yet. Indeed, new permittivity characterizations of blood–glucose solutions keep on being published [18], looking for a trustable dielectric model for blood which takes into account the glucose contribution. Hence, further research is advisable in this field. In this sense, it is convenient to regard pure water as a simplified model for blood, since blood is composed of roughly 80% of water. This yields to wieldier experimentations which, although in an approximate manner, allow to identify the contribution of glucose to the dielectric behavior of the solutions, as well as to measure and model the effects reported by Park et al. [2, 19, 20]. The accurate explanation of the relaxation processes in water is still open to discussion, as its hydrogen bonded cluster structure is still a point waiting for light to be shed on [21]. It has still to be fathomed whether its relaxation phenomena are due to the reorientation of the macroscopic dipolar moment of the water structure by means of extended large angle jumps [22–24], or to the aggregate effect of microscopic continuous rotational diffusion of the molecules [25, 26]. Recent advances have even proposed other alternative explanations, based on proton cascade effect leading to cluster reorientation [21]. The use of open-ended coaxial probes to measure water–glucose solutions has been reported [16, 27], measuring glucose contents fairly greater than the physiological ones, with qualitative description objectives. The use of other techniques based upon microstrip circuits with several configurations has also been proposed [28]. Notwithstanding all these advancements, this scientific debate is still open. Some recent contributions are [29–31], for example. In the next sections, a dielectric characterization method based upon transmission/reflection techniques with a coaxial line is proposed. These methods are not as common as open-ended coaxial probes due to their greater complexity and the lack of commercially available units, although they have been studied in different configurations and their advantages have been highlighted [32, 33]. It consists in an empty coaxial line (i.e., with no dielectric between the inner and outer conductors) filled

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71

with the liquid to be characterized (the MUT), which acts as the coaxial line dielectric. The relative permittivity of the solutions can be obtained from the electrical response of the line filled with each water–glucose solution. This method allows to obtain two complex magnitudes (transmission and reflection coefficients of the line) instead of the one that is given by an open-ended coaxial probe (only reflection coefficient). As logical, this advantage allows for a more accurate characterization. An in-depth discussion on the use of this method will be given in Sect. 3.2, with a special focus on the theoretical estimation of the relative permittivity of the liquids to be characterized, and the ways to represent them. The measurement process will be described in Sect. 3.3, showing the main guidelines for its implementation. In Sect. 3.4 the obtained results will be shown and explained. Finally, the discussion on the overall work and the conclusions reached will be examined in Sects. 3.5 and 3.6, respectively.

3.2 Materials and Methods When performing dielectric spectroscopy in water or aqueous solutions, the microwaves range of frequencies is usually deemed as one of the most interesting. This is because it is at these frequencies when the dominant relaxation processes of water take place [34]. The relative permittivity of water has been widely studied and characterized under many circumstances, up to 100 GHz, as well as fitted to Debye, Cole–Cole and Cole–Davidson dispersion functions [35]. This study revealed how the dielectric parameters of water depend on the temperature. The results showed that, for pure water at a given stable temperature and at microwave frequencies, its dielectric dispersion can be fitted to a simple Debye function, within a certain experimental uncertainty. Since water is a polar dielectric, in a first approximation it may be seen as an ideal system of permanent dipoles. Hence, it is a suitable medium to dissolve the substances that are to be characterized from a dielectric point of view, in order to analyze the dielectric dispersion of the resulting solutions. It is also an interesting medium for biological purposes since it is the main component of blood and other biological fluids. Given the characteristic relaxation times of water, the microwave region seems a good option for characterizing this kind of phenomena. In the context of broadband dielectric spectroscopy, specifically at microwave frequencies, methods based on guided waves become very interesting. Among these methods, open-ended coaxial lines and transmission/reflection (T/R) line methods are very popular. In order to have a more accurate characterization thanks to a greater amount of information available, in this chapter T/R line methods will be considered, which provide two complex parameters [32], instead of only one in open-ended coaxial probes. The proposed method consists in measuring the properties of a coaxial line when it is filled with the MUT. These properties are usually described in terms of the scattering parameters (S-parameters). These parameters are complex magnitudes

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defined in relation to the characteristic impedance Z 0 of the unaltered line (50  for most coaxial lines) [36, 37]. When dealing with high-frequency circuits, such as microwave networks, there is a practical problem because direct measurements often involve the magnitude (inferred from power) and phase of a wave travelling in a given direction or of a standing wave. In order to get a fair representation of the incident, reflected and transmitted waves according to these direct measurements, the S-parameters are frequently employed in experimental procedures. Thus, these parameters are the components of the scattering matrix, i.e., the matrix that relates the voltage waves incident on the ports of the network and the voltage waves reflected from the ports [38]. For instance, if an N-port network is considered, where V n + and V n − are the voltage amplitudes of the waves entering and leaving, respectively, the network at port n, supposing for the sake of simplicity that all the ports have the same characteristic impedance, the scattering parameters are defined as follows: ⎡ ⎢ ⎢ ⎢ ⎣

V1− V2− .. .

VN−

⎤

⎡

⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎦ ⎣

S11 · · · S1N S21 · · · S2N . .. . . . .. . SN 1 · · · SN N

⎤⎡ ⎥⎢ ⎥⎢ ⎥⎢ ⎦⎣

V1+ V2+ .. .

⎤ ⎥ ⎥ ⎥ ⎦

(3.1)

VN+

Thereby, a single element of [S] (an S-parameter) is generically defined as:  Vi−  Si j = +  Vj 

(3.2) Vk+ =0 for k= j

The measuring networks used in the present application often have only two ports. However, although in those networks there are four S-parameters (S11 , S12 , S21 , and S22 ), these systems are usually reciprocal (a condition met by isotropic, linear and passive media) and satisfy S12 = S21 . If they are also symmetrical, S11 = S22 . Thus, when these conditions are met, only two scattering parameters need to be considered, commonly S11 and S21 , to account for transmission and reflection. These parameters, of course, may be complex and frequency-dependent. Therefore, for measuring purposes, the scattering parameters of the network are measured with a VNA as a function of frequency, and they can be related to the complex impedance of a line of length l containing the MUT, Z(ω), and its propagation constant, γ(ω). This relation involves the reflection coefficient in the interface between the input line and the line section with the MUT, (ω), as well as the transmission coefficient along this line section, T (ω), in the following way: (ω) =

Z (ω) − Z 0 Z (ω) + Z 0

(3.3)

3.2 Materials and Methods

73

T (ω) = e−γ l

(3.4)

The coefficients  and T can be obtained from the measured S-parameters with a method presented later in this section. In this chapter, a T/R line method has been utilized to carry out the dielectric characterization of a set of water–glucose solutions at different concentrations, most of them of interest for biological purposes [1]. The measurement setup was connected to the VNA (Rhode & Schwartz ZVRE, with capabilities for measuring up to 4 GHz) by means of accurate 50  coaxial lines, and the measured S-parameters were recorded for later computer analysis. To gain accuracy in the results, as well as to allow for comparison, two different empty coaxial line sections were used: SMA male–male and N female–female. This way, different lengths of the MUT could be studied, providing for more accurate broadband characterization. All the solutions were measured with both probes. After all the measurements, the dielectric dispersion of each solution was obtained from computer processing of the recorded scattering parameters. The measurement process is schematically depicted in Fig. 3.1, whereas a picture of the N coaxial line section filled with a solution is shown in Fig. 3.2, and the setup for the empty SMA probe can be seen in Fig. 3.3. The frequencies seen in the measurements are within the microwave region, which, as discussed in Sect. 2.1.2, are convenient for exploring many dielectric dispersions in Fig. 3.1 T/R measurement process. Reprinted from [1] © (2017) with permission from Elsevier

Fig. 3.2 N coaxial line section filled with a solution. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

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3 Dielectric Characterization of Water–Glucose Solutions

Fig. 3.3 Empty SMA coaxial line section used in the measurements. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

biological systems [39]. Specifically, for this study the most relevant dielectric relaxation is that of water. Although being temperature-dependent, pure water has dielectric relaxation times around 10 ps as shown in [34, 40], and more recently in [29]. Due to these reasons, the measurements were made with frequency sweeps covering 100 MHz–4 GHz range, exploring the interesting relaxations of the solutions. With regard to the solutions, glucose concentrations of interest for diabetes purposes were chosen: 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 1000, 5000, and 10,000 mg/dL. The first ones belong to a range likely to find in the daily life of a person with diabetes, whilst the rest were chosen to provide for a further study of the observed phenomena and their trends. Overall, the study was aimed to extract conclusions for further development of sensors for diabetes context, but they could also be broadened for other applications thanks to the higher concentrations. The experimental procedure for making any measurement was as follows. First, the VNA was properly calibrated for the above-mentioned frequency range up to the input and output planes of the measuring coaxial line section. Then, in order to avoid the presence of air bubbles inside the coaxial section (which would have perturbed and introduced errors in the measurements), a special structure was set up. It consisted of a tripod and two grippers disposed to hold the coaxial section vertically. Later, the inner and outer conductor of the coaxial section were connected to the lower 50  I/O VNA line, held by one gripper. After that, the vertical empty coaxial section was carefully filled with the corresponding solution by means of an accurate pipette, which allowed the air out during the filling, and the upper 50  I/O VNA line was connected and held by the other gripper. A picture of the setup while a measurement was being carried out can be seen in Fig. 3.4. After the measurements, the obtained S-parameters were analyzed and processed for the extraction of the complex frequency-dependent permittivity of each solution. To do that, the permittivity of the dielectric inside a coaxial guide can be obtained by means of the well-known Nicolson-Ross-Weir (NRW) method [41, 42]. This procedure has been widely studied and used for dielectric characterization purposes, and wieldy numerical adaptations have been described [43–45]. A recent review can be seen in [46].

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75

Fig. 3.4 T/R line setup during a measurement. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

Basing on the theory of multiple reflections, NRW expressed the measured Sparameters as a function of the effective reflection and transmission coefficients [defined in Eqs. (3.3) and (3.4)] as follows:

(ω) 1 − T 2 (ω) S11 (ω) = 1 −  2 (ω)T 2 (ω)

T (ω) 1 −  2 (ω) S21 (ω) = 1 −  2 (ω)T 2 (ω)

(3.5)

(3.6)

In NRW algorithm, two parameters (A and B) are defined directly from the measured scattering parameters: A ≡ S21 (ω) + S11 (ω)

(3.7)

B ≡ S21 (ω) − S11 (ω)

(3.8)

And a third parameter X is defined from A and B:

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3 Dielectric Characterization of Water–Glucose Solutions

X≡

1 − AB A−B

(3.9)

Therefore, applying some substitutions within Eqs. (3.5)–(3.9) the effective reflection coefficient can be expressed as: (ω) = X ±



X2 − 1

(3.10)

where the right sign for the square root is chosen by requiring |(ω)| ≤ 1 to account for the appropriate impedance and propagation constant values. Then, substituting for the effective transmission coefficient, it can be shown to be: T (ω) =

A − (ω) 1 − A(ω)

(3.11)

Consequently, for a coaxial line section, NRW method allows to obtain in a simplified manner the complex frequency-dependent permittivity of the MUT from the effective transmission coefficient in Eq. (3.11) as shown below [1]:

2 c lnT (ω) ε∗ (ω) = − ωl

(3.12)

being c the speed of light in vacuum and l the length of the line. The latter is a crucial parameter and must be estimated as much accurately as possible. It should be noticed that, given that T (ω) is a complex magnitude as defined in Eq. (3.4) (since so it is the propagation constant), its natural logarithm required for computing Eq. (3.12) has infinite solutions, which are given by: lnT (ω) = ln|T (ω)| + j(θ + 2π n)

(3.13)

where θ is the phase term of the effective transmission coefficient, and n can be any integer number. Thus, the proper solution for the algorithm must be chosen by comparing and seeking the most accurate match of the theoretical τtheor and measured τmeas group delay, obtained as: τtheor

d =l df

τmeas = −

√ ∗ ε (ω) λ0

(3.14)

1 dφ 2π d f

(3.15)

being λ0 the free space wavelength and φ the chosen phase for T (ω). It is important to note that the discussion so far is only valid for coaxial lines with constant cross-section. In the case of other geometries, the calculations become more complex, and simulation methods are usually concerned for permittivity extraction, as it will be shown in Sect. 3.1. NRW method also has some drawbacks, chiefly

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77

concerning the electrical thickness of the MUT [47], as well as an accuracy drop for low reflecting materials [46]. Finally, when the complex relative permittivity is obtained from Eq. (3.12), there are several ways to plot it for further discussion. A usually manner is plotting the real and imaginary part independently as a function of frequency (often with a logarithmic plot). In this case, the main disadvantage is the independence in the representation of both parts of the permittivity, which are indeed related to each other, since each one can be obtained from the variation of the other throughout the whole frequency range, as given by the well-known Kramers–Kronig relation [3]. Though, a convenient way to represent the results and allow for comparison of the dielectric behavior of all the solutions studied is by means of a Cole–Cole plot. This is made by representing the real part of the permittivity against its imaginary part in an Argand diagram [48]. Effectively, Eqs. (2.24) and (2.25) for the real and imaginary part of the permittivity in a single Debye dispersion can be combined (neglecting the effect of the conductivity), yielding [3]: 2   2 1 1  εr (ω) − (εs + ε∞ ) + εr (ω) = (εs − ε∞ )2 2 4

(3.16)

This way, as Cole and Cole suggested [49], the function εr (εr ) can be evaluated and plotted for each frequency value, leading to a semi-circle in the complex plane Er *(ω), as shown in Eq. (3.16). Each point of the semi-circle corresponds to a specific frequency point, which evolves counterclockwise. Consequently, the Cole–Cole plot for representing Er *(ω) gives a semi-circle centered at εr = (E∞ + Es )/2 with radius (E∞ − Es )/2, whose top is given at ωτ = 1. A generic Cole–Cole plot is shown in Fig. 3.5. The main disadvantage of this representation is the absence of explicit values for the frequency, although it can be tracked by going through the semi-circle. The Cole–Cole plot can have shapes different from semi-circles, if no only single Debye dispersion is concerned. Indeed, a perfect semi-circle Cole–Cole diagram implies that only a single Debye dispersion is taking place [50]. In this chapter only single Debye relaxations will be considered, as it is a characteristics of water for the studied frequencies, as discussed previously. In the next section, the measurements carried Fig. 3.5 Cole–Cole plot

78

3 Dielectric Characterization of Water–Glucose Solutions

out to get the information needed to obtain the dielectric dispersion of the solutions under test will be described.

3.3 Measurements The measurements for all the water–glucose solutions studied were performed with the experimental procedure described in the prior section. However, before these experiments, several calibration tasks had to be carried out. In dielectric spectroscopy, calibration is essential for the reliability of the results, and this aspect is even more crucial for transmission/reflection methods due to the higher complexity and larger number of parameters concerned [32, 51]. Specifically, when NRW algorithm is involved, the length of the sample l must be very accurately determined to avoid significant errors in the permittivity calculations [32]. Therefore, the values of the lengths l of the inner sections of the SMA and N coaxial lines filled with the solutions had to be determined before the measurement process. There is a considerable difficulty for measuring this parameter directly, since it depends on the inner geometry of the coaxial section. This is the length of the line section occupied by the solution to be measured, without involving the threads at the input and output of the section. Due to this reason, the determination of its value was made by simulation techniques, based on real measurements of known liquids and computing a parameter optimization to match the obtained response to the theoretical one. With this aim, the T/R method described in Sect. 3.2 was simulated with Keysight Technologies’ Advanced Design System (ADS) software. A real measurement with the SMA probe (Fig. 3.3) filled with pure water (triple distilled water) was performed and the scattering parameters were recorded and introduced into the simulations. Then, the dielectric characteristics and Debye parameters reported for pure water by Kaatze [34] were used to model the inner dielectric of the SMA coaxial line section in the software. With this configuration, simulations were run to optimize the value of l, considered as a parameter in the simulations, so that the best match between the measured and simulated S-parameters was achieved. The result was l = 15.017 mm, which was consistent with the approximate direct measurements made with the real SMA coaxial section. This was the final value considered in Eq. (3.12) when solving the NRW solution in the follow-on measurements. Figure 3.6 shows the simultaneous plot of the measured S11 parameter for pure water and the simulated S11 parameter for the model of pure water with Kaatze’s dielectric parameters [34] and the obtained value of l. As it can be seen, the match is good for the region of interest. An alike procedure was carried out for the calibration of the N coaxial line. This time the difficulty was higher, as there were three different inner sections with different radius. An electromagnetic model developed in ADS with three cascaded coaxial lines accounted for the three inner sections. The radius of each one in the ADS model was selected according to the description of each inner section in the datasheet

3.3 Measurements

79

Fig. 3.6 Measured and simulated S11 parameter for pure water. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

of the real N coaxial line. Then, the length of each section was obtained with a similar procedure, involving pure water measurement as well as simulation and optimization for the lengths. As a result, the same length for each section was obtained, 9.73 mm, which is consistent with the symmetry of the real line. Consequently, a total length of l = 29.19 mm was set, which is almost twofold the length of the SMA line. This length difference is a propitious feature since it allows to broaden the study to higher frequencies (thanks to the SMA coaxial section) and to two different MUT lengths, providing for more accurate characterization. Indeed, for liquid characterization, measurements with different liquid lengths are convenient since they allow to determine precisely the permittivity of the samples and compensate for calibration errors (to a certain extent). Due to these reasons, this kind of measurement techniques involving several liquid lengths are often considered for the accurate characterization of reference liquids [34, 40, 52], used in other permittivity determination methods. Thus, after ensuring a proper calibration and accurately determining l for both coaxial lines, the measurements with the water–glucose solutions were carried out. The experimental procedure was as described in Sect. 3.2, involving glucose solutions at concentrations ranging 50–10,000 mg/dL. Initial broadband measurements with these solutions were performed up to 26 GHz, but no significant changes between the solutions were seen above 4 GHz. Therefore, in order to reach precise conclusions for the future development of glucose concentration sensors, the main discussion was focused on frequencies up to 4 GHz. All the measurements were made at a room temperature of 25 ± 0.1 °C, with a 47% humidity. The next section will show the experimental results.

3.4 Results The scattering parameters measured for the different solutions showed little variations between them, as expected. This is logical because the glucose concentrations of the

80

3 Dielectric Characterization of Water–Glucose Solutions

measured solutions were very low, as corresponding to typical values in the diabetes context. That said, although little, these changes in the S-parameters can only be attributed to the variations in the glucose concentration, since this was the only varying parameter in the measurement process. In Fig. 3.7 the magnitude of the measured S11 (a) and S21 (b) parameters for a selection of solutions with glucose concentrations from 50 to 1000 mg/dL with the SMA coaxial line are plotted from 100 MHz to 4 GHz. To give a clearer representation of the results, more related to diabetes purposes, the glucose concentrations 5000 and 10,000 mg/dL have been removed because they exceeded too much the studied range. Notwithstanding, these high concentrations were actually involved in the experimental procedure, and comments on them will be provided further on. The measurements with the N coaxial line (not shown) led to a very similar behavior.

Fig. 3.7 Magnitude of measured S11 (a) and S21 (b) parameters with SMA coaxial line filled with water–glucose solutions at 50 (filled circle), 250 (open circle), 350 (×), 400 (+), 500 (*) and 1000 (open square) mg/dL. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

3.4 Results

81

Frequency of min S11 (GHz)

Frequency position of min S11 against the glucose concentration 1.25 1.2 1.15 1.1 1.05 1

0

100

200

300

400

500

600

700

800

900

1000

Glucose concentration (mg/dl)

Fig. 3.8 Evolution of the minimum amplitude of S11 with respect to the glucose concentration in SMA line measurements. The single points are marked with open circle. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

In order to see the effect of the glucose concentration in the electrical response, the exact frequencies of the minimum amplitudes of S11 were plotted in Fig. 3.8 for aqueous glucose solutions up to 1000 mg/dL. In this figure only the results for the SMA measurements are shown, given that those for N measurements were similar, as well as the corresponding results in S21 parameter for both coaxial lines. The relative error of each point in the plot is ±0.01 GHz. Concerning the estimation of the dielectric permittivity of each solution, a single relaxation Debye model was considered, following the suggestions of Kaatze [35]. This way, once the lengths of the coaxial lines had been determined (as explained before), the software models for the experimental assemblies could be used for permittivity estimation. A MUT whose permittivity was defined as a single Debye relaxation, as shown in Eq. (2.22), was used as the dielectric of the coaxial lines. In this configuration, the MUT’s Es , E∞ and τ were taken as parameters to optimize. Hence, following a similar procedure to when the inner lengths of the coaxial sections were defined, the measured S-parameters for each solution were introduced in the simulations. Then, the simulation for each solution was run and the Debye model parameters were tuned and optimized so that the simulated results were matched to the experimental scattering parameters. The dielectric parameters obtained from the random and gradient optimizations for all the water–glucose solutions involved in the study are shown in Table 3.1. The data appearing in the table is mean of the results from SMA and N coaxial lines measurements. The results of both lines showed good matching, and the relative errors were acceptable. The relative permittivities for the SMA line measurements were also computed by means of the NRW method (as explained in Sect. 3.2), yielding results coherent with the permittivities obtained with the Debye model and the data in Table 3.1. Finally, a clearer representation of the dielectric behavior of the aqueous solutions at varying concentrations was sought. To get it, only the solutions from 100

82 Table 3.1 Obtained parameters of the dielectric dispersion of water–glucose solutions with different concentrations. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

3 Dielectric Characterization of Water–Glucose Solutions Concentration (mg/dl)

εs

τ (ps)

ε∞

0

79.86 ± 0.08

11.27 ± 0.20

5.4 ± 0.3

50

80.35 ± 0.09

10.10 ± 0.14

5.3 ± 0.2

100

87.85 ± 0.02

10.02 ± 0.20

6.0 ± 0.5

150

84.72 ± 0.01

10.99 ± 0.29

5.2 ± 0.4

200

81.59 ± 0.08

10.01 ± 0.14

4.7 ± 0.3

250

82.38 ± 0.07

10.21 ± 0.32

5.1 ± 0.4

300

83.94 ± 0.01

10.82 ± 0.12

5.2 ± 0.1

350

84.33 ± 0.05

10.77 ± 0.23

5.2 ± 0.2

400

85.90 ± 0.02

10.62 ± 0.25

5.3 ± 0.4

450

86.26 ± 0.07

10.86 ± 0.22

5.5 ± 0.3

500

86.93 ± 0.01

10.93 ± 0.18

6.2 ± 0.4

1000

88.73 ± 0.02

10.47 ± 0.19

5.8 ± 0.1

5000

84.04 ± 0.01

11.91 ± 0.15

5.9 ± 0.3

10,000

81.36 ± 0.01

13.20 ± 0.26

7.6 ± 0.4

to 500 mg/dL were concerned, with constant steps of 100 mg/dL. Thus, the relative permittivities of these solutions, computed with the Debye parameters in Table 3.1, were plotted in a Cole–Cole diagram, which is suitable for dielectric behavior characterization (as discussed in Sect. 3.2). In this diagram, the real part of the relative permittivity was plotted against its imaginary part, resulting in a semi-circle for each solution (as expected since single Debye models were considered). In the semi-circles, the lower frequencies (starting in this case at 100 MHz) are in the first right points, and the higher frequencies (ending in 4 GHz) are in the last left points, thus evolving counterclockwise. The final plot is shown in Fig. 3.9.

3.5 Discussion Analyzing the results shown in the previous section, it can be noticed that not a linear or monotonic behavior between the electrical responses obtained for all the solutions was found (Fig. 3.7), although some concentrations ranges may be pointed to show monotonic responses. The glucose concentrations from 250 to 500 mg/dL, for example, resulted in an almost linear increase of the frequencies of the minimum S11 and maximum S21 as the glucose concentration increments. In addition, the measurements for 50 and 1000 mg/dL also fit within this behavior. This can be more clearly seen in Fig. 3.8. It is difficult to state it, but these changes are expected to be provoked by changes in the real part of the permittivity, directly affecting the dispersion of the obtained electrical responses. Another interesting feature is the remarkable change in the

3.5 Discussion

83

Imaginary relative permittivity

Complex plot of relative permittivity of water glucose solutions 40

30 100 mg/dl 200 mg/dl 300 mg/dl 400 mg/dl 500 mg/dl

20

10

0

0

10

20

30

40

50

60

70

80

90

Real relative permittivity

Fig. 3.9 Cole–Cole diagram of the relative permittivity of the water–glucose solutions with concentrations 100 (open square), 200 (open circle), 300 (×), 400 (open down triangle) and 500 (open up triangle) mg/dL. Reprinted from Juan et al. [1] © (2017) with permission from Elsevier

magnitude of the S11 minimum (Fig. 3.7a), which also seems to be in accordance with the selected solutions range. This is also seen in the magnitude of the S21 maximum (Fig. 3.7b) with more slight changes, although relatively comparable in terms of amplitude level. These changes can be put down to the variations in the imaginary part of the permittivity, or to the losses in the solutions, thus changing the measured amplitude level. This phenomenon will be deeply studied in Chaps. 4, 5 and 7. Further analysis of the graphs in Fig. 3.7 allows to state that the proposed measurement system gives useful information up to 3 GHz, becoming the responses too much noisy from this frequency on (chiefly in S21 parameter). This is also logical since water is a noisy dielectric. Thereby, the results of this work can be useful for the dielectric study of water–glucose solutions and the development of sensors at frequencies approximately ranging 0.5–3 GHz. More specifically, the most relevant information of the measurements proposed can be extracted from frequencies between 1.0 and 1.2 GHz, at which the maximum transmission (S21 ) and minimum reflection (S11 ) take place. In the light of these results, the deep analysis of the phenomena seen in this frequency range is worthwhile. Notwithstanding the above-mentioned behaviors for some solutions, not a stable relationship was found between the electrical responses for all the solutions in the study. When the frequency of the minimum of S11 or the maximum of S21 was computed, some alternating behaviors were seen, leading to a certain valley in the overall responses for the concentrations raging 100–400 mg/dL (Fig. 3.8). Specifically, the concentrations from 100 to 250 mg/dL showed a linear decaying behavior opposite to that from the concentrations ranging 250–500 mg/dL. This valley was seen for both SMA and N coaxial lines measurements with a relative similarity. Given the low concentrations considered (close to or within the biological range) and the importance of a highly accurate calibration for the measurement and data acquisition process, this behavior might be attributed to instrumental or resolution

84

3 Dielectric Characterization of Water–Glucose Solutions

errors. However, the specific valley seen is in accordance with the initial work by Hayashi et al. [11]. In that work, the relative permittivity of several saline erythrocytes solutions was related to the glucose concentration, reporting a valley similar to the one seen in Fig. 3.8, roughly at the same glucose concentrations, although at lower frequencies. The measurements by Park et al. [2], involving water–glucose solutions (as in this case), without the influence of erythrocytes, did not report such a valley. That said, those measurements ranged up to 100 MHz, the initial frequency in this work, and the data at their highest frequencies were not as clear as desirable, and might point to a change of behavior. Indeed, for specific measurements at 10 kHz the relative permittivity was plotted against the glucose concentration, showing not strictly a valley but a different proportionality or relationship for the same glucose concentrations involved in the valley of Fig. 3.8, mainly for the imaginary part. For all these reasons, although the instrumental error must be considered as a possible cause, the reported valley seems to be consistent with reference works in the literature. A physical explanation for this behavior is still to be provided. Regarding the rest of measurements, the solutions with 5000 and 10,000 mg/dL (not shown) yielded comparatively low frequencies for S11 minimum: 1.09 and 1.12 GHz respectively for the SMA coaxial line measurements [1]. The interpretation of these results is not straightforward, as they are far from the rest of concentrations. A possible conclusion is that the observed behaviors do not follow the same rules for relatively larger concentrations. Other possible explanation might point out to the existence of more valleys induced by other types of polarization and dielectric dispersion mechanisms (as explained in Sect. 2.1.1), which prevents the identification of global behaviors for extended glucose concentration ranges. Anyhow, solutions with more concentrations would be needed to further study these principles in these concentration ranges, which fall too far from diabetes interest. Concerning the permittivity extraction, the data reported in Table 3.1 allows for further discussion. As it can be seen, the first row (0 mg/dL) corresponds to the measurements of pure water. This result is coherent with the data reported by Kaatze [34] and Ellison [40], two reference works as far as dielectric dispersion of water is concerned. This is a logical result because Kaatze’s data were used in the calibration process for the determination of l, as explained in Sect. 3.3. The rest of data in Table 3.1 are consistent with the results of this work. For example, the static permittivity values show the above-mentioned valley for the rows from 100 to 250 mg/dL. Also, this parameter for the extreme concentrations 5000 and 10,000 mg/dL shows a different behavior than the rest of solutions, as commented previously. However, τ and E∞ seem to keep some relationship with the rest of solutions, maybe pointing to a general behavior for these parameters. The information in Table 3.1 can be very useful for modeling, simulating and designing future glucose sensors, always bearing in mind the limitations of the experimental procedure. With regard to the Cole–Cole diagram shown in Fig. 3.9, it is important to note that, in this graph, the 100 mg/dL solution is inside the above-mentioned valley. With this exception, the other solutions seem to grow to higher real relative permittivities as the glucose level raises, mainly at low frequencies (right side of the semi-circle).

3.5 Discussion

85

This is also logical given the frequency range considered in this study, and the increment of the real part of the permittivity for low frequencies is consistent with the data reported by Park et al. [2]. This behavior is opposite for higher frequencies in Fig. 3.9, which is also coherent with [2] and even with studies regarding quite larger glucose concentrations [16]. With this plot, a general behavior of the relative permittivity for aqueous glucose solutions can be defined, although affected by the valley. This is especially important for hyperglycemia detection in concentrations above 200 mg/dL. These results are also coherent with the data in Table 3.1, as well as with the specific results of the electromagnetic simulations and optimizations, and the theoretical calculations of the permittivity of the solutions with NRW method. Moreover, the Cole–Cole plots in Fig. 3.9 are similar to the ones provided by Ellison [40] for pure water. This is logical as well, given that the glucose concentrations involved in this study are quite low, and hence low permittivity variations are expected. Overall, the analysis of the results highlights that, with these experiments, dielectric characterization of water–glucose solutions based upon reliable data up to 3 GHz has been provided. Thereby, the results shown point to the frequency range under 2 GHz as the most interesting to extract information and conclusions from these measurements, although the broadening of the data to higher frequencies provided for more accurate processing. This frequency limitation might have a relationship with the lengths of the coaxial lines, as well as with the technology. Broader analysis would require more MUT lengths and coaxial sections working well at higher frequencies. The observed valley in the general behavior of the electrical responses for the low glucose concentrations (50–500 mg/dL) prevents a general behavior to be identified. Thus, unfortunately not a full dielectric characterization can be given for the solutions with concentrations likely to be found in the daily life of a person with diabetes. It must be pointed out that the experimental error could account for this valley, even though scientific evidence for this phenomenon has been provided by other authors. Having analyzed the data, the dielectric dispersions reported can be useful for the future design of glucose sensors basing on the dielectric properties of glucosecontaining solutions. In this sense, the information given in this chapter finds its maximum relevance in the frequencies ranging 1.0–1.2 GHz, at which the major dispersions have been seen. If willing to design a microwave microstrip resonator sensor basing on these data, the resultant resonant frequency should be close to 1.2 GHz when placed next to the medium to be measured, with a null glucose concentration. Since Table 3.1 suggests that the relative permittivity seems to increase with the glucose concentration (although not for all the concentrations), the resonant frequency is expected to decrease as the glucose concentration arises. As the permittivity of the medium without glucose is expected to be much greater than the vacuum permittivity, the resonator should be designed to have a resonant frequency higher in free space, roughly 1.3–1.6 GHz, in order to decay to the desired range in presence of the MUT [1]. However, the data reported in this work can be used to develop accurate software models of the whole environment (at least for water–glucose solutions

86

3 Dielectric Characterization of Water–Glucose Solutions

measurements) and search for the most proper sensor design. In addition, the idea of the contribution of glucose to the increment of the dielectric losses of the solution discussed previously should also be considered in the sensor design.

3.6 Conclusions Having seen the difficulties reported in the scientific literature to develop glucose sensors with microwave technology, as well as the absence of comprehensive dielectric characterizations of glucose solutions within physiological ranges (in the context of diabetes), in this work the dielectric properties of water–glucose solutions have been studied. To do it, glucose concentrations likely to be found in a person with diabetes have been considered, as well as some other extended ones to see further behaviors. Therefore, this chapter has presented a dielectric characterization of glucose in aqueous solutions in order to shed some light on the pursue of the desired non-invasive glucose sensor. As dielectric spectroscopy technique, a transmission/reflection line method has been developed, with two different coaxial sections. The aim is to benefit from the increment of information available compared to the conventional coaxial probes so that more accurate data can be obtained. In this regard, theoretical calculations have been combined with comprehensive electromagnetic simulations and computer optimization to retrieve the permittivity parameters in a reliable manner. Also, as a first approach, water was chosen as simplified case of blood, so that the observed behaviors can only be attributed to the presence of glucose. The measuring methods shown had the objective of identifying the contribution of the variations of glucose in the dielectric dispersion of the solutions. A key feature is that the observed changes in the electrical responses and the obtained dielectric permittivities can only be put down to the existence of different glucose concentrations, since this was the only varying parameter in the measurement system. For this reason, the results reported for the dielectric permittivity of the solutions (Table 3.1) can help to understand the dielectric dispersion of glucose and its influence in the overall permittivity of the solutions. All the phenomena seen have been discussed, even some particular concentrations that do not follow the general behavior observed. Discussion on further development of microwave glucose sensors has been offered. The conclusions have set that the most relevant information obtained in this work applies for sensors intended to work in the 1.0–1.2 GHz frequency range. Some guidelines for the design of future sensors have been offered, highlighting two main ideas. On the one hand, the overall real permittivity seems to increase with the glucose level at low frequencies and decrease at high frequencies. On the other, the variations in the imaginary part of the permittivity yields to different dielectric losses according to the glucose level, which can be observed in the magnitude of the electrical responses. These aspects should be considered when developing glucose sensors, since they can play crucial roles. In addition, the selection of the working frequency must be thoroughly studied due to the different dielectric behaviors.

3.6 Conclusions

87

The reader should be aware that the conclusions reached in this chapter are only strictly valid for water–glucose solutions, not for blood solutions. Notwithstanding, the dielectric behavior of glucose in blood is expected to have a close relationship to the ones exposed here due to the its high water content. As a matter of fact, the results reported in this work have agreed to a certain extent with data from experiments in erythrocyte solutions [11]. Further studies should be conducted to see if the presence of more components or different processes in blood leads to divergent dielectric dispersions. Despite the commented limitations, this study has provided useful information for the understanding of the dielectric dispersion of glucose and its effect in glucose-containing solutions. The work developed throughout this chapter was published in a JCR journal [1]. To sum up, the main contributions are listed below: • A transmission/reflection line method with two different coaxial sections has been developed for the accurate dielectric characterization of liquids. • The dielectric characterization of water–glucose solutions at concentrations of interest for diabetes purposes has been shown. • Different dielectric behaviors attributed to the presence of glucose have been identified, and the dielectric dispersion of glucose-containing solutions at physiological concentrations has been described. The results are coherent with the existing literature. • Useful discussion for understanding the effect of glucose in the overall permittivity of the solution has been offered. • Debye models of the studied solutions have been given, in order to provide for further research and sophisticated sensors design. • Guidelines for future glucose sensors design in the studied frequency range have been discussed, within the limitations of the experimental procedure.

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29. Ahmed S, Pasti A, Fernández-Terán RJ, Ciardi G, Shalit A, Hamm P (2018) Aqueous solvation from the water perspective. J Chem Phys 148(23):234505 30. Sasaki K, Popov I, Feldman Y (2019) Water in the hydrated protein powders: dynamic and structure. J Chem Phys 150(20):204504 31. Banerjee P, Bagchi B (2019) Ions’ motion in water. J Chem Phys 150(19):190901 32. Shenhui J, Ding D, Quanxing J (2003) Measurement of electromagnetic properties of materials using transmission/reflection method in coaxial line. In: Proceedings of the Asia-Pacific conference on environmental electromagnetics, 2003 (CEEM’2003), Hangzhou, China 33. Sheen J (2009) Comparisons of microwave dielectric property measurements by transmission/reflection techniques and resonance techniques. Meas Sci Technol 20(4):042001 34. Kaatze U (2007) Reference liquids for the calibration of dielectric sensors and measurement instruments. Meas Sci Technol 18(4):967–976 35. Kaatze U (1989) Complex permittivity of water as a function of frequency and temperature. J Chem Eng Data 34(4):371–374 36. Collin RE (1990) Field theory of guided waves, 2nd edn. Wiley-IEEE Press, New York 37. Collin RE (2001) Foundations for microwave engineering, 2nd edn. Wiley-IEEE Press, New York 38. Pozar DM (1998) Microwave network analysis. In: Pozar DM (ed) Microwave engineering, 2nd edn. Wiley, Hoboken, pp 182–250 39. Kaatze U, Feldman Y, Ben Ishai P, Greenbaum A, Raicu V (2015) Experimental methods. In: Raicu V, Feldman Y (eds) Dielectric relaxation in biological systems: physical principles, methods, and applications. Oxford University Press, Oxford, pp 109–139 40. Ellison WJ (2007) Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25 THz and temperature range 0–100 ºC. J Phys Chem Ref Data 36(1):1–18 41. Nicolson AM, Ross GF (1970) Measurement of the intrinsic properties of materials by time domain techniques. IEEE Trans Instrum Measur im-19(4):377–382 42. Weir W (1974) Automatic measurement of complex dielectric constant and permeabihty at microwave frequencies. Proc IEEE 62(1):33–36 43. Baker-Jarvis J (1990) Transmission/reflection and short-circuit line permittivity measurements. National Institute of Standards and Technology (NIST), Boulder 44. Baker-Jarvis J, Janezik MD, Jr Grosvenor JH, Geyer RG (1992) Transmission/reflection and short-circuit line methods for measuring permittivity and permeability. National Institute of Standards and Technology (NIST), Boulder 45. Baker-Jarvis J, Janezic MD, Riddle BF, Johnk RT, Kabos P, Holloway CL, Geyer RG, Grosvenor CA (2005) Measuring the permittivity and permeability of lossy materials: solids, liquids, metals, building materials, and negative-index materials. National Institute of Standards and Technology, Boulder 46. Costa F, Borgese M, Degiorgi D, Monorchio A (2017) Electromagnetic characterisation of materials by using transmission/reflection (T/R) devices. Electronics 6(4):95 47. Arslanagi´c S, Hansen TV, Mortensen NA, Gregersen AH, Sigmund O, Ziolkowski RW, Breinbjerg O (2013) A review of the scattering-parameter extraction method with clarification of ambiguity issues in relation to metamaterial homogenization. IEEE Anten Propag Mag 55(2):91–106 48. Powles JG (1993) Cole-Cole plots as they should be. J Mol Liq 56:35–47 49. Cole KS, Cole RH (1941) Dispersion and absorption in dielectrics I. Alternating current characteristics. J Chem Phys 9(2):341–451 50. Fang PH (1965) Cole-Cole diagram and the distribution of relaxation times. J Chem Phys 42(10):3411–3413 51. Fossion M, Huynen I, Vanhoenacker D, Vander Vorst A (1992) A new and simple calibration method for measuring planar lines parameters up to 40 GHz. In: Proceedings of the 22nd European Microwave Conference (EuMC), Helsinki, Finland, pp 180–185 52. Gregory AP, Clarke RN (2012) Tables of the complex permittivity of dielectric reference liquids at frequencies up to 5 GHz. National Physical Laboratory, Teddington

Chapter 4

Glucose Concentration Detection in Aqueous Solutions with Microwave Sensors

If I have seen further it is by standing on the shoulders of Giants. Isaac Newton

4.1 Introduction In this chapter, the application of microwave microstrip resonators for glucose sensing in aqueous solutions is thoroughly studied [1]. This work is inspired in part by the permittivity variations in water–glucose solutions observed and discussed in the preceding chapter [2], as well as in other works [3]. Hence, the following study is built upon the idea that the permittivity changes can be measured with properly designed microwave sensors, and they can eventually be related to the glucose content. In this regard, sensors aimed to measure dielectric properties of the materials have been widely studied for a great deal of applications [4]. Among all the known techniques for obtaining the relative permittivity of a MUT, the most common ones are the parallel-plate capacitor, resonant cavities and transmission line techniques [5, 6] (see Sect. 2.1). In order to select the most adequate one, different factors must be considered. The frequency range, the approximate expected values of the relative permittivity, the desired accuracy in the measurements, the physical state of the MUT, or the sample size must be studied to choose the right method [7–9]. For low-frequency applications (up to a few GHz) with low- or medium-loss materials, parallel-plate capacitor techniques work well [10, 11]. When not very lossy MUTs are involved at microwave frequencies, resonant cavity techniques find a potential field of application with many configurations [12–16]. In order to achieve the widest frequency range of measurement, however, transmission lines must be considered whether in reflection or transmission/reflection modes. These techniques can provide reliable measurements from RF to roughly 60 GHz. Within them, if the MUT is remarkably lossy, coaxial probes are a good option, although a considerable sample size is required in this case [17]. As discussed in Sect. 2.1.2, these probes are commercially available and they are widely used for

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_4

91

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characterization of liquids [3, 18, 19]. Notwithstanding, if a low- or medium-loss MUT is to be measured but only small samples are available, other resonant transmission line techniques seem to be suitable [20–24]. These techniques may provide reasonably high sensitivities in the measure of the MUT permittivity, and, given the small sample sizes needed, they might be convenient for measuring the concentration of solutions with low availability. Specifically, glucose concentration sensing in aqueous solutions is a very interesting application due to several aspects. The benefits in diabetes context are evident since proper sensors would considerably contribute towards the desired NIBGM systems. Also, this technology can find potential applications in the food industry processes where glucose plays important roles. The use of this kind of systems in other industry contexts has also been proposed by other authors [25]. In this sense, the control of the production of glucose-containing drinks, like juices or sodas, seems to be a good context for these sensors [1]. The glucose content is an essential parameter for these products since its level highly influences their flavor and texture. This control is also fundamental to abide by the health regulations. The common methods to measure the glucose level and check it is the proper one are based upon chemical probes. These probes must be soaked into a liquid sample [26], which entails a certain waste of the liquid produced. The repetition of the needed controls finally leads to economic loss. The increase of time between controls to minimize the liquid waste also produces a reliability decrease. Sensors that require very small amounts of sample could contribute to enhance this process. Another possible field of application is the production of beers, wines and spirits, which requires the use of glucose as a fermentation substrate. The glucose level in this process is crucial for the final result, and it has to be periodically checked. Many methods are used for glucose detection in the industry, based upon different principles [27]. Among them, for instance, enzymatic methods for controlling the glucose level during the wine yeast fermentation are frequently employed [28, 29]. Also, intense recent research activity can be seen on non-enzymatic glucose sensors in consumable or industrial ethanol production processes [30], although these methods still need to be reinforced by other techniques to provide for fully reliable measurements [27]. Therefore, the same conclusions may be applied to these contexts, and thus the research on microwave sensors for glucose detection is so active nowadays. Some attempts for such a sensor development have been made with different technologies, as for example waveguide techniques [31, 32]. Notwithstanding, hitherto promising results have been obtained with microstrip resonator techniques, which seem to be suitable for measuring the dielectric properties of a MUT in their upper space. Indeed, it was shown how the electrical properties of a microstrip transmission line change depending on the material placed over it [33, 34], with special emphasis on the characteristic impedance, the dielectric losses and the quality factor (also related to the overall losses). In an approximate manner, it can be said that the electric field interacts with the MUT, which leads to variations in the attenuation constant of the microstrip line [33]. As a matter of fact, theoretical methods for the determination of the relative permittivity of a superstrate (that could be the MUT) over a microstrip line have

4.1 Introduction

93

been studied, like the integral equation method [35, 36], the relaxation method [37], or the variational method [38, 39]. As an illustrative case of a theoretical general procedure for MUT’s permittivity extraction from a microstrip line configuration, one of the most popular methods for superstrate analysis, the conformal mapping method [40], will be reviewed in the following paragraphs. Consider a standard transversal section of a microstrip line of height h and width w in a substrate with relative permittivity Er1 , in the complex plane z = x + jy. Consider also a superstrate with relative permittivity Er2 , being the total height of the ensemble h2 , as depicted in Fig. 4.1, with the ensemble covered by air. Then, the conformal mapping is applied to take the ensemble from z plane to g = u + jv plane [41], as shown in Fig. 4.2. Note that the interfaces between different permittivity regions are also transformed. The width of the line in the z plane has been transformed to its effective width weff in the g plane. The degree of filling this cross section of the ensemble by each dielectric in the transformed g plane is given by a filling factor for each one: q1 and q2 Fig. 4.1 Standard transversal section of a microstrip line with a superstrate

Fig. 4.2 Microstrip line with superstrate transformed into g plane

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4 Glucose Concentration Detection in Aqueous Solutions …

[41]. The conformal mapping method defines each filling factor as the ratio between its corresponding area, S 1 and S 2 , and the total area S T of the transversal section of the ensemble [40, 42]. Therefore: S∈1 ST − S0 − S∈2 S0 + S∈2 = =1− ST ST ST

(4.1)

S∈2 ST − S0 − S∈1 S∈1 S0 S0 = =1− − = 1 − q1 − ST ST ST ST ST

(4.2)

q1 = q2 =

Approximating the boundaries of S 0 and S 2 as elliptical curves, considering a narrow microstrip line (w/h ≤ 1), and applying the functions defined by the conformal mapping [43], it is possible to define the filling factors as functions h, h2 and w [41]. Then, the elliptic-shaped areas in Fig. 4.2 can be approximated by squareshaped areas without losing precision, as shown in Fig. 4.3. This yields to a wieldier configuration for the analysis of the permittivity, while areas S 0 , S 1 and S 2 remain unaltered. In this configuration, and considering the previously defined filling factors, the overall relative effective permittivity can be shown to be [41]: εr, eff = εr1 q1 + εr2

(1 − q1 )2 εr2 (1 − q1 − q2 ) + q2

(4.3)

The reader should note that Eq. (4.3) relates the relative permittivity of the superstrate (or the MUT), i.e., the target variable, to the relative permittivity of the substrate, the filling factors, and the relative effective permittivity. The relative permittivity of the substrate is known from the fabrication process. The filling factors can be computed with the conformal mapping functions [43]. The effective relative permittivity can be obtained from direct measurement if a proper configuration is chosen. Therefore, rearranging Eq. (4.3) the superstrate relative permittivity can be solved from known parameters as shown below: Fig. 4.3 Microstrip line with superstrate transformed into g plane with square-shaped areas

4.1 Introduction

95

εr2 =

q2 (1−q1 )2 εr, eff −εr1 q1

+ q1 + q2 − 1

(4.4)

Thus, considering the changes in the relative permittivity of the solutions due to the variations in the glucose level, microwave sensors have been proposed with different configurations, putting the solutions as superstrate. Specifically, microwave resonators, as described in Sect. 2.2, have been studied due to the influence of the relative effective permittivity. Following the theoretical approach, a way to determine Er,eff [required for solving for Er2 in Eq. (4.4)] from direct measurement of a generic microwave resonator with a lossy dielectric is discussed next. As usual, the relative effective permittivity is defined from its real and imaginary part as: εr, eff = εr, eff − jεr, eff

(4.5)

From the measurements, the resonant frequency fr and the bandwidth BW can be easily obtained. From them, the quality factor Q can also be determined as shown in Eq. (2.44). In microstrip resonators, as shown in Sect. 2.2, the quality factor can also be expressed as a function of the complex propagation constant γ , depending on the attenuation constant α and the phase constant β, as shown in Eqs. (2.71) and (2.79): Q = β/2α. In this case, according to general electromagnetic waves propagation in lossy media theory [44], these terms can be expressed as: 

   μεr, eff  1 + tan2 δ − 1 Np/m α=ω 2   μεr, eff  β=ω 1 + tan2 δ + 1 [rad/m] 2

(4.6)

(4.7)

where μ is the magnetic permeability, and tan δ is the loss tangent, given by: tan δ =

εr, eff εr, eff

(4.8)

If the loss tangent is defined in terms of Q, one condition to determine the two terms in Er,eff (real and imaginary part) from direct measurement will be achieved. Hence, if Eqs. (4.6) and (4.7) are substituted into Eqs. (2.71) or (2.79), after some rearrangement yields: √ 4Q = √ 2

1 + tan2 δ + 1 1 + tan2 δ − 1

Developing Eq. (4.9) to find tan δ leads to the next quadratic expression:

(4.9)

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4 Glucose Concentration Detection in Aqueous Solutions …

   tan2 δ 16Q 4 − 8Q 2 + 1 tan2 δ − 16Q 2 = 0

(4.10)

One possible solution is tan δ = 0. However, this is not a valid one since it implies E r,eff = 0, which is not true for lossy media, neither for real measurements. Thus, solving for the term in brackets in Eq. (4.10) leads to: 16Q 2 4Q tan2 δ =  2 ⇒ tan δ = 2−1 2 4Q 4Q − 1

(4.11)

Note that the negative solution for the loss tangent is not considered since neither tan δ nor E r,eff nor E r,eff can be negative. It is convenient to show the natural and squared expressions for the follow-on development. Therefore, Eq. (4.11) relates tan δ to Q, which is determined directly from the measurement. The second condition for solving for Er,eff is obtained in a way dependent on the resonator configuration and type. For instance, for a close-loop resonator, the wavelength at the resonant frequency λr equals to the total length of the line l. At this point the values of voltage and intensity from both sides of the line are equal (due to the short-circuit in the ends of the line), and hence maximum power transfer occurs. From general transmission line theory [45], λr is defined as: λr =

2π β

(4.12)

Then, considering λr = l and applying Eq. (4.7) in Eq. (4.12), yields: l=

ω



μεr, eff 2

2π √ 1 + tan2 δ + 1

(4.13)

Taking into account that ω = 2πf , with f = f r in this case (since λr = l condition is satisfied at f r ), rearranging Eq. (4.13) gives:

μεr, eff  1 2δ+1 = 1 + tan l 2 f r2 2

(4.14)

Solving for E r,eff leads to: εr, eff =

μl 2 f r2

√

2

1 + tan2 δ + 1

(4.15)

Since the presence of magnetic materials is not considered, μ = μ0 . Then, the expression of tan δ (or tan2 δ) from Eq. (4.11) can be used in Eq. (4.15), giving: εr, eff =

μ0

 l2

f r2

2 1+

16Q 2 (4Q 2 −1)2

+1

(4.16)

4.1 Introduction

97

Finally, E r,eff can be easily obtained from E r,eff thanks to the definition of the loss tangent in Eq. (4.8) and its expression as a function of Q in Eq. (4.11). The imaginary part of the relative effective permittivity is therefore given by: εr, eff = εr, eff

4Q 4Q 2 − 1

(4.17)

This way, a definition for E r,eff and E r,eff which only depends on intrinsic factors of the resonator (l) and parameters from the direct measurement (f r and Q) has been reached. This means that Er,eff can be determined from direct measurement with a microwave resonator, and hence the permittivity of what is placed upon the resonator can be obtained as shown before. Basing on the principles discussed so far, some microwave resonators have been proposed for glucose sensing in aqueous solutions put in the immediately upper space. The dielectric dispersion of pure water has been widely studied in the scientific literature [46]. The variation of the resonant frequency depending on the permittivity of the superstrate was effectively shown [47]. Metal patch resonators were investigated at millimeter wave frequencies [48]. A proposal based on U-shaped resonators was explored [49]. A close-loop ring microstrip resonator was considered for microfluidic measurements of water–glucose solutions [50], and a further attempt with a λ/2 strip line resonator was made [51]. A good work with spiral resonators was developed involving aqueous solutions and ad hoc phantoms [52, 53]. These works usually relied upon the fact that the changes in the permittivity of the solutions yield variations in the resonant frequency. These variations have been seen in some works, but they are relatively too small to provide for accurate sensing [54]. A wide variety of reports have been offered, but no convincing results have been seen yet, and the research remains actively open. In this chapter, a concept based upon open-loop microstrip resonators aimed to explore the variations in the dielectric losses of water–glucose solutions under a new measurement paradigm is proposed. In the following sections, three glucose concentration sensors for microlitervolume aqueous solutions will be discussed. The sensors are made of open-loop microstrip resonators with special dielectric liquid holders (with volumes of 5 and 25 μL) glued onto the gap between the line ends. The three single resonant frequencies are within the 2–7 GHz range. The sensors will be assessed and models with electromagnetic software, whose simulations properly match the experimental results. The main novelty of this approach is the use of Q factor and the maximum of S21 parameter as sensing magnitudes. The open-loop microstrip resonator is a popular circuit frequently used for many applications, like for example developing microwave filters [55]. This chapter studies the use of this circuit for sensing purposes under a new approach: the quality factor as a sensing magnitude. The low sensitivity of the resonant frequency to the glucose concentration is discussed, from which the convenience of looking at the quality factor is shown. The results obtained in the experimental procedures described in

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4 Glucose Concentration Detection in Aqueous Solutions …

Sects. 4.2–4.4 reinforce this view, pointing to higher sensing sensitivities than those obtained with other techniques. Actually, the convenience of analyzing the quality factor when a lossy covering is on a microstrip line was highlighted many years ago [33]. The new losses affect the characteristic impedance, which is reflected in the quality factor as defined in Sect. 2.2. These changes in the characteristic impedance, related to the Q factor, have been seen for measurements with water–glucose solutions [56, 57]. Indeed, the pathbreaking work by Park et al. [58] showed significant changes of the imaginary part of the relative permittivity with the glucose level variations in aqueous solutions. This parameter is closely related to the losses, which have a direct impact on the quality factor. Several configurations have been studied for the determination of the dielectric permittivity of lossy MUTs involving Q factor measurements [59]. Guidelines, techniques and discussions have been offered for measurements of Q factor in microwave resonators [60–63]. Thus, the investigation of this approach seems convenient. Another key feature of this approach is the small amount of solution sample required for the measurements. This sample size, in the range of microliters, is a remarkable benefit in comparison with the volumes required by other techniques. As described before, this is a quite desirable characteristic for many applications, chiefly for industrial processes in which the control of the glucose level of the solutions being produced is essential. This small volume would therefore enhance the control by tracking more samples throughout the production process without incrementing the waste, hence shortening the sampling period and providing for more reliable control. On the other hand, at the expense of maintaining the same sampling period, this small volume could also allow to reduce the waste (and hence the final cost) of the solution produced. Furthermore, this technique requires neither sample preprocessing, nor reactive chemicals, nor enzymatic reagents, nor disposable items. For all these reasons, the study of these sensors is worthwhile. It is also important to note that this research could find application in diabetes context. Indeed, the relative permittivity of blood does not differ much from that of water [64]. Although the solutions and glucose concentrations involved in this study are far from real blood samples for glucose level estimation, this study is necessary to take a step forward in understanding the effect of glucose in the dielectric properties of the solutions, and how to measure it. In this sense, the small volume of the sample is again an important factor because large amounts of blood cannot be used due to practical reasons. The microwave range is especially interesting for developing NIBGM systems because of the typical penetration depths, comparable to human skin depths [65, 66]. This parameter gives an estimation of the interaction of the field with matter as it travels into the material. The penetration depth δ (not to be confused with the loss tangent) is defined as [44, 67]: δ=

1 1 = [m] ωμσ α 2

(4.18)

4.1 Introduction

99

It determines the distance the field must penetrate into a material so that its intensity is reduced by 1/e (∼37%). As it can be seen, δ decreases as the frequency increases. In the frequency range concerned in this chapter (2–7 GHz), the penetration depths for the tissues in human skin (dermis and epidermis) range from 4 mm to 3 cm [68], approximately. These depths are convenient since they are comparable to the usual depth of human skin (roughly 3–4 mm). Higher frequencies lead to too short depths, whereas lower frequencies yield too large circuit sizes to be wieldy attached to the body. Furthermore, the ionic conductivity can dominate the imaginary part of the relative permittivity of some body fluids (like blood) for frequencies under 2 GHz, masking the influence of glucose in the overall losses. Therefore, the proposed study can also be helpful in the pursue of NIBGM technology. Recent reviews have pointed out the lack of confidence with the resonant frequency approach in microwave sensors for NIBGM and the need for improvements [69–71]. In this regard, this chapter introduces a new approach which benefits from the above-mentioned advantages of microwave technology, but explodes the variations of the dielectric losses to gain sensitivity. In the next section the focus will be put on the sensors design and implementation. A discussion on the different options and how to choose the right one will be given, and the sensing strategy will be analyzed. In Sect. 4.3 the measurements carried out will be explained in detail. The results obtained from the experimental study will be shown in Sect. 4.4. To finish, the discussion on the results obtained and their implications, as well as the conclusions reached in this investigation will be examined in Sects. 4.5 and 4.6, respectively.

4.2 Materials and Methods The proposal developed in this chapter is based upon open-loop microstrip resonators performing as glucose content sensors [1]. A key feature is the placement of the MUT in the gap between the open ends of the lines, thus directly affecting the coupling between them. As it will be seen later, the electric field in this region is more intense, and therefore the influence of the MUT is greater. To provide for a generic theoretical analysis, an open-loop half-wave microstrip line with characteristic impedance Z 0 , attenuation constant α, phase constant β, length l, and the ends connected by a load (the MUT) is considered, as depicted in Fig. 4.4. The load can be modeled as a  circuit in which the shunt impedances, connected to ground, account for the parasitic capacitances C p between the line ends and the ground plane of the microstrip line. For the sake of handiness, admittances will be considered, as shown in Fig. 4.5. Then, as a first approximation, it can be defined Y p = jωC p . Regarding the series impedance Z s , it represents the capacitance between both ends of the line, as well as the existing resistance. Without loss of generality, it can be defined Z s = Rs + jX s , regardless the frequency dependence of Rs and X s . If the line was completely open,

100

4 Glucose Concentration Detection in Aqueous Solutions …

Fig. 4.4 Open-loop microstrip line with the ends connected by a load

Fig. 4.5 -pad model for the load

with both ends totally isolated between them, the first resonance would correspond to l = λ/2, with a corresponding odd voltage distribution (as shown in Fig. 2.16 for n = 1). This can be inferred from the fact that, if there is no physical connection between the ends of the line, not the same potential can appear in both of them, yielding to odd voltage distribution. Then, the first resonance of the considered resonator in Fig. 4.4 has a similar voltage distribution, i.e. an odd one. Therefore, an electric wall (ground plane) can be set in the middle of the resonator, as it can be seen in Fig. 4.6 for the resonator and the load model. This leads to the transmission line model of half resonator shown in Fig. 4.7. Then, from general transmission line theory [45], the input admittance of the half resonator is given by:

Fig. 4.6 Resonator with an electric wall in the middle

4.2 Materials and Methods

101

Fig. 4.7 Transmission line model of half resonator



l Yin = − jY0 cot β 2

+ Yp +

2 Zs

(4.19)

being Y 0 = 1/Z 0 the characteristic admittance. The analysis can be simplified by modeling the series impedance of the load as a parallel capacitance C ps with a conductance Gps . This leads to the model seen in Fig. 4.8 for the whole load. Then, after splitting again the circuit into two parts by means of the odd mode analysis, the input admittance is now given by:    l + jω Cp + 2Cps + 2G ps Yin = − jY0 cot β 2

(4.20)

The condition for the resonance, i.e. null imaginary part of the input admittance (as discussed in Sect. 2.2), yields: 

l Y0 cot β 2

  = ω Cp + 2Cps

(4.21)

Then, at resonance, the capacitance C ps , which is due to the load, is:   cot β 2l Cp − Cps = Y0 2ω 2

(4.22)

Which can also be written as a function of the angular resonant frequency for the resonator with isolated line ends (with no load), ωr , considering Eqs. (2.63)–(2.65), as follows: Fig. 4.8 Model for the load with parallel capacitance and conductance

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4 Glucose Concentration Detection in Aqueous Solutions …

Cps = Y0

cot

π ω 2 ωr



2ω

−

Cp 2

(4.23)

This means that the frequency response of the resonator depends on the capacitance of the load, which is closely related to its relative permittivity. For example, for an open-loop microstrip resonator with line width w, substrate height h and open-end gap length s, supposing typical values of w/h = 0.5 and s/w = 2.5, from the curves in [72] the values of C p and C ps can be approximately estimated to be 10 and 5 fF, respectively, in the absence of the load. Then, considering the frequency response, if the left side of Eq. (4.21) is developed as a second order Taylor series, and the relationship of the phase constant with the frequency is considered, the next expression is valid near the resonant frequency f r : f ∼ =

fr   1 + 4Z 0 f r Cp + 2Cps

(4.24)

This way, considering that these capacitances are in the range of femtofarads, the denominator will be very close to 1, and the changes in the frequency response due to the capacitance of the load will be very slight. As for the Q factor, it can be defined as: Q=ω

UT Pdis

(4.25)

where U T is the total energy stored in the resonator, and Pdis is the power dissipated. As an initial approach, it can be considered that the losses in the series conductance in the gap predominate over any other losses. Therefore, the power dissipated is given by: Pdis

 2 G ps 2Vgap 2 = 2G ps Vgap = 2

(4.26)

being V gap the voltage amplitude in each end of the line in the absence of the load. Since the voltage distribution is odd, voltages of different signs are to be found at each end of the line, and hence there is a difference voltage of 2V gap between them. As discussed in Sect. 2.2, the total energy stored equals to the maximum electric energy or to the maximum magnetic energy. In this case the maximum magnetic energy is easier to obtain, as long as the magnetic energy associated to the conductance is neglected, considering only the energy in the line. The voltage distribution along the line is defined as: V (x) = V0 sin(βx)

(4.27)

In this expression V 0 is the voltage wave amplitude, and x is measured starting from the center of the line.

4.2 Materials and Methods

103

Then, at resonance, in the open ends (x = ± l/2 = ± λr /4), Eq. (4.27) can be expressed as follows: V (x = ±l/2) = ±Vgap

  βl π f = ±V0 sin = V0 sin ± 2 2 fr

(4.28)

Therefore:  Pdis =

2G ps V02

sin

2

π f 2 fr

(4.29)

whereas, assuming a current I(x) = I 0 cos(βx), the maximum magnetic energy (total energy) can be obtained as: l 2

UT = ∫

− 2l



    π f L C V02 l |I (x)|2 d x = · · · = 1 + 4 f r Cp + 2Cps Z 0 sin2 2 4 2 fr (4.30)

being L and C the inductance and capacitance per unit length of the line, respectively. Hence, considering Eqs. (4.25), (4.29) and (4.30), the quality factor is given by:    Cl 1 + 4 f r Cp + 2Cps Z 0 sin2 π2

Q=ω 8G ps sin2 π2 ffr

f fr

 (4.31)

Rearranging and applying Eq. (4.21) into (4.31) leads to:

Q=ω

   2   Cl 1 + ωZ 0 Cp + 2Cps + 4 f r Z 0 Cp + 2Cps 8G ps

(4.32)

Again, at frequencies relatively near f r and applying Eq. (4.24) to Eq. (4.32), after rearranging yields:  2  ω ωZ 0 Cp + 2Cps + ωr ∼ Q= 16 f r Z 0 G ps

(4.33)

Thus, the quality factor depends on two intrinsic parameters of the load, C ps and Gps , instead of depending only on C ps as it happened with the frequency response. The form of the Eqs. (4.24) and (4.33) also allows to predict a higher variation in Q factor than in f r due to variations in the load, and it could provide for more noticeable contribution. The presence of C ps in the numerator in Eq. (4.33), instead of in the denominator in Eq. (4.24), also allows to expect slightly greater influence in the Q factor.

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4 Glucose Concentration Detection in Aqueous Solutions …

In addition, these parameters are related through the relative permittivity of the material. For a homogeneous material at frequencies high enough to neglect the conductivity, it must be satisfied the following relationship: G ps ωε = r Cps εr

(4.34)

Therefore, the idea of using the Q factor as sensing magnitude seems worthwhile investigating. Since Eq. (4.34) relates the components of the circuit model of the load to its relative permittivity, such a configuration seems suitable for measuring the variations of the permittivity of a MUT placed in the gap between the ends of the lines. In this chapter, three sensors based upon open-loop microstrip resonators at microwave frequencies are presented, which a special sample holder placed in the gap, to be filled with the solutions under measurement [1]. The sensors are used to track the glucose concentration of aqueous solutions be means of the Q factor. In this sense, remarkable variations of the dielectric parameters of aqueous solutions at different glucose concentrations were shown in [3]. As discussed in Sect. 2.1.1, the dielectric behavior depends on the frequency, and therefore the investigation of different frequencies is interesting. Hence, three microstrip resonators, hereinafter named R1 , R2 , and R3 , were designed and implemented, with resonant frequencies of 2.0, 5.7, and 8.0 GHz in free space (with no load) respectively (see Sect. 2.2). This implies a characterization of three specific frequency points in a 6 GHz range. Each sensor is composed of a microstrip resonator with a small dielectric sample holder placed upon it. The sample holder was specifically designed to be filled with the solution to be characterized, and it was made of polytetrafluoroethylene (PTFE), a low-loss, low-permittivity material. This material allows to reduce the influence of the sample holder in the measuring setup, thus emphasizing the contribution of the solution. PTFE also has low chemical reactivity, thus providing for the characterization of a wide variety of liquids. After placing the corresponding sample holders and filling them with pure water, the measured resonant frequencies of the resonators moved to roughly 1.9, 5.2, and 7.2 GHz. These points seem to be convenient for identification of dielectric changes in water–glucose solutions according to the electromagnetic signature of the solutions reported in [3]. In the design of the resonators, folded open-loop half-wave microstrip resonators were considered. A folded design was preferred to a circular one to enhance the I/O couplings, which are very relevant for sensing purposes. For these resonators, the resonant frequency may be defined as: fr =

c √ 2l εr,eff

(4.35)

where c is the speed of light in free space, Er,eff is the effective relative permittivity, and l is the length of the line. The final resonant frequencies differed slightly from

4.2 Materials and Methods

105

the expected ones from Eq. (4.35) due to the placement of the PTFE sample holders. A low-loss, low-permittivity substrate (Taconic TLX-8, Er = 2.55, tan δ = 0.0017) was chosen with the objective of lowering its influence in the measurements, since the liquids to be characterized were expected to have high permittivities and high losses. The selected substrate thicknesses were 1220 μm for R1 and 800 μm for R2 and R3 . A schematic of the developed resonators can be seen in Fig. 4.9. An open-loop design was selected due to the above-mentioned benefits of the gap between the ends of the lines as sensing area. Thus, in this gap a high electric field region is created for the first resonant mode, as shown in Fig. 4.10, in which the measurement setup can also be seen. At resonance, voltage maxima with opposite signs will be given at the open-end positions. Figure 4.11 illustrates this by depicting the surface current density distribution for R1 at resonance, which is inversely proportional to the voltage

Fig. 4.9 Schematic of the design of a R1 , b R2 , and c R3 resonators. All the dimensions are in millimeters. © [2019] IEEE. Reprinted, with permission, from [1]

VNA

micropipette liquid sample holder

microstrip lines

electric field lines

substrate

50

lines

sensor

ground plane

Fig. 4.10 Measurement setup and electric field distribution in the open-end gap, from [73]

106

4 Glucose Concentration Detection in Aqueous Solutions …

Fig. 4.11 Surface current density for R1 at the resonant frequency

distribution. For these reasons, this is the place where the electric interaction with the sample is expected to be the highest. All the design was optimized to increase the sensitivity of the electrical response to the circumstances in the gap region. Looking at Fig. 4.10, high electric field intensity is desirable so that the interaction with the MUT increases. To increment the field intensity at the open ends, high characteristic impedances of the microstrip lines are needed. Thus, the voltage wave amplitude V 0 for the first resonant mode can be easily shown to be: V02 = 8U Z 0 f r

(4.36)

being Z 0 the characteristic impedance of the line, and U the energy stored in the resonator. Therefore, for a given U, the voltage amplitude is proportional to Z 0 , and hence high characteristic impedances are required to increase the field intensity. Due to this reason, within fabrication possibilities, relatively narrow strip widths of 600 μm were chosen (as shown in Fig. 4.9). The resulting impedances, which also depend on

4.2 Materials and Methods

107

the substrate permittivity and thickness, were 117 for R1 and approximately 100 for R2 and R3 . In addition, broad lines are not convenient because they could prevent the energy from being concentrated in the central area of the gap, which is the region of maximum interest in this design. It is also convenient to have a low-permittivity substrate in this regard, which allows the electric field to go through the biggest space section in the gap. Once designed, coupled-line sections were used to couple the resonators to 50 I/O lines. The coupling strength is an essential parameter to consider, too. It depends on the coupling section geometry, and the result of the coupling has a remarkable influence in the shape and the amplitude of the resonant peak, both in transmission and reflection responses [74]. Hence, a strong coupling gives loaded quality factors noticeably influenced by the external loads of the I/O ports, worsening the resolution in the resonant frequency and unloaded quality factor. However, a weak coupling yields to low-amplitude resonant peaks, and the noise starts masking important information. A trade-off between these effects had to be selected, and the coupling parameters (including line widths, spacing and length) were set to give a maximum transmission (S21 parameter) peak in the amplitude range from −15 to −12 dB for a measurement in the absence of sample. Finally, coaxial connectors were welded to the I/O lines to provide for VNA measurement. Also, the length of the gap between the ends of the lines is a critical parameter, since it has a direct effect in how the fields are affected by the presence of the sample holder and the sample. A too short gap would yield to an electric field chiefly concentrated in the substrate–sample holder interface, being scarcely aware of the presence of the sample. For a too long gap, although having an electric field more homogeneously distributed in the space around the gap, the field intensity could be too low and the resolution would worsen significantly. Therefore, anew a trade-off choice had to be taken, trying to get the benefits of both situations and providing for processable measurements. Finally, 1600 μm gap for R1 and R2 was selected, and 1200 μm gap for R3 . In this sense, all the design dimensions (line widths, gap I/O coupling distance…) were carefully selected to ensure a sufficient safety margin not to be affected by dispersions of the fabrication. The difference in R3 is due to line length reasons (given the higher resonant frequency), although this led to the implementation of a sample holder with a volume five times smaller. Hence, two models of PTFE sample holder were used. The big model for R1 and R2 had an inner volume (solution volume) of 25 μL, whilst the inner volume of the small model for R3 was 5 μL. The sample holders and their transversal sections are shown in Fig. 4.12. After fabrication, each sample holder was glued onto the open-end gap of its corresponding resonator using a very thin layer of epoxy resin. In Fig. 4.13 a picture of the final version of the three sensors can be seen. In the next section the optimization of the sensors will be discussed and the measurement procedure will be described.

108 Fig. 4.12 Sample holders used in the sensors: a top view, and transversal sections of the small b and big c sample holders. © [2019] IEEE. Reprinted, with permission, from [1]

Fig. 4.13 Sensors developed. © [2019] IEEE. Reprinted, with permission, from [1]

4 Glucose Concentration Detection in Aqueous Solutions …

4.3 Measurements

109

4.3 Measurements With the aim of assessing the sensors designed, models in ANSYS® HFSS software for electromagnetic simulation were developed, including the resonators, the sample holders, the samples and the glue. For example, the model for R2 is shown in Fig. 4.14a, with a specific screenshot of the model of the sample holder in Fig. 4.14b. In the models, several parameters referring to physical or geometrical properties of the objects involved were not known accurately enough to provide for trustable simulations. No data were available for modeling the thickness and complex permittivity of the glue used to attach the sample holders to the resonators. Furthermore, the inner shapes of the sample holders were designed to be hemispherical, so that the air could flow during the filling process, and the air bubbles presence in the sample could be avoided. However, only the small sample holder had an acceptable hemispherical inner shape (Fig. 4.12b). In the case of the big one, due to fabrication non-idealities, its inner shape was modeled in a more reliable manner by a filleted cylinder (Figs. 4.12c and 4.14b), whose fillet radius was difficult to measure directly.

Fig. 4.14 ANSYS HFSS model for R2 sensor. a 3D view of the whole resonator and the PTFE sample holder (without sample). b Cross section of the sample holder. © [2019] IEEE. Reprinted, with permission, from [1]

110 Table 4.1 Dielectric parameters of reference liquids

4 Glucose Concentration Detection in Aqueous Solutions … Liquid

Er 

tan δ

References

Water

76.84

0.134

[3, 76, 78]

6.62

0.952

[77–80]

Ethanol Methanol

20.54

0.653

[75, 77]

Nitrobenzene

34.82

0.014

[81]

Acetonitrile

35.76

0.016

[82]

Formamide

77.86

0.620

[81, 83]

© [2019] IEEE. Adapted, with permission, from [1]

To determine these parameters, retrofit simulations were performed in HFSS taking data from real measurements with the implemented sensors. In these measurements, some reference liquids were selected, given that their dielectric parameters had been previously determined with precision by other authors [3, 75–83]. Then, the real and imaginary part of the permittivity of the glue, in addition to the fillet radius of the inner shape of the big sample holder, were taken as parameters to be tuned and optimized in the retrofit simulations. The optimizations were made in order to obtain the least difference between the simulated and the incorporated measured response of each sensor with each reference liquid. For example, the dielectric parameters for the reference liquids concerned, at 2 GHz and 25 °C, are shown in Table 4.1. After all the simulations and optimization processes, taking the average results, the glue was modeled as a dielectric layer with the same base shape than the sample holder basis, and a height of 50 μm. Its dielectric parameters were set to Er  = 3.55 and tan δ = 0.01. Also, the fillet radius of the filleted cylinder used to model the inner shape of the sample holder was computed to be 0.5 mm. With these parameters the electromagnetic models reproduced well the results obtained in real experimentation. The proper setup of the sample holder is crucial for the right performance of the sensors, and it has remarkable implications in the final sensitivity. To ensure the best configuration, further simulations were run to study the influence of some critical parameters of the design of the sample holder, and identify the best values. The simulations were performed with R2 sensor without loss of generality. Since the sensors are intended to perform as glucose trackers, water–glucose solutions were concerned for these simulations. The data for modeling the solutions were extracted from [3], considering three water–glucose solutions at 0% (pure water), 5%, and 10% mass content. The first parameter to study was the exact position of the sample holder with respect to the center of the open-end gap. Therefore, as shown in Fig. 4.15a, this position was changed from the center of the gap (centered) 1 mm inward (− 1 mm) and 1 mm outward (+ 1 mm). The results can be seen in Fig. 4.15b. Effectively, the best results in terms of sensitivity to the glucose content were obtained for the centered position, since it yielded the greatest variations of the unloaded Q factor. As logical, the center position seems to be the best option, since in the other ones the plain lower area of the inner shape of the sample holder is getting far from the gap, so

4.3 Measurements

111

(a) Simulations for sensitivity of R2 varying the position of the sample holder 7 Center

6

+1 mm

unloaded Q change

-1 mm

5 4 3 2 1 0 0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(b) Fig. 4.15 Variation of the position of the sample holder: a positions simulated; b results of unloaded Q against the glucose concentrations. © [2019] IEEE. Reprinted, with permission, from [1]

the field lines have to travel through a larger sample holder volume before reaching the solution. All the sample holders were therefore centered in their corresponding gap. Setting the sample holder fixed in the center of the gap, further simulations were run to investigate its lower thickness, another crucial parameter. This thickness was varied from 150 to 400 μm, as depicted in Fig. 4.16a. The results, plotted in Fig. 4.16b, suggest that the thinner the base of the sample holder is, the more volume of liquid the electric field travels through, and therefore the more sensitive it is to the dielectric properties of the liquid. Hence, the shortest thickness was applied during the fabrication of the sample holders, within fabrication possibilities, which resulted in 190 μm. This thickness allows for trustable fabrication and its results were proven not to be remarkably worse than those for 150 μm, the best case simulated. Another parameter to take into account is the sample holder material. A new set of simulations was run considering the above-mentioned parameters and changing the real part of the relative permittivity of the sample holder material, considering

112

4 Glucose Concentration Detection in Aqueous Solutions …

(a) Simulations for sensitivity of R2 varying the lower thickness of the sample holder

7

150 um

6

190 um (real)

unloaded Q change

250 um

5

300 um

4

400 um

350 um

3 2 1 0 0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(b) Fig. 4.16 Variation of the bottom thickness of the sample holder: a thicknesses simulated; b results of unloaded Q against the glucose concentrations. © [2019] IEEE. Reprinted, with permission, from [1]

lossless materials. Several values were considered, from 1 (the ideal case) to 10, including PTFE (with its reported losses). The results, shown in Fig. 4.17, point that the lower the permittivity, the better the sensitivity. Indeed, the closest match to the ideal case is provided by PTFE (Er  = 2.1), including the losses, with little difference. Also, in addition to the low sensitivities obtained for Er  = 5, 10, the unloaded Q factors obtained in these cases were too low for practical measurements.

4.3 Measurements

113

Simulations for sensitivity of R2 varying the permittivity of the sample holder 7 eps=1 PTFE (eps=2.1) eps=5 eps=10

unloaded Q change

6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

Fig. 4.17 Results of unloaded Q against the glucose concentrations for the simulations of different sample holder materials. © [2019] IEEE. Reprinted, with permission, from [1]

Thus, as expected, the material with the lowest relative permittivity is convenient for the sample holder, and PTFE seems the best option. Finally, the permittivity of the substrate was also investigated with simulations with different substrates. Setting the previous parameters, the ideal case of air substrate (Er  = 1) was simulated along with Taconic TLX-8 (Er  = 2.1) and a higher case (Er  = 10). Full redesign of the circuit for each permittivity value was needed in these simulations. The results are shown in Fig. 4.18. As it can be seen, the greater Simulations for sensitivity of R2 varying the permittivity of the substrate

unloaded Q change

8 eps=1 TLX (eps=2.55) eps=10

6

4

2

0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

Fig. 4.18 Results of unloaded Q against the glucose concentrations for the simulations of different substrate permittivities

114

4 Glucose Concentration Detection in Aqueous Solutions …

the permittivity of the substrate is, the more confined the fields are into it, and the less affected they are by the elements in the upper space. Thus, the sensitivity decreases when the substrate permittivity increases. Then, the chosen low-permittivity substrate provides a good option. This way, after ensuring an optimized configuration of the sensors, measurements were carried out. The measurement process was as follows. Before starting, the VNA was properly calibrated for the frequency range of interest of each sensor, and the sensor was connected to it. With the aim of ensuring repeatability, the response (Sparameters) of the sensor with the sample holder empty was saved and frozen in the VNA’s screen. Then, the measurements for each specific study were made. Each one consisted in filling the sample holder with the solution or liquid to be measured by means of a micropipette, saving the obtained S-parameters, and carefully cleaning the sample holder with ethanol until the scattering parameters for the empty case frozen in the screen were matched with the measured S-parameters. A couple of pictures of the experimental procedure can be seen in Fig. 4.19. For the 25 μL sample holder, a micropipette with 0.5 μL resolution was used, whereas the 5 μL sample holder was filled with a micropipette with 0.1 μL resolution. In absolute terms, this means an instrumental error of 2% in the liquid volume, which is not expected to affect noticeably the measurement. With the reference liquids, the measurements were carried out in order from lowest to highest Er ’, whilst with the water–glucose solutions the measurements were made from lowest to highest glucose concentration, having the first and the last measurement of deionized water to check Fig. 4.19 Pictures of the experimental procedure: a R2 with liquid; b setup for R3 measurements. © [2019] IEEE. Reprinted, with permission, from [1]

4.3 Measurements

115

repeatability and absence of drift. The experiments were always carried out at room temperature ranging 22–25 °C in general, with changes lower than 1 °C for the same measurement session. In addition, the measurements were made at Miguel Hernández University of Elche, Elche, Spain, as well as at University of Brest, Brest, France, getting very similar results. This circumstance indicates good reproducibility. One of the main novelties of this work was the use of the quality factor as sensing parameter. Since the measurements provide the scattering parameters, the Q factor must be computed from them. In this case, due to the fact of having two ports and hence being transmission resonators, the Q factor was computed considering the exact 3 dB fall from the maximum in S21 parameter, as described in Eq. (2.44). However, as explained in Sect. 2.2, this leads to the loaded Q factor QL , which also accounts for the effects of the VNA. The desired parameter is the unloaded Q factor Qu , which only refers to the quality factor of the sensor, getting rid of loading effects. Therefore, QL was obtained from the measurements and then Qu was computed as [62, 63]: Qu =

QL 1 − S21max,lin

(4.37)

where S21max,lin is the magnitude of the maximum amplitude of S21 parameter in linear scale. Henceforth, all Q factors regarded are unloaded Q factors. It should be noted that the measurements provided signals made out of discrete (frequency, S21 ) points, not always falling in the exact required points, like the maximum in S21 or the exact 3 dB fall. Hence, linear interpolation or fitting strategies were followed to obtain the exact parameters and have a more reliable calculation of the QL , to later obtain Qu by means of Eq. (4.37). In Appendix A a method to fit the discrete signal to a quadratic function and obtain the desired parameters is shown. In a first approach, the devices were evaluated as permittivity sensors using the reference liquids and their dielectric parameters listed in Table 4.1. Data for this study were obtained both from real measurements and simulations of the devices with the sample holders filled with these liquids. The real part of the permittivity was expected to be related to the obtained resonant frequency, while the loss tangent was expected to produce variations in Qu [1]. To see this, in Fig. 4.20a the measured and simulated resonant frequencies are plotted against the Er  of the liquid, whereas the unloaded Q factors against the loss tangent are shown in Fig. 4.20b. Similar results were obtained for the rest of resonators (not shown). The good agreements between the measurements and simulations indicate that the software models are reliable. As it can be seen, variations were reported both for the resonant frequency and for Qu , related to variations in the dielectric properties of the liquids under measurement. However, the changes in the unloaded quality factor were comparatively larger. This first approach points the convenience of considering Qu as sensing parameter, as proposed [1]. In this sense, the use of Q factor, regardless the kind, for applications with microwave resonators has been described in many works [60, 61]. The different types of quality factors, with special emphasis on Qu , haven been described, and methods for computing them in any configuration have been discussed [62, 63].

116

4 Glucose Concentration Detection in Aqueous Solutions …

Fig. 4.20 Measurements and simulations for reference liquids with R1 : a resonant frequencies; b unloaded Q factors. Blue circles for real measurements and red asterisks for simulations. © [2019] IEEE. Reprinted, with permission, from [1]

Then, this work proposes this parameter for a new application: glucose concentration tracking. As to water–glucose solutions, reference data were taken from [3]. Deionized water, as well as water–glucose solutions at 5 and 10% mass content (labeled water, G5, and G10, respectively) were measured with the sensors proposed. Volumes of 10 mL of each solution were prepared with deionized water and d-(+)-glucose anhydrous from Panreac (ref. 131341) with a Sartorius analytical balance with 0.1 mg resolution (ref. BP61S). All the measurements were made in the same conditions described for the reference liquids. In the VNA configuration, a frequency step of 2 MHz was set. In the worst case, R1 sensor, this implied 15 frequency points available in the 3 dB bandwidth of the S21 response. The S21 peak widths used in the calculation of the Q factors were computed by linear interpolation of the experimental points closest to S21max (dB) - 3 dB.

4.3 Measurements

117

Concerning the temperature, since the sensors intrinsically required the liquid to be sampled and placed into the sample holder, by considering the volume needed and the temperature inertia, one can consider that the temperature should not be a relevant cause of error in the measurements, as they were intended to work at room temperature. Indeed, although existing, impact of the temperature upon the sensor itself (material dilatations) is very weak compared to the variation of the properties of the glucose solutions with temperature changes. The room temperature was recorded in every measurement, and the variations throughout a whole measurement session were always lower than 1 °C for all the sessions. Some results of others authors for water–glucose solutions measured with resonant techniques can give an estimation of the variation in Q due to the temperature. Measurements of water–glucose solutions at several temperatures using a resonant cavity technique at 4.5 GHz were shown in [84]. Albeit that technique is different from the one in this document, in both cases the main factor affecting the quality factor is the loss tangent of the sample. In that work, the data at 25 °C indicate that

Q/ T ∼ = 0.09/°C for 1% glucose concentration (being T the temperature), and

Q/ T ∼ = 0.11/°C for 10%. Thus, within that concentration range, which corresponds to the range presented in this chapter, it can be estimated that Q/ T ∼ = 0.10/°C for any sample. With these data, the expected error in Q because of the variations in the temperature can be approximated as Q = Q/ T × T = 0.10/°C × 1 °C = 0.10, for measurements in a same session. The maximum temperature variation for different sessions was of roughly 3 °C, leading to an estimated error in Q of 0.30. For these reasons, provided that the measurements are made at room temperature with low variations, which is a reasonable premise for many industry or clinical applications, it seems an acceptable error. As a matter of fact, during this study the measurement sessions were repeated many times in different moments and places, at different room temperatures, yielding the same results. This is also a good sign as far as reproducibility and repeatability are concerned. On the other hand, regarding the extrapolation to different temperature ranges, the loss tangent of the water–glucose solutions is highly affected by the temperature. This is mainly because of the high impact of the temperature upon the viscosity of those solutions [85]. Viscosity directly impacts the loss tangent as it creates friction efforts to the movement generated thanks to the excitation of the dipolar momentum or ionic displacement. Those effects are of high interest and worth being studied but, as they mainly concern the behavior of the glucose/water mix from a physico-chemical standpoint, they are out of the scope of this dissertation. Finally, as an illustrative example, in Tables 4.2 and 4.3 the results obtained in the measurements and simulations for the resonant frequency and the unloaded quality factor of sensor R2 with deionized water, G5 and G10 can be seen. The subscripts m and s refer to measurements and simulations, respectively, whilst stands for the percentage change of a glucose solution with respect to deionized water. Although a new good matching between measurements and simulations was seen, this time, considering only aqueous solutions, the changes in f r were too small for measuring purposes, too much close to the VNA resolution. Hence, notwithstanding the fact that

118

4 Glucose Concentration Detection in Aqueous Solutions …

Table 4.2 Results for the resonant frequency measurements and simulations of R2 with deionized water, G5 and G10 Liquid

Er  at ∼5 GHz

f rm (GHz)

f rm (%)

Water

73.007

5.1534

–

5.1546

–

G5

70.043

5.1544

0.0194

5.1556

0.0194

G10

66.052

5.1559

0.0485

5.1570

0.0466

f rs (%)

f rs (GHz)

© [2019] IEEE. Reprinted, with permission, from [1]

Table 4.3 Results for the unloaded quality factor measurements and simulations of R2 with deionized water, G5 and G10 Liquid

tan δ at ∼5 GHz

Qum

Qum (%)

Qus

Qus (%)

Water

0.261

67.102

–

66.926

–

G5

0.286

62.981

6.141

62.881

6.044

G10

0.312

60.519

9.810

60.384

9.775

© [2019] IEEE. Reprinted, with permission, from [1]

the sensors had been proven to measure f r and Qu variations between different liquids (see Fig. 4.20), when only low-concentration water–glucose solutions are considered the greatest sensitivity was obtained measuring the unloaded quality factor, as proposed. The results for the whole experimental procedure will be shown in the next section.

4.4 Results According to the measurements and simulations discussed in the preceding section, especially for Qu sensitivities (see Table 4.3), further assessment of the sensors was carried out. To do it, more water–glucose solutions sets were prepared at concentrations ranging 1.25–10.00% in mass, equally spaced. Henceforward, the solutions are labeled Gx.xx, being x.xx the glucose mass content percentage. All these solutions were measured with each sensor, and simulations were run as well. Data for modeling the solutions in the simulations were obtained from [3], albeit only data for deionized water, G5.00 and G10.00 were available. Since no more data were found in the literature, the rest of solutions were modeled with dielectric parameters lineally interpolated from the above-mentioned solutions. Regarding R1 performance, the magnitude of the measured S21 parameters around the resonant frequency for the set of solutions are plotted in Fig. 4.21a. The reader can note that the changes in f r are quite small, almost negligible. Notwithstanding, it is clear how S21 magnitude decreases as the glucose concentration raises. In this sense, this plot illustrates well the idea of the greater exploitability of dielectric losses

4.4 Results

119

Water-glucose measurements for R1 Water

-21

G1.25 G2.50

mag(S21) (dB)

G3.75

-21.5

G5.00 G6.25 G7.50

-22

G8.75 G10.00

-22.5

-23 1.91

1.92

1.915

1.93

1.925

f (GHz)

(a) Glucose concentration vs Q factor change for R1 5 Measured Simulated

Q factor change

4

3

2

1

0 0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (% mass)

(b) Fig. 4.21 Results of the assessment of R1 with water–glucose solutions: a measured S21 parameters; b absolute changes in Qu . © [2019] IEEE. Reprinted, with permission, from [1]

(seen as amplitude losses) against the resonant frequency by means of a microstrip resonator [1]. As discussed hereinbefore, the unloaded Q factor is a good candidate to account for these changes in the dielectric losses. Therefore, Fig. 4.21b shows the absolute changes in Qu for all the solutions relative to deionized water measurement. These changes are plotted against the glucose concentration of each solution, both measured and simulated with R1 . The plot evidences the convenience of using Qu as sensing magnitude for the glucose concentration, given the well-nigh linear relationship obtained, which facilitates the retrieval of the glucose level in unknown solutions.

120

4 Glucose Concentration Detection in Aqueous Solutions …

On the other hand, when the resonant frequencies were plotted against the glucose concentration a random distribution of points was obtained (not shown), in a range comparable to the frequency resolution of the VNA. Thus, the convenience of Qu instead of f r is clearly seen in Fig. 4.21. It is important to see the good agreement found between measurements and simulations, accounting for the validation of the software models and of the experimental procedure. Concerning R2 sensor, the results are shown in Fig. 4.22. As it can be seen in Fig. 4.22a, the magnitude S21 parameters next to the resonance were similar to those found with R1 , with a clear relationship between the S21 peak amplitude and the Water-glucose measurements for R2 Water

-25.5

G1.25 G2.50

-26

mag(S21) (dB)

G3.75 G5.00

-26.5

G6.25 G7.50

-27

G8.75 G10.00

-27.5 -28 -28.5 5.11

5.12

5.13

5.14

5.15

5.16

5.17

5.18

5.19

5.2

f (GHz)

(a) Glucose concentration vs Q factor changes for R2 7 Measured

Q factor change

6

Simulated

5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (% mass)

(b) Fig. 4.22 Results of the assessment of R2 with water–glucose solutions: a measured S21 parameters; b absolute changes in Qu . © [2019] IEEE. Reprinted, with permission, from [1]

4.4 Results

121

glucose concentration. In Fig. 4.22b the performance of R2 as glucose concentration sensor with Qu as sensing magnitude can be seen both for measurements and simulations. Again, an almost linear relationship between the unloaded Q factor and the glucose concentration was obtained, with a random distribution of points for f r measurements. Finally, as to R3 , the results can be seen in Fig. 4.23. Near the resonance, the measured S21 parameters shown in Fig. 4.23a had a similar behavior to R1 and R2 , with S21max following the changes in the glucose concentration. It should be noted that, this time, despite the five times smaller volume of the sample holder, the Water-glucose measurements for R3 Water

-22.5

G1.25

mag(S21) (dB)

G2.50 G3.75

-23

G5.00 G6.25 G7.50

-23.5

G8.75 G10.00

-24

-24.5 7.12

7.13

7.14

7.15

7.16

7.17

7.18

7.19

7.2

7.21

f (GHz)

(a) Glucose concentration vs Q factor change for R3 2.5 Measured Simulated

Q factor change

2

1.5

1

0.5

0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(b) Fig. 4.23 Results of the assessment of R3 with water–glucose solutions: a measured S21 parameters; b absolute changes in Qu . © [2019] IEEE. Reprinted, with permission, from [1]

122

4 Glucose Concentration Detection in Aqueous Solutions …

measured and simulated Qu plotted in Fig. 4.23b also presented similar behaviors to the other sensors, with Qu slightly lower, perhaps due to the smaller sample volume. Therefore, the proposed sensor design was proved to work well as glucose concentration retrieving system with sample volumes as small as 5 μL, remaining the same conclusions reached for sensors with higher sample volumes unaltered [1]. With reference to the measurements error, plots in Figs. 4.21b, 4.22 and 4.23b do not include error bars in Qu because the estimated error magnitudes were, in the worst case, comparable to the symbol size. In this sense, the chief error sources can be, on the one hand, instrumental error in the VNA measurement and, on the other, error in the sample volume (approximately 2%). The VNA measurement error in the unloaded Q factor can be estimated to be ∼ 2% in the worst case for the abovementioned measuring conditions. A theoretical method to compute the instrumental error in Qu is shown in Appendix B, and a further discussion can be seen in [86]. Regarding the influence of instrumental error in the sample volume, it is difficult to estimate due to the need of defining the electric field distribution throughout the sample, which is unknown. Conversely, given that the design is thought for an electric field highly concentrated in the bottom of the sample, the possible variations in the solution volume filling the sample holder are expected to have negligible impact in the measured Qu . Concerning higher glucose concentrations, further measurements were performed with solutions up to 20% glucose mass content. The aim was to see if the reported linearity of Qu with respect to the variations in the glucose concentration remained the same. The results (not shown) confirmed this behavior even for 20% glucose solutions, which are fairly far from biological purposes, but might be interesting for some industry applications, like sugared drinks production or fermentation control processes in the making of spirits (as explained in Sect. 4.1).

4.5 Discussion The results shown in this chapter, in general, indicate a good performance of the proposed devices as dielectric permittivity sensors for liquids with a wide variety of permittivity values (see Fig. 4.20). Remarkable changes of the resonant frequency and unloaded quality factor were seen for different liquids, which could be related to the actual values of Er  and tan δ of the liquids. Therefore, with the measurement of two parameters, f r and Qu , the real and imaginary part of the permittivity at the sensor frequency could be identified. This behaviors account for dielectric permittivity sensing and liquid identification, within a certain error. To study this behavior, some simple estimations of the sensitivities of the resonant frequency and unloaded Q factor with respect to the glucose concentration in mass percentage C can be done. Figure 4.20a shows a slope f r / Er  of roughly − 1.5 × 105 Hz in the region of water, whilst Fig. 4.20b shows a slope Qu /( tan δ) of approximately − 100 in the same region. As a first approximation, the sensitivities of f r and Qu can be calculated as:

4.5 Discussion

123

f r ∼ f r εr =

C

εr C

Q u

Q u ∼ Q u (tan δ) = =

C

(tan δ) C

(tan δ)

(4.38)

εr  ε

C r

ε

− Cr εr εr 2

(4.39)

The missing terms in Eqs. (4.38) and (4.39) can be obtained from [87]. In that work, measurements of pure water and 0.292 M water–glucose solutions at 5.2% in mass, approximately, were made with a commercial open probe at 300 K (~ 27 °C). At 2 GHz (roughly the frequency of the measurements of R1 shown in Fig. 4.20), it can be extracted from the plots in [87] with a slight uncertainty that Er  / C(%) ≈ −0.4/% and Er  / C(%) ≈ 0.2/%. Thus, solving for the sensitivities of f r and Qu in Eqs. (4.38) and (4.39) yields: Hz

fr ≈ 6 × 105

C %

(4.40)

Q u −0.4 ≈

C %

(4.41)

These values suggest that the estimated variation of the resonant frequency is negligible in relative terms (600 kHz for a 1% increment in C vs. an f r value of several GHz). This indicates that, although being able to see considerable variations in the real part of the relative permittivity when liquids of different nature are concerned, the variations expected with water–glucose solutions are too low, since no such great changes in Er  will take place. Therefore, no full dielectric characterization for these solutions can be made in a trustable way with the proposed sensors. However, the sensitivity of Qu shown in Eq. (4.41) seems convenient for glucose concentration sensing purposes, and further discussion is advisable. In this sense, concerning Qu as sensing magnitude for glucose concentration in water–glucose solutions, the proposed sensors showed good performance, as it can be seen in Figs. 4.21b, 4.22 and 4.23b. Good linearity between the unloaded quality factor and the glucose concentration was found, even for very small sample volumes (5 and 25 μL). Then, a crucial feature of the sensors is their sensitivity as glucose trackers, i.e., the variation found in a sensor’s output magnitude due to a change in the glucose concentration. This can be easily obtained from the experimental results (Figs. 4.21, 4.22 and 4.23). In Table 4.4 the Qu sensitivities for the three sensors are shown, while Table 4.5 offers the sensitivities of S21max , obtained as the maximum amplitude of the peaks plotted in Figs. 4.21a, 4.22 and 4.23a. Comparison with related works by other authors is provided in both tables. As shown in Table 4.5, the results reported for S21max compare well with the work carried out by Kim et al. [31]. In that work a dielectric waveguide probe in reflection mode was developed and used for measuring aqueous glucose solutions at concentrations up to 30% in mass, by considering the minimum reflection at resonance. This work was made at frequencies comparable to R1 range. The same

124 Table 4.4 Qu sensitivities of the three sensors for water–glucose measurement

4 Glucose Concentration Detection in Aqueous Solutions … f r (GHz)

Qu / C (/%)

[54]

1.00

0.384

This work [1]

1.92 (R1 )

0.468

5.16 (R2 )

0.658

7.16 (R3 )

0.414

© [2019] IEEE. Reprinted, with permission, from [1]

Table 4.5 S21max sensitivities of the three sensors for water–glucose measurement

f r (GHz)

S21max / C (dB/%)

[31]

2.15

0.028

[84]

4.50

0.030

This work [1]

1.92 (R1 )

0.047

5.16 (R2 )

0.084

7.16 (R3 )

0.048

© [2019] IEEE. Reprinted, with permission, from [1]

group developed a more complex setup in [84], based upon a high-Q dielectric resonator perturbed by a near-field probe placed at 1 μm over the solution sample, at frequencies near R2 range. With reference to Qu (Table 4.4), the research by Saeed et al. [54] analyzed the unloaded quality factor of a microstrip λ/2 resonator for characterizing water–glucose solutions at frequencies close to R1 region. In Tables 4.4 and 4.5 the results reported in this chapter, published in [1], are compared to those studies. It should be also noticed that the sensitivities obtained for Qu are coherent with the sensitivity estimations made in Eqs. (4.39) and (4.41). In addition, the results for R3 sensor, showing slower sensitivities than R2 , are logical given the fivefold smaller sample holder volume. Indeed, the Q factors are smaller as the circuit dimensions decrease, since the global energy is more concentrated in the sample, which shows significant dielectric losses. In general, results in Tables 4.4 and 4.5 show the convenience of paying attention to the dielectric losses variations in the solutions for sensing purposes. Both S21max and Qu have shown good performance as glucose concentration trackers, which are parameters related to the losses, thus reinforcing this idea [1]. Since S21max has a remarkable dependence on the feeding and measurement process, Qu is proposed as sensing magnitude for this purpose. Hence, this chapter has described and assessed a good technique for developing glucose concentration sensors in aqueous solutions with microwave resonators. It is based on the exploitability of the unloaded Q factor for measuring purposes. In fact, measurements of dielectric properties of the MUT with quality factor of microstrip line devices have been proposed and supported in other contexts [33], especially when the dielectric losses are considerable. Since Qu is closely related to the dielectric losses, this supports the idea that the main contribution of glucose to the dielectric behavior of the solutions comes in the form of losses [1].

4.5 Discussion

125

This view has been recently supported by some authors. In [88] the importance that the loss tangent variations have in blood glucose level measurement by microwave sensors was highlighted. Guidelines for microwave sensors design aimed to biomedical applications have been provided, emphasizing the need for considering the dielectric constant and loss tangent contribution in the measurements [89]. Accurate dielectric models for the real and imaginary part of the relative permittivity have been investigated for their use in the design of microwave glucose sensors, given the essential role that the losses play in this context [90]. This chapter has provided contributions in this line [1], which are also consistent with the discussion in Chap. 3. Thus, the development of microwave sensors for glucose concentration tracking exploiting the dielectric losses of the sample is recommended.

4.6 Conclusions This chapter has presented a glucose concentration sensor design for μL-volume water–glucose solutions. The sensor is composed of an open-loop microstrip resonator with a dielectric sample holder glued onto the gap between the open ends of the lines. The solutions to be measured are placed filling the sample holder. The chapter has shown three versions of this design at frequencies of approximately 2, 5 and 7 GHz. Their implementation and evaluation have been discussed. It has been shown how, after tuning some design parameters, accurate software models have been developed. The measurements and simulations carried out have reproduced well the complex permittivities of reference liquids. The proposed devices have been assessed as glucose concentration sensors in water–glucose solutions. In this sense, the unloaded quality factor has been selected as the measuring magnitude due to the contribution of glucose to the losses in the medium, following the conclusions in Chap. 3 (Sect. 3.6). The results have shown the convenience of this parameter instead of the resonant frequency, since greater variations in the loss tangent than in the real part of the permittivity are expected. The results concerning the maximum amplitude of the S21 parameter at resonance have also supported this. The sensitivities obtained for Qu and S21max have compared well with works by other authors involving microwave sensors at similar frequencies and glucose concentrations. Since most of the resonators proposed for glucose sensing in the scientific literature have focused on resonant frequency measurements, one of the main novelties in this work is the use of Qu . Another fundamental novelty is found in the low sample volume needed for the measurements. It has been shown that the sensitivities to glucose concentration keep allowing for glucose tracking even for the lowest sample volume (5 μL) with promising results. This is a key feature in many industry or biomedical applications, as discussed in Sects. 2.1.2 and 4.1, and it becomes a remarkable contribution in this regard. It should be noted that the conclusions reached throughout this chapter apply only for glucose tracking in aqueous solutions by means of microwave microstrip

126

4 Glucose Concentration Detection in Aqueous Solutions …

resonators. Therefore, although they might find application in industry, they are far from real BGL measurement contexts. That said, the results and discussion find good agreement with the points discussed by other authors for BGL measurement [88–90], and even with the dielectric losses evolution with the glucose level reported in some well-known works [58, 91, 92]. Therefore, a contribution has also been provided in this line. Within the commented limitations, this chapter has effectively shown the development of microwave sensors for glucose concentration detection in aqueous solutions. The work developed in this chapter was published in a JCR journal [1]. In short, the main contributions are the following: • Glucose concentration detection in aqueous solutions has been achieved by means of microwave microstrip resonator sensors. • The main contribution of glucose to the dielectric behavior of the solution has been shown to be in the form of losses, a highly exploitable fact for sensing purposes if a proper configuration is chosen. • Sensors design guidelines have been offered and discussed. • The unloaded Q factor has been proposed as sensing parameter, leading to promising sensitivities. • The obtained sensitivities have compared well with other works in the scientific literature, even for the lowest sample volume. • Very small sample volumes (5 and 25 μL) were needed in the measurement process, which is convenient for many industry and biomedical applications.

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Chapter 5

Glucose Concentration Detection in Biological Solutions with Microwave Sensors

An experiment is a question which science poses to Nature, and a measurement is the recording of Nature’s answer. Max Planck

5.1 Introduction A study based upon the identification of the glucose concentration in human blood plasma samples with the previously discussed sensors is presented in this chapter [1]. This research is motivated by the promising results in glucose tracking with the sensors described in Chap. 4 [2]. Therefore, a step ahead towards biomedical applications is taken here by trying to detect the glucose concentration in biological solutions with microwave sensors. The use of a new measurement paradigm, focused on losses-related parameters (such as Qu ) as discussed in the prior chapter, is applied to a biological context to investigate its viability and potential. As discussed in Sect. 2.3.5, when a biological context is concerned, glucose has been shown to change the complex frequency-dependent dielectric permittivity of erythrocytes [3]. This is due in a qualitative way to changes in the cell membrane capacitance because of the presence of glucose, which were latter quantified [4]. Hence, as an outcome of this effect there are variations in the dielectric permittivity of blood. Indeed, it was shown how the rheological and electrical behavior of blood is linked to the blood glucose concentration [5]. Not only that, but also other works showed a relationship between the dielectric permittivity and the glucose content in aqueous solutions [2, 6–10]. Thus, this accounts also for the solely contribution of the glucose presence itself to the variations in the permittivity. In addition, these changes have been reported to be noticeably greater for the imaginary part of the relative permittivity, being therefore related to the dielectric losses. In this context, some attempts for in vivo BGL measuring with microwave sensors able to detect the dielectric permittivity variations due to the glucose concentration have been made. The use of resonant circuits was proposed since these phenomena were described, yielding interesting results for human BGL measurement [11, 12], © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_5

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5 Glucose Concentration Detection in Biological Solutions …

although far from real application. An attempt relying on a wideband antenna for BGL measurement in individuals showed promising results in simulation [13], but did not succeed the same with real measurements after implementation [14]. Spiral resonators have been studied for sensing the glucose concentration [15–17], although no further works have been published during the last five years. More interesting is the approach by Choi et al. with a proposal based on a double split-ring resonator, built through several works. Such a device was implemented and used for measuring the BGL in volunteers [18]. The sensor, in addition to temperature correction, tracked f r and BW. A further study was carried out with in vitro and in vivo measurements [19]. This time, in addition to glucose, the effect of the variations of other components in blood was studied, such as common sugars, vitamins and metabolites. The results showed that the rest of components have a lower influence in the measurements that glucose. Notwithstanding, they should also be concerned since as a result too high glucose levels were needed in the experiments to see changes in the measurements. Also, not a good agreement between in vivo and in vitro results was reported. Some enhancements based on multiple measurement and statistical analysis have been shown [20], although leading to a non-portable device. Notwithstanding these attempts, it seems that further research is needed to achieve a successful device. The good results reported for simple media (aqueous solutions) show a considerable contrast with the lack of success when real, complex media are involved. This points to a remarkable complexity in the real context, with so many variables taking place, which leads to uncertainties in the measurement process that must be solved. In this sense, in vitro studies in controlled scenarios emulating real biological contexts are desirable to shed some light on the phenomena to be identified. The effect of varying the concentrations of other components different to glucose seems also worthy of further investigation. In this chapter, this problem is analyzed in a controlled, semi-real biological medium, made out of solutions of human blood plasma and some additional components: glucose, ascorbic acid and lactic acid. An intermediate step between simple media measurements and real context measurements is taken with the use of the technology developed in the previous chapter [2] to carry out a glucose concentration retrieval study in blood plasma solutions. One of the main aims is the comparison with the water–glucose solutions results and the assessment of the performance of the sensors in a more realistic context. The evaluation of the contribution of the other components concentrations to the measurement process could lead to the identification of guidelines for more effective designs for diabetes purposes. As an approach to BGL measurement, human blood plasma is considered in this study. Water is the major constituent in the vast majority of biological tissues, including blood. The water in those tissues is commonly referred to as biological water. However, the dielectric properties of biological water do not seem to perfectly match those of pure water [21, 22]. Many researches have been done to characterize the dielectric relaxation processes, conductivity and diffusion of biological water, in comparison to pure water. For instance, water in muscles has been shown to exhibit a relaxation time 50% longer than pure water [23]. Such variations can have remarkable implications in dielectric measurement systems, given the high water

5.1 Introduction

135

content in biological tissues. In this sense, although the dielectric properties of a wide variety of biological tissues have been thoroughly reported [22, 24–29], the study on the measurement of human blood plasma solutions with different glucose concentrations by means of the proposed sensors seems advisable. This way, the feasibility of such a technology in biological contexts can be investigated. Thus, in the next sections, the three microwave sensors presented in Chap. 4 will be used to track the glucose level of different human blood plasma solutions. Specifically, the preparation of the solutions for the experimentation will be explained in detail in Sect. 5.2, as well as the experimental procedure. Section 5.3 will outline the measurements carried out in this study. The obtained results will be shown in Sect. 5.4. Finally, Sect. 5.5 will discuss the overall results of the study and Sect. 5.6 will examine the conclusions reached.

5.2 Materials and Methods The sensors studied in Chap. 4 were used in a further experimental procedure involving human blood plasma solutions. The main objective was to characterize and acquire useful information about the performance of the developed sensors when measuring more realistic biological solutions. Therefore, sensors R1 , R2 and R3 (Chap. 4) were employed, with resonant frequencies in the absence of sample holder of 2.0, 5.7 and 8.0 GHz, taking advantage of the reported promising sensitivities for aqueous solutions. For preparing the solutions, O+ blood plasma from an unknown healthy donor was mixed with several additional substances, namely glucose, lactic acid (hereinafter labeled LA), and ascorbic acid (hereinafter labeled AA). Both acids were selected to provide for solutions with more components different from glucose with varying concentrations. Specifically, AA and LA acids were selected due to their considerable range of possible concentrations in healthy people [30]. There were five sets of solutions prepared in total, each one with a different fixed concentration of added LA or AA. Each set was composed of five single solutions, made by adding always the same amounts of glucose, so that added glucose concentrations of 0, 2.5, 5.0, 7.5 and 10.0% in mass were achieved. This yielded to an aggregate amount of 25 solutions. The glucose concentrations were selected to provide for comparison with [2]. In Table 5.1 the concentrations of AA and LA for the five solutions sets can be seen, as well as the label given to each set. Their preparation was carried out by directly adding the corresponding solutes to the plasma samples, not mixing the plasma with the previously diluted substance. The two values for AA concentration involved, as well as the two ones for LA, correspond to their respective low and high physiological limits [30]. This way, the effects of varying each acid throughout its expected whole range can be studied. An important fact that should be noted is that the initial concentrations for any components were unfortunately unknown, and all the concentrations expressed in this

136 Table 5.1 Sets of solutions involved in the study

5 Glucose Concentration Detection in Biological Solutions … Label

Concentrations of AA or LA added to the plasma

P

No additional components

AAL

AA at low limit (6 × 10−6 g/cm3 )

AAH

AA at high limit (20 × 10−6 g/cm3 )

LAL

LA at low limit (4.5 × 10−5 g/cm3 )

LAH

LA at high limit (19.8 × 10−5 g/cm3 )

chapter are referred to added amounts of the component. That said, the initial glucose concentration in the plasma sample is expected to be within the normal physiological range, and it therefore may be considered negligible when compared to the added glucose amounts. Furthermore, no variations are expected in this parameter since all the solutions were prepared from the same blood plasma sample, and it has no effect in the glucose concentration raise between two different samples. Conversely, AA and LA initial concentrations (also unknown) can be considered as concentration offsets. In the lack of more accurate data, these offsets can be approximately estimated as the mean value of their normal physiological concentration ranges, i.e., 13 × 10−6 g/cm3 for AA and 12.15 × 10−5 g/cm3 for LA. In addition, a sixth set of solutions was prepared by adding AA and LA to the plasma sample. Both acids were added to obtain half their respective limit concentration (AA at 10 × 10−6 g/cm3 and LA at 9.9 × 10−5 g/cm3 ). The aim of preparing this set was to analyze the aggregate effects of the simultaneous presence of both acids. This set was labeled ‘Mix’. A volume of 5 mL for each solution was prepared. The samples taken were of 5 µL (R3 measurements) and 25 µL (R1 and R2 measurements), thus reducing remarkably the possible concentration or volume errors. The components used in preparing the samples were d(+)-Glucose anhydrous from PanReac AppliChem (ref. 131341), lAscorbic acid from Sigma-Aldrich® (ref. A7631) and l(+)-Lactic acid from Scharlau (ref. AC1381). The measurements carried out during the experimental procedure will be described in the next section. These measurements, as well as the discussion on the results, were published in [1].

5.3 Measurements Although some studies have characterized the dielectric parameters of biological solutions (for instance [31, 32]), very few have done it with sensing purposes (see [19]), and none has analyzed the retrieval of glucose concentration including AA and LA variations. To do it, in this chapter all the solutions described in Sect. 5.2 were measured with the sensors presented in Chap. 4, thus performing 90 measurements in total. Following the experimentation guidelines discussed in [2], the frequency response of the sensors (the scattering parameters) were recorded with a properly calibrated

5.3 Measurements

137

VNA in each measurement. As shown in Sect. 4.3, for each sensor, the S-parameters having the sample holder empty were saved and held in the VNA screen. Then, the sample holder was filled with the corresponding solution by means of a micropipette. The response for each measurement was measured, and then the sample holder was carefully cleaned with ethanol until the empty-case scattering parameters held in the screen were perfectly matched again. Thereby, the system was ready for a new measurement. For each sensor, all the sets were measured following the next order: P, AAL, AAH, LAL, LAH, and Mix. The same empty-case S-parameters were held in the VNA screen for the whole experimentation with the same sensor, regardless the solutions set, and no measurements were made until the current response absolutely matched them. For each set, the measurements were carried out in order from the lowest (0%) to the highest (10%) added glucose concentration. Moreover, deionized water and an unaltered sample of the blood plasma used to prepare the solutions were measured both at the beginning and end of each measurement session, to account for repeatability. In all these control measurements, the obtained responses were identical. All the measurements were performed at stable room temperature of roughly 25 °C, with variations lower than 1 °C for each measurement session. Given the complexity of the solutions and the frequencies involved, Maxwell–Wagner polarization effects are expected to take place (see Sect. 2.1.1). The static conductivity reported for biological tissues in many works ([22, 25], for example) starts weakening and lets the relative permittivity lead the dielectric behavior. In this sense, it has been estimated that the relaxation frequency of the biological compound could exhibit a temperature coefficient of up to 2%/°C [21, 23], which is consistent with the possible error estimations in Sect. 4.3. Other estimations consider the temperature error in the dielectric permittivity of many biological tissues negligible for temperatures lower than 50 °C [33]. The results obtained in the measurements will be shown in Sect. 5.4.

5.4 Results After the measurements, the obtained responses for each set with each sensor were plotted together, so that the possible behaviors could be identified. As an example, in Fig. 5.1 the magnitude of the obtained S21 parameters for the measurements of plasma (P set) with the three sensors are plotted. Like in Chap. 4, the solutions are labeled as Px.x, where x.x is the added glucose mass percentage in the plasma solution. The rest of sets, concerning AA and LA, presented similar behaviors (not shown). These graphs indicate that there is a relationship between the frequency response and the sample glucose concentration. Figure 5.1 shows that the effect of changing the added glucose concentration does not seem to entail variations in the resonant frequency, but in the bandwidth and in the maximum amplitude of S21 (S21max ). This is in direct accordance with the behaviors seen in Chap. 4 for aqueous solutions. Therefore, considering the BW and S21max alterations, as well as the conclusions

138

5 Glucose Concentration Detection in Biological Solutions … Plasma measurements for R1 P0.0 P2.5 P5.0 P7.5 P10.0

-22.2

mag(S21) (dB)

-22.3 -22.4 -22.5 -22.6 -22.7 -22.8 -22.9 -23 1.914

1.916

1.92

1.918

1.922

1.924

1.926

f (GHz)

(a) Plasma measurements for R2 P0.0 P2.5 P5.0 P7.5 P10.0

-25

mag(S21) (dB)

-25.2

-25.4

-25.6

-25.8

-26 5.15

5.155

5.16

5.165

5.17

5.175

5.18

5.185

5.19

5.195

5.2

f (GHz)

(b) Plasma measurements for R3 P0.0 P2.5 P5.0 P7.5 P10.0

mag(S21) (dB)

-22.6 -22.8 -23 -23.2 -23.4 -23.6 7.13

7.14

7.15

7.16

7.17

7.18

7.19

f (GHz)

(c) Fig. 5.1 Magnitude of the obtained S21 parameter for P set with R1 (a), R2 (b) and R3 (c), from [1]

5.4 Results

139

in the preceding chapter, the unloaded quality factor (Qu ) seems a good tracking parameter to investigate. The changes in the S21 amplitude according to the added glucose concentration suggest an increase in the dielectric losses of the solutions as glucose is added. In fact, the variations of the real part of the permittivity of the solutions should induce changes in the resonant frequency, whereas the variations of its imaginary part are related to the dielectric losses in the medium, and they should thereby be visible in Qu and S21 . This means that noticeable changes in the loss tangent can be expected as the added glucose varies, and hence the sensing strategy described in Chap. 4 seems also suitable for this kind of solutions. The parameter S21max actually depends on the coupling between the resonator and the VNA, and it is therefore indirectly influenced by the losses. Hence, considering the almost negligible variations in f r and the significant changes in S21max and Qu seen in the measurements, it seems that, in the studied frequency range, the glucose concentration has a major impact on Er  than on Er  . This initial result is consistent with the data reported in [6]. This is also coherent with the idea discussed in the previous chapter and in [2] that for these frequencies the main contribution of glucose to the dielectric properties of the solution comes in the form of losses. Hence, a thorough evaluation of the S21max and Qu data obtained from the measurements was performed. All the f r were computed and plotted as well (not shown), but no conclusive results were achieved, as discussed previously, since random variations comparable to the VNA resolution were obtained. Concerning S21max and Qu parameters, they were computed for all the sets and added glucose concentrations. The results, grouped for each sensor and without involving Mix set, can be seen in Figs. 5.2, 5.3 and 5.4. In these figures, the absolute difference in S21max and the percentage change in Qu referenced to the 0% added glucose measurement in each set are represented. The resulting data are plotted against the added glucose concentration in mass percentage for the measurement of each solution. This representation permits to identify the contribution of glucose to the dielectric changes in the solutions seen by the sensors. It is easy to see that there is a clear relationship between both sensing parameters and the glucose level, which is almost linear in many cases. This relationship also shows some dependence on the acids content since a different slope for each set is shown. While similar tendencies for the responses with reference to the added glucose concentrations are seen for all sets, the sensitivity is different for each one, finding the greatest in P set and the lowest in LAH set concerning Qu , and the other way round concerning S21max , in general. Besides, the results obtained for Mix set presented an intermediate behavior between the results for AAH and LAH sets. This seems logical given that the solutions in Mix set have half the acids concentrations than the solutions in AAH or LAH sets, as explained in Sect. 5.2. This points out that their effects are additive. To illustrate it, in Fig. 5.5 the Qu percentage changes related to the 0% measurements for the Mix set are compared to those for AAH and LAH sets, involving R2 . The rest of measurements for Mix set concerning Qu and S21max with all the sensors (not shown) yielded similar behaviors.

140

5 Glucose Concentration Detection in Biological Solutions … Added glucose concentration vs max(S21) change for R1

0.35 P AAL AAH LAL LAH

max(S21) change (dB)

0.3

0.25

0.2

0.15

0.1

0.05

0

0

1

2

3

4

5

6

7

8

9

10

9

10

Added glucose concentration (mass %)

(a) Added glucose concentration vs unloaded Q change for R1 P AAL AAH LAL LAH

unloaded Q factor % change

2

1.5

1

0.5

0

0

1

2

3

4

5

6

7

8

Added glucose concentration (mass %)

(b) Fig. 5.2 Results for the measurements with R1 : a magnitude changes in S21max ; b percentage changes in Qu . Reprinted from [1]

5.4 Results

141 Added glucose concentration vs max(S21) change for R2

0.45 P AAL AAH LAL LAH

0.4

max(S21) change (dB)

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

0

1

2

3

4

5

6

7

8

9

10

Added glucose concentration (mass %)

(a) Added glucose concentration vs unloaded Q change for R2 9 P AAL AAH LAL LAH

8

unloaded Q factor % change

7 6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

Added glucose concentration (mass %)

(b)

Fig. 5.3 Results for the measurements with R2 : a magnitude changes in S21max ; b percentage changes in Qu . Reprinted from [1]

142

5 Glucose Concentration Detection in Biological Solutions … Added glucose concentration vs max(S21) change for R3 0.25 P AAL AAH LAL LAH

max(S21) change (dB)

0.2

0.15

0.1

0.05

0 0

1

2

3

4

5

6

7

8

9

10

Added glucose concentration (mass %)

(a) Added glucose concentration vs unloaded Q change for R3 6 P AAL AAH LAL LAH

unloaded Q factor % change

5

4

3

2

1

0 0

1

2

3

4

5

6

7

8

9

10

Added glucose concentration (mass %)

(b)

Fig. 5.4 Results for the measurements with R3 : a magnitude changes in S21max ; b percentage changes in Qu . Reprinted from [1]

5.5 Discussion

143

Added glucose concentration vs unloaded Q change for Mix, AAH, and LAH with R2 5 AAH

4.5

LAH Mix

unloaded Q factor % change

4 3.5 3 2.5 2 1.5 1 0.5 0 0

1

2

3

4

5

6

7

8

9

10

Added glucose concentration (mass %)

Fig. 5.5 Results regarding Qu percentage changes for Mix, AAH and LAH sets with R2 , from [1]

5.5 Discussion The previous section showed the results of this study concerning S21max and Qu . In this section the corresponding discussion will be offered with the main focus put on Qu as sensing parameter for retrieving the glucose concentration C g . Despite having shown the potential of S21max for alternatively measuring C g , both parameters are related to each other, as shown in Eq. (4.37), and they therefore provide basically the same information about the glucose concentration. Having Qu the advantage of not depending on the external coupling, as discussed in Sect. 2.2, being thereby an intrinsic property of the resonator, its analysis seems more interesting. Regarding the added glucose concentration, according to [34] the densities for aqueous solutions of d-glucose at 5% and 10% in mass are, respectively, 1.019 and 1.038 g/ml at 17.5 °C. This means that, in practice, there is almost no difference between expressing the concentrations in mass percentage or in mg/mL, or in g/100 g, or in g/100 cm3 (as the concentrations for the acids were expressed). For example, for the middle concentration in this chapter, 5% in mass equals to a glucose concentration of 50.95 mg/mL = 5095 mg/dL. These concentrations, although out of the common blood glucose level limits in people with diabetes, can give a clear vision on how the sensors work, especially when other components vary. The behavior of the obtained Qu with respect to C g for all the sensors is approximately linear for the added glucose concentrations involved (0–10%) in all the solutions sets. When other solutes are added the slope varies, but the behavior keeps linear. It should be noticed that, in this section, the possible chemical reactions between the

144

5 Glucose Concentration Detection in Biological Solutions …

Table 5.2 Qu sensitivities of the sensors for all the sets Sensor

S Q = Qu /C g (%/%) [2]

P

AAL

AAH

LAL

LAH

R1

0.609

0.185

0.163

0.125

0.122

0.126

R2

0.978

0.829

0.683

0.488

0.360

0.346

R3

0.584

0.571

0.408

0.292

0.315

0.298

added components and the blood plasma are not taken into account. This discussion assumes glucose to be the only component in the solutions with a noticeably higher concentration than the usual physiological ones. In Table 5.2 the obtained sensitivities for the unloaded quality factor measurements (S Q ) resulting from a simple least squares adjustment are shown. It should be noticed that the increases in C g yield decrements in Qu . However, the resulting negative sign is not included in S Q since the variations are calculated in percentage difference, related to the Qu values measured for the 0% added glucose solution (denoted Qu0 ) in each set. These reference values can be seen in Table 5.3. In both tables comparison with the results of the sensors measuring water–glucose solutions [2] is given. Hence, the linearity of the measurements is good in general terms, as it can be seen in Figs. 5.2, 5.3, 5.4 and 5.5. The adjustments led to R2 values over 0.98 for sensors R2 and R3 . Sensor R1 , conversely, showed a less linear behavior, with an R2 value of 0.90 for P set and 0.94 for AAL set, the worst cases. The sensing parameter Qu presents a good correlation with the glucose concentration, as shown in the correlation coefficients (R) obtained for the three sensors with all the solutions sets, shown in Table 5.4. These results are coherent with those from water–glucose Table 5.3 Reference Qu0 values obtained for the 0% added glucose measurement in each set, used for computing the Qu percentage difference Sensor

Qu0 [2]

P

AAL

AAH

LAL

LAH

R1

76.454

70.531

70.346

70.296

70.001

69.909

R2

60.652

58.159

57.710

57.647

57.543

55.984

R3

72.682

64.992

64.987

64.963

64.967

64.965

Table 5.4 Correlation coefficients obtained for all the sensors with all the sets Sensor

Correlation coefficient [2]

P

AAL

AAH

LAL

LAH

R1

0.999

0.966

0.979

0.998

0.994

0.997

R2

0.997

0.999

0.999

0.999

0.991

0.997

R3

0.994

0.989

0.998

0.999

0.997

0.999

5.5 Discussion

145

measurements (Chap. 4), which points that the measurement principle seems right, being the differences found in the sensitivity, not in the linearity. An important fact is that in all cases and for all the sensors the obtained sensitivities for the blood plasma study are always lower than those from the water–glucose solutions [2], as it can be noted in Table 5.2. A logical explanation for this result can be reached if the sensitivity S Q is theoretically estimated. To do it, it is assumed that the only loss factor in the system is the solution sample, disregarding the ohmic and radiation losses in the line, as well as the substrate dielectric losses. Hence, Qu is considered to be influenced only by the permittivity of the sample, specifically by its imaginary part. In other words, it is considered Qu ∼ = K/Er  , being K a constant. Therefore, considering Qu as a percentage difference of Qu0 , the sensitivity can be defined as: SQ =

100 −d Q u 100 −d Q u dεr · = · · Q u0 dCg Q u0 dεr dCg

(5.1)

Applying the estimated definition for Qu to Eq. (5.1) and rearranging: S Q ≈ 100

Q u 1 εr · · Q u0 εr Cg

(5.2)

Equation (5.2) gives a clear view of how a loss increment leads to a sensitivity decrease. When blood plasma is considered, at least two additional loss factors can be identified compared to water solutions at identical glucose concentrations: a greater ionic conductivity, due to the presence of electrolytes, and a greater viscosity, associated to the presence of several organic molecules. In this sense, the extra losses because of the ionic conductivity, which are greater at low frequencies, could explain the sensitivity drop found in sensor R1 , as shown in Table 5.2. Regarding viscosity, when it raises the frequency at which Er  reaches it maximum is displaced towards lower values [35, 36]. This phenomenon occurs thanks to the proportional relationship between the dielectric relaxation time and the viscosity [37]. In pure water, the maximum of Er  is found at approximately 20 GHz [38, 39]. At the frequencies of measurement of the considered sensors, within the 2–7 GHz range, this leads to higher values of Er  and hence dielectric losses increment, due to the growing tendency of Er  at frequencies lower than the relaxation frequency (see Fig. 2.2). This was clearly illustrated in Fig. 1 in [40]. This expected raise of losses account for the sensitivity decrease with respect to pure water solutions. The experimental values obtained for the sensitivities of Qu shown in Table 5.2 are consistent with the expectations that can be drawn from Eq. (5.2). In the measurements presented in this chapter, the term Qu /Qu0 can be estimated to be slightly lower than 1 (as it can be derived from Tables 5.2 and 5.3). Also, it can be assumed Er  ∼ 20 (a usual value for water in the frequency range of interest, see [6]). Concerning the term Er  /C g , it can be estimated from other works with the data shown in Table 5.5.

146 Table 5.5 Values for estimating the term Er  /Cg obtained from the scientific literature

5 Glucose Concentration Detection in Biological Solutions … Reference

Medium

f (GHz)

Er  /C g (wt%)

[40]

Water + glucose

2–3

0.19

[41]

Water + glucose

5

0.25

[10]

Water + glucose

6.5

0.5

[17]

Pig blood

7.7

0.17

Therefore, an average value of 0.25 wt% can be set for Er  /C g considering Table 5.5. If all these assumptions are applied to Eq. (5.2), solving for the sensitivity gives S Q ∼ 1.2 (%/%). As it can be seen, the estimated value is comparable to the experimental sensitivities shown in Table 5.2 for plasma solutions measurements. The differences, as discussed, can be explained by the higher losses found in plasma due to several physico-chemical principles. Regarding the sensitivities to C g for AA and LA sets measurements, both at their high and low limits, they are in all cases lower than the sensitivity obtained for P sets, as it can be seen in Fig. 5.6 (P sets are the dots at 0 acid concentration). Specifically, the sensitivities for AAL with respect to P decrease to 88.11%, 82.39% and 71.45% for R1 , R2 and R3 , respectively, whereas those for LAL with respect to P decrease to 69.95%, 43.43% and 55.17%. It should be noted that the concentrations in Fig. 5.6 refer to the added acids, being unknown the previous concentrations. In consequence, all the points should suffer an unknown displacement offset towards higher acid concentration values, remaining the behavior unaltered. This offset can be roughly estimated as the mean value of the physiological range for each acid. As for the sensitivities obtained with the Mix set, they are approximately the average of the sensitivities obtained for AAH and LAH sets (see Fig. 5.5). The plots in Fig. 5.6 give a clear view of how an increment in LA or AA concentration yields a decrement in the sensors sensitivity. This effect does not seem to be linear, especially for LA, and it could be more related to a saturation effect. In

Fig. 5.6 Sensitivities of the sensors to the added acids concentrations, from [1]

5.5 Discussion

147

other words, the obtained sensitivity seems to evolve towards a limit value as the acid concentrations raise (at least within the physiological range). This phenomenon is more evidenced in LA, whose concentrations are ten times greater than AA concentrations. For the specific case of LA sets measured with R1 , it seems that the saturated state has been reached, and therefore the unexpected very small sensitivity increment of LAH with respect to LAL (see Table 5.2) could be put down to instrumental errors. An important fact to be noticed from Table 5.2 and Fig. 5.6 is that the sensitivity decrease from the measurements with the low concentration to those with the high concentration for AA sets are comparable to those for LA sets. This is an interesting result considering that AA concentrations are one order of magnitude lower than LA concentrations. The explanation could be found in a more remarkable influence, in relative terms, of AA due to its larger molecular size (6 carbon atoms in the AA molecule, C6 H8 O6 , for 3 in the LA molecule, C3 H6 O3 ), as shown in Fig. 5.7. Effectively, the molecular mass of AA is 176.12 g/mol, for 90.08 g/mol in LA (approximately half AA). Very few data are available concerning the dielectric properties of these acids in solutions. In [42] the relative dielectric permittivity of LA in an aqueous solution was studied by means of open-ended coaxial probe techniques. From their data it can be approximated for a water–LA solution at 14.6% in mass that, at 2.45 GHz and ∼25 °C, the effective relative permittivity is Er,eff * ∼ 9 − j5.5. At the same frequency and temperature, the real part of the permittivity of pure water is roughly 77, and its imaginary part 10 [6, 38, 39]. With these data, the Maxwell–Garnett formula in Eq. (2.27) can be applied to obtain the relative dielectric permittivity of LA.

Fig. 5.7 3D models for the lactic acid and ascorbic acid molecules. Gray spheres: C, red: O, white: H

148

5 Glucose Concentration Detection in Biological Solutions …

Table 5.6 S21max sensitivities of the sensors for all sets Sensor

S Q = S21max /C g (dB/%) [2]

P

AAL

AAH

LAL

LAH

R1

0.047

0.017

0.020

0.023

0.019

0.032

R2

0.084

0.028

0.031

0.037

0.034

0.041

R3

0.048

0.015

0.018

0.021

0.020

0.023

Hence, rearranging Eq. (2.27) yields: ∗ εr,eff = ε1

ε2 (1 + 2v) + 2ε1 (1 + v) ε2 (1 − v) + ε1 (2 + v)

(5.3)

being E1 and E2 the relative permittivities of the solvent (water) and the solute (LA), respectively, and v the volume fraction of the solvent. The volume fraction v can be approximated as the mass fraction, which is not strictly true but induces low error in aqueous solutions. Then, solving for E2 in Eq. (5.3) gives E2 (LA) ≈ 1.18 − j4.75. This result, although lacking of a great accuracy, gives a clear view of the contribution of LA to the dielectric losses in the solution, relative to its concentration. This is consistent with the results exposed in this chapter. Unfortunately, no data are available to perform such calculations for AA, although the experimental results suggest a similar or even greater contribution to the dielectric losses. After analyzing the results for Qu , the experimental results for the sensitivity of S21max to C g can be seen in Table 5.6. The unloaded quality factor and the maximum amplitude of the S21 parameter are related to each other, as shown in Eq. (4.37). Consequently, a theoretical relationship between their sensitivities can be obtained. Considering S21max as the maximum amplitude of S21 in dB and S21max,lin as the maximum amplitude of S21 in linear scale, verifying S21max = 20log10 S21max,lin , the sensitivity of S21max to C g can be expressed as: dS21max,lin dS21max 20 8.686 dS21max,lin · = ≈ · dCg S21max,lin ln 10 dCg S21max,lin dCg

(5.4)

Equation (4.37) gives Qu in terms of S21max,lin and QL (the loaded quality factor). Rearranging Eq. (2.80) gives an alternative expression for QL : QL =

Qe Qu Qe + Qu

(5.5)

Then, applying Eq. (5.5) in Eq. (4.37) and solving for S21max,lin leads to: S21max,lin = 1 − and rearranging it for isolating Qe gives:

QL Qu = Qu Qe + Qu

(5.6)

5.5 Discussion

149

Qe = Qu

1 − S21max,lin S21max,lin

(5.7)

The unknown term in Eq. (5.4) dS21max,lin /dC g can be expressed as: dS21max,lin dS21max,lin d Q u Qe d Qu = · = · 2 dCg d Qu dCg (Q e + Q u ) dCg

(5.8)

where it should be noted that S Q = dQu /dC g . Therefore, applying Eq. (5.8) in Eq. (5.4) yields: 8.686 Qe dS21max ≈ · · SQ dCg S21max,lin (Q e + Q u )2

(5.9)

Finally, applying Eq. (5.7) in Eq. (5.9) and rearranging gives the following expression relating the sensitivities of Qu and S21max to C g : S 21max 1 − S21max,lin ≈ 8.686 · · SQ Cg Qu

(5.10)

It should be noted that this relationship is not constant, since it depends on the S21max,lin and Qu values obtained for each measurement. Anyway, the theoretical estimations made with Eq. (5.10) for the sensitivities in Table 5.2 and the measurements made in this chapter give similar results to the sensitivities in Table 5.6. The slight differences can consequently be attributed to instrumental errors in the experimental process. Overall, given the drops of the sensitivities concerning blood plasma solutions compared to the sensitivities obtained for water–glucose solutions (Chap. 4), it seems that further research is advisable. This could point to a limitation, especially for microwave sensors based upon dielectric permittivity variations. Indeed, the results suggest that more components different from glucose have an influence in the sensitivity and the measurements, as it has been predicted in other works [43], and hence one single measuring principle could not be enough. This also means that, for a hypothetical future device, individual calibration would be a key feature, as suggested also in other works [43]. Therefore, the results showed in this chapter point to the need of broadening the study of the glucose influence in the dielectric behavior of plasma to other frequency bands. The influence in other physical principles able to be sensed with other technological approaches seems also worthy for consideration.

5.6 Conclusions Motivated by the previous promising results of the developed sensors when measuring the glucose concentration of water–glucose solutions, this chapter has

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assessed their performance when blood plasma solutions are involved. The good results reported by some authors with sensors of several kinds and technologies in aqueous solutions contrast strikingly with the lack of success when they are applied to real contexts. This suggests that the sensors should be analyzed in controlled, in vitro scenarios with real biological solutions before real application, as it has been done in this chapter. The analysis carried out included, in addition to glucose, variations of the lactic acid and ascorbic acid in the plasma solutions. The results in Sect. 5.4 show how the three sensors responses vary with the glucose level concentration. They are therefore able to track this parameter provided that the concentration of the rest of components is known. The study developed in this chapter have identified and characterized the performance of microwave sensors when biological solutions are concerned, as well as when the variations of the concentrations affect not only to glucose, but also to more components. These results provide a contribution towards the application of NIBGM systems in real, complex scenarios. The obtained sensitivities (see Sect. 5.5) point to a better performance of R2 and R3 sensors, having R1 not as good results. This suggests that higher frequencies can be interesting and worthwhile investigating in future designs. Another fundamental contribution has evidenced the need of multi-component tracking and individual calibration for better results in real contexts. The achievement of a painstaking modeling of the real application environment is proposed in this sense, since it is crucial for leading to accurate and successful novel designs. The data reported in this chapter can help building such a modeling. In general, this chapter shows the need for further research intended to the design, evaluation and implementation of new sensing devices taking advantage of the principles discussed. The investigation of different frequencies and measurement processes, involving other physical principles and technologies, seems essential for more successful attempts. In this sense, the different data generated by such devices could be used as feed for machine learning algorithms, as it has been proposed for other similar contexts [44]. A system able to build comprehensive reliable models for the real application scenario from the information processed by these algorithms with the sensors data could remarkably help to understand all the underlying phenomena taking place. With the appropriate techniques, such a system could build individualized models for each user, identify the contribution of the main parameters (including the blood glucose level), and solve for their composition from the data provided by the sensors. The work shown throughout this chapter accounts for the glucose concentration detection in biological solutions with microwave sensors [1]. In summary, the main contributions of this work are listed below: • Glucose concentration detection in real biological solutions with several components varying their concentration has been achieved by means of microwave sensors. • The convenience of having Qu as the sensing parameter has been highlighted, especially for more lossy media.

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• The contribution of glucose, ascorbic acid and lactic acid to the dielectric losses in blood plasma solutions has been identified. • The need for individual calibration has been shown, which should be considered for future developments. • The need for multi-component tracking has been evidenced, which could be faced with multi-technology approaches, as well as broadening the frequencies under study. • The convenience of an accurate modeling of the most realistic possible measurement environment for further research (both in single- or multi-technology attempts) has been shown.

References 1. Juan CG, Bronchalo E, Potelon B, Quendo C, Sabater-Navarro JM (2019) Glucose concentration measurement in human blood plasma solutions with microwave sensors. Sensors 19(17):3779 2. Juan CG, Bronchalo E, Potelon B, Quendo C, Ávila-Navarro E, Sabater-Navarro JM (2019) Concentration measurement of microliter-volume water–glucose solutions using Q factor of microwave sensors. IEEE Trans Instrum Meas 68(7):2621–2634 3. Hayashi Y, Livshits L, Caduff A, Feldman Y (2003) Dielectric spectroscopy study of specific glucose influence on human erythrocyte membranes. J Phys D Appl Phys 36(4):369–374 4. Livshits L, Caduff A, Talary MS, Feldman Y (2007) Dielectric response of biconcave erythrocyte membranes to D- and L-glucose. J Phys D Appl Phys 40(1):15–19 5. Desouky OS (2009) Rheological and electrical behavior or erythrocytes in patients with diabetes mellitus. Rom J Biophys 19(4):239–250 6. Potelon B, Quendo C, Carré J-L, Chevalier A, Person C, Queffelec P (2014) Electromagnetic signature of glucose in aqueous solutions and human blood. In: Proceedings of MEMSWAVE conference, La Rochelle, France, pp 4–7 7. Park J-H, Kim C-S, Choi B-C, Ham K-Y (2003) The correlation of the complex dielectric constant and blood glucose at low frequency. Biosens Bioelectron 19(4):321–324 8. Tura A, Sbrignadello S, Barison S, Conti C, Pacini G (2007) Impedance spectroscopy of solutions at physiological glucose concentrations. Biophys Chem 129(2–3):235–241 9. Yoon G (2011) Dielectric properties of glucose in bulk aqueous solutions: influence of electrode polarization and modeling. Biosens Bioelectron 26(5):2347–2353 10. Lin T, Gu S, Lasri T (2017) Highly sensitive characterization of glucose aqueous solution with low concentration: application to broadband dielectric spectroscopy. Sens Actuators A 267:318–326 11. Caduff A, Hirt E, Feldman Y, Ali Z, Heinemann L (2003) First human experiments with a novel non-invasive, non-optical continuous glucose monitoring system. Biosens Bioelectron 19(3):209–217 12. Caduff A, Dewarrat F, Talary M, Stalder G, Heinemann L, Feldman Y (2006) Non-invasive glucose monitoring in patients with diabetes: a novel system based on impedance spectroscopy. Biosens Bioelectron 22(5):598–604 13. Freer B, Venkataraman J (2010) Feasibility study for non-invasive blood glucose monitoring. In: Proceedings of the 2010 IEEE antennas and propagation society international symposium, Toronto, ON, Canada 14. Venkataraman J, Freer B (2011) Feasibility of non-invasive blood glucose monitoring: In-vitro measurements and phantom models. In: Proceedings of the 2011 IEEE international symposium on antennas and propagation (APSURSI), Spokane, WA, USA

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15. Jean BR, Green EC, McClung MJ (2008) A microwave frequency sensor for non-invasive blood-glucose measurement. In: Proceedings of the 2008 IEEE sensors applications symposium (SAS), Atlanta, GA, USA 16. Yilmaz T, Foster R, Hao Y (2014) Towards accurate dielectric property retrieval of biological tissues for blood glucose monitoring. IEEE Trans Microw Theory Tech 62(12):3193–3204 17. Melikyan H, Danielyan E, Kim S, Kim J, Babajanyan A, Lee J, Friedman B, Lee K (2012) Non-invasive in vitro sensing of d-glucose in pig blood. Med Eng Phys 34(3):299–304 18. Choi H, Nylon J, Luzio S, Beutler J, Porch A (2014) Design of continuous non-invasive blood glucose monitoring sensor based on a microwave split ring resonator. In: Proceedings of the 2014 IEEE MTT-S international microwave workshop series on RF and wireless technologies for biomedical and healthcare applications (IMWS-Bio), London, UK 19. Choi H, Naylon J, Luzio S, Beutler J, Birchall J, Martin C, Porch A (2015) Design and in vitro interference test of microwave noninvasive blood glucose monitoring sensor. IEEE Trans Microw Theory Tech 63(10):3016–3025 20. Choi H, Luzio S, Beutler J, Porch A (2017) Microwave noninvasive blood glucose monitoring sensor: human clinical trial results. In: Proceedings of the 2017 IEEE MTT-S international microwave symposium (IMS), Honolulu, HI, USA, pp 876–879 21. Vander Vorst A, Rosen A, Kotsuka Y (2006) RF/Microwave interaction with biological tissues. Wiley, Hoboken, NJ, USA 22. Gabriel C (2006) Dielectric properties of biological materials. In: Barnes FS, Greenebaum B (eds) Handbook of biological effects of electromagnetic field: bioengineering and biophysical aspects of electromagnetic fields, 3rd edn. Taylor & Francis Group, LLC, Boca Raton, FL, USA, pp 51–100 23. Foster KR, Schawn HP (1996) Dielectric properties of tissues. In: Polk C, Postow E (eds) Handbook of biological effects of electromagnetic fields. CRC Press, Boca Raton, FL, USA 24. Gabriel C, Gabriel S, Corthout E (1996) The dielectric properties of biological tissues: I. Literature survey. Phys Med Biol 41(11):2231–2249 25. Gabriel S, Lau RW, Gabriel C (1996) The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 41(11):2251–2269 26. Gabriel S, Lau RW, Gabriel C (1996) The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues. Phys Med Biol 41(11):2271–2293 27. Takashima S, Gabriel C, Sheppard RJ, Grant EH (1984) Dielectric behavior of DNA solution at radio and microwave frequencies (at 20 °C). Biophys J 46(1):29–34 28. Michaelson SM, Lin JC (1987) Biological effects and health implications of radiofrequency radiation. Plenum, New York, NY, USA 29. Thuery J (1992) Microwaves: industrial, scientific and medical applications. Artech House, Boston, MA, USA 30. Rodak BF, Carr JH (2013) Clinical hematology atlas, 4th edn. Elsevier, St. Louis, MO, USA 31. Dai T, Adler A (2009) In vivo blood characterization from bioimpedance spectroscopy of blood pooling. IEEE Trans Instrum Meas 58(11):3831–3838 32. Zhadobov M, Augustine R, Sauleau R, Alekseev S, Di Paola A, Le Quément C, Mahamoud YS, Le Dréan Y (2012) Complex permittivity of representative biological solutions in the 2–67 GHz range. Bioelectromagnetics 33(4):346–355 33. Faktorová D (2008) Temperature dependence of biological tissues complex permittivity at microwave frequencies. Adv Electr Electron Eng 7(1–2):354–357 34. O’Neil MJ (2013) The Merck index: an encyclopedia of chemicals, drugs, and biologicals. Royal Society of Chemistry, Cambridge, UK 35. Levy E, Puzenko A, Kaatze U, Ben Ishai P, Feldman Y (2012) Dielectric spectra broadening as the signature of dipole-matrix interaction. I. Water in nonionic solutions. J Chem Phys 136(11):114502 36. Levy E, Puzenko A, Kaatze U, Ben Ishai P, Feldman Y (2012) Dielectric spectra broadening as the signature of dipole-matrix interaction. II. Water in ionic solutions. J Chem Phys 136(11):114503

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37. Grant EH (1957) Relationship between relaxation time and viscosity for water. J Chem Phys 26(6):1575–1577 38. Ellison WJ (2007) Permittivity of pure water, at standard atmospheric pressure, over the frequency range 0–25 THz and temperature range 0–100 °C. J Phys Chem Ref Data 36(1):1–18 39. Kaatze U (1989) Complex permittivity of water as a function of frequency and temperature. J Chem Eng Data 34(4):371–374 40. Shiraga K, Suzuki T, Kondo N, Tajima T, Nakamura M, Togo H, Hirata A, Ajito K, Ogawa Y (2015) Broadband dielectric spectroscopy of glucose aqueous solution: analysis of the hydration state and the hydrogen bond network. J Chem Phys 142(23):234504 41. Turgul V, Kale I (2018) Permittivity extraction of glucose solutions through artificial neural networks and non-invasive microwave glucose sensing. Sens Actuators A 277:65–72 42. Nakamura T, Nagahata R, Suemitsu S, Takeuchi K (2010) In-situ measurement of microwave absorption properties at 2.45 GHz for the polycondensation of lactic acid. Polymer 51(2):329– 333 43. Sharma NK, Singh S (2012) Designing a non invasive blood glucose measurement sensor. In: Proceedings of the IEEE 7th international conference on industrial and information systems (ICIIS), Chennai, India 44. Zhao H, Zhao C, Gao F (2018) An automatic glucose monitoring signal denoising method with noise level estimation and responsive filter updating. Biomed Signal Process Control 41:172–185

Chapter 6

Microwave Resonator for NIBGM: Proof of Concept

A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective. Edward Teller

6.1 Introduction This chapter shows the development of a portable version of the measuring glucose concentration measuring system based on microwave sensors [1] for its proof of concept in two real clinical scenarios [2]. This study was prompted by the previous positive results of the sensors with aqueous [3] and biological solutions [4] in Chaps. 4 and 5. In this chapter, a contribution towards real NIBGM was made by assessing this concept in a real context, aimed to validate the measuring hypothesis (based upon the unloaded Q factor as sensing parameter, as discussed in the prior chapters). Another main objective was to identify constraints in this measuring paradigm and factors to be faced for real implementation in future research. As discussed in Sect. 2.3.1, self-management of BGL is essential for dealing with diabetes. The common BGL self-measurement processes involve invasive, painful and uncomfortable methods. Therefore, an appropriate, painfulness non-invasive measuring device would be desirable for diabetes treatment. In this sense, considerable amounts of research have been carried out during the last years to develop potential technologies for the desired NIBGM system, which could doubtlessly enhance the life of people with diabetes and contribute stopping this burden which is threatening the global population. Following the initial discussion in Sects. 2.3.4 and 2.3.5, some attempts for NIBGM have been made from different approaches, being the electromagnetic devices one of the most studied ones. Effectively, the development of these sensors was initially motivated by the finding that the BGL changes provoke variations in the cell membrane of erythrocytes, which lead to variations in the dielectric permittivity © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_6

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of blood, as shown by Hayashi et al. [5]. The sensors are designed to be sensitive to the variations of the permittivity of the surrounding medium, and these measured permittivity changes are tried to be related to the BGL. In biological cells, the membrane is a biomolecular lipid structure serving as functional boundary, composed of proteins and carbohydrates. This membrane is a thin (∼10 nm) semipermeable dielectric that allows some ionic interchange [6]. The chemical exchange across the cell is regulated by electrochemical forces across the membrane. The medium inside the cell is called cytoplasm, whereas the medium outside the cell is called interstitial fluid (ISF). Both media are mainly composed of water carrying several ions. This way, the concentrations of these ions in cytoplasm and ISF give the cell electric potential, called the Nernst potential [7, 8]. If there is a difference in the concentration of a specific kind of ions in cytoplasm and ISF, an electrochemical force across the membrane is generated [9]. In general, when being quiescent, the membrane potential usually ranges form –60 to −95 mV, depending on the kind of cell (as a convention the inside of the cell is taken negative with relation to its outside). This is called the resting membrane potential. This potential may be altered by a higher concentration of ions in cytoplasm or ISF. Given the usual values for the transmembrane potential and membrane thinness, the electric field inside the membrane can reach very high values (in the order of MV/m). Therefore, a common cell membrane seems to act as a charged capacitor close to the breakdown voltage, being its charge the result of metabolic processes. This charge is usually in the order of μF/cm2 [6]. Thus, the membrane can be deemed as a semipermeable dielectric with a certain capability for ionic interchange. It should be notices that its ionic permittivity is not constant, since it varies depending on the ions involved. For all these reasons, the electrodynamics of the cell membrane has been widely studied (for example [10– 13]), and electrical models for the membrane have being proposed [14–18]. Thus, the main conclusion is that, from an electrical point of view, the cell membrane acts as a varying capacitance depending on the composition of the ISF [19]. In this context, the work by Hayashi et al. [5] raised awareness about how this capacitance is affected by the presence of glucose (specifically d-glucose) in ISF, with the consequent changes in the relative dielectric permittivity of the cells as well as in the effective relative permittivity of the medium. Other works have supported [20] and quantified [21] this phenomenon, in addition to showing its relevance for diabetes applications [22]. Specifically, the presence of glucose itself was shown to change the relative permittivity of the medium, with remarkable variations of its imaginary part [23–25]. Relying on these principles, some attempts for NIBGM devices were made with electromagnetic sensors sensitive to the variations of Er in the surrounding media. The use of resonant techniques was proposed and investigated since the publication of the above-mentioned findings, leading to promising results [26, 27]. Research on other resonant options, like spiral resonators, also showed the potential of this technology [28]. Wideband antennas were also proposed, showing good results in simulation [29] but not conclusive results in real implementation [30]. An interesting approach based on double split-ring resonator showed good agreement with invasive glucometer [31],

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but it also highlighted the dependence on other components different to glucose, as well as some constraints to be faced in further research, like multiple measurements followed by statistical analysis. In fact, the errors due to other substances different to glucose have been recently deemed as worthy investigating even in invasive CGM devices [32]. In addition to the sensitivity of these sensors to the relative permittivity of the medium, another important parameter is the penetration depth. This feature allows the electromagnetic response of a circuit nearby to be affected by most of the layers of the skin [33]. In fact, it is known that the dermal interstitial fluid glucose has a strong correlation with BGL [34–36]. Therefore, it seems convenient to perform measurements in this medium, although some aspects have to be considered. The skin consists of three major layers Fig. 6.1, namely epidermis (the outermost), dermis and hypodermis (the deeper subcutaneous tissue). The area of ISF where glucose concentration is intended to be measured with these sensors is located in the epidermis, at roughly 100 μm from the surface (stratum corneum). The glucose concentration in this ISF was correlated to BGL with ∼10 min delay in average [37], although other works have reported BGL–ISF glucose time lags up to 45 min [35, 38], depending on the concentration range. Thus, when carrying out intermittent glucose measurements, this lag may have impact on measurements accuracy [39]. As a matter of fact, many invasive CGM devices make measurements in ISF by means of microneedles [40] (see Sect. 2.3.3), and some errors have been reported Fig. 6.1 Skin layers

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6 Microwave Resonator for NIBGM: Proof of Concept

due to the BGL–ISF glucose lag [41, 42]. To overcome this, some authors have developed algorithms to relate BGL to ISF glucose and predict the former from the latter [43–45]. Metabolites and proteins diffuse into the ISF on their way from capillaries to cells, which actually leads to a strong correlation of BGL and ISF glucose concentration within the physiological range, as confirmed in clinical trials [40]. In addition, in the ISF small-to-moderate sized molecules (like glucose or ethanol) are present in the same proportion as in blood. Consequently, the diffusion process leads to a delayed increase of the glucose concentration in the ISF, which is estimated to be between 5 and 15 min [46], although the lag between BGL and ISF glucose can be greater at low BGL levels, as shown above. Concerning the correlation for decreasing glucose concentration, although some uncertainty persists [47, 48], some authors have pointed to a shorter time delay due to the high glucose clearance from epidermal ISF [43, 45]. Conversely, the outer skin layers have a greater time delay and smaller glucose concentration maxima. The outermost, the stratum corneum, consisting of cell remains (i.e. dead cells), acts as a barrier to protect the human body from mechanical, chemical or microbiological impacts from the surrounding. Moreover, it is responsible to prevent transepidermal water loss. This layer is only 10–20 μm thin (except at the sole of foot and the palm, where it can reach up to several mm). It has a water content of approximately 10% and it contains marginal amounts of glucose [49], which points that measurements in deeper areas are convenient. Therefore, all these reasons claim that in vivo glucose sensing (either intermittent or continuous) should involve skin layers deeper than the stratum corneum, mainly focusing on ISF. Indeed, recent works have even wondered if it would be more convenient to consider ISF glucose instead of BGL for taking therapeutic decisions (selecting insulin doses) in diabetes [47]. Due to these reasons microwave technology can play an important role in pursuing the development of NIBGM devices, given its ability to measure in ISF. However, not a conclusive solution has been hitherto reached for NIBGM. Many in vitro attempts have been made, some of them showing good results, but the number of in vivo tests is lower and the results are not convincing. Indeed, recent reviews on this technology have pointed out the lack of confidence with the results and the need for enhancements, thus stating challenges for the future [50–52]. Hence, some enhancements must be made to microwave sensors for NIBGM before real application. The positioning errors, the study of more capacitive sensors or the pressure have been recently emphasized as possible error factors to be faced [53]. In this sense, the need for an accurate study of these sensors in complex, real scenarios is therefore evident. Problems and possible error sources in real applications must be identified in order to implement the required improvements. The results in Chaps. 4 and 5 suggest the application of the developed sensors in [3] in a real clinical environment to test them in real application and thereby identify possible future research lines. Hence, this chapter takes a step forward by evaluating the performance of one of the sensors in two real clinical scenarios. A portable version of the NIBGM candidate device was developed and assessed in two hospital with real volunteers,

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as a proof of concept. A total amount of 352 individuals made measurements with the device, with 1217 measurements in aggregate. The implementation of such a device, including all the required components, will be comprehensively explained in Sect. 6.2. In Sect. 6.3 the measurement method will be shown, and the measurements made during this study will be commented. The results obtained after the measuring period will be gathered and shown in Sect. 6.4. To finish, a discussion on the obtained results will be offered in Sect. 6.5, whilst the main conclusions reached will be outlined in Sect. 6.6.

6.2 Materials and Methods In this chapter a portable NIBGM sensor was developed [1] and tested in a multicenter clinical scenario [2]. So far, very few works have evaluated candidate NIBGM devices in real application contexts (see [31]), none of them being absolutely portable and ready to be used by health practitioners. Therefore, this chapter will give relevant information about the behavior of these kind of sensors in real use conditions. This study will allow to detect future research lines for enhancing this technology that cannot be observed in in vitro experiments. The developed NIBGM device works measuring the electrical response of a microwave microstrip resonator when an individual places their tongue onto it. After the measurements, the changes in the obtained responses were evaluated and related to the BGL of the individuals. The selection of the body area used to perform the measurement is crucial and it has remarkable implications in the final results, even for invasive CGM devices, as it has been recently shown [54]. In this work, the tongue was selected due to several reasons, like its thermal stability or its intense blood circulation. Also, its dielectric behavior is highly desirable for making measurements related to dielectric losses (as shown in [3, 4]), as it will be discussed below. When selecting the body area for the measurements, the tissue-blood ratio, i.e., the relative content of blood in the tissue, is an important parameter. For ensuring that all the measurements are made in the same conditions, this parameter must be as constant as possible. This is a good reason to select the tongue, since it shows a relative stability in this sense, being weakly affected by blood pressure or heart rate variations (in the general case). Its tissue-blood ratio common values are also convenient. Not only a stable tissue-blood ratio is desirable, but also it should reach high values. This is another reason for selecting the tongue. Effectively, the ratio found in the tongue is higher than in other tissues also showing a constant (but low) ratio, like fat. This means more presence of blood, which accounts for a better sensitivity of the sensor. In addition, the low thermic variations in the tongue constitute another desirable characteristic, too. Furthermore, the dielectric properties of the tongue are really convenient for dielectric measurements in which the losses play a remarkable role. Following the conclusions reached in Chaps. 4 and 5, the major contribution of glucose to the

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6 Microwave Resonator for NIBGM: Proof of Concept Loss tangent of the human tongue

1 0.9

Loss tangent

0.8 0.7 0.6 0.5 0.4 0.3 0.2

109

1010

Frequency (Hz)

Fig. 6.2 Loss tangent of human tongue tissue according to [55, 56], from Juan et al. [2]

changes in the dielectric permittivity of the medium is expected to be in the form of dielectric losses. In this regard, a body area with low dielectric losses is highly convenient. This would make the losses variations due to the blood glucose level more noticeable. The loss tangent values of the human tongue are plotted in Fig. 6.2, according to the data provided in [55, 56]. It is easy to notice that the tongue shows convenient low values for frequencies approximately ranging 1–6 GHz. Indeed, the lowest values of tan δ are given between 2 and 3 GHz, and therefore it seems that choosing the tongue for dielectric measurements in this frequency range is a good option. To carry out the in vivo experimentation, three units of the proposed device were implemented. Two of them were setup in two different hospitals, providing for a multicenter proof of concept, whereas the third one was kept as a reserve unit, in case any repairment or replacement were needed for any of the two other units. Fortunately, there was no need to use the reserve unit throughout the whole study. The final three units can be seen in Fig. 6.3. Each device was composed of an ad hoc case, a microwave resonator acting as the sensor, the data acquisition electronics, a tactile screen serving as user interface, the driving and data saving electronics, a memory card for storage, and the structure to ensure that the measurements are made always in the same position. The device was aimed to measure the electrical response of the resonator when the user put their tongue onto it. Then, a study was performed to identify if there was any relationship between the plasma glucose level of the user (checked by a clinical analysis) and the obtained response, as suggested in [3] and in Chaps. 4 and 5.

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Fig. 6.3 Three units of the device developed, from Juan et al. [2]

The most crucial part of the device is the sensor. Following the design guidelines discussed in [3, 30] (see Chap. 4), an open-loop microstrip resonator was designed to perform as glucose level sensor. The results in Chap. 4 suggest good sensitivity for frequencies between 2 and 7 GHz, having promising sensing results even for the lowest frequency. Therefore, with the objective of simplifying the driving electronics and easing the implementation and the reproducibility, low frequency (up to 2.5 GHz) was considered. Specifically, the resonator was designed at 2.44 GHz, given that its electrical response is expected to move only towards lower frequencies during the measurement process. This frequency was selected also due to its high convenience for dielectric measurement in the tongue, as it can be inferred from Fig. 6.2. As discussed in previous chapters, the open-loop configuration provides for a resonator highly sensitive to the changes in the dielectric characteristics of the media upon the open-end gap. Due to this reason, the measurements were made by placing the user’s tongue onto this gap, to benefit from the principles discussed in [3]. The design of this gap, as well as the rest of parameters such as the characteristic impedance (strip width), substrate material, substrate thickness or I/O lines was performed according to the design criteria in Chap. 4, leading to the design depicted in Fig. 6.4 in Taconic TLX-8 substrate. The response of the resonator for an empty measurement (with no user) recorded with the developed device is shown in Fig. 6.5. Given the high sensitivity of the gap between the ends of the resonator to the permittivity of the material placed upon it, the placement of the user’s tongue exactly onto this gap and always in the same position is essential. To ensure it, a special structure was designed and incorporated to the case to guide the tongue and make sure that the same placement and posture were adopted during each measurement. To do it, a silicone mouthpiece with a small hole in the middle was used. This piece was designed to fit in the structure always in the same position, being its hole always upon the open-end gap of the resonator. This way, the user introduced the tongue in the hole, and the tongue was guided through it to the proper position. This piece was intended to account for the repeatability and reproducibility of the measurements, which allows to make comparison between different measurements. Some design

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Fig. 6.4 Open-loop microstrip resonator designed to perform as sensor. © (2019) IEEE. Reprinted, with permission, from García et al. [1]

Fig. 6.5 Frequency response of the resonator measured with the device with no user, from Juan et al. [2]

sketches of the mouthpiece are shown in Fig. 6.6, whose absolute dimensions are 60.25 × 35.90 × 5.80 mm. In order to have all the measurements aseptic, in each measurement a new thin disposable plastic square was placed between the resonator and the mouthpiece, to avoid the tongue directly touching the resonator. This plastic square was previously tested and proved not to influence in the measurement.

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Fig. 6.6 Silicone mouthpiece used to ensure the proper placement of the tongue, from Juan et al. [2]

The sensor holding structure was composed of a resonator support, a movable sample holder and a bumper block. All these pieces were implemented in polylactic acid (PLA) thermoplastic with a 3D printer. The resonator was inserted and firmly held in the resonator support thanks to its lateral and lower inner grooves. Then, the bumper block was screwed to the resonator support to provide for a stable structure. Finally, the movable holder was set in its right position, next to the resonator, and held thanks to two aluminum handles passing through the front holes in the bumper block. This way, the movable holder could be moved horizontally with the handles, between the resonator support and the bumper block. A sketch of this structure can be seen in Fig. 6.7. For the experimentation in the hospitals, a sufficiently large number of mouthpieces were provided. This way, a different mouthpiece could be used for each measurement throughout the day, and they finally could be sterilized and prepared for a new use before the next measurement session. In the setup, the mouthpiece and the plastic square fitted perfectly into the movable holder. This piece could be grabbed by two aluminum handles to slightly remove it from the resonator support. Then, the set was easily prepared putting the mouthpiece and the plastic square in the right position in the movable holder. After that, also by means of the aluminum handles, the movable holder (already carrying the mouthpiece and plastic square) was put back to its proper position, anew integrated in the resonator support. To finish, a couple of grippers were applied always in the same position, gripping the mouthpiece, movable holder and plastic square, to ensure their position and pressure were always the same. A photograph of the structure with the setup ready for a new measurement can be seen in Fig. 6.8.

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6 Microwave Resonator for NIBGM: Proof of Concept

Fig. 6.7 Sensor holding structure

Being the user and the setup in the right position, the measurement could be carried out. The sensor driving electronics was made of a low-cost scalar network analyzer. This system is able to obtain the transmission signal given between the input and output ports of any microwave device under test (DUT), in the frequency range 1.6–2.7 GHz. The subparts concerned to develop this system are listed in Table 6.1. The voltage-controlled oscillator (VCO), fed with the signal provided by the microcontroller unit (MCU) (see Fig. 6.9), can generate a linear frequency sweep voltage signal ranging 1600–3200 MHz for a linear variable input tuning voltage growing from 0.5 to 20 V. The required time for the user to perform a measurement is mainly determined by the speed of the oscillator to respond to a change in the tuning voltage. After characterizing the VCO and checking its proper functioning when integrated into the system, the obtained transition between consecutive frequencies was 5 ms, which led to overall measurement time of approximately 3.5 s. A low-pass filter is used immediately after the VCO’s output (Fig. 6.9), with the purpose of eliminating the spurious harmonics from the oscillator tuning. The filter was implemented and integrated into the system by means of common microstrip stub techniques [57, 58]. Thanks to it, the undesired harmonics are prevented from disturbing the detection of the desired signal by the RF detector.

6.2 Materials and Methods

165

Fig. 6.8 Structure of the sensor holding setup ready for a measurement. © (2019) IEEE. Reprinted, with permission, from García et al. [1]

Table 6.1 Electronic components used in the design of the device Analog

Digital

Component

Model

Manufacturer

Voltage-controlled oscillator

CVCO55BE-1600–3200

Crystek

Directional coupler

X3C19E2-20S

Anaren

RF Gain detector

AD8302

Analog Devices

Attenuators

PAT1220

Susumu

Low-pass filter

4th order, microstrip line

Home-made

Microcontroller unit

PIC32-PINGUINO-OTG

Olimex

Tactile screen

SK-gen4-32PT

4D Systems

At the output of the filter, the directional coupler (Fig. 6.9) divides the signal coming from the oscillator into two new equal signals: firstly, the signal directly driven to the input of the DUT—in this case the 2.44 GHz resonator; secondly, the signal used as reference to obtain the magnitude response only attributed to the DUT.

166

6 Microwave Resonator for NIBGM: Proof of Concept

MCU V Tune

VCO

DUT

Gain

Attenuator

Screen

AD8302

Attenuator

50 Ω

Low-Pass Filter Directional Coupler

Fig. 6.9 Schematic for the scalar network analyzer. © (2019) IEEE. Reprinted, with permission, from García et al. [1]

To ensure its proper functioning, the isolated port of the coupler is loaded with its characteristic input impedance by means of the 50  resistance FC0603E50R0BTBST1 from Vishay® . The RF detector uses these two signals to provide the transmission signal of the DUT (Fig. 6.9). The purpose of this component is to supply in its output the magnitude difference between the signal driven from the output of the DUT to one of its inputs and the reference signal driven from the coupler to another of its inputs. This way, the magnitude S21 signal of the DUT is obtained at the output of the detector. It should be noted that both the reference signal and the signal from the DUT are also loaded with 50  resistances, to match the characteristic impedance of the input ports of the detector. The obtained S21 signal is finally driven to the MCU for further processing. The detector requires a power reference level of −30 dBm for optimal functioning. However, the amplitude of the DUT’s signal can range from 0 to −60 dBm. Therefore, a couple of attenuators must be used to adapt the power levels supplied at the output of the directional coupler to the detector input requirements. They are placed at the convenient inputs of the detector (Fig. 6.9), so that they can be used to provide for accurate adjustment and compensation of the power levels from the reference and the DUT transmission signals. Thanks to them, the proper power ratio can be ensured for any DUT. In this case, given the passive device condition of the DUT (since it is a microwave resonator), a 10 dB attenuator was employed for the reference signal input, whereas a 3 dB attenuator was used in the DUT signal input. These attenuators provided for the largest detection range according to the detector characteristics.

6.2 Materials and Methods

167

Coaxial Connector AD8302 Attenuator 3 dB Resistance 50 Ω V_Gain

Directional Coupler

V_in Attenuator 10 dB

V_Tune

VCO

Low-Pass Filter

Fig. 6.10 Implementation of the RF scalar network analyzer. © (2019) IEEE. Reprinted, with permission, from García et al. [1]

The resulting RF circuit for this measuring system was implemented in fiberglass substrate ABC16 from CIF (Er = 4.4, h = 0.6 mm). In order to allow the connection of the DUT, two coaxial connectors were welded at the proper output of the directional coupler (DUT input) and at the proper input of the RF detector (DUT output). Also, the required ground connections were drilled and filled with suitable 0.8 mm diameter copper wire, welded to the copper in both faces of the circuit. A picture of the implemented RF circuit can be seen in Fig. 6.10. To start the RF stage, the input voltage sweep signal required by the VCO is generated by the MCU, which can be seen in Fig. 6.11. Among other characteristics, the most convenient ones for the purpose of this work are that it can work at frequencies up to 80 MHz, it has digital and analog input and output port, and it has capabilities for data storage in an extern SD memory card. The signal generated for the VCO

Fig. 6.11 Microcontroller unit used in the system, from Olimex [59]

168

6 Microwave Resonator for NIBGM: Proof of Concept

input is a voltage stepped ramp ranging 0.5–9.5 V, with a period of approximately 2 s. This signal is provided by the MCU in one of its digital outputs, and it is driven to the V_Tune input of the VCO (as shown in Figs. 6.9 and 6.10). In parallel, as the frequency sweep is generated in the VCO and the RF stage develops its process, all the gain voltage values generated in V_Gain port at the output of the detector (which constitute the S21 signal of the DUT) are driven to the MCU, where they are saved in a new data array for each measurement. The reader should note that these values are voltage values, as a result of the RF detector functioning. Once all the resulting voltage signal has been digitally saved in the MCU, the dB conversion of the detected voltages is carried out. This is done by means of a calibration file previously stored in the memory card. This file contains the relationship between the different voltages generated in the detector for all the single frequencies in the sweep while connecting specific precise attenuators (from MiniCircuits® ) to the DUT output port. These attenuators accounted for all the amplitude detection range, and they had been previously characterized in an accurate manner with a commercial network analyzer E8363B from Keysight. Therefore, this file allows the MCU to directly convert the detected voltage values to their corresponding dB values. With the obtained values, the S21 parameter of the DUT is finally written in a new S2P file and stored in the memory card. The general powering of the device is provided by the power supply SW4307 from PowerPax. The power supply is directly connected to the MCU, and then the different feeding voltage signals are generated in the MCU and driven to the corresponding parts of the system (like V_in signals for the RF circuit, as it can be seen in Fig. 6.10). All these electronics was safely kept inside a white methacrylate case, acting as a protecting box, of dimensions 210 × 154 × 160 mm. A picture of the final device can be seen in Fig. 6.12. Finally, to provide for user handling, the tactile screen was embedded in the top face of the methacrylate case (as it can be seen in Fig. 6.12). The screen was connected to the MCU with a communication bus UART. It provides for graphic user interface, and it allows to introduce the data, launch the measurement and see the plot of the obtained S21 parameter. The user interface will be briefly outlined next. The graphic user interface starts with the start screen showing the button for a “new measure”, as it can be seen in Fig. 6.13a. After pressing it, the data screen is shown (Fig. 6.13b) with an alphanumeric keyboard in order to introduce the practitioner code (a), the patient identifier (SIP) (b), the date in dd/mm/yy format (c), the hour (d) and the glucose level obtained with a pricking glucometer (e) in mg/dl. The active data field is underlined in red. The data are introduced with the alphanumeric keyboard in the lower half of the screen, pressing the red “ 1 (over-coupled resonator). In the case k = 1, there is critical coupling, and 0 = 0 (there is perfect adaptation between the resonator and the generator), and Qu = 2QL (3 dB). Due to all these reasons, it is convenient to design the sensor with a relatively high Qu value for the no-glucose measurement, and it is interesting to investigate different coupling strengths. The sensors presented in this section (Figs. 7.1 and 7.3) were studied for comparison with R2 (the best case of the sensors presented in Chap. 4) and R3 (the only sensor in Chap. 4 with the same sample holder volume), having one less port and different couplings. The main characteristics of these sensors (R4 and R5) are summarized in Table 7.1, in which also the comparison with R2 and R3 is provided. Once the sensors were implemented, an analysis similar to the one exposed in Chap. 4 was applied by measuring water–glucose solutions, to see the results and compare them with the results obtained with R2 and R3 [4]. The same solutions at the same concentrations were used, and the same experimental procedure was followed. After the measurements, the Qu and the minimum of the S11 parameter, S11min (due to the reflection nature of the resonators) were computed and plotted. It should be noted that, due to having a weaker coupling, the bandwidth required for computing QL had to be considered at 2 dB for R4 measurements (instead of the usual 3 dB BW) as defined in Eq. (2.44), although common Qu were later concerned by means of Eq. (7.36), to allow for general comparison. The obtained S11 responses near to the resonance and the variations in the computed Qu and S11min for the measurements with R4 and R5 are shown in Figs. 7.16 and 7.17, respectively. The resulting sensitivities of the Qu (S Q ) and for the S11min (S S1 ) to the glucose concentration are shown in Table 7.2, in comparison with the results obtained for R2. It should be noticed that, in the latter case, there is comparison between sensitivities in S11 parameter (R4 and R5) and S21 parameter (R2). Thus, this parameter should

202

7 Microwave Sensors for Glucose Detection: Open Lines Water-glucose measurements for R4 -1.8

Water G1.25 G2.50 G3.75 G5.00 G6.25 G7.50 G8.75 G10.00

mag(S11) (dB)

-2 -2.2 -2.4 -2.6 -2.8 -3 -3.2 4.3

4.32

4.34

4.36

4.38

4.4

4.42

f (GHz)

(a) Glucose concentration vs unloaded Q factor change for R4

unloaded Q factor change

6

5

4

3

2

1

0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(b) Glucose concentration vs min(S11) changes for R4

min(S11) change (dB)

0.25

0.2

0.15

0.1

0.05

0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(c) Fig. 7.16 Results of the measurements of water–glucose solutions with R4: a magnitude of S11 responses, b Qu changes, c S11min changes

7.2 Simplification of the Electronic System

203

Water-glucose measurements for R5 -10 Water G1.25 G2.50 G3.75 G5.00 G6.25 G7.50 G8.75 G10.00

mag(S11) (dB)

-11 -12 -13 -14 -15 -16 4.32

4.33

4.34

4.35

4.36

4.37

4.38

4.39

4.4

4.41

4.42

f (GHz)

(a) Glucose concentration vs unloaded Q factor change for R5

4

unloaded Q factor change

3.5 3 2.5 2 1.5 1 0.5 0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(b) Glucose concentration vs min(S11) change for R5 1.4

min(S11) change (dB)

1.2 1 0.8 0.6 0.4 0.2 0

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

(c)

Fig. 7.17 Results of the measurements of water–glucose solutions with R5: a magnitude of S11 responses, b Qu changes, c S11min changes

204 Table 7.2 Obtained sensitivities for R4 and R5 measuring water–glucose solutions

7 Microwave Sensors for Glucose Detection: Open Lines S Q (/%)

S S1 (dB/%)

R2

0.658

0.084

R3

0.414

0.048

R4

0.594

0.024

R5

0.384

0.140

not be taken as a fair comparative item between the performances of the sensors, although it gives a good vision of their potential. As it can be seen, the sensors proposed provide for a simpler system, which would have a smaller size and would work at lower frequencies (especially compared with R3, the sensor with the same sample holder volume). All these circumstances would ease the required driving electronics and the data processing, leading to a less complex system, as desired. In addition, this simplification would also reduce the possible error sources, yielding more reliable measurements. Also, the measuring area has been reduced, and a more capacitive configuration has been used, characteristics that have been shown to be convenient for glucose sensing by microwave means [6]. Analyzing the sensitivities in Table 7.2, it can be seen that the S Q loss is acceptable for R4 (which is under-coupled, as R2 and R3) compared to R2 (the best case in Chap. 4): 90.27%, having five times smaller sample holder. The sensitivity for the same sample holder volume (R3) is noticeable greater: 143.48%, which suggests the convenience of the approach proposed with an under-coupled sensor. The S Q values obtained for R5 (critically coupled) are not as good in comparison, and hence this kind of coupling seems not to be the best option. On the other hand, S S1 values for R5 are comparatively better than those from the prior sensors, yielding to sensitivity increases of 166.67% and 291.67% in comparison with R2 and R3, respectively. It therefore seems that the critical coupling yields more noticeable variations in the magnitude response, which is logical, and hence this approach seems a good idea for having S11min as the measuring parameter. However, as discussed in previous chapters, Qu seems a more convenient parameter to look at, and hence approaches based upon R4 are advisable. In conclusion, in this section it has been shown how new designs for the sensors can be exploitable to simplify the overall system without losing sensitivity (it could be even increased if a proper design is selected). This could be an important aspect to consider when addressing the drawbacks and required improvements highlighted in Chap. 6. A novel technique to remarkably increment the sensitivity will be shown in the next section.

7.3 Sensitivity The sensors presented so far have proven their feasibility to track the variations in the glucose concentration in aqueous and biological solutions. In this regard,

7.3 Sensitivity

205

the sensitivity plays a role of the utmost importance. In the preceding section, new designs to simplify the overall system while keeping the sensitivity almost unchanged have been shown, aimed to address some of the future issues highlighted in Chap. 6. However, some applications, whether related to industry or health (see Sect. 4.1), may require higher sensitivities to properly track the low glucose concentrations involved, requiring or not simplified electronics for a portable device. In this section, a novel sensing approach is presented, which shows a notorious increment of the sensitivities of the measurement parameters to the glucose concentration. The original work has been published as a full contribution to an international conference [1]. The novelty of the work shown in this section is on the exploitability of interresonator couplings. Starting from the design principles studied in Chap. 4 [4], a sensor composed of two mutually coupled open-loop microstrip resonators is proposed. General microstrip band-pass filter design guidelines [11] were applied to design the microwave network depicted in Fig. 7.18, hereinafter referred to as RR. This circuit is composed of two slow-wave open-loop resonators electrically coupled, as described in [12]. Also, slightly asymmetrical I/O lines were designed with the aim of taking advantage of the expected unbalance due to the presence of the sample. The same substrate than in the other sensors (Taconic TLX-8, 800 μm thin) was used due to the reasons discussed in Chap. 4. The electrical response of coupledresonator filters is highly sensitive to the coupling between the resonators (1 mm slot in Fig. 7.18). Given that this device is not to be user for filter applications, matching throughout the band pass is not required. Instead, the design was adjusted to provide for optimum sensitivity of the response to the inter-resonator coupling. The dimension of this slot is thereby the result of trading off between the electric field strength in the coupling area and the most adequate electric field distribution in each resonator, both between the strips and the ground and through the open-end gaps. Therefore, considering the design guidelines in [4], the coupling slot, especially its section between the open-end gaps of both resonators, seems the best option to place the sample holder. A new sample holder was designed (also with PTFE), with a new elongated shape adapted to the new characteristics of the measuring area. It Fig. 7.18 Design of the sensor based on inter-resonator couplings (RR). All dimensions are in mm. © [2019] IEEE. Reprinted, with permission, from [1]

206

7 Microwave Sensors for Glucose Detection: Open Lines

was designed with the purpose of maximizing the interaction of the sample with the electric field while keeping the same inner volume and ease of fabrication. The inner volume remained 5 μL, as in R3, the smallest in Chap. 4 [4]. Its top-view design is depicted in Fig. 7.19. The total height is 1.65 mm and the height from its base to the bottom of the container is ~60 μm. The circuit and the sample holder were implemented, and the sample holder was glued onto the right place (with the same glue than in the rest of sensors). A picture of the final device can be seen in Fig. 7.20, while the detail of the real sample holder is shown in Fig. 7.21. The electrical response had two differentiated poles (as expected from the two-resonator configuration). The measured poles frequencies before placing the sample holder were 4.40 and 4.51 GHz. Finally, these peaks moved to 4.32 and 4.46 GHz after having glued the sample holder between the open-end gaps. A similar experimental procedure than the one described in Chap. 4, with aqueous solutions at the same glucose concentrations, was applied to evaluate this sensing Fig. 7.19 Top view of the design of the new sample holder. All the dimensions are in mm. © [2019] IEEE. Reprinted, with permission, from [1]

Fig. 7.20 Implemented sensor. The scale is in cm. © [2019] IEEE. Reprinted, with permission, from [1]

7.3 Sensitivity

207

Fig. 7.21 Detail of the sample holder. All dimensions are in μm. © [2019] IEEE. Reprinted, with permission, from [1]

approach. All the measurements were made at stable room temperature (~22 °C), and the obtained S21 parameters were plotted together. The resulting plot for the frequency range of interest can be seen in Fig. 7.22. As shown, the sensor has a noticeable sensitivity to the changes in the glucose concentration. The coupling between the resonators is affected by the dielectric permittivity of the solution filling the sample holder, which in this case depends on the glucose concentration. Hence, Water-glucose measurements Water G1.25 G2.50 G3.75 G5.00 G6.25 G7.50 G8.75 G10.00

mag(S21) (dB)

-12

-14

-16

-18

-20

-22 4.05

4.1

4.15

4.2

4.25

4.3

4.35

4.4

4.45

4.5

f (GHz)

Fig. 7.22 Magnitude of the measured S21 parameters with RR in the frequency range of interest for all the water–glucose solutions. © [2019] IEEE. Reprinted, with permission, from [1]

208

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs max S21

3.5 Measured Simulated

max S21 change (dB)

3 2.5 2 1.5 1 0.5 0 -0.5

0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

Fig. 7.23 Absolute changes in the S21max of the first peak against the glucose concentration. © [2019] IEEE. Reprinted, with permission, from [1]

different glucose concentrations lead to different inter-resonator couplings, which yield different electrical responses of the device. Figure 7.22 suggests that there is a certain relationship between the glucose concentration and the maximum amplitude of the S21 parameter (S21max ). This happens in both peaks, but it seems more clearly evidenced in the first one, as it covers a larger amplitude range. This phenomenon is consistent with one of the main points discussed in Chap. 4, which refers to a more noticeable contribution of the glucose concentration variations to the overall dielectric losses, instead of to the real part of the effective permittivity. To investigate this, the changes in the S21max of the first peak for each measurement related to the deionized water measurement were computed and plotted against the glucose concentration in Fig. 7.23. In the plot the corresponding regression line can also be seen, besides the results from electromagnetic simulation of the measurements. According to the discussion in Chap. 4, the unloaded Q factor of the first peak for each measurement was meaningful to analyze. However, this time it was not convenient to compute the bandwidth at −3 dB for calculating the loaded Q factor, since it could be influenced by the second peak due to their proximity. To avoid this, the QL were obtained with the 2 dB fall from S21max . Later, in order to provide for the comparison of the results with the rest of sensors, the QL (2 dB) values were converted to common QL (3 dB) before obtaining the Qu values, which are not dependent on the bandwidth selected. This conversion was made with the method described in [13], using the following expression:  1 Q L ( p) = δ( p)

1− p ∼ fr = 0.765 p BW (2 dB)

(7.38)

7.3 Sensitivity

209 Glucose concentration vs unloaded Q factor change Measured Simulated

unloaded Q factor change

20

15

10

5

0 0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

Fig. 7.24 Absolute changes in the Qu of the first peak against the glucose concentration. © [2019] IEEE. Reprinted, with permission, from [1]

where δ(p) is the fractional bandwidth at the power fraction p, f r is the resonant frequency (the frequency of S21max , in this case), and BW (2 dB) is the bandwidth at S21max −2 dB. It should be noted that the approximated equivalence to the right in Eq. (7.38) only holds for fractional bandwidths at −2 dB. The differences in the resulting Qu for each measurement relative to the deionized water measurement were plotted against the glucose concentration in Fig. 7.24. The regression line and the results from the simulations are also shown. In this study, some variations in the resonant frequencies of both poles could be identified, which had not happened with the prior sensors. This could be due to the remarkable influence of the inter-resonator coupling on the final frequency response. As a result, the difference between the frequencies of both poles was different for each measurement. To study the correlation between the differences in the frequencies of the poles and the glucose concentration, the coupling factor k was computed for each measurement. In the case of coupled resonators, this factor depends on the resonant frequencies of the first (f 1 ) and the second (f 2 ) peaks as [14]: k=

f 22 − f 12 f 22 + f 12

(7.39)

The obtained k for all the measurements were plotted in Fig. 7.25 against the glucose concentration, along with the regression line and the simulation results. The results plotted in Figs. 7.23, 7.24, 7.25 remark the exploitability of the coupling between the resonators for sensing purposes. The correlations found between the glucose concentration of the solutions and up to three different parameters retrievable from the raw measurement give a clear view of the potential of this approach as glucose concentration sensor. These results show coherence with the results in Chap. 4 [4], in addition to presenting an improvement. They highlight the

210

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs K

0.025 Measured Simulated

0.0245 0.024 0.0235

K

0.023 0.0225 0.022 0.0215 0.021 0.0205 0.02 0

1

2

3

4

5

6

7

8

9

10

Glucose concentration (mass %)

Fig. 7.25 Obtained k values against the glucose concentration. © [2019] IEEE. Reprinted, with permission, from [1]

appropriateness of tracking the glucose concentration by means of its contribution to the dielectric losses. As a matter of fact, besides the already studied measuring parameters in previous chapters, this approach has revealed for the first time variations in the resonant frequencies (through the coupling factor) linked to the glucose concentration. Regarding the sensitivity, the values for the unloaded quality factor (S Q ), S21max (S S2 ) and coupling factor (S k ) with RR are gathered in Table 7.3. The table also shows the comparison with R2 (best case in Chap. 4, although with a sample holder volume of 25 μL) and R3 (same sample holder volume than RR). In Table 7.4 the achieved percentage improvements (increase of the corresponding sensitivity) with RR compared to R2 and R3 are shown. The improvement in terms of sensitivity is Table 7.3 Sensitivities obtained with the new sensor compared to the results with R2 and R3 Sensor

S.H. volume (μL)

S Q (/%)

S S2 (dB/%)

S k (/%)

R2

25

0.658

0.084

–

R3

5

0.414

0.048

–

RR

5

1.962

0.340

2.49 × 10−3

Sensor being compared

S Q % improvement

S S2 % improvement

R2

298

405

R3

473

708

Table 7.4 Sensitivity increments achieved with the new sensor

7.3 Sensitivity

211

clear, and this approach thereby opens a new line which could lead to highly sensitive sensors which could be suitable to address the main enhancement points spotlighted in the conclusions of Chap. 6. Further research on these sensing techniques is consequently advised [1].

7.4 Selectivity The selectivity is another challenge this kind of sensors must face. In the context of sensors, the selectivity is the ability of the device to provide information uniquely related to the targeted variable [15, 16]. The response of sensors intended to provide the user with their BGL should be only affected by variations in the BGL. Yet, the experimental results found in [17] and Chaps. 5 and 6, as well as by other authors [18], suggest that variations in other components indeed have a certain influence in the final response. Besides, the literature has pointed out the need of individual calibration for NIBGM [2, 19] (as it was also discussed in the previous chapter) and CGM devices [20], which means that other factors linked to the individual affect the performance of the sensor. The sensitivity of the sensors to other components different from BGL entails a lack of selectivity to BGL, whose investigation is deemed as imperative to develop a future reliable BGL measuring system. In Chap. 5, the selectivity for R1–R3 was indirectly studied and discussed. In this section, this aspect is studied for the approaches presented in Sects. 7.2 and 7.3. Specifically, sensors R4, R5 and RR are now tested with new solutions sets composed of distilled water, salt (NaCl), albumin (Sigma-Aldrich A2153) and glucose. Distilled water was chosen as solving medium to provide for comparison with the previous studies, and help identifying the contribution only due to salt, glucose and albumin. Salt was always used at a fixed 0.6 g/100 g concentration, corresponding to the normal physiological value [21]. Then, 5 different sets of solutions were prepared, each one at a fixed albumin concentration of 0, 2, 3, 4 and 5 g/100 g (labeled Ab0, Ab2, Ab3, Ab4 and Ab5, respectively), which provides albumin relative concentration variations between sets similar to the ones for the glucose inside each set. Thus, in each set, 5 solutions were prepared keeping their fixed salt and albumin concentrations, and having a varying glucose concentration of 0, 1.5, 3.0, 4.5 and 6.0 g/100 g (which is equivalent to mass %, as discussed in Sect. 5.5), which allow for comparison with the previous studies. It should be noted that the albumin values are within the usual healthy range [21], since albumin is the main protein in human blood, thereby being worthwhile investigating. Hence, there were 25 solutions in aggregate, measured with R4, R5 and RR, yielding 75 measurements in total for this study. A volume of 10 mL for each solution was prepared, requiring only 5 μL for each measurement. The measurements were made and the data were analyzed following the same experimental procedure described in Sect. 7.2 for R4 and R5, and in Sect. 7.3 for RR. The room temperature was constant, ranging 22–23 °C. The results for S11min and Qu with R4 are plotted in Figs. 7.26 and 7.27, respectively, whereas the results for S11min and Qu

212

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs min(S11) changes for R4

0.6 Ab0 Ab2 Ab3 Ab4 Ab5

min(S11) change (dB)

0.5

0.4

0.3

0.2

0.1

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs min(S11) changes vs albumin concentration for R4 Ab0 Ab2 Ab3 Ab4 Ab5

min(S11) change (dB)

0.6 0.5 0.4 0.3 0.2 0.1 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.26 Results for S11min for albumin sets with R4: 2D (a) and 3D (b)

with R5 are plotted in Figs. 7.28 and 7.29, respectively. Finally, the results for k, S21max and Qu with RR are plotted in Figs. 7.30, 7.31 and 7.32, respectively. In all these figures the results are plotted in 2D and in 3D, due to having a new variable (albumin concentration). Analyzing the results, it can be seen how, in a general sense, there is some interference of the albumin concentration in the sensitivity to the glucose. Thus, although good matching has been obtained, it seems that not a robust selectivity only for the glucose concentration is observed, as it also happened for R1–R3 in Chap. 5. This selectivity is not constant and it depends on the sensor. Therefore, this kind of studies

7.4 Selectivity

213 Glucose concentration vs unloaded Q factor changes for R4

3 Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

2.5

2

1.5

1

0.5

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs unloaded Q factor changes vs albumin concentration for R4 Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

3 2.5 2 1.5 1 0.5 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.27 Results for Qu for albumin sets with R4: 2D (a) and 3D (b)

are useful to identify the different behaviors and select the best configuration in terms of selectivity to the glucose concentration. However, there will be a limit which will be very hard to surpass, since the existence of several variables (several components varying) is unlikely to be efficiently handled with only one sensor [15]. The results for R4 when S11min is concerned show a certain lack of linearity, and they seem to be likely to be affected by instrumental errors. The results for the Qu seem more robust, with good linearity for glucose detection but slightly different slopes for the different albumin concentrations. This interference should be considered and solved otherwise for accurate glucose detection in multi-component solutions. As to

214

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs min(S11) changes for R5

0.25 Ab0 Ab2 Ab3 Ab4 Ab5

min(S11) change (dB)

0.2

0.15

0.1

0.05

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs min(S11) changes vs albumin concentration for R5 Ab0 Ab2 Ab3 Ab4 Ab5

min(S11) change (dB)

0.25 0.2 0.15 0.1 0.05 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.28 Results for S11min for albumin sets with R5: 2D (a) and 3D (b)

R5, not good glucose tracking concerning Qu has been seen (as expected from the discussion in Sect. 7.2), but the results show less interference for S11min , although the sensitivity has been reduced (maybe due to the presence of more lossy components in the solutions). Finally, the results for RR have yielded more dispersed detected glucose concentrations in the general case, although they keep showing promise for k, S21max and Qu . The interference persists in the three parameters, and it thus must be faced by other means. The resulting sensitivities for S11min (S S1 ), S21max (S S2 ), Qu (S Q ) and k (S k ) in this study are shown in Tables 7.5 and 7.6 for R4 and R5, respectively, and in Table 7.7

7.4 Selectivity

215 Glucose concentration vs unloaded Q factor changes for R5

2.5

Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

2

1.5

1

0.5

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs unloaded Q factor changes vs albumin concentration for R5 Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

2.5 2 1.5 1 0.5 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.29 Results for Qu for albumin sets with R5: 2D (a) and 3D (b)

for RR. In all the tables the results are compared to the ones obtained for the water– glucose (WG) solutions measurements with R4 and R5 in Sect. 7.2 and with RR in Sect. 7.3. Table 7.8 shows the percentage difference (% dif.) of the sensitivities of the three sensors for the Ab0 set measurements relative to the WG measurements, which allows to see the effect due to the salt. Table 7.9 shows this difference for the Ab5 set measurements, to see the aggregate effect due to the presence of salt and the highest albumin concentration. These tables give a clear idea of the performance of the sensors presented in this study when multi-component solutions are concerned. The presence of more

216

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs K for RR

0.023 Ab0 Ab2 Ab3 Ab4 Ab5

0.0225

0.022

K

0.0215

0.021

0.0205

0.02

0.0195

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs K vs albumin concentration for RR

Ab0 Ab2 Ab3 Ab4 Ab5

0.023 0.0225

K

0.022 0.0215 0.021 0.0205 0.02 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

3

2

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.30 Results for k for albumin sets with RR: 2D (a) and 3D (b)

components in the solutions is likely to account for an increase of the dielectric losses, which should lead to lower amplitudes of the recorded S-parameters. The results for S S1 and S S2 with R4 and RR confirm this aspect, since S S1 increases and S S2 decreases with lower amplitudes. The results obtained in this sense for R5 do not seem to be in accordance with the logical expectations, as the behavior of the sensor when critically coupled is not easy to predict. Thus, a configuration similar to R4 seems more convenient. The remarkable increases in S S1 with R4 for all the cases could point to an excessive influence of the losses in this configuration, which could finally disturb the measurement process and the accuracy. Due to this reason, slightly lower couplings

7.4 Selectivity

217 Glucose concentration vs max(S21) changes for RR

3 Ab0 Ab2 Ab3 Ab4 Ab5

max(S21) change (dB)

2.5

2

1.5

1

0.5

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs max(S21) changes vs albumin concentration for RR Ab0 Ab2 Ab3 Ab4 Ab5

max(S21) change (dB)

3 2.5 2 1.5 1 0.5 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(b) Fig. 7.31 Results for S21max for albumin sets with RR: 2D (a) and 3D (b)

could be of interest to provide for more reliable sensors. However, the results for S S2 and S Q with RR allow to select this configuration as the most robust one. RR’s S S2 variations show even a certain increase due to the presence of salt (a highly ionic component), which is logical considering the high sensitivities achieved with this sensor, and they also present the expected decrease when albumin is involved. As to S Q , the most interesting tracking parameter, RR is barely affected by the presence of salt, and the decrease due to the presence of albumin at concentrations comparable to the ones used for glucose is acceptable, bearing in mind its high sensitivity. The

218

7 Microwave Sensors for Glucose Detection: Open Lines Glucose concentration vs unloaded Q factor changes for RR

12

Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

10

8

6

4

2

0

0

1

2

3

4

5

6

Glucose concentration (mass %)

(a) Glucose concentration vs unloaded Q factor changes vs albumin concentration for RR Ab0 Ab2 Ab3 Ab4 Ab5

unloaded Q factor change

12 10 8 6 4 2 0 5 4 3 2

Albumin concentration (g/100g)

1 0

0

1

3

2

4

5

Glucose concentration (mass %)

(b) Fig. 7.32 Results for Qu for albumin sets with RR: 2D (a) and 3D (b) Table 7.5 Sensitivities for all the albumin sets with R4

Results for R4 Solutions set

S S1 (dB/%)

S Q (/%)

WG

0.024

0.594

Ab0

0.085

0.467

Ab2

0.092

0.447

Ab3

0.094

0.442

Ab4

0.095

0.434

Ab5

0.096

0.429

6

7.4 Selectivity

219

Table 7.6 Sensitivities for all the albumin sets with R5 Results for R5 Solutions set

S S1 (dB/%)

S Q (/%)

WG

0.140

0.384

Ab0

0.037

0.358

Ab2

0.039

0.343

Ab3

0.039

0.336

Ab4

0.040

0.330

Ab5

0.041

0.312

Table 7.7 Sensitivities for all the albumin sets with RR Results for RR Solutions set

S k (/%)

S S2 (dB/%)

S Q (/%)

WG

2.49 ×

10−3

0.340

1.962

Ab0

2.14 × 10−3

0.418

1.957

Ab2

2.07 ×

10−3

0.408

1.847

Ab3

2.14 × 10−3

0.331

1.351

Ab4

2.14 × 10−3

0.307

1.283

Ab5

10−3

0.276

1.195

2.11 ×

Table 7.8 Percentage differences (% dif.) of the sensitivities of R4, R5 and RR for the Ab0 set measurements relative to the water–glucose measurements Percentage differences for the Ab0 set Sensor

S S1 % dif

S S2 % dif

S Q % dif

S k % dif

R4

354.16

–

78.61

–

R5

26.43

–

93.23

–

RR

–

122.94

99.75

85.94

Table 7.9 Percentage differences (% dif.) of the sensitivities of R4, R5 and RR for the Ab5 set measurements relative to the water–glucose measurements Percentage differences for the Ab5 set Sensor

S S1 % dif

S S2 % dif

S Q % dif

S k % dif

R4

400.00

–

72.22

–

R5

29.29

–

81.25

–

RR

–

81.18

60.91

84.74

220

7 Microwave Sensors for Glucose Detection: Open Lines

comparison between R4 and R5 for S Q could point to a higher convenience for R5, but its lack of stability for the S11 response prevents from advising its use. This way, the sensors have proven their capability to track glucose even for multicomponent solutions. Notwithstanding, the change in the sensitivities for the different levels of albumin concerned points to a certain lack of selectivity. This means that, with these solutions, the albumin level should be known beforehand to provide a reliable measurement of the glucose concentration. A similar behavior was observed in Chap. 5 for R1–R3 with plasma multi-component solutions, and both studies seem to be in accordance. This is a logical result since the monitoring of a single parameter inside a system where more parameters are varying requires more than one source of information. Therefore, it seems evident that multi-sensor approaches should be considered for this purpose. Studies like the one presented in this section are hence needed to select the proper measurement techniques.

7.5 Discussion The use of one-port sensors accounts for the simplification of the electronic system complexity, a desirable feature as pointed out in the conclusions of Chap. 6. The investigation of coplanar resonators with a highly capacitive open end (R4 and R5) has led to promising results comparable to the ones obtained with two-port sensors (R2 and R3), even for the smallest sample holder volume, as shown in Table 7.2. The results seem to highlight a better performance of couplings far from being critical, and hence a comprehensive study in this way could even provide for more accurate oneport sensors. The investigation of this kind of sensors is desirable, especially from the point of view of the development of portable devices. The behaviors observed suggest that there is room for improvement to be exploited, and further research in this field is advised. This could doubtlessly contribute to reduce the possible noise sources (both electronic and relative to external aspects, such as sensor placement, user’s posture, etc.) and address some of the improvement aspects remarked in Chap. 6. The convenience of highly capacitive couplings for sensing purposes (as discussed throughout this dissertation, as well as pointed out by other authors [6]) has led to a new approach aimed to increase the sensitivity. The use of inter-resonators couplings has been investigated and the results show notable sensitivity increments, as it can be seen in Tables 7.3 and 7.4. These results open a new research line to be exploited that could lead to highly sensitive sensors able to efficiently detect the glucose level variations even when small biological glucose contents are concerned. Consequently, the application of filter design techniques to provide for highly sensitive inter-resonators couplings should be considered as future scope. Notwithstanding the previous results, the selectivity of the measuring system is still to be faced with new techniques. The measurements for multi-component solutions suggest some interference of the rest of components, i.e., they are not only sensitive to the glucose level (see Figs. 7.26, 7.27, 7.28, 7.29, 7.30, 7.31 and 7.32). Such a behavior must be thoroughly characterized, and all the influencing factors should

7.5 Discussion

221

be identified and tracked to provide for reliable readings of the desired parameter, especially when aiming to applications in real clinical or biological contexts. The multi-component nature of the targeted biological solutions, as well as the considerable deal of varying factors in the real application environment, account for the complexity of the whole measuring system. As a matter of fact, this entails the existence of many variables having a remarkable influence in the measurements, which will be very difficult to manage with a single sensor, however precise it can be. The comprehensive study and characterization of all these variables seems advisable [22], since not even individual calibration seems able to solve this aspect [19, 20]. In this sense, a multi-sensor approach may be a good way to address the lack of selectivity and provide enough information to track all the processes involved. Very few attempts have been made so far in this regard [23–27], all of them trying to measure BGL parallelly by several means. This idea can provide for more robust measurement, but it does not seem to be adequate for addressing the selectivity problem. Instead, an interesting approach can benefit from a multi-sensor system to track not only glucose concentration, but also the rest of parameters involved. This attempt could eventually provide suitable information to solve the interferences and the influence of the components and factors affecting the measurement process. Within this system, microwave sensors can play an essential role due to their proven convenience, as discussed throughout this document. Furthermore, such a system could be beneficially combined with a precise, painstaking computational model of the whole measurement environment for all the measurement principles concerned. Thus, the information gathered from the multisensor system could be used to solve the model for all the variables considered, being the BGL among them. The investigation of this kind of models, describing the dielectric parameters (or other required physical characteristics) of the environment as a function of the targeted variables (such as BGL) is expected to be extensively useful for this and many other applications [28]. Some work has been done for modeling the relative dielectric permittivity of blood as a function of the glucose level [29–32], in addition to provide dielectric models for human tissues and cell aggregates [33–38]. This field of research provides sophisticated descriptions of the permittivity for many biological contexts under different principles, which are suitable for the development of accurate computational models [39, 40]. The proper models for the multi-sensor approach should be as thorough as possible, even considering aspects like the variations in the placement and pressure of the sensors [6, 41]. Therefore, the investigation of these models can provide the research community with useful insights to develop the proposed multi-sensor system, whose data can be used in turn to solve the models for real application. It should be noticed that this discussion is in direct accordance with the conclusions reached in Chap. 5.

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7 Microwave Sensors for Glucose Detection: Open Lines

7.6 Conclusions The current open lines in the design and development of NIBGM sensors have been studied in this chapter, to address the remaining challenges [6]. Specifically, as a consequence of the prior studies [2, 4, 17], the simplification of the electronic system, the sensitivity and the selectivity have been identified as critical aspects to be improved for further progress. The first two ones have been successfully addressed in this chapter, showing promising results, while the third one remains still open, waiting for further developments. One-port sensors provide remarkable simplifications in the required driving and data acquisition electronics. They can also yield to significant size reductions, both of the sensor and the whole device. Due to these reasons, portable attempts should be based upon this kind of sensors. In the design process, the couplings must be comprehensively studied and optimized to obtain the desired sensitivity for each measurement parameter. Previous studies [4] point to Qu as the most interesting one, for which it has been seen the convenience of non-critical couplings. A new approach based on inter-resonators couplings has also been studied [1], and its potential to increase the sensitivity has been shown. Further investigation of this effect is expected to provide remarkable progress, since the expected sensitivities really show promise. The study of new configurations according to general filter theory [12] is advised to maximize the performance of these devices as glucose concentration trackers. The selectivity of the measurements only to the glucose level remains an open line. The performance of all the proposed devices in this document with multicomponent solutions has been good, but information about the rest of components is required in all cases. The need for different pieces of information is complicated to be faced with a single sensor, and hence multi-sensor systems are proposed. These systems should provide a precise tracking of all the important parameters affecting the measurements. Such an approach would conveniently combine with painstaking computational models of the whole measurement environment. These models could be solved with the information from the sensors to retrieve the contribution of the involved parameters, and identify the targeted ones (such as BGL). Microwave sensors are expected to be a fundamental part of these multi-sensor approaches. In this regard, attempts under the idea shown with RR are convenient to provide for robust, highly-sensitive measurements, whereas designs in the line of R4 lead to simpler (and maybe smaller) systems while keeping acceptable performances (although not as good as if RR approach is considered). The final choice will depend on the overall characteristics and requirements of the whole system, as well as on the specific application. This chapter has therefore provided the reader with an introduction to the current open lines in NIBGM devices development field. Part of the work shown in the prior sections yielded a full contribution to an international conference [1]. As a summary, the main conclusions reached throughout this chapter are listed below:

7.6 Conclusions

223

• One-port coplanar resonators can provide for convenient simplification of the electronic system without loss of sensitivity. • The sensitivity can be noticeably improved by means of inter-resonators coupling techniques. • The selectivity of the system will hardly be addressed with a single sensor: a multi-sensor system is desirable. • A multi-sensor system should track all the parameters and factors influencing the measurements to gather the suitable information from them all. • The development of painstaking computational models of the real measurement environment is advised. These models could be solved with the information from the multi-sensor system to identify the BGL (among other parameters). • Microwave sensors with proper designs and configurations can potentially be a fundamental part of these multi-sensor systems.

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13. Bray JR, Roy L (2004) Measuring the unloaded, loaded, and external quality factors of oneand two-port resonators using scattering-parameter magnitudes at fractional power levels. IEE Proc Microw Antennas Propag 151(4):345–350 14. Hong J-S (2011) Coupled resonator circuits. In: Hong J-S (ed) Microstrip filters for RF/microwave applications, 2nd edn. Wiley, pp 235–272 15. Peveler WJ, Yazdani M, Rotello VM (2016) Selectivity and specificity: pros and cons in sensing. ACS Sens 1(11):1282–1285 16. Wang F, Cao S, Yan R, Wang Z, Wang D, Yang H (2017) Selectivity/specificity improvement strategies in surface-enhanced Raman spectroscopy analysis. Sensors 17(11):2689 17. Juan CG, Bronchalo E, Potelon B, Quendo C, Sabater-Navarro JM (2019) Glucose concentration measurement in human blood plasma solutions with microwave sensors. Sensors 19(17):3779 18. Choi H, Naylon J, Luzio S, Beutler J, Birchall J, Martin C, Porch A (2015) Design and in vitro interference test of microwave noninvasive blood glucose monitoring sensor. IEEE Trans Microw Theory Tech 63(10):3016–3025 19. Barman I, Kong C-R, Dingari NC, Dasari RR, Feld MS (2010) Development of robust calibration models using support vector machines for spectroscopic monitoring of blood glucose. Anal Chem 82(23):9719–9726 20. Rossetti P, Bondia J, Vehí J, Fanelli CG (2010) Estimating plasma glucose from interstitial glucose: the issue of calibration algorithms in commercial continuous glucose monitoring devices. Sensors 10(12):10936–10952 21. Rodak BF, Carr JH (2013) Clinical hematology atlas, 4th edn. Elsevier, St. Louis, MO 22. Sharma NK, Singh S (2012) Designing a non invasive blood glucose measurement sensor. In: Proceedings of the IEEE 7th international conference on industrial and information systems (ICIIS), Chennai 23. Sobel SI, Chomentowski PJ, Vyas N, Andre D, Toledo FGS (2014) Accuracy of a novel noninvasive multisensor technology to estimate glucose in diabetic subjects during dynamic conditions. J Diabetes Sci Technol 8(1):54–63 24. Caduff A, Talary MS, Mueller M, Dewarrat F, Klisic J, Donath M, Heinemann L, Stahel WA (2009) Non-invasive glucose monitoring in patients with type 1 diabetes: a multisensor system combining sensors for dielectric and optical characterisation of skin. Biosens Bioelectron 24(9):2778–2784 25. Harman-Boehm I, Gal A, Raykhman AM, Zahn JD, Naidis E, Mayzel Y (2009) Noninvasive glucose monitoring: a novel approach. J Diabetes Sci Technol 3(2):253–260 26. Caduff A, Mueller M, Megej A, Dewarrat F, Suri RE, Klisic J, Donath M, Zakharov P, Schaub D, Stahel WA, Talary MS (2011) Characteristics of a multisensor system for non invasive glucose monitoring with external validation and prospective evaluation. Biosens Bioelectron 26(9):3794–3800 27. Acciaroli G, Zanon M, Facchinetti A, Caduff A, Sparacino G (2019) Retrospective continuoustime blood glucose estimation in free living conditions with a non-invasive multisensor device. Sensors 19(17):3677 28. Costanzo S (2017) Non-invasive microwave sensors for biomedical applications: new design perspectives. Radioengineering 26(2):406–410 29. Topsakal E, Karacolak T, Moreland EC (2011) Glucose-dependent dielectric properties of blood plasma. In: Proceedings of the XXXth URSI general assembly and scientific symposium, Istanbul 30. Karacolak T, Moreland EC, Topsakal E (2013) Cole-Cole model for glucose-dependent dielectric properties of blood plasma for continuous glucose monitoring. Microw Opt Technol Lett 55(5):1160–1164 31. Costanzo S, Cioffi V, Raffo A (2018) Complex permittivity effect on the performances of non-invasive microwave blood glucose sensing: enhanced model and preliminary results. In: Rocha A, Adeli H, Reis LP, Costanzo S (eds) Proceedings on WorldCIST’18 2018: trends and advances in information systems and technologies, Naples, pp 1505–1511

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Chapter 8

Conclusions

Everything is theoretically impossible, until it is done. Robert A. Heinlein

8.1 Summary and Conclusions This dissertation has shown and discussed state-of-the-art techniques for designing and developing microwave sensors for glucose concentration detection in aqueous and biological solutions. The main approach has singled out the microwave resonator as the fundamental element for the development of such sensors, although other techniques have been investigated as well. Theory fundamentals have been deeply reviewed with the aim to adapt them to the application context. From them, design guidelines have been discussed, intended to provide for sensors with maximized sensitivity. The proposed designs have been implemented and thoroughly tested with different sorts of in vitro experimentations. An application-oriented approach has even been developed and assessed in an in vivo environment. The results of all these experiments have provided the researchers with useful insights on the real performance of the devices, from which improvement aspects, more adequate design guidelines and future research open lines have been inferred. Indeed, some of the proposed enhancements and open lines have already been approached during the last works collected in this document. The results obtained during this period have been published in highly-ranked JCR journals and international conferences. The main conclusions derived from all these studies will be summarized throughout the next paragraphs. In Chap. 3 a transmission/reflection line technique for measuring the dielectric properties of liquids was presented [1], based on emptied (i.e. with no dielectric between the inner and outer conductors) coaxial lines. With this technique, the dielectric characterization of water–glucose solutions at concentrations of interest for diabetes purposes was performed. Thanks to this work, the effect of glucose in the effective permittivity of the solution could be comprehensively discussed. As a result,

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0_8

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8 Conclusions

Debye models and Cole–Cole diagrams of the solutions studied were provided. This work led to the identification of basic guidelines for the design of microwave sensors for glucose concentration detection, within the frequency range studied. The design and assessment of three microwave sensors for glucose concentration tracking [2] was shown in Chap. 4. The glucose concentration detection in aqueous solutions was effectively achieved by means of microwave microstrip resonator sensors equipped with a special sample holder. The sensor design guidelines were developed and deeply discussed, aiming to maximize their sensitivity. One of the main conclusions pointed that the main contribution of glucose to the overall dielectric behavior of the solutions is seen in the dielectric losses. Consequently, the Qu was selected as the proper sensing parameter. The detection of the glucose concentration was achieved for very small sample volumes (5 and 25 µL), which yields evident benefits for health and industry applications. The obtained sensitivities compared well with the results by other authors utilizing different techniques. Chapter 5 studied the performance of the previously proposed sensors when measuring biological solutions [3]. The solutions were made by adding glucose, ascorbic acid and lactic acid to a sample of human blood plasma. The glucose concentration detection in these solutions with several components varying their concentration was achieved and thoroughly discussed, remarking the need to characterize the concentration of some other components (not only glucose). The conclusions reinforced the convenience of using Qu for sensing purposes, especially for more lossy media. The contribution of some blood components such as glucose, ascorbic acid and lactic acid to the overall dielectric losses in blood plasma were identified, which should be taken into account for future developments. A main conclusion foresaw the need for individual calibration when aiming to real application due to the influence of other blood components, as it has also been suggested by other authors [4]. The need for multi-component tracking was also remarked, leading to the convenience of multi-technology approaches and broader frequency ranges. The accurate modeling of the measurement environment based on the observed data was proposed as well. After the previous in vitro studies, a comprehensive in vivo experimentation was shown in Chap. 6. A portable NIBGM device aimed to conduct experiments in clinical scenarios was developed and assessed [5], leading to a proof of concept of this technology in a multicenter clinical context [6]. In this chapter, guidelines for the design and implementation of portable, application-oriented, user-friendly NIBGM devices were offered. The developed device was tested in a multi-center clinical environment, and it was used by a large number of individuals. A database with more than 1200 measurements by more than 350 different users was obtained and analyzed. The conclusions showed the specific cases in which the device showed promise as in vivo glucose concentration tracker, and they also identified its limitations and possible error sources. Consequently, interesting enhancements were proposed, such as the use of different measurement principles in parallel, individual calibration (as suggested also by other authors [7, 8]), tracking of external parameters (like the pressure applied against the sensor), structure modifications and electronics simplification.

8.1 Summary and Conclusions

229

Finally, basing upon the conclusions reached throughout the prior chapters, Chap. 7, discussed and approached the current open lines in the development of microwave sensors for NIBGM. Specifically, three main aspects were studied: simplification of the electronic system, sensitivity and selectivity. One-port coplanar resonators with a suitable configuration were proved to simplify the required driving and data acquisition electronics, as well as the overall size, without loss of sensitivity. New techniques based on inter-resonators coupling were shown to remarkably increase the sensitivity to the glucose concentration [9]. However, the selectivity still remains to be improved. Achieving a suitable selectivity seems to require a multi-sensor system. This kind of systems should allow to track all the parameters and factors affecting the measurement process. In addition, the development of realistic, painstaking computational models of the measurement environment is advised. These models could be solved with the information from the measurements of the multi-sensor system to retrieve the parameters of interest (like BGL). In this sense, the potential of microwave sensors to become an essential part of these systems has been proven.

8.2 Future Scope The conclusions reached in this dissertation allow the key aspects that must be overcome in order to achieve truly reliable NIBGM to be roadmapped. In this sense, some research lines that should be addressed in the near future are discussed below: • Sensitivity. According to the findings in Sect. 7.3 [9], the study of new sensing techniques exploiting inter-resonators couplings is desirable. The low glucose concentration values found in real biological applications require a considerable increase of the sensitivity, which seems attainable with these techniques. The design of RR sensor is based in a second-order band-pass microstrip filter, and hence further order and configurations should be studied seeking to maximize the sensitivity. • Comprehensive dielectric characterization. Given the influence of other parameters different from the glucose concentration (as concluded in Chaps. 5–7), the identification and thorough dielectric characterization of them all seems mandatory. Indeed, some works (although very few) start currently to be published in this regard [10, 11]. This kind of works could help gathering the required information to comprehensively understand and accurately describe the relevant physical phenomena occurring in the measurement process. If such a situation was met, proper sensing strategies according to the aggregate phenomena seen could be easily identified. • In vivo experimentation. The development of improved portable NIBGM devices considering the conclusions reached in Chaps. 6 and 7 is advised. These devices could be used to carry out large in vivo experimentations useful to build extensive databases regarding different measurement techniques. With these databases, the

230

8 Conclusions

application of big data techniques to analyze them and recognize patterns, aiming to the achievement of qualitative descriptions of the phenomena occurring during the measurement process in real application, could lead to remarkable progresses. • Computational models. As discussed in the previous chapter, the development of painstaking computational models involving all the pertinent physical principles in the measurement process is desirable. The electromagnetic signature of many parameters interfering in the glucose measurement should be characterized and modeled [12]. Specifically, work towards the accurate description and modelling of the permittivity and dielectric losses of blood (and, if possible, other relevant tissues) as a function of the glucose concentration and the rest of influencing parameters seems worthy [13]. These models should also investigate and include any possible external factors, so that the most precise model involving real patientoriented conditions is provided [14]. In this sense, the conclusions reached in studies like those discussed in the previous two bullet points could significantly contribute to the development of these models. • Multi-sensor systems. One of the main conclusions in this dissertation points to the need for multi-sensor approaches for advancing towards reliable NIBGM systems. Not only aimed at glucose concentration, but able to track all the required parameters in an aggregate manner and relying on different principles and technologies, these systems could provide information of the utmost importance for an accurate glucose level reading. Only measuring all the relevant parameters, the desired information will be able to be discerned. Extensive in vitro and in vivo experimentation is also advised to test and perfectionate these multi-sensor systems. • Solve the models from the measurements. Once progress enough on the prior two bullet points have been achieved, a system combining the multi-sensor device and the models might be developed. In this point, the application of machine learning techniques to develop algorithms able to solve the models when fed with the information obtained from the sensors is advised. Such a system should be able to discern the contribution to the measurement of every single parameter tracked with the multi-sensor (like BGL), and compute their actual value. In addition, with a proper training, it could also provide the user with a convenient individual calibration.

References 1. Juan CG, Bronchalo E, Torregrosa G, Ávila E, García N, Sabater-Navarro JM (2017) Dielectric characterization of water glucose solutions using a transmission/reflection line method. Biomed Signal Process Control 31(1):139–147 2. Juan CG, Bronchalo E, Potelon B, Quendo C, Ávila-Navarro E, Sabater-Navarro JM (2019) Concentration measurement of microliter-volume water–glucose solutions using Q factor of microwave sensors. IEEE Trans Instrum Meas 68(7):2621–2634

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3. Juan CG, Bronchalo E, Potelon B, Quendo C, Sabater-Navarro JM (2019) Glucose concentration measurement in human blood plasma solutions with microwave sensors. Sensors 19(17):3779 4. Sharma NK, Singh S (2012) Designing a non invasive blood glucose measurement sensor. In: Proceedings of the IEEE 7th international conference on industrial and information systems (ICIIS), Chennai, India 5. García H, Juan CG, Ávila-Navarro E, Bronchalo E, Sabater-Navarro JM (2019) Portable device based on microwave resonator for noninvasive blood glucose monitoring. In: Proceedings of the 41st annual international conference of the IEEE engineering in medicine and biology society (EMBC), Berlin, Germany, pp 1115–1118 6. Juan CG, García H, Ávila-Navarro E, Bronchalo E, Galiano V, Moreno O, Orozco D, SabaterNavarro JM (2019) Feasibility study of portable microwave microstrip open-loop resonator for noninvasive blood glucose level sensing: proof of concept. Med Biol Eng Comput 57(11):2389– 2405. Available: https://rdcu.be/bP1T6. Accessed 1 Sept 2019 7. Barman I, Kong C-R, Dingari NC, Dasari RR, Feld MS (2010) Development of robust calibration models using support vector machines for spectroscopic monitoring of blood glucose. Anal Chem 82(23):9719–9726 8. Rossetti P, Bondia J, Vehí J, Fanelli CG (2010) Estimating plasma glucose from interstitial glucose: The issue of calibration algorithms in commercial continuous glucose monitoring devices. Sensors 10(12):10936–10952 9. Juan CG, Potelon B, Quendo C, Bronchalo E, Sabater-Navarro JM (2019) Highly-sensitive glucose concentration sensor exploiting inter-resonators couplings. In: Proceedings of the 49th European microwave conference (EuMC), Paris, France, pp 662–665 10. Chevalier A, Potelon B, Benedicto J, Quendo C, Roquefort P, Aubry T, Simon S (2019) Caractérisation électromagnétique hyperfréquence de marqueur physiologique : application au Lactate de sodium. In: XXIèmes Journées Nationales Microondes, Caen, France 11. Koutsoupidou M, Cano-Garcia H, Pricci RL, Saha SC, Rana S, Ancu O, Draicchio F, Mackenzie R, Kosmas P, Kallos E (2019) Dielectric permittivity of human blood of different lactate levels measured at millimeter waves. In: Proceedings of the 41st annual international conference of the IEEE engineering in medicine and biology society (EMBC), Berlin, Germany, pp 1183–1186 12. Choi H, Naylon J, Luzio S, Beutler J, Birchall J, Martin C, Porch A (2015) Design and in vitro interference test of microwave noninvasive blood glucose monitoring sensor. IEEE Trans Microw Theory Tech 63(10):3016–3025 13. Costanzo S, Cioffi V, Raffo A (2018) Complex permittivity effect on the performances of non-invasive microwave blood glucose sensing: enhanced model and preliminary results. In: Rocha A, Adeli H, Reis LP, Costanzo S (eds) Proceedings on WorldCIST’18 2018: trends and advances in information systems and technologies, Naples, Italy, pp 1505–1511 14. Lunze K, Singh T, Walter M, Brendel MD, Leonhardt S (2013) Blood glucose control algorithms for type 1 diabetic patients: a methodological review. Biomed Signal Process Control 8(2):107– 119

Appendix A

Fitting the Measured Raw Data to a Quadratic Function to Obtain f r , S21max and BW

This appendix offers a mathematical method to fit the measured raw data into a parabola, as shown in Fig. A.1. This is made so that the interesting parameters can be computed in a more precise manner. The measured raw data will be fitted into the next quadratic function: y = a0 + a1 x + a2 x 2

(A.1)

being y the fitted abs[S21 ] (dB) signal and x the frequency. This fitting is made for a selection of N points around the resonance peak. To do the fitting, the parameters a1 , a2 and a3 must be determined. To this end, chi-square function (χ2 ) is defined as follows:    yn − a0 − a1 xn − a2 xn 2 2 χ = σn 2 2

(A.2)

Fig. A.1 Fitting the raw data into a parabola

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0

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234

Appendix A: Fitting the Measured Raw Data to a Quadratic Function to Obtain f r , …

where σn 2 is the variance of each piece of data with respect to its corresponding expected (fitted) value. In this case, σn 2 = 1 can be assumed as a good approximation. Therefore, the optimization for the three required parameters can be done:   ∂χ 2 = −2 yn − a0 − a1 xn − a2 xn2 = 0 ∂a0   ∂χ 2 = −2 yn − a0 − a1 xn − a2 xn2 xn = 0 ∂a1   ∂χ 2 = −2 yn − a0 − a1 xn − a2 xn2 xn2 = 0 ∂a2

(A.3)

Developing Eq. (A.3) and rearranging it as a matrix system leads to: 2 ⎞−1 ⎛ ⎞ ⎛ ⎞ a0 xn N xn yn 2 3 ⎝ a1 ⎠ = ⎝ x x x ⎠ ⎝ y x ⎠ n2 n 3 n 4 n n2 xn xn xn yn xn a2 ⎛

(A.4)

Equation (A.4) can be solved to obtain the values of a1 , a2 and a3 , and hence the fitted data defined in Eq. (1). From these data, the desired parameters can be easily determined. For example, the resonant frequency is the frequency (f r ) at which the S21 parameter reaches its maximum: ∂y a1 = 0 ⇒ xmax = f r = − ∂x 2a2

(A.5)

Then, the S21max is the value of the S21 parameter at the resonant frequency, i.e., the maximum value of the fitted parabola ymax : ymax = y(xmax ) ⇒ ymax = S21max = a0 −

a12 4a2

(A.6)

In addition, the bandwidth at 3 dB (BW) is determined by the frequency points in which the S21 (y) falls 3 dB (y3dB ) from its maximum (ymax ): 2 y3dB = y(x3dB ) ⇒ ymax − 3 = a0 + a1 x3dB + a2 x3dB

(A.7)

Substituting Eq. (A.6) into Eq. (A.7) and rearranging yields: a2 x3dB 2 + a1 x3dB +

a1 2 +3=0 4a2

Solving Eq. (A.8) for x 3dB gives the frequency points delimiting the BW:

(A.8)

Appendix A: Fitting the Measured Raw Data to a Quadratic Function to Obtain f r , …

x3dB =

235

 2 a1 −a1 ± a1 2 − 4a2 4a + 3 2 2a2

(A.9)

The BW is obtained as the difference between the highest and the lowest x 3dB , i.e. x 3dB,2 − x 3dB,1 . Thus, applying this definition to Eq. (A.9) leads to:

BW =

 2 a1 a1 2 − 4a2 4a + 3 2 a2

(A.10)

This way, the raw data can be fitted to a quadratic function, and the desired parameters can be accurately obtained from it. In summary, the measured raw data must be used to solve the system in Eq. (A.4) and obtain the fitted model. Then, f r , S21max (in dB) and BW are defined by means of Eqs. (A.5), (A.6) and (A.10), respectively. Finally, QL is computed from these data with Eq. (2.44) and then Eq. (4.37) can be applied to obtain Qu .

Appendix B

Calculation of the Instrumental Error in the Unloaded Quality Factor

This appendix offers a theoretical description of the instrumental error that might be found in the measured unloaded quality factor (Qu ), and how it can be computed. It is important to bear in mind the definition of Qu given in Eq. (4.37): Qu =

QL 1 − S21max,lin

(B.1)

where S21max,lin is the magnitude of the maximum amplitude of the measured S21 parameter in linear scale, and QL is the loaded quality factor, defined in Eq. (2.44) as: QL =

fr BW

(B.2)

being f r the measured resonant frequency and BW the bandwidth at 3 dB from resonance, as explained in Sect. 2.2. In computing Qu , the measured variables are f r , BW and S21max,lin . They are obtained by adjusting the local response of S21 parameter (in dB) around the resonance with N experimental points pairs (f n , S21n ). Therefore, two instrumental errors should be considered. The precision in the frequency measurement is defined as f = f n+1 − f n , whereas the precision in S21lin is denoted S21lin . One can note that, if S21lin is constant (i.e., it does not depend on S21lin value), then the precision in S21dB (in dB) is not constant since: S21lin = 10S21dB /20 ⇒ ln S21lin =

S21dB ln 10 20

(B.3)

and therefore: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0

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238

Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor

∂S21lin ∂S21dB ln10 = S21lin 20

(B.4)

Thus, the error in S21dB is not constant and depends on each measured point. The RMS error in S21dB for the point n is denoted σn . Locally, the S21dB (f ) response near the resonance can be assumed to be quadratic as a good approximation (see Appendix A), having: y( f ) = ym −

12 ( f − f r )2 BW2

(B.5)

where y(f ) ≡ S21dB (f ) and ym is an adjustment parameter. Applying Eq. (B.2) into Eq. (B.5): y( f ) = ym −

12Q L 2 ( f − f r )2 fr 2

(B.6)

The parameters ym , QL , BW and f r can be obtained by optimization of the χ2 function:  N  yn − y( f n ) 2 χ = σn n=1 2

(B.7)

This model is not linear for the parameters f r and BW (or QL ), but it is linear for the parameters defined next: 12 f r2 = yn − 12Q 2L BW2 fr QL p1 ≡ 24 = 24 2 BW BW −12 p2 ≡ BW2

p0 ≡ yn −

(B.8)

With these new parameters, the model of S21dB (f ) is expressed as: y( f ) =

2 

pk f k

(B.9)

k=0

Then, the optimization of χ2 function with this new model leads to a solution in the form of: − → − → p = [M]−1 Y

(B.10)

Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor

239

where: ⎛

N

yn σn 2

⎜ n=1 ⎜ N − → ⎜ yn f n Y =⎜ ⎜ σ 2 ⎜ n=1 n ⎝ N 2 n=1

yn f n σn 2

⎞ ⎟ ⎛ ⎞ ⎟ N M0 M1 M2  ⎟ fn k ⎟, [M] = ⎝ M1 M2 M3 ⎠, Mk = ⎟ σ 2 ⎟ n=1 n M2 M3 M4 ⎠

(B.11)

The errors in the parameters defined in Eq. (B.8) are given by the covariance matrix, which can be expressed as: ⎛ ⎞ −1 −1

−1 C00 C01 C02   1 1 ∂ 2χ 2 ⎝ ⎠ 2[M] C p ≡ C01 C11 C12 = = = [M] 2 ∂ pi ∂ p j 2 C02 C12 C22

(B.12)

Then, the matrix [M]−1 can be explicitly calculated as: ⎞ M2 M4 − M3 2 M2 M3 − M1 M4 M1 M3 − M2 2 1 ⎝ = M2 M3 − M1 M4 M0 M4 − M2 2 M1 M2 − M0 M3 ⎠ |M| M1 M3 − M2 2 M1 M2 − M0 M3 M0 M2 − M1 2 ⎛

[M]−1

(B.13)

being the determinant of M given by:   |M| = M0 M2 M4 − M3 2 − M1 2 M4 + 2M1 M2 M3 − M2 3

(B.14)

The calculation of the covariance matrix gets noticeable simplified by considering that all the variances in the data (denoted σn 2 ) are equal. Usually, the frequency range covering the data is comparable to the BW. In this interval, the variation of σn 2 is within a factor 2 between the limits and center data. Hence, not an excessive error is assumed in considering all the values for σn 2 equal to a certain value σ intermediate between the center and limit values. In this case, the elements of the matrix [M] are: Mk =

N 1  k fn σ 2 n=1

(B.15)

where f n can be expressed as f n = f 1 + (n − 1)f , being f 1 the frequency of the first piece of data. To simplify the calculations, it can be considered that the frequency range of the data is centered with respect to a certain center frequency f c . It is also assumed that the number of available data is odd, and there is therefore the same amount of data to the left and to the right of f c . Normally, f c will be close to f r . Although

240

Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor

there is no reason why these conditions will always be met, they are in fact not very restrictive (except if the number of available data is too low), and hence the data for the computation can be suitably selected to meet them. Then, solving for the single elements in the matrix [M] yields: M0 = M1 = M2 = M3 = M4 =

N σ2 N fc = f c M0 σ2   N N2 − 1 2 2 f + f ( ) σ2 c 12   N fc 2 N 2 − 1 2 f + f ( ) c σ2 4    2   2 N − 1 3N 2 − 7 N N −1 2 4 2 4 f + f c ( f ) + ( f ) σ2 c 2 240

(B.16)

It must be noted that, for the usual values of f c (in the order of GHz for conventional microstrip resonators), f (in the order of MHz) and N (Nf close to the BW), the matrix [M] is close to become singular and it could therefore have null determinant. This could be a problem for the calculation. Parallel to the pk parameters defined in Eq. A.8, the original parameters are defined → within the − q vector: ⎛

⎞ ym − → q = ⎝ QL ⎠ fr

(B.17)

Now, the covariance matrix for the parameters of the original (nonlinear) model, [C q ], can be related to the covariance matrix for the pk parameters of the linearized model, [C p ], defined in Eq. (B.12), as follows:      Cq = [J ] C p J T

(B.18)

where [J] is the Jacobian matrix evaluated for the optimal pk parameters: ⎛ ∂q1 ⎜ [J ] = ⎝

∂ p0 ∂q2 ∂ p0 ∂q3 ∂ p0

∂q1 ∂ p1 ∂q2 ∂ p1 ∂q3 ∂ p1

∂q1 ∂ p2 ∂q2 ∂ p2 ∂q3 ∂ p2

⎞ ⎟ ⎠

(B.19) op

The relationship between pk and qk parameters can be obtained from Eqs. (B.2) and (B.8), and it is given by:

Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor

p1 2 ym = p0 − , 4 p2

 p1 QL = 12

−3 , p2

fr =

p1 2 p2

241

(B.20)

Since the main interest is on Qu , the parameters qk could be disregarded and Qu could be directly expressed as a function of parameters pk . However, the calculations are wieldier if parameters qk are considered, although dispensing with f r , which is not considered in Qu definition in Eq. (B.1). In this case, the Jacobian matrix reads:  [J ] =

∂ ym ∂ ym ∂ ym ∂ p0 ∂ p1 ∂ p2 ∂ QL ∂ QL ∂ QL ∂ p0 ∂ p1 ∂ p2



⎛ =⎝

op

1 0

 2 − p1 p1 2 p2 2 p2 √1 √− p1 4 −3 p2 8 −3 p2 3

⎞ ⎠

(B.21) op

Involving Eqs. (B.12), (B.18) and (B.21), the covariance matrix for ym and QL is therefore expressed as: 

 C ym ym C ym Q L C ym Q L C Q L Q L

⎛

⎞  ⎞ ⎛ 1 0 −p p1 2 C00 C01 C02 ⎜ − p1 1 2p1 √1 ⎜ ⎟⎜ 2 p 2 p2 2 ⎝ ⎠ = ⎝ C01 C11 C12 ⎠⎜  2 4 −3 p2 ⎝ p 2 − p1 0 √1 1 4 −3 p2 8 −3 p2 3 op C 02 C 12 C 22 − p1 2 p2 8 −3 p2 3 ⎛

⎞ ⎟ ⎟ ⎟ ⎠ op

(B.22) where, as shown in Eq. (B.12), [C p ] = [M]−1 . Developing Eq. (B.21) finally leads to: C ym ym = σ y2m = C00 − 2C01 f r + (2C02 + C11 ) f r2 − 2C12 f r3 + C22 f r4  1  C11 − 2C12 f r + C22 f r2 C Q L Q L = σ Q2 L = −48 p2   1 C ym Q L = √ C01 − (C11 + C02 ) f r + 2C12 f r2 − C22 f r3 (B.23) 4 −3 p2 Finally, as for Qu , considering its definition in Eq. (B.1) and the covariance matrix expression in Eq. (B.18), it is satisfied: σ Q2 u

=



∂ Qu ∂ Qu ∂ ym ∂ Q L

   ∂ Qu σ2 C ym Q L ym ∂ ym ∂ Qu C ym Q L σ Q2 L ∂ QL

(B.24)

Solving the derivatives and considering Eq. (B.23), leads to the final expression of the variance of Qu for calculating the instrumental error in the unloaded quality factor from the data from the measurement:

σ Q2 u =

Qu QL

2  Q u S21max,lin

 

ln10 2 ln10 σ ym Q u S21max,lin + 2C ym Q L + σ Q2 L 20 20 (B.25)

242

Appendix B: Calculation of the Instrumental Error in the Unloaded Quality Factor

− → In summary, starting for the N experimental data pairs (f n , S21n ), the vector Y and the matrix [M] can be calculated with Eqs. (B.11) and (B.16), respectively. Then, the parameters pk and the matrix [C p ] are obtained from Eqs. (A.8) and (B.12). After that, the parameters qk and the matrix [C q ] are computed by means of Eqs. (B.20) and (B.23). Finally, Qu and its variance can be obtained thanks to Eqs. (B.1) and (B.25).

About the Author

Carlos G. Juan Carlos G. Juan was born in Petrer, Spain, on 2 July 1991. He received the MSc degree in telecommunication engineering and the Ph.D. degree in electronics engineering (with honors) from Miguel Hernández University of Elche, Elche, Spain, in 2014 and 2019, respectively, where he joined the Neuroengineering Biomedical (nBio) Research Gruop as a research fellow. He was a visiting researcher with the Lab-STICC Group, Université de Bretagne Occidentale, Brest, France, in 2016 and 2018. Since 2014, he has been a research fellow with the nBio Research Group, Department of Systems Engineering and Automation, Miguel Hernández University of Elche. During 2019 and 2020 he was an adjunct professor with the Department of Materials Science, Optics and Electronic Technology, Miguel Hernández University of Elche. Since 2020 he is a postdoctoral research fellow with Lab-STICC, Université de Bretagne Occidentale. His main research interests include microwave engineering, biomedical sensors, antenna and propagation, electronics and computer science applied to bioengineering. His research work is focused on the development of microwave sensors for biomedical applications. Dr. Juan was a recipient of the CEA-Springer Award to the Best Ph.D. Thesis in Bioengineering 2020, awarded by the Spanish Committee in Automatic Control (CEA). He held an FPU research grant, a competitive predoctoral grant from the Spanish Government, and a competitive postdoctoral grant from the Brittany Government. He serves as a regular reviewer for more than 10 highlyimpacted journals, including Scientific Reports (Nature Research), Sensors (MDPI), IEEE Sensors Journal (IEEE) or IEEE Microwave and Wireless Components Letters (IEEE). Since 2015, he has authored more than 20 scientific publications.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 C. G. Juan, Designing Microwave Sensors for Glucose Concentration Detection in Aqueous and Biological Solutions, Springer Theses, https://doi.org/10.1007/978-3-030-76179-0

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