Manual of Vibration Exercise and Vibration Therapy [1st ed.] 9783030439842, 9783030439859

Table of contents :
Front Matter ....Pages i-xi
Front Matter ....Pages 1-1
The Physics of Vibration (Jörn Rittweger, Redha Taiar)....Pages 3-21
The Biology of Vibration (Eddy A. van der Zee)....Pages 23-38
Design Principles of Available Machines (Rainer Rawer)....Pages 39-54
Safety and Contraindications (Danny A. Riley, Jörn Rittweger)....Pages 55-65
Front Matter ....Pages 67-67
Biomechanics of Vibration Exercise (Darryl Cochrane, Jörn Rittweger)....Pages 69-85
Cutaneous and Muscle Mechanoreceptors: Sensitivity to Mechanical Vibrations (Edith Ribot-Ciscar)....Pages 87-107
Electromyographical Recordings During Vibration (Ramona Ritzmann, Ilhan Karacan, Kemal S. Türker)....Pages 109-120
Supraspinal Responses and Spinal Reflexes (Ramona Ritzmann, Katya Mileva)....Pages 121-133
Assessing Reflex Latencies in Responses to Vibration: Evidence for the Involvement of More Than One Receptor (Ilhan Karacan, Kemal S. Türker)....Pages 135-142
Metabolic Responses to Whole-Body Vibration Exercise (Jörn Rittweger)....Pages 143-153
Circulation Effects (Darryl Cochrane, Jörn Rittweger)....Pages 155-167
Hormonal Responses to Vibration Therapy (Eloá Moreira-Marconi, Danubia da Cunha de Sá-Caputo, Alessandro Sartorio, Mario Bernardo-Filho)....Pages 169-184
Front Matter ....Pages 185-185
Warming-Up (Darryl Cochrane)....Pages 187-202
Modulation of Neuromuscular Function (Pedro J. Marín)....Pages 203-211
Application in Athletes (Darryl Cochrane)....Pages 213-228
Using Whole-Body Vibration for Countermeasure Exercise (Patrick J. Owen, Daniel L. Belavy, Jörn Rittweger)....Pages 229-244
Front Matter ....Pages 245-245
How to Design Exercise Sessions with Whole-Body Vibration Platforms (Christina Stark, Jörn Rittweger)....Pages 247-254
Whole-Body Vibration in Geriatric Rehabilitation (Martin Runge, Jörn Rittweger)....Pages 255-268
Application of Vibration Training for Enhancing Bone Strength (Debra Bemben)....Pages 269-278
Whole-Body Vibration Exercise as a Treatment Option for Chronic Lower Back Pain (Jörn Rittweger)....Pages 279-284
Pediatric Rehabilitation (Christina Stark, Ibrahim Duran, Eckhard Schoenau)....Pages 285-317
Chronic Obstructive Pulmonary Disease (COPD) (Rainer Gloeckl)....Pages 319-327
Urinary Incontinence (Volker Viereck, Marianne Gamper)....Pages 329-335
Primary Muscle Disorders (Ibrahim Duran, Christina Stark, Eckhard Schoenau)....Pages 337-341
Application of Vibration Training in People with Common Neurological Disorders (Feng Yang)....Pages 343-353
Whole-Body Vibration Therapy in Patients with Pulmonary Hypertension and Right Heart Failure: Lessons from a Pilot Study (Felix Gerhardt, Stephan Rosenkranz)....Pages 355-362
Vibration Exercise and Vibration Therapy in Metabolic Syndrome (Laisa Liane Paineiras-Domingos, Danúbia da Cunha de Sá-Caputo, Mario Bernardo-Filho)....Pages 363-380
Whole-Body Vibration Exercise in Cancer (Patrícia Lopes-Souza, Danúbia da Cunha de Sá-Caputo, Redha Taiar, Mario Bernardo-Filho)....Pages 381-396

Citation preview

Manual of Vibration Exercise and Vibration Therapy Jörn Rittweger  Editor

123

Manual of Vibration Exercise and Vibration Therapy

Jörn Rittweger Editor

Manual of Vibration Exercise and Vibration Therapy

Editor Jörn Rittweger Institute of Aerospace Medicine Department of Muscle and Bone Metabolism, German Aerospace Center (DLR) Cologne Germany Department of Pediatrics and Adolescent Medicine

University of Cologne Cologne Germany

ISBN 978-3-030-43984-2    ISBN 978-3-030-43985-9 (eBook) https://doi.org/10.1007/978-3-030-43985-9 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved 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, express 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

Preface

After two decades of research, and after one decade of ample clinical application, vibration exercise and vibration therapy have conquered their positions, both in the local gym and in highly specialized centres for rehabilitation medicine. Physically, vibration exercise differs from most other types of exercise because it transfers mechanical energy into the human body and also because it induces movements that are much faster, and also smaller than with other types of exercise. Moreover, vibration can be combined with many other types of traditional exercise. Realistically, the proven effects by the vibration are often not superior, or at least not much superior, than could be achieved with more traditional forms of exercise. In many cases, however, addition of vibration leads to faster and easier achievement of the therapeutic target (see Chap. 13 on warming up). Thus, vibration has established itself as an option for people who do not want to do other types of physical exercise. Alternatively, vibration can yield additional therapeutic benefits that would be difficult to reap in other ways. This is foremost the case where the patients’ compliance is limited, because of physical or behavioural limitations, and where ‘passive’ types of exercise are needed. For example, introduction of vibration into paediatric rehabilitation (see Chap. 21) has been a tremendous success. This is because it helps children, who can normally not move, to expose their bodily systems to challenges that would normally only arise when children run or play. Metaphorically speaking, action and reaction is reversed in these rehabilitated children, as the vibration machines are working ‘on the children’. Likewise patients with depression (see Chap. 21) can benefit from such a reversal, highlighting the former tenet. Another, much more speculative field where vibration could have unique benefits would be to exploit the neurophysiological effects (Chaps. 6 and 8) in order to pre-condition for training or performance optimization (Chap. 14)—readers are invited to study these chapters and to come up with their own ideas and trials! However, general euphoria is out of place. Firstly, the evidence in support of vibration is still feeble in many areas. This is because many studies have been rather small, have tested only few endpoints that have not always been clinically relevant, and because of a lack of well-defined control groups in many studies. The reason for this lack of high-class studies is not only a lack of funding, but also a lack of knowledge of the widespread effects of vibration on the human organism certainly has also played a role. The primary aim of this book, therefore, is to provide an v

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Preface

overarching platform of information for those who work with vibration. Thus, the book combines physical and biological principles of vibration with physiology and clinical application. Moreover, there is a specific chapter on the mechanical design principles of vibration exercisers (Chap. 3), which may help the reader understand what is possible in terms of machine design, and also what is available on the market. Unfortunately, though, the representative of only one company has accepted the invitation to contribute to Chap. 3, although I have made quite an effort to also involve other key manufacturers on the market. The second aim of the book is to sensitize readers to the importance of the physical parameters of vibration therapy, such as vibration frequency and amplitude, duration, etc. Although many studies have demonstrated effectiveness of vibration interventions, we are still ignorant of exact dose-response relationships. It is hoped, therefore, that the next generation of vibration studies will establish such dose-­ response relationships, and thereby increase the effectiveness of the physical intervention. Thirdly, safety aspects have to date been only sporadically considered in the field of vibration exercise and vibration therapy. Although there are only extremely few reports on adverse events in the published literature, it must be suspected that some events have gone unreported. Hence, this book is also meant to encourage the awareness of safety aspects. Indeed, it is here proposed to proactively collect information on occurrence and non-occurrence of adverse events. I would like to end by saying thank you to all authors of this book, who have been extremely helpful and good to work with. Finally, I am also grateful for the unconditional support that I have received from my wonderful wife, Natia, and from my children whilst working on this book. Cologne, Germany February 2020

Jörn Rittweger

Contents

Part I The Fundamentals 1 The Physics of Vibration����������������������������������������������������������������������������   3 Jörn Rittweger and Redha Taiar 2 The Biology of Vibration ��������������������������������������������������������������������������  23 Eddy A. van der Zee 3 Design Principles of Available Machines�������������������������������������������������  39 Rainer Rawer 4 Safety and Contraindications�������������������������������������������������������������������  55 Danny A. Riley and Jörn Rittweger Part II Physiological Responses 5 Biomechanics of Vibration Exercise ��������������������������������������������������������  69 Darryl Cochrane and Jörn Rittweger 6 Cutaneous and Muscle Mechanoreceptors: Sensitivity to Mechanical Vibrations��������������������������������������������������������������������������  87 Edith Ribot-Ciscar 7 Electromyographical Recordings During Vibration������������������������������ 109 Ramona Ritzmann, Ilhan Karacan, and Kemal S. Türker 8 Supraspinal Responses and Spinal Reflexes�������������������������������������������� 121 Ramona Ritzmann and Katya Mileva 9 Assessing Reflex Latencies in Responses to Vibration: Evidence for the Involvement of More Than One Receptor������������������ 135 Ilhan Karacan and Kemal S. Türker 10 Metabolic Responses to Whole-Body Vibration Exercise���������������������� 143 Jörn Rittweger 11 Circulation Effects ������������������������������������������������������������������������������������ 155 Darryl Cochrane and Jörn Rittweger

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Contents

12 Hormonal Responses to Vibration Therapy�������������������������������������������� 169 Eloá Moreira-Marconi, Danubia da Cunha de Sá-Caputo, Alessandro Sartorio, and Mario Bernardo-Filho Part III Use of Vibration for Training 13 Warming-Up���������������������������������������������������������������������������������������������� 187 Darryl Cochrane 14 Modulation of Neuromuscular Function ������������������������������������������������ 203 Pedro J. Marín 15 Application in Athletes������������������������������������������������������������������������������ 213 Darryl Cochrane 16 Using Whole-Body Vibration for Countermeasure Exercise ���������������� 229 Patrick J. Owen, Daniel L. Belavy, and Jörn Rittweger Part IV Clinical Applications 17 How to Design Exercise Sessions with Whole-Body Vibration Platforms ���������������������������������������������������������������������������������� 247 Christina Stark and Jörn Rittweger 18 Whole-Body Vibration in Geriatric Rehabilitation�������������������������������� 255 Martin Runge and Jörn Rittweger 19 Application of Vibration Training for Enhancing Bone Strength �������� 269 Debra Bemben 20 Whole-Body Vibration Exercise as a Treatment Option for Chronic Lower Back Pain ������������������������������������������������������������������������ 279 Jörn Rittweger 21 Pediatric Rehabilitation���������������������������������������������������������������������������� 285 Christina Stark, Ibrahim Duran, and Eckhard Schoenau 22 Chronic Obstructive Pulmonary Disease (COPD)���������������������������������� 319 Rainer Gloeckl 23 Urinary Incontinence����������������������������������������������������������������������������   329 Volker Viereck and Marianne Gamper 24 Primary Muscle Disorders������������������������������������������������������������������������ 337 Ibrahim Duran, Christina Stark, and Eckhard Schoenau 25 Application of Vibration Training in People with Common Neurological Disorders������������������������������������������������������������������������������ 343 Feng Yang

Contents

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26 Whole-Body Vibration Therapy in Patients with Pulmonary Hypertension and Right Heart Failure: Lessons from a Pilot Study���� 355 Felix Gerhardt and Stephan Rosenkranz 27 Vibration Exercise and Vibration Therapy in Metabolic Syndrome���� 363 Laisa Liane Paineiras-Domingos, Danúbia da Cunha de Sá-Caputo, and Mario Bernardo-Filho 28 Whole-Body Vibration Exercise in Cancer���������������������������������������������� 381 Patrícia Lopes-Souza, Danúbia da Cunha de Sá-Caputo, Redha Taiar, and Mario Bernardo-Filho

List of Videos

Video 1.1  Excitation of a tuning fork, as an example of a natural oscillation Video 1.2  Playground swing, as an example of a driven oscillation Video 5.1  The suspended pendulum as a stable equilibrium Video 5.2  The inverted pendulum as an un-stable equilibrium Video 5.3 Ultrasound movies of the gastrocnemius muscle during vibration at 4 Hz and 16 Hz Video 17.1  Squatting exercise on a side-alternating vibration platform Video 17.2  Deep squats on a side-alternating vibration platform Video 17.3  Calf raises on a side-alternating vibration platform Video 17.4  Pelvic twist on a side-alternating vibration platform

xi

Part I The Fundamentals

1

The Physics of Vibration Jörn Rittweger and Redha Taiar

1.1

Introduction

Vibrations are mechanical oscillations, which are closely linked to the concept of waves [1]. For whatever reason, standard textbooks of biomechanics are devoid of chapters on oscillation, vibration or waves [2, 3], and so are text books of physiotherapy. Hence, we anticipate that a good fraction of the readership will not be very familiar with the concept of oscillations. However, understanding them is very useful for practically working in vibration exercise and vibration therapy. Hence, we will be starting the chapter with a more intuitive outline of the questions and concepts, and we will be arriving at a more ‘mathematical’ level toward the end of this foundation chapter.

Electronic Supplementary Material The online version of this chapter (https://doi. org/10.1007/978-3-030-43985-9_1) contains supplementary material, which is available to authorized users. J. Rittweger (*) Institute of Aerospace Medicine, German Aerospace Center (DLR), Cologne, Germany Department of Pediatrics and Adolescent Medicine, University of Cologne, Cologne, Germany e-mail: [email protected]; [email protected] R. Taiar Department of Physical Exercise, Université Reims Champagne-Ardennes, Reims, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Rittweger (ed.), Manual of Vibration Exercise and Vibration Therapy, https://doi.org/10.1007/978-3-030-43985-9_1

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4

1.2

J. Rittweger and R. Taiar

How Oscillations Emerge

Periodic movements are very common. Think, for example, of your legs during walking, a leaf shaking in the wind, or a child on a swing. Physicists refer to such periodic movements by the wider term of ‘oscillation’. When discussing how they emerge, we have to distinguish two different kinds of oscillations. Firstly, something can start oscillating by itself. This is called a natural oscillation, and a typical example would be a tuning fork (Fig. 1.1 left). Secondly, one thing can be driven to oscillate by another thing. This is then called a ‘driven oscillation’, and a typical example would be a playground swing (Fig. 1.1 right). Natural oscillations emerge from an energy transferal that excites the oscillating system so that it starts to move. Within the oscillating system, there is a continuous transformation from one type of energy into another. In the case of the tuning fork, this elastic energy is periodically transferred to kinetic energy and vice versa. The rate of energy transferal, which is determined by the physical properties of the oscillator, defines its natural frequency, which is also called the eigenfrequency. Other typical examples of natural oscillations can be found in musical instruments. For string instruments, the energy transferal can be either by a single impulse as in picking a guitar string, or it can be continuous as when a violin string is touched with a bow. Of course, a violin string can also be excited in picking (pizzicato), and it will produce a tone with the same pitch in either case. Some more examples of oscillations that occur during daily life are given in Table 1.1. The situation is very different for driven oscillations: here, the frequency is imposed from an actuator onto a dynamic system. Often, the actuator is an engine, such as a car engine, or indeed a vibration platform. Whilst a vibration platform is purposefully built to operate at a given frequency, the vibration of a car engine is a by-product of its design. In the old days cars were much noisier, and truck seats were vibrating  heavily until the 1980s to an extent that was even detrimental to

Fig. 1.1  Natural oscillation vs. driven oscillation. Mechanically speaking, the tuning fork (left) is excited once by a finger snap (= energy transferal). The two tines of the fork then naturally start oscillating to produce a specific tone, the pitch of which is defined by the structural properties of the tines. By contrast, the oscillation of the swing (right) is driven by the human ‘operator’. When the operator repeatedly agitates the swing at the right time points (= phase), the excursions augment with each cycle, and the energy stored within the swing system can accumulate. Of note, the swing oscillates at a specific frequency only, and it is in this sense physically similar to the tuning fork

1  The Physics of Vibration

5

Table 1.1  Typical real-world examples of oscillators in our daily life Real-world example Tuning fork String of a musical instrument Metronome

Physical principle Spring pendulum Spring pendulum Torsion pendulum

Balance spring (e.g., in mechanical clocks) Pan’s pipe

Torsion pendulum

Trumpet

Spring pendulum (lips) Helmholtz-resonator (pipe) Oscillator circuit Pendulum

Transistor radio Swing

Helmholtz-resonator

Important properties Stiffness and mass Stiffness and mass Stiffness and moment of inertia Stiffness and moment of inertia Air density and tube dimensions Air density and tube dimensions Capacitance and inductance Suspension length and gravity

spinal health (see Chaps. 4 and 20). Modern cars are much more comfortable, simply because they are designed to reduce vibrations. So, why do vibrations emerge in cars at all, and how is it possible to reduce them? Within any complex mechanical structure, there will be some elements that behave in a way that is comparable to some kind of pendulum (Table 1.1). Thus, parts will start to oscillate when energy is transferred to them. Whenever the eigenfrequency of a given part matches the engine’s pace, this will lead to the phenomenon of resonance. Resonance is also the mechanism by which swings in children’s playgrounds work (Fig. 1.1): to augment the excursions, the child has to invest energy, and this energy investment has to be in a certain temporal relationship. Physically speaking, the periodic action of the actuator (e.g., child) and the resonator (swing)  occur in phase. In this way, energy storage within the system can accumulate over time. When car engineers aim at avoiding resonance, they have to shift the parts’ eigenfrequencies away from the engine’s actuation frequency. Musical instruments, on the other hand, are purposefully designed to amplify certain frequencies. This is beautifully exemplified in a trumpet, where the natural oscillations of the lips get amplified by the resonating pipe. It is of particular note within the context of this book that most side-synchronous vibration platforms rely on the principle of resonance. Accordingly, these systems can struggle to maintain identical vibration frequency and amplitude for persons with different weight. Due to their make-up, most side-alternating systems do not encounter that problem.

1.3

How to Describe Oscillations

Since periodic movements, or oscillations, are somehow monotonous, one can simplify their description by a set of variables. The most useful descriptors are frequency, amplitude and phase (see Box 1.1).

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J. Rittweger and R. Taiar

Box 1.1

• The oscillation frequency (Fig. 1.2a) tells us how many cycles occur per unit time (a cycle being one full repetition of the movement). Sometimes, the periodicity or oscillation period is mentioned. It describes the time required for one cycle. Mathematically, it is therefore inversely related to the frequency. In other words, frequency and period convey the same information. • The amplitude (Fig. 1.2b) tells us how large the movement is in each cycle. There is an important caveat: Whilst mathematically speaking the amplitude describes the movement from equilibrium to the maximal excursion, the so-called peak-to-peak amplitude describes the distance between the two maxima on either side of the equilibrium. Obviously, the distinction between amplitude and peak-to-peak amplitude is crucial. Unfortunately, this distinction is not always made, even not in the scientific literature. Therefore, one needs to be very explicit when reporting the amplitude of vibrations [4]. • The phase information defines the timing of the movement (Fig.  1.2c). Although phase is at least as important as frequency and amplitude information (or in some instances even more important [5]), it is often neglected. We will see further down how important phase information is, in particular when two oscillators interfere with each other. • The shape of an oscillation is more difficult to define—it is more of an intuitive concept. The standard mathematical approach to oscillations is by so-called Fourier analysis, which regards sinus waves as basis of all oscillations. It is important to realize, therefore that Fourier analysiscan misinterpret the shape factor of an oscillation. Accordingly, when an oscillation’s shape deviated significantly from a sine curve, we need to use more advanced techniques (e.g., wavelet analysis of pattern recognition algorithms) in order to adequately quantify frequency, amplitude and phase in our signals.

When engineers speak about oscillations, they usually imply sinusoidal oscillations. This is because sinusoidal oscillations are more convenient to produce in machines than other types of oscillations, and also because the mathematical concept of harmonic oscillation yields sine curves as a result. Moreover, sinusoidal functions are very convenient, as one can easily compute position, velocity and acceleration from each other when assuming a sinusoidal shape (Fig.  1.2). And, more complex wave forms can be generated, or simulated, by adding harmonics. These are oscillations with frequencies that are multiples of the fundamental frequency (Fig. 1.3d). However, there are many other different types of periodic movements and oscillations, in particular in biological systems. The heartbeat, hormonal cycles or nerve cell discharges may serve as well-known examples for this (see Fig. 1.2d). Still, we can describe such anharmonic oscillations in terms of frequency, amplitude and phase—it is just that they have a different shape.

1  The Physics of Vibration

a

7

b

Frequency

Amplitude

f = 1/1s = 1Hz A=1 A=1/2

f = 1/2s = 0.5Hz

c

d

Phase

Physiological Signals

φ=90º

φ=±180º 0.0

0.5

1.0

1.5

2.0

0.0

Time [s]

0.5

1.0

1.5

2.0

Time [s]

Fig. 1.2  Illustration of the concepts of frequency, amplitude, phase and shape in oscillations. Whilst curves in (a–c) are mathematically constructed sine curves, the curve in (d) depicts genuine physiological signals. (a) The red oscillation’s period is 1 s, and its frequency thus 1/s or 1 Hz. The blue oscillation’s frequency is half that of the red oscillation. (b) The blue oscillation’s amplitude is half as large as the amplitude of the red oscillation. (c) The blue curve lags behind the red curve, and the green curve is antiphase to the red curve. Thus, the blue and green curves are said to be in phase relationship of −π/2 and - π = −90° and 180°, respectively, with the red curve. (d) Arterial blood pressure (red) and electrocardiogram (blue) as physiological signals of oscillatory character

1.4

Interference of Oscillations

The superposition of two oscillators is called interference. When two oscillations have identical frequency and phase, their amplitudes will add (Fig. 1.3a). That is called constructive interference, and the constructive effect is the greatest when both oscillations are fully in phase. When they get out of phase, an opposite phenomenon may emerge: destructive interference (Table 1.2). Although both oscillations have identical frequency, the maxima of one oscillation coincide with the minima of another (Fig.  1.3b). They are antiphase and thus ‘destroy’ each other. When both oscillations have identical amplitudes, they can even cancel each other out entirely, which is the physical foundation of active noise cancellation. Interesting phenomena may also arise when oscillations with different frequencies are superposed. For example, their frequency ratios are integer numbers, i.e., when one oscillation is 2, 3 or n times faster than the lowest frequency. This lowest frequency is then called the fundamental frequency, and the higher ones are called harmonics (sometimes also formants). Harmonic oscillations in musical instruments can emerge from simultaneous oscillations of strings at their full length and

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a

Constructive Interference

b

Destructive Interference

c

Phase Shift

d

Harmonics

e

0.0

f

Beat Frequency

0.5

1.0 Time [s]

1.5

2.0

Modulation

0.0

0.5

1.0

1.5

2.0

Time [s]

Fig. 1.3  Interference of oscillations. (a) Constructive interference: As the blue and green oscillations are in phase, the resulting red oscillation has greater amplitude then the red or green oscillation; (b) Destructive interference: The blue and green curves have been shifted so that they are antiphase. This is resulting in a substantial reduction of the red curve’s amplitude; (c) Phase Shift: Phase lags between the blue and the green oscillations lead to a phase shift that results in the red oscillation; (d) Harmonics: Superposition of frequencies with integer ratio results in ‘interesting’ periodic oscillations. The red curve is, simply spoken, the sum of the first harmonic (also called mode or fundamental frequency, shown in yellow colour) and the 2nd and 3rd harmonics (yellow and blue, respectively). Note that the red and yellow curves are identical with regards to cycles per time, but obviously have a different shape. The more complex shape of the red curve almost resembles physiological signals such as blood pressure (see Fig. 1.2d); (e) Beat frequency: Superposition of two oscillations with a similar frequency results in the red curve. The blue and green oscillations are in-phase at 0, 1 and s, but antiphase at 0.5 and 1.5. This causes a waxing and waning of the resultant red oscillation. Such a variation in air pressure can be  perceived by humans as a new tone with its own frequency (depicted by yellow line); (f) Modulation: Although the phenomenon of amplitude modulation resembles beat frequency, it is mathematically distinct. Frequency modulation (blue) is technically advantageous over amplitude modulation (red)

1  The Physics of Vibration

9

Table 1.2  Overview of different types of superpositions by two or several oscillators Phenomenon Constructive interference Destructive interference Phase shift

Frequency Identical

Phase Identical

Result Amplitude enhanced, phase unchanged

Identical

Opposed

Identical

Harmonic oscillation Beat frequency

Integer Relationship Similar, but not identical

Any other Identical

Amplitude reduced (up to cancellation), phase unchanged Amplitude reduced, phase changed

Variable

Enrichment of information content Emergence of a new oscillation

Note that the oscillators themselves do not interact (example: two instruments played in the same room), but that the resulting signal does

at ½, 1/3 or 1/n of their length (Fig.  1.3d). In music, harmonic oscillations are always more pleasant to hear than a pure sinus tone, and harmonics constitute the ‘acoustic color’ or ‘timbre’ of a given instrument. In human speech, harmonics or formants make up the difference between the different vowels and are thus an important source of information. Conversely, harmonics usually have undesirable effects in electric circuits, where they may emerge from some miss-behaving electrical devices. A very interesting phenomenon is the so-called beat-frequency (Fig.  1.3e). It emerges from oscillations with similar but different frequencies. As a result, the phase relationship is variable, and constructive interference alternates with destructive interference. This results in two different frequencies that emerge from this, a carrier frequency that is defined by the mean of the two foundation frequency, and the beat frequency, which is defined by their difference. One can use this phenomenon, for example, when tuning an instrument: two tones have identical frequency when the beat frequency has disappeared. Note that although the beat frequency may resemble amplitude modulation of a signal, the two are mathematically not identical (Fig. 1.3f), and that they can be distinguished by spectral analysis.

1.5

Resonance and Damping

Whilst the previous section dealt with the interference as a mere superposition of oscillations, we now have to discuss interactions by which two oscillators affect the action of each other. Consider an oscillating actuator (e.g., a vibration platform) that drives a resonator. If the actuator’s excitation frequency matches the resonator’s eigenfrequency, and if the actuator and resonator are in phase, then this can lead to an accumulation of energy, even to an extent that is disruptive. This phenomenon is referred to as resonance catastrophe. To avoid this catastrophic event, soldiers (here: actuator) are required to march out-of-phase when crossing bridges (here: resonator). There are several ways to avoid resonance catastrophe. We have already discussed above that engineers can structurally design parts to

10

J. Rittweger and R. Taiar Amplitude Resoncance Function 4 D=0

m

Transmissibility

3 k

D = 0.2

b

2 0.4 1/√2

1

2 5

0 0

1

2

3

Normalized frequency

Fig. 1.4  Resonance in a damped mass-spring oscillator (see inlet). The resonance frequency is defined by mass m, stiffness k and friction b. Now imagine the blue plate in the inlet to be driven by an actuator at variable frequencies. Transmissibility is defined as the ratio of amplitudes in the resonator and in the actuator, and plotted against the frequency of the actuator, expressed in multiples of the resonance frequency (= normalilzed frequency). The damping coefficient D (see also Fig. 1.8) affects both transmissibility as well as resonance frequency. Amplitude amplification, i.e., transmissibility >1 occurs only when there is little damping. Figure reproduced from [6]

reduce or increase the resonator’s eigenfrequency. An alternative way is to introduce damping elements. Dash-pots in the shock-absorbers of a car are an example (Fig. 1.4). Damping has two effects on the resonator: firstly, it withdraws a certain amount of energy from the oscillation. Second, damping reduces the eigenfrequency of the resonator. With regards to vibration exercise, it is important that muscles have such damping properties [7], and that they can act as shock absorbers in our body. However, any mechanical damping will lead to the absorption of energy and thus generate heat. In order to practically assess whether resonance occurs in a given system, one can assess the presence of ‘amplitude amplification’. This test makes use of the fact that resonance enhances movements within the resonator (example: swinging child). Thus, if any part of the system oscillates with greater amplitude, or with greater acceleration than the actuator, then this is indicative of resonance. Of course, such resonance phenomena occur only at certain actuation frequencies, so one usually has to test a range of different frequencies. To test for resonance of the human body during whole body vibration, for example, one can affix accelerometers to the platform and to the human body [8, 9]. Division of the acceleration signals (after subtracting Earth’s gravity) will then yield the amount of amplitude amplification. However, most of the times, transmissibility of vibration signals is low, and amplitude amplification does not occur. It is thus apparent that amplitude amplification can only occur if there is little damping. Moreover, not all amplitude amplification

1  The Physics of Vibration

11

causes resonance catastrophe, as this will happen only if the generated forces exceed the resonator’s structural strength. Nevertheless, resonance should be prevented in vibration exercise, e.g., by alteration of muscle stiffness and thus ω0 [7].

1.6

Waves

When parts of or body are vibrated, then the tissue deformations tend to spread out within our body. We therefore have to introduce the concept of waves. In physics there are three main categories of waves: gravitational waves, mechanical waves— such as swell, seismic waves or sound waves—and electromagnetic waves—such as light. A wave is defined as a periodic movement, which can normally be described by a sinusoidal function (Fig. 1.2a and Eq. 1.1). However, the propagation of the wave is not equivalent to transport of matter. In fact, the wave per se does not transport any matter. Each wave is characterized by different quantities that are specific to it. According to these quantities, we can understand the nature of the wave, its properties and its consequences. Transversal propagation: During the passing of the wave deformation, the different points of the environment move perpendicular to the direction of propagation, and the deformation is a transversal signal (Fig. 1.5a). Longitudinal propagation: During the passing of the wave deformation, the different points of the environment move in the direction of propagation, and the deformation is a longitudinal signal (Fig. 1.5b). Transverse and longitudinal waves can have different velocities. The wave length is one of the characteristics specific to each wave, whatever its nature. It is noted using the Greek letter lambda (λ). It represents the spatial periodicity of the oscillations, i.e., the distance between two maximum oscillations, for a

b

Fig. 1.5 (a) Transversal wave signal obtained when the different points move perpendicular to the direction of the propagation). In (b) a longitudinal wave signal results from the different points move in the direction of the propagation

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J. Rittweger and R. Taiar Incident wave

Reflected wave Wall

Fig. 1.6  Illustration of the reflection of the wave. The reverse reflected pulse is represented by the blue curve and after striking the wall

example. The wavelength is also the distance travelled by the wave during a period of oscillation. Thus, it is inversely proportional to frequency. The wave length also depends on the speed at which the wave propagates in the environment. Thus, when a wave passes from one environment to another by changing velocity, its wave length will change, but the frequency remains the same. All this is described by the following relationship: λ = v* Td= v/f, where v corresponds to the wave velocity, Td to the oscillation period and f to its frequency. Reflection of waves occurs when the wave hits a fixed obstacle. After the collision, the wave propagates in the same environment, but in a different direction. A wave that strikes an object or an obstacle or shows discontinuity in the environment is partially reflected. For instance, we consider the case of a disturbance propagating along a rope. When the pulse reaches the end of the rope at its support point (Fig. 1.6), it exerts an upward force and the support opposes a downward force. The force exerted by the support creates the reverse reflected pulse. The pulse inversion corresponds to a 180° phase change. However, waves are not necessarily reflected, but can also be absorbed by an object.

1.7

Some Mathematical Background

Sinusoidal oscillations can naturally emerge, mathematically speaking, in cases that are described by 2nd-order differential equations. Such a situation is given in the suspended pendulum (Fig. 1.7), where the restoring force is opposite and proportional to the magnitude of the sideways deflection. Force is naturally related to acceleration, and acceleration is the 2nd derivative of deflection. Similar proportionalities can be found for other natural oscillators (see Table 1.3). It is this proportionality between deflection and its 2nd derivative that leads to the general solution by a sinusoidal function [1].

1  The Physics of Vibration

13 Pivot

of L

θ

d Ro

Deflection

eng th /

FR S Equilibrium Point

Fig. 1.7  Illustration of a suspended pendulum. Deflection of the pendulum away from the equilibrium by angle θ leads to vertical displacement s, and thus potential energy. If let loose, the mass (red bob) will have transformed all of its potential energy into kinetic energy at the equilibrium point, and then continue to swing to the other side until all of the kinetic energy is transformed into potential energy. This transferal of energy is affected by rod length l (the greater l, the slower the transfer), and by gravity (a pendulum will swing slower on the moon), but independent of the bob’s mass. Mathematically speaking, the restoring force FR is proportional to deflection angle θ, at least for small deflections. Therefore, the pendulum can be described by a 2nd order differential equation (for more information, see text books on physics) Table 1.3  Eigenfrequency of some natural oscillators Eigenfrequency (f) Pendulum f =

g 1 ´ L 2p

Spring-mass f =

k 1 ´ m 2p

Instrument string fn =

n T ´ 2L m

Variables π = circular number (3.1415) g = gravity (9.81 m/s on Earth) L = length of the string [m] π = circular number (3.1415) k = stiffness of the spring [N/m] m = mass of the spring [kg] n = number of harmonic (e.g., 1st, 2nd, etc) T = tension of the string [N] μ = mass per unit length [kg/m] L = length of the string [m]

Note that these equations apply to idealized conditions, where there is complete conservation of energy. Note also that numerators (gravity, stiffness, tension) are positively associated with the eigenfrequency, whilst denominators (length, mass) are negatively associated. This is because the numerators foster the relative energy transferal, whilst denominators hamper it.

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The basic equation for sinusoidal oscillations is (1.1) y ( t ) = A ´ sin (j + t ´ w ) Where y is the displacement, A is the amplitude, φ is phase, and t is time. These variables have been illustrated in Fig. 1.2. The circular frequency ω is given as

w = 2p f (1.2) And the peak-to-peak amplitude Ap2p is defined as Ap 2 p = 2 × A (1.3) It follows from Newton’s second axiom that the maximal force exerted on a rigid body scales with the maximal acceleration (amax), which can be collated as amax = w 2 ´ A (1.4) which is usually given in multiples of acceleration on Earth (g). The first derivative of the sine function in Eq. (1.1) is a cosine function (1.5) y ¢ ( t ) = A ´ w ´ cos (j + t ´ w ) and the sine function corresponds to the cosine function through a phase shift by π æ æ p öö cos ( t ) = sin(t ´ ç w + ç ÷ ÷ è 2 øø è

(1.6)

Conversely, integration of a sine function yields a cosine function. Finally, damped oscillations are described as y ( t ) = A ´ sin (j + t ´ w ) ´ e -d ´t (1.7) where e is Euler’s number and δ is the damping constant. If the damping is constant, then it will only affect the amplitude of the oscillation. If the damping is proportional to velocity (also called viscous damping), then it reduces the amplitude and frequency. The damping constant can be graphically determined from the logarithmic decrement λ (Fig. 1.8), which is related to δ and the oscillation period Td by

l = d ´Td (1.8)

Fig. 1.8  In damped oscillations, the logarithmic decrement λ can be calculated by Eq. (1.8), or it can be graphically assessed as the ratio yˆ 1 / yˆ 2 , or equally by yˆ 2 / yˆ 3 , etc.

Damped Oscillation

^y 1

^y 2

^y 3

f = 1 Hz, δ = 0.2 Hz 0

1

2

3 Time [s]

4

5

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1.8

15

Analysis of Periodic Signals

There are several ways possible by which we can analyze the oscillatory components of signals with regards to their frequency, amplitude, phase and shape. Each of them has its specific strengths and weaknesses, and we can describe only a small selection here.

1.8.1 Spectral Analysis This classical method is based on Fourier’s theorem, which states that any periodic signal can be thought of as a composition of sine and cosine waves. When discussing the emergence of harmonics (Fig.  1.3d), we had already seen that superposition of sinusoidal waves can generate complex periodic patterns. The principle idea behind Fourier transforms is to back-trace harmonic superposition and to decompose empirical data into a hypothetical set of sinusoidal oscillations. Technically speaking, decomposition of N samples of a given time series yields N/2 frequency components as well as N/2 phase components. Thus, the entire information is conserved, which is a great strength of Fourier transforms. However, whilst interpretation of the amplitude information is straightforward (Fig.  1.9), humans typically struggle to comprehend the phase information, which is why this information is typically neglected. This can give rise to misinterpretations, namely when authors refer to ‘higher frequencies’ when in reality they speak of harmonics, i.e., the shape factors or formants. To avoid such confusion, the term ‘frequency components’ should be used (rather than ‘higher frequencies’), and it should be understood that such higher frequency components typically result from deviations from the idealized sinusoidal curves, rather than by additional oscillations. For example, the vibration signals from riveting hammers and from other hand-held power tools are very rich in harmonics (Chap. 4), and they must surely not be confused with frequencies originating from other primary oscillations. Another example would be impacts that emerge from collisions with vibrating platforms, which can occur when affixment to the platform is insufficient (see Chap. 7). This is important, as higher frequency components are thought to be particularly provocative for vibration-­related problems in occupational medicine (see Chap. 4). Fourier transforms are not only useful for quantitative analysis of periodic signals, they also offer the mathematical foundation for frequency-selective filtering. This can often be useful in signal processing tasks.

1.8.2 Wavelet Transforms To overcome the Fourier transform’s limitations in assessing phase and shape information, wavelet analysis has been introduced in the early 1980s. The idea is here to a priori define the shape of the periodic oscillations, and to the approximate

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d

-1.5

-0.5

0.5

1.5

a

0.0

0.5

1.0 Time [s]

0.0 0.2 0.4 0.6 0.8 1.0

b

0

1

2

0.0 0.2 0.4 0.6 0.8 1.0

c

0

1

2

1.5

2.0

0.0

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1.0 Time [s]

e

3 4 Frequency [Hz]

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4 3 Frequency [Hz]

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6

2.0

0

1

2

3 4 Frequency [Hz]

5

6

0

1

2

3 4 Frequency [Hz]

5

6

f

6

1.5

Fig. 1.9  Spectral Analysis of sinusoidal signals (left column) and of physiological signals (right column). (a) A pure sine wave (red curve) and an oscillation curve with 2nd and 3rd harmonic (blue curve, identical with Fig. 1.3d); (b) amplitude spectrogram of the red curve in A, showing that only one oscillation is present at 1 Hz; (c) amplitude spectrogram of the blue curve in A, showing peak at the fundamental frequency (1st harmonic, 1 Hz), as well as at the 2nd and 3rd harmonic (2  Hz and 3  Hz, respectively). (d) Blood pressure (red) and electrocardiogram (ECG, in blue) signals, which are identical with Fig. 1.2d; (e) amplitude spectrogram of the ECG in (d). Although the blood pressure curve looks quite similar to the red curve in (a), its harmonics have much greater amplitude. In the jargon of engineers, these are called ‘higher frequency components’, and they are often seen as shape factors. The greater the harmonic power, the ‘edgier’ is the oscillation; (f) amplitude spectrogram of the ECG signal. Here, the amplitude of the harmonics is even greater than the amplitude of the fundamental frequency. Note also that acceleration curves from riveting hammers (see Chap. 4) can look similar to an ECG

its occurrence in a given signal (time-frequency location). Mathematically, this works by generating a family of functions deduced from the same function (called mother wavelets) by translation and dilation operations (see Fig.  1.10). Thus, whilst Fourier transforms decompose a given signal into a set of sine waves that

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0.5

1.0

σ=1 σ=2 σ=3

-0.5

Coefficient

1.5

Ricker Wavelet

-6

-4

-2

0

2

4

6

Times [s]

Fig. 1.10  The Ricker wavelet, also called ‘Mexican hat’ wavelet, is derived from the Gaussian function. It thus assumes a shape for which the frequency content scales with the parameter σ. As for the sine function, the curve oscillates around a mean value of 0. However, whilst the sine curve is unlimited, wavelets are limited in time.

extend over the entire signal, the wavelet approach is decomposing into wave elements that are limited in time. However, whilst the fundamental ideas behind wavelet transforms are promising, they have so far not become very popular among researchers.

1.8.3 Averaging Methods Spectral analysis and wavelet analysis are extremely useful to analyze technical and physical signals. However, their strength is at decomposing signals, and not at recognizing patterns. Therefore, they are not so straightforward to use with physiological signals (see Fig.  1.9f). Hitherto, averaging methods provide an easy-to-use, intuitive alternative. The principle idea is to analyze signal sweeps in relation to a time signal. Often, the time signal is an external stimulus, e.g., a light flash, a sound or an electric stimulus that is given to a test subject at regular (or irregular) intervals. That stimulus then serves as a timing event (ET), and sweeps from another physiological signal (S) are overlayed and averaged. This approach is routinely used in clinical neurophysiology, e.g., for visually evoked potentials (ET = light flash, S = electro-­ encephalogram (EEG)) or for brainstem auditory evoked potentials (BAEP, ET = sound, S = electro-encephalogram (EEG)). In neurophysiology, a related technique called peri-stimulus time histogram (PSTH) uses external stimuli and the discharge of a given neurone signal. Obviously, neuronal discharge is better modelled as an event than as a continuous signal. Hence, PSTH uses counts per time bin for its display, which requires some smart reasoning about the width of the time bin [10]. Using averaging methods in other fields of physiological data processing is straightforward. Triggering an ECG, for example, is as easy as triggering neural

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160

200

240

280

ECG

0.0

0.5

1.0

lag [s]

60

80

120

160

Blood Pressure

0.0

0.5

1.0

lag [s]

Fig. 1.11  Illustration of how averaging methods can help. Here, the ECG signal has been thresholded at a value of 240 to yield a series of timing events ET. Next, sweeps of the blood pressure signal are overlayed such that they range from 0.15 s before (=negative lag) until 1.35 s after ET (=positive lag). The individual sweep data are displayed as grey curves in the resulting peri-­ stimulus plot. In this plot, all ET coincides with lag = 0 (indicated by yellow line), and the blue curve denotes the averaged blood pressure over the cardiac cycle. In this example, the 95% confidence interval is indicated by red curves. Note from the upper figure that peri-stimulus plots can also be used to quickly judge the accuracy of the triggering process: Accuracies in the triggering reveal themselves by grey curves that do not follow the averaged curve

discharge (see Fig. 1.11). This can be used to get an averaged blood pressure, to check the accuracy of the ECG-triggering, and also to look at relationships between the cardiac rhythm and other oscillatory processes in the body. As illustrated by Fig.  1.11, the approach is very powerful in assessing the shape of an oscillatory process when the physiological signal does not follow any analytical mathematical function. Averaging methods are also straightforward for the analysis of human vibration exercise. Either the position of the vibration platform or an accelerometric signal can be used for ET, and S could consist in signals as varied as perfusion, joint angle or muscle fascicle length [11].

1  The Physics of Vibration

1.9

19

How to Quantify Signal Amplitude and Magnitude

Finally, we need to shortly discuss the concept of amplitude in some more detail. This is important, as the different measures of amplitude are frequently confused in the literature [4]. All is simple if we are to deal with sine curves. Then the positive peak amplitude APeak is given by the displacement between ϕ = 0° and ϕ = 0° (see Eq. 1.1 and Fig. 1.12a). As the sine wave is symmetric, the peak-to-peak amplitude a

Sine Curve

ARMS

APeak AP2P

b

ECG

APeak ARMS

AP2P

APeak2

0.0

0.5

1.0

1.5

2.0

Time [s]

Fig. 1.12  Illustration of the different measures for signal amplitude. (a) sine curve. Peak amplitude is defined as the difference between mean value and the extreme value, both positive as well as negative. In the case of the sine function, the excursions are symmetrical, and AP2P is simply 2 × APeak. The sinus function’s absolute value is displayed as grey area, and its average is referred to as

( )

ARMS (indicated in yellow), where RMS stands for root-mean-square ( RMS = mean x ). RMS is mathematically equivalent to (mean(|x|)). This value is quite important, as it is directly related to the mechanical power of the vibration. (b) ECG signal. Because of the asymmetry of the signal, the positive and negative APeak have different extent, and AP2P cannot simply be calculated, but has to be processed from the data. For similar reasons, ARMS gets relatively smaller in relation to AP2P for ‘edgy’ signals such as ECG 2

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AP2P is simply 2 × APeak (Eq. 1.3). In addition, the averaged absolute amplitude ARMS can be calculated for sinusoidal functions as APeak / 2 . Thus, as long as we know at least one of the three (APeak, AP2P or ARMS), the other two can be calculated in the specific case of sinusoidal functions. This changes dramatically when we deviate from sinusoidal oscillations and turn to real-world data. As can be seen from Fig. 1.12b, the negative and positive APeak may have different magnitude. As a result, we cannot simply compute AP2P, or ARMS from APeak, but rather have to assess those empirically. This can have a strong bearing on comparisons between different vibration devices. For example, if one of the systems produces relatively more higher frequency components than the other, then it also has, for the same ARMS, a greater AP2P. Thus, the comparison of vibration amplitudes is not as straightforward as it may seem. Another term that is often used in the field of vibration exercise is the so-called vibration magnitude [12], which is defined as the peak acceleration amax. For sinusoidal functions, it can be easily calculated (Eq. 1.4), and its importance consists in the fact that acceleration scales with the force that the body is exposed to. However, as for ARMS, amax strongly depends on the oscillation’s shape, and one can normally not rely on calculations from the vibration frequency and the targeted APeak. In summary, the different descriptors APeak, AP2P, ARMS and amax must not be used interchangeably. Moreover, each of them has its specific implications for vibration exercise and therapy. Whilst APeak and AP2P indicate the range of motion, ARMS scales with the mechanical power, and aPeak is related to the peak force. Given that many vibration exercise devices generate vibrations that deviate substantially from the sinusoidal shape, it seems mandatory for scientific and medical publications to report at least AP2P, ARMS and amax.

References 1. Tipler PA, Mosca G.  Physics for scientists and engineers. New  York: W.H.  Freeman and Company; 2008. 2. Nigg BM, Herzog W, editors. Biomechanics of the musculo-skeletal system. 3rd ed. Chichester: Wiley; 2007. 3. Özkaya N, Nordin M. Fundamentals of biomechanics. New York: Springer; 1998. 4. Rauch F, Sievanen H, Boonen S, Cardinale M, Degens H, Felsenberg D, et  al. Reporting whole-body vibration intervention studies: recommendations of the International Society of Musculoskeletal and Neuronal Interactions. J Musculoskelet Neuronal Interact. 2010;10(3):193–8. 5. Oppenheim AV, Lim JS. The importance of phase in signals. Proceed IEEE. 1981;69:529. 6. Rittweger J. Vibration as an exercise modality: how it may work, and what its potential might be. Eur J Appl Physiol. 2010;108(5):877–904. 7. Wakeling JM, Nigg BM, Rozitis AI.  Muscle activity damps the soft tissue resonance that occurs in response to pulsed and continuous vibrations. J Appl Physiol. 2002; 93(3):1093–103. 8. Kiiski J, Heinonen A, Jarvinen TL, Kannus P, Sievanen H.  Transmission of vertical whole body vibration to the human body. J Bone Miner Res. 2008;23(8):1318–25. 9. Caryn RC, Dickey JP.  Transmission of acceleration from a synchronous vibration exercise platform to the head during dynamic squats. Dose-Response. 2019;17(1):1559325819827467.

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10. Shimazaki H, Shinomoto S. A method for selecting the bin size of a time histogram. Neural Comput. 2007;19(6):1503–27. 11. Cochrane DJ, Loram ID, Stannard SR, Rittweger J.  Changes in joint angle, muscle-tendon complex length, muscle contractile tissue displacement, and modulation of EMG activity during acute whole-body vibration. Muscle Nerve. 2009;40(3):420–9. 12. Cardinale M, Rittweger J. Vibration exercise makes your muscles and bones stronger: fact or fiction? J Br Menopause Soc. 2006;12(1):12–8.

2

The Biology of Vibration Eddy A. van der Zee

2.1

General Introduction

The function and features of vibrations has a history as a study field in natural science (e.g., physics), but only modestly so in life sciences, and even less so in biomedical sciences. Nevertheless, it is already known since 2007 that vibrations affect the development of stem cells and hence most likely played a key role in the development of life [1]. This may not come as a surprise knowing that around us, all things are continuously vibrating, including objects that seem to be stationary. These objects are constantly in motion, vibrating at various frequencies (see Box 1.1, Chap. 1). These vibrations also include regular oscillations and resonance, observed when an object (or protein for example) oscillates between two preferred (morphological) conditions. We are surrounded by both biotic and abiotic vibrations of natural and anthropogenic (man-made) origins. Natural vibrations come, for example, from running water or, at the coast, from breaking waves, which in shallow water generate vibrations between 10 and 800  Hz [2]. Thunderstorms produce brief vibrations with peaks at 10–30 and 100–300 Hz [3]. A rain drop falling on a leaf produces a vibratory signal of typically 5.7–10.5 Hz, whereas wind-induced oscillations of a leaf are typically below 15  Hz of vibrations (see the videos of the vibrating leaf in Chap. 1). Irregular vibrations induced by the movement of air can lead to vibrations up to 25 kHz [4]. Also creatures generate vibrations. Striking examples can be found throughout the animal kingdom and illustrate how ubiquitous vibrations are

E. A. van der Zee (*) Department of Neurobiology, Groningen Institute for Evolutionary Life Sciences (GELIFES), University of Groningen, Groningen, The Netherlands e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Rittweger (ed.), Manual of Vibration Exercise and Vibration Therapy, https://doi.org/10.1007/978-3-030-43985-9_2

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E. A. van der Zee

being used. For example, animals digging in noncohesive materials (granular materials) such as sand or dry snow do this with least resistance if they use a digging strategy with vibrations of 50–200 Hz and an amplitude of ~10 μm [5]. Man-made vibrations, often below 200 Hz, include, among many others, sounds from ships, drilling, explosions, wind turbines and seismic research in the marine environment. However, most of these vibrations are below detection-­ threshold for humans. The natural vibrations are too low in intensity to be consciously detected by humans, although we are endowed with different mechanoreceptors in the skin which are highly sensitive to most frequencies generated by nature. In contrast, in an urban environment people are exposed to well-­ perceived vibrations from different transport sources including heavy (truck) traffic, tramways, railways, or subways. In this chapter, I set out to illustrate that the detection of vibration is used for several functions, and that the human capacity to detect and utilize vibrations can be traced back to our early mammalian ancestors. Humans are sensitive to vibrations and it could be further employed to serve us. Notably the field of whole body vibration (WBV; using a mechanically vibrating platform to transmit vibration to the one standing or sitting on the platform) may profit from a better awareness of the origins of vibration detection and the future potentials it may have.

2.2

The Ancient Nature of Vibrational Communication

It has been argued that vibrational communication, next to chemical communication, most likely evolved from eukaryotic cell communication in the earliest animals [6–8]. A study with amoebas (Dictyostelium discoideum), a unicellular organism, in 1993 raised considerable interest in different fields of biology for the notion that vibrational movements of these amoebas were considered an essential component of self-organization in their shape [9]. More recently, vibrational studies in cell cultures revealed that also mesenchymal cells (multipotent cells that can differentiate into a variety of cell types) respond morphologically. Mechanical vibrations of 300 Hz (with a maximum amplitude of 10 μm) to mesenchymal cells caused the cells to align in a specific direction. The vibrations increased the metabolic activity of the cells during the differentiation process [10]. Another recent example is the finding that the formation of cell spheroids in cell cultures showed a 70-fold increase in the spheroid volume due to 60  Hz mechanical vibration [11]. It is suggested that the level of cell-cell interactions increases due to the vibration, which results in a change in the morphology. The observed finding is relevant for 3D cell cultures and optimally preparing cells for in vivo transplantation. Part of the above described findings can be viewed as cell-to-cell communication. A wealth of evidence exists about multicellular species using vibrational communication. Some of them will be touched upon below.

2  The Biology of Vibration

2.3

25

 ow Vibrations Are Being Used for Communication H in the Animal Kingdom

A common use of vibration detection is found in the domain of communication, either to exchange information between individuals of a species or between species [12, 13]. A challenge in the use of vibrational information is that due to physical constraints, the vibration signal quickly loses energy, faces filtering and gets distorted. This made many scientists believe it could not be used as a reliable source of information. However, nature found a way to cope with this. An array of evolutionary strategies have been developed to enable and promote the use of vibrational information despite the inevitable physical constraints existing in the habitats of all species (see [6], for review; see Box 2.1). Hence, vibration detection and vibrational information is used throughout the animal kingdom, including humans. What can we learn from the detection of vibrations by other species, and how is it used in nature?

Box 2.1 Evolutionary Aspects of Vibration

The sensory system responding to vibrations is relatively often overlooked by researchers. Sensory systems are primary drivers of evolution, as processing of the input from sensory organs during development determines the rewiring and adaptation of the brain and hence the behavior over generations. This is true for vibrational sense as well. Vibrations are all around us, assumingly already during the origin of life. The overall meaning of vibration in biology is to “keep in touch” with one’s environment, and to scan it. The main purpose of being able to detect vibration is, as is for all other sensory domains, to keep “in touch” with one’s environment. Vibrations are even more important for species or individuals with poor visual, auditory or olfactory senses. The vibration sense is being used in the animal kingdom to (1) detect prey, (2) avoid or threaten predators, (3) assess and navigate within a habitat or environment, (4) search for food and (5) communicate (for example, to find a mate, to ward off a competitor, to provide social interactions, or to send out an alarm signal). The enormous variation (called evolutionary radiation or adaptive radiation) of types of sensors to detect vibrations as well as devices to produce vibrations between and within animal taxa clearly demonstrates how important it is for survival and reproductive success to utilize vibrations. The fact that in mammals so many different brain regions (which dictate at large our behavior) are involved in the detection and processing of vibration signals further indicate the evolutionary relevance of this type of sensory domain. The evolutionary value in terms of survival (and the subsequent chance of having offspring) by detecting vibrations is nicely illustrated by egg-laying avian species. Recent findings showed that before hatching (and before the chick embryos produce sounds), chick embryos communicate with their siblings in

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a nest of eggs via vibrations (caused by embryos moving in their shell). Embryos move more if they hear alarm calls from their parents. Eggs not exposed to alarm calls but put in that nest experimentally were found to pick up the information by the “alarmed” nest-mates. It turned out that the alarmed chick embryos are physiologically better prepared to survive in their environment than the eggs that were never exposed to alarm calls or were not in contact with “alarmed eggs” [14]. Evolution has shaped life on earth, and clearly used vibrations as one of its tool boxes.

Vibrations are used, among others, by bacteria, mollusks, insects, spiders, amphibians, fish and mammals. It can be demonstrated across all animal taxa. When adhering to a surface, bacteria demonstrate random, nanoscopic vibrations around their equilibrium positions (see also Fig. 2.3E). It is assumed that these vibrations are a result of their metabolic activity and cell membrane dynamics. When giving glucose to bacteria, this further augments the vibrations. This hints at a possible relationship between metabolic activity and nanoscale bacterial movements [15]. These nanoscale movements are currently used to test antibiotics, as it was found that bacteria exposed to antibiotics stop producing nanoscopic vibrations. Some bacteria can grow faster if exposed to vibrations. When kept in syringes containing media, vibrations of either 0.33 or 1 Hz augmented their growth. Beyond single-­ celled organisms, probably all multicelled organisms respond to (or even employ) vibrations. To illustrate this, I will provide examples organized by the way the vibrations are transmitted: waterborne, substrate-borne or airborne. Together, these vibrations contribute to a vibrational landscape in biology (Fig. 2.1A).

2.4

Waterborne Vibrations

Life developed in water. Water is the active matrix of life, and creatures living in it are sensitive to waterborne vibrations. Examples of the use of vibrations in species that live in or around water are widespread, ranging from unicellular organisms to the largest whales. Various species of mollusks respond to waterborne vibrations. Some species have special organs to detect water vibrations, such as the abdominal organ in pectens (saltwater clams) [16]. Many studies have been performed using marine mollusks, showing their highest vibrational sensitivity in the range of 10–200  Hz ([17] and references therein). For example, Oysters transiently close their valves in response to water-borne vibrations in the range of 10–1 kHZ), on 1–4 Hz frequencies, but later studies made clear that frequencies between 20 and 90 Hz (seismic/substrate-­ borne vibrations) are typically generated, depending on the walking style [48]. Such vibrations in combination with the generated sound can become a disturbing issue in buildings and cause stress to the inhabitants. The vibrations generated by walking can also be employed. Seismic sensors are being used to detect anomalous vibrations within specific regions, such as at a border or near a military base that needs protection against unauthorized intrusion. Human and animal steps generate both substrate-borne vibrations, but their patterns differ as do the patterns of individuals. Although detection by sensors can be challenging due to a variety of reasons including differences in the composition of the ground and weather conditions, techniques are being developed to selectively discriminate human footsteps [49]. It is unclear to what extent human-raised vibrations are consciously perceived by other humans, but if they predominate at 20–90 Hz predominate, they fall within the sensitivity range of the Meissner corpuscles (sensitive between 5 and 150 Hz, with a peak sensitivity around 10–65 Hz; see Chap. 7). Due to harmonics it will also activate another skin mechanoreceptor, the Pacinian corpuscles (or pressure receptors, deeply placed in the skin, sensitive between 20 and 1000 Hz, with a peak sensitivity around 250 Hz). The human brain knows “the address” of skin mechanoreceptors, at least in the fingers and therefore most likely everywhere. This underlines our sensitivity to vibrations. The fact that there we have different mechanoreceptors responding to vibrations, with partly overlapping sensitivity to frequencies and varying adaptation speeds, already suggests that somewhere during the evolution of mammals, vibrations were important for the interaction between the host and the environment. Next to the environment, it is also used in the interaction between individuals (either of the same species or between different species). We inherited this sensitivity, and due to its evolutionary ancient nature, vibration detection is hard-wired in the body and brain (see Box 2.1).

2.8

Conclusion

It can be concluded that the meaning of vibration in biology is to “keep in touch” with one’s environment. The natural origin of vibrations and the large variety of solutions across the animal kingdom to employ them is eminent. All creatures create, consciously or subconsciously, vibrations. Eavesdropping on them can help the listener gain a significant advantage over those that do not or do worse. Because vibrations are an essential part of nature, it also provided humans with vibrational sense. Besides being able to detect them, humans also produce vibrations in various ways. Some of the anthropogenic vibrations can have serious downsides. These are predominantly in relation to unnatural, mechanical vibrations generated by

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mankind since the start of the industrial revolution. It should be realized that anthropogenic noise is not only about dBs but also about vibrations. For example, there is an increasing concern about the impact of noise on the marine environment, as water-­borne vibrations carry very far. As mentioned earlier, the sound of whales, as a water-borne vibration, is known to travel around the globe. Can whales maintain this type of communication? Increased awareness on the nature of vibrations and the positive and negative aspects of them is warranted, specifically in the field of WBV. WBV research has showed that vibrations when used appropriately can stimulate our muscles, physiology and brain. They can, for example, enhance attention and cognitive performance (see [50] and references therein). Notably the brain stimualtion by WBV illustrates that WBV can be of health benefit beyond the muscle stimulation for which it is best known.

References 1. Robertson SN, Campsie P, Childs PG, Madsen F, Donnelly H, Henriquez FL, Mackay WG, Salmerón-Sánchez M, Tsimbouri MP, Williams C, Dalby MJ, Reid S. Control of cell behaviour through nanovibrational stimulation: nanokicking. Philos Trans A Math Phys Eng Sci. 2018;376(2120):20170290. https://doi.org/10.1098/rsta.2017.0290. 2. Haxel JH, Dziak RP, Matsumoto H.  Observations of shallow water marine ambient sound: the low frequency underwater soundscape of the central Oregon coast. J Acoust Soc Am. 2013;133:2586–96. https://doi.org/10.1121/1.4796132. 3. Dubrovsky NA, Frolov VM. Thunderstorm as a source of sounds in the ocean. In: Buckingham MJ, Potter JR, editors. Sea surface sound ’94. Lake Arrowhead: University of California; 1996. p. 112–24. 4. Casas J, Bacher S, Tautz J, Meyhöfer R, Pierre D.  Leaf vibrations and air movements in a leafminer-parasitoid system. Biol Control. 1998;11:147–53. 5. Darbois Texier B, Ibarra A, Melo F.  Low-resistive vibratory penetration in granular media. PLoS One. 2017;12(4):e0175412. https://doi.org/10.1371/journal.pone.0175412. 6. Mortimer B. Biotremology: do physical constraints limit the propagation of vibrational information? Animal Behaviour. 2017;130:165–74. 7. Endler JA. The emerging field of tremology. In: Crofort RB, Gogala M, PSM H, Wessel A, editors. Studying vibrational communication. Heidelberg: Springer; 2014. p. vii–x. 8. Hill PS, Wessel A.  Biotremology. Curr Biol. 2016;26:R187–91. https://doi.org/10.1016/j. cub.2016.01.054. 9. Killich T, Plath PJ, Wei X, Bultmann H, Rensing L, Vicker MG.  The locomotion, shape and pseudopodial dynamics of unstimulated dictyostelium cells are not random. J Cell Sci. 1993;106:1005–10013. 10. Safavi AS, Rouhi G, Haghighipour N, Bagheri F, Eslaminejad MB, Sayahpour FA. Efficacy of mechanical vibration in regulating mesenchymal stem cells gene expression. In Vitro Cell Dev Biol Anim. 2019;55(5):387–94. https://doi.org/10.1007/s11626-019-00340-9. 11. Beckingham LJ, Todorovic M, Tello Velasquez J, Vial ML, Chen M, Ekberg JAK, St John JA.  Three-dimensional cell culture can be regulated by vibration: low-frequency vibration increases the size of olfactory ensheathing cell spheroids. J Biol Eng. 2019;13:41. https://doi. org/10.1186/s13036-019-0176-1. 12. Hill PS. Vibration and animal communication: a review. Am Zool. 2001;41:1135–42. 13. Hill PS.  How do animals use substrate-borne vibrations as an information source? Naturwissenschaften. 2009;96:1355–71. https://doi.org/10.1007/s00114-009-0588-8. 14. Mariette MM, Buchana KL. Good vibrations in the nest. Nat Ecol Evol. 2019;3(8):1144–5. https://doi.org/10.1038/s41559-019-0955-6.

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15. Şeker E. Bacterial vibrations. Sci Transl Med. 2013;5(196):196ec126. https://doi.org/10.1126/ scitranslmed.3007046. 16. Zhadan PM.  Directional sensitivity of the Japanese scallop Mizuhopecten yessoensis and Swift scallop Chlamys swifti to water-borne vibrations. Russ J Mar Biol. 2005;31: 28–35. 17. Charifi M, Sow M, Ciret P, Benomar S, Massabuau JC. The sense of hearing in the Pacific oyster, Magallana gigas. PLoS One. 2017;12:e0185353. https://doi.org/10.1371/journal. pone.0185353. 18. Coombs S, Gorner P, Munz H. The mechanosensory lateral line: neurobiology and evolution. New York: Springer; 1989. 19. Kasumyan AO. Sounds and sound production in fishes. J Ichthyol. 2008;48:981–1030. 20. Fine ML. Mismatch between sound production and hearing in the Oyster Toadfish. In: Tavolga WN, Popper AN, Fay RR, editors. Hearing and sound communication in fishes. New York: Springer; 1981. p. 257–63. 21. Cokl A, Virant-Doberlet M.  Communication with substrate-borne signals in small plant-­ dwelling insects. Annu Rev Entomol. 2003;48:29–50. 22. Hunt JH, Richard F-J. Intracolony vibroacoustic communication in social insects. Insect Soc. 2013;60:403–17. 23. Siehler O, Bloch, G. Colony volatiles and substrate-borne vibrations entrain circadian rhythms and are potential mediators of social synchronization in honey bee colonies. 2019. www. biorxiv.org, https://doi.org/10.1101/850891 24. Vallejo-Marin M.  Buzz pollination: studying bee vibrations on flowers. New Phytol. 2019;224:1068–74. 25. Shaw S. Detection of airborne sound by a cockroach ‘vibration detector’: a possible missing link in insect auditory evolution. J Exp Biol. 1994;193:13–47. 26. Kuszewska K, Miler K, Filipiak M, Woyciechowski M. Sedentary antlion larbae (Neuroptera: Myrmeleontidae) use vibrational cues to modify their foraging strategies. Anim Cogn. 2016;19:1037–41. https://doi.org/10.1007/s10071-016-1000-7. 27. Michelsen A, Nocke H. Biophysical aspects of sound communication in insects. Adv Insect Physiol. 1974;10:247–96. 28. Hayashi Y, Yoshimura J, Roff DA, Kumita T, Shimizu A.  Four types of vibration behaviors in a mole cricket. PLoS One. 2018;13(10):e0204628. https://doi.org/10.1371/journal. pone.0204628. 29. Schafer RM.  The soundscape: our sonic environment and the tuning of the world. Alfred Knopf: Rochester Vt, Destiny Books; 1977. 30. Klauer G, Burda H, Nevo E. Adaptive differentiations of the skin of the head in a subterranean rodent, Spalax ehrenbergi. J Morphol. 1997;233:53–66. 31. Nevo E, Heth G, Pratt H.  Seismic communication in a blind subterranean mammal: a major somatosensory mechanism in adaptive evolution underground. Proc Natl Acad Sci. 1961;88:1256–60. 32. Nevo E. Observations on Israeli populations of the mole rat, Spalax ehrenbergi Nehring 1898. Mammalia. 1961;25:127–44. 33. Catania KC. A nose that looks like a hand and acts like an eye: the unusual mechanosensory system of the star-nosed mole. J Comp Physiol A. 1999;185:367–72. 34. Gunther RH, O’Connell-Rodwell CE, Klemperer SL. Seismic waves from elephant vocalization: a possible communication mode? Geophys Res Lett. 2004;31(L11602):1–4. 35. Mortimer B.  A spider’s vibration landscape: adaptations to promote vibrational information transfer in orb webs. Integr Comp Biol. 2019;59(6):1636–45. https://doi.org/10.1093/ icb/icz043. 36. Caldwell MS. Interactions between airborne sound and substrate vibration in animal communication. In: Studying vibrational communication, animal signals and communication, vol. 3. Berlin Heidelberg: Springer-Verlag; 2014. https://doi.org/10.1007/978-3-662-43607-3_6. 37. Cocroft RB, Rodriguez RL.  The behavioral ecology of insect vibrational communication. Bioscience. 2005;55:323–34.

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38. Bennet-Clark HC.  Size and scale effect as constraints in insect sound communication. Phil Trans R Soc Lond B. 1998;353:407–19. 39. Ryan MA, Cokl A, Walter GH.  Differences in vibratory sound communication between a Slovanian and an Australian population of Nezara viridula (L.) (Heteroptera: Pentatomidae). Behav Processes. 1996;36:183–93. 40. Eriksson A, Anfora G, Lucchi A, Lanzo F, Virant-Doberlet M, Mazzoni V. Exploitation of insect vibrational signals reveals a new method for pest management. PLoS One. 2012;7(3):e32954. 41. Nieri R, Mazzoni V. Vibrational mating disruption of Empoasca vitis by natural or artificial disturbance noises. Pets Manag Sci. 2019;75:1065–73. https://doi.org/10.1002/ps.5216. 42. Mankin RW, Anderson JB, Mizrach A, Epsky ND, Shuman D, Heath RR, Mazor M, Hetzroni A, Grinshpun J, Taylor PW, Garrett SL. Broadcasts of wing-fanning vibrations recorded from calling Ceratitis capitata (Diptera: Tephritidae) increase captures of females in traps. J Econ Entomol. 2004;97:1299–309. 43. Polajnar J, Eriksson A, Lucchi A, Anfora G, Virant-Doberlet M, Mazzoni V.  Manipulating behaviour with substrate-borne vibrations—potential for insect pest control. Pest Manag Sci. 2015;71:15–23. 44. Mankin RW, Hodges RD, Nagle HT, Schal C, Pereira RM, Koehler PG. Acoustic indicators for targeted detection of stored product and urban insect pests by inexpensive infrared, acoustic, and vibrational detection of movement. J Econ Entomol. 2010;103:1636–46. 45. Pumphrey RJ. Hearing. Symp Soc Exp Biol. 1950;4:3–18. 46. Levänen S, Hamdorf D. Feeling vibrations: enhanced tactile sensitivity in congenitally deaf humans. Neurosci Lett. 2001;301:75–7. 47. Arnason BT, Hart LA, O’Connell-Rodwell CE. The properties of geophysical fields and their effects on elephants and other animals. J Comp Psychol. 2002;116:123–32. 48. Ekimov A, Sabatier JM.  Vibration and sound signatures of human footsteps in buildings. J Acoust Soc Am. 2006;120:762–8. 49. Faghfouri AE, Frish MB.  Robust discrimination of human footsteps using seismic sig nals. Proceedings of the International Society for Optical Engineering. 2011. https://doi. org/10.1117/12.882726. 50. Boerema AS, Heesterbeek M, Boersma SA, Schoemaker R, de Vries EFJ, van Heuvelen MJG, Van der Zee EA.  Beneficial effects of whole body vibration on brain functions in mice and humans. Dose Response. 2018;16(4):1559325818811756. https://doi. org/10.1177/1559325818811756.

3

Design Principles of Available Machines Rainer Rawer

3.1

Introduction

There is a plethora of vibration exercise devices available on the market, which makes it difficult even for professionals to have an overview. The situation is complicated by the fact that (mis)reporting of performance features by manufacturers is often inconsistent. Hence, the present chapter gives an overview of the main design principles for vibration platforms and the consequences that the design principles have for vibration parameters, application, quality, and durability. The oscillation parameters of a vibration device have an essential influence on its possible application for training and for therapy. The most relevant parameters are amplitude, frequency, and oscillation movement (e.g., sinusoidal wave-form). The most obvious difference of available devices is the movement principle of the platform (the plate the user is typically standing on). The majority of vibration training devices can be categorized according to [1]: 1.  Vertical movement The complete platform is moving up- and downward only. 2.  Side-alternating (pivotal) movement The platform acts like a see-saw with a central axis; therefore, while one side (foot) moves upward the other one moves downward. 3.  Circular horizontal movement The platform moves in a circle in the horizontal plane. 4.  3D movement Although some manufacturers use the term 3D movement as a marketing tool, all currently available systems use movements in only one or two dimensions plus rotation in the resulting plane. Therefore, the term 3D is a misleading concept.

R. Rawer (*) Research & Development Department, Galileo Training & Therapy, Novotec Medical GmbH, Pforzheim, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2020 J. Rittweger (ed.), Manual of Vibration Exercise and Vibration Therapy, https://doi.org/10.1007/978-3-030-43985-9_3

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Table 3.1  Oscillation parameters of the most common vibration training and therapy devices

Parameter Amplitude (mm) Frequency (Hz) Acceleration (g)b Application time (min)c Publicationsd Cost in US$

Vertical home use 1–2

Vertical high class 1–2

Vertical low magnitude