The Dielectric Properties of Biological Specimens at Microwave Frequencies

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tftg BIELlOfjBXC ¥%QfW6fftM OP BIOLOGICAL S$86BM$ AT MICiSOWAfB f’ SUSQOBHOIM

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It earn new be mom that if I5 « ||

k2 f equation (a*22) redness to

sere indicating no reflection while aquation (2*23) become* ecjtaal to Otto for total tntniBdssio&i fiirfiiii»i,y the impedances are matched at tlxo second boundary and thus if medium 3 la lossless then all the incident power wUX he transferred to medium 2. It la therefore important to know the dieleetrie properties of ell tissues su-eb as fat,

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4 wave of intensity 2 Just inside the first surfsee of a dieleetrie ie attenuated te a value of 1(a) at a distance *** in the aaterial a« shown in fig*. 2* this attenuated wave ie expressed byi -•PC*

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* 3T-^JS"tan S »(*) V Be A u

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fhe wave 1# thus decreased te 1 (about 37 per cent) of its original value ie a distance* *•

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this distastes is defined as the depth of penetration of ttte wave* Blues the heat produced by a save is proportional to the intensity, It ie of Interest to detemine the depth of penetration of heat for various materials* the offsets of heat conduction or radiation era neglected and the eaterlal Is considered to he of uniform dielectric properties. iseuwe a material such as polystyrene with k * 2*5 and tan S m 0*0004 at a wavelength of 10 cm* fhe depth of penetration

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la by Eq* 2.3»*

(0*0004)

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the transmitted wave travels 5*000 am* Into the dieleotrle before of it* intensity In the material* How eonslder a material snob an salt water with k « 81 and tsn S * 0*20* the depth of penetration becomes * »

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tht dltitottlo properties of a material dotsniae the amount of electromagnetic radiation refloated and tbo depth of penetration or depth of boating*

3*0 Measurement of Dleleatrio Propertiea Thor© are many methods for measuring the dielectric constant and leas tangent of materials* Bash method haa son© limitation such as frequency range* else of sample required* ©to* k study of the various method* was made to determine the one neat suitable for measuring biological specimens* done of the basis methods are deearibed briefly for eomperlsem*

5*1 Sueeeptance Variation Method* One of the nest widelyused methods for measuring the dieleetrie properties of materials at loser frequencies has been deeerlbsd by Hartshorn and Ward (12). the dieleetrie sample to be measured is mounted between parallel plates

ef the same area a* the sample* % e n the dieleetrle under test is replaced by air (vacuum) , the electrode spacing and alignment re* mslnlng unchanged* and neglecting edge or fringing correction®* the equivalent parallel capacitance Cp will become the *inter«leetrodc capacitance," % *

By definition, the dielectric constant k la given

bsn 0*1} the dielectric constant is therefore determined by the change in capacitance due to the dielectric sample* The loss tangent le found by the change in dleelpation factor or 1/Q of a resonant circuit due to addition of the dielectric sample* 4 eireuit diagram of one sueeeptaitee variation method is shown in Fig* 4* 4 radio*frequency oscillator furnishes to reeleter & a constant current which le measured fcgr the radio~frequeney ammeter 4* the resonant circuit le composed ef a fixed inductor 1 and & calibrated variable air capacitor 6* A vacuum tube voltmeter V is connected to measure the voltage developed aeroas G* the dissipation factor of the entire eireuit is the ratio of the voltage drop across the reeleter I due to current 1 from the oscillator to the voltage developed across with a known 1 and H* the voltmeter can he calibrated directly in terms ef Q* measurement of the dielectric sample is accomplished as follows!

Fig,

4 - Susceptance

variation

method

19

x O

H h

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(ft) fhe eireuit la tuned to resonance as indicated by aarlamwtvoltage byadjusting the capacitor 0 or the

frwpoasy of the

oscillator* (b) headings of the voltmeter and capacitor are designated as % and % respectively* (a) the specimen capacitor, eitli electrodes affixed, is thenoonduoted by short iow resistance leads to the terminals of the capacitor 0% the eireuit is rebaned to resonaaee by reducing capacitor g and the readings of voltage and capacitance % and €2 *re noted* (3.2)

then* (3.3) (3.4)

Dharal Gp m capacitance of the epeeiawa is alero-nierofarads % « oapaeitanoe of the standard air capacitor without specimen, in ailereHnierofarads §2

m eapaeitanee of the standard air capacitor with speci­ men, in mtero-mierofarade

C* * calculated »alr capacitance* of the sample holder plates

0 » .2249 is

Ay * « m of the specimen holder plates In square inches d » measured thickness of the specimen, la inches % * dissipation factor indicated by voltmeter with specimen disconnected * dissipation fatter Indicated by voltmeter with specimen eomneoted la fperelftel When the voltmeter it. calibrated la terms ef storage faster Q, Sq« 3*1 l) beeomesi tan£

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where! % « storage factor with sample disconnected 02 ** storage faetor with sample connected This method ha» been satisfactory for frequencies fro* XO kilocycles per second up to 100 megacycles par second. the measurements are greatly facilitated by a test Instrument Incorporating the oscillator, vacuum tube voltmeter, ammeter and calibrated capacitor in one unit* Such am instrument is called a 0*Mater end is shown in fig# 5*

3.2

BtwnHW» StaaUEt BsSbat* it frequencies above 10®

megacycles per second the dimension* of the coll and capacitor become unusually smell#, the Q values of lumped constants such as a coil and capacitor bseome too lew to measure the less factor of low-1©*#

Fig,

5 - Q-meter

n

22

23

materials* Also land inductance and stray capacitance become critical and eater as measurement errors* d method ef measuring dielectric properties at frequeneies above 1GQ megacycles par second has been described by Works (13) An wfeicti a closed resonant cavity we* substituted for the aoil and capacitor circuit* The cavity resonator la essentially « abort* circuited quarter wavelength coaxial transmission Una with capacity loading at tha open and of tha line* the capacitor causes the physical length of Una to ha less than an actual one-fourth wavelength* the cavity described la a doubly ra*antrant cylindrical cavity having a gap la tha center conductor near one and of tha cavity* Tha width of this gap which represent* a lumped capacitance is variable ty scans of a micrometer mounted on tha top of the cavity* Oscillator energy la coupled to and frost the cavity by snail loop* placed at currant maximum paints* Output from tha cavity is rectified by a crystal rectifier and tha resultant current read by a sensitive galvanometer or microammeter* Measurement of a sample la made as follows* (a)

Tha sample of the same diameter as the center post

is centered between the electrodes*

Tha cavity is closed and the top

electrode brought into contact with the sample* The sample then fills tha gap in the canter post* The electrode separation with sample in place is determined by the micrometer and is designated D^*

u

(b)

lb# frequency of the oscillator is varied until the

resonant frequency (maximum response) of the cavity is found* fit# cttipui voltage 1# read as ?x*

(ft was determined that the output

current of the crystal was proportional to

in the cavity*)

(0) With the oscillator remaining at th# resonant frequency, th# Sample is removed fro# the cavity. fb* cavity i# reiuaed to resonance by closing th# gay and th# electrode separation Bg f* noted* Heading of output voltage i« designated a# f0i Weglecting fringing and other correction# to be discussed later, the equation# for k and tan S arc th# same a# in the coil and capacitor ncthod previously cit#d a# the electrode separation is pro* portions! to the capacitance of the gay with fined area* fhle method offer# the following advantaged (1) the samples required are of simple diak shape and are small* (2) Beth measurement* and calculations are simple, msking possible rapid determination of both dielectric constant and power factor* (3) Measurement# can be mad# quickly. (4) The equipment involved Is not too elaborate. 3«3 flfoiyjfog Wave Measurements, Another method of measuring dieleetrie properties of materials has bean described by Boherte and Won Bippel (14)* this method is based on the principle that any

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impedance terminating a transmission lime can be evaluated is terms of the characteristic impedance of the line by measurement of the relative magnitudes of tb© field strength maxima and minima (standing wave ratio) end their location with respeet to the terminating loHteea Xa this method the terminating impedance consists of a sample-filled portion of waveguide eloeed by a short-circuiting plug which approximates an ideal reflecting surface* A determination of the impedance of this sample-filled line (by the standing wave method) permits the calculation of its propagation function *hloh9 combined with the measured length of the saaple, can in turn be need to evaluate the dielectric properties of the material*

A diagram of this standing

nave method is shown la fig* 6* the calculation of the propagation function of the material being tested is rather complex bat la summarised as foXlowsi The ration ^m/Seam* the distances \ and d and wavelength A * are measured* from these measured values 0 and $ are calculated from the following equation* ^max

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that the change froa room tespenature bo body temperature should pro**«• * negligible Chang* in the results* Although aaiaal specimens were measured# the resalta should eonpare with food accuracy to the properties of him m speeinens* 10*0 Conclu*!opg It in evident froa the results of the meaeureaenbs that the dielectric properties of nosb body constituents one not significantly different from the properties of salt water* thin and ousels containing rather high percentage water content hare approximately the enae dielectric constant as water#

Speeisezis with

lower water content such as fat and hone here much lower dielectric constants* the influence of miter content on the dielectric constant of Materials mis observed in the calibration of the cavity#

Addition of

leas than 5 per cent water to dried ethylene glycol increased the dielectric constant froa approximately 12*5 to 26*

So discussion of

the dielectric constant as a resalt of airing Materials of different dielectric constants was found in the literature* Whole bleed was measured and then allewed to coagulate in the sample cup chile measurement was being node* Mo change in the dleleetrle properties of the bleed was observed during coagulation* Xi was again concluded that the high water content of the bleed determined the dielectric constant.

tfsasarsnsnt* of ski* spoeisens froiwrtloo similar to water.

prediissa disleetrle

f h m tfee akin layer of tbs M y i*

•nffioiont to m m # a high perssatage of tbs incident pens* i» ir~ radioUon to to reflected at the surface.

fatty tissas, boas and boa* starrs* nsssttrsd loo dlelesirls constants and loos tangents* these materials hews loo water content •ad are thus fairly b at i p t m l to aiorowavo radiation*. A layer of subcutaneous fat any possibly set as a natchlag ,section to dsejwr tissue# The aaoauat of energy passing through the akin should bo rather blab due to tbs thismoos of the ekla layer. Reflection* fron the akin to fat and free the fat to ansels boundaries aboald bo decreased by tbs fat layer* Also if tbs fat layer is m Sid mltlple of a qaartozMvars la thickness# an impedance natch nay occur as described previously* baraia tissue bas a rather hi#i dielectric constant bat a Is* loss tangent* Ibis indicates that although sons energy say bs reflected at tbs brain surface, tbs transmitted power sill penetrate rather dssjOy before being absorbed*

Tbs thin section of shall boas

say also toad to serve as a matching section to reduce reflection at the braia surface* fbs results of tbs measurements are of the same magnitude as tboss reported by otber experimenters. Sharpies and SftgJend (6) find tbs disisetrie constants of blood sad akin range from 50 to 70 sad tbs dielectric constant# of fat sad boas rang® froa 4 to 7*

flMMMi v m a M m m X m ihew that high mte* eonient iaereaee* the ^ 'OXeetipie conetftnt#

X0*X ffmntrr- **»*• Ssfeeetigettos resulted Is the develop »«nt of e Bethod of manuring the dielectric jwopeYtie* of biological 'epeelaese et slez'oveee frequencies.

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