resistivity of body tissues at low...

Resistivity of Body Tissues at Low Frequencies

By Stanley Rush, Ph.D., J. A. Abildskov, M.D., andRichard McFee, Ph.D.

• A theoretical model capable of explainingthe relationship between the EMP generatedby the heart and the electrocardiographiclead voltages must be based on quantitativeknowledge of the resistivities of the tissuesof the thorax. At the time this study wasundertaken, the most recent investigations oftissue resistivity in living animals were thosewhose results are summarized in the firstthree columns of table I.1'2> 3 More recently,the results summarized in column 4 werepublished.4 Differences in results range from40% for lung to 400% for heart muscle,and no two groups of investigators are insubstantial agreement on all measurements.

An additional investigation of animal tis-sue resistivity is reported here and the con-clusions are presented in column 5 of table 1.A limited attempt was made to discover thesources of the discrepancies in previouslypublished data. This was done by repeatingthe reported measurement procedure, bytheoretical studies and by reviewing the workof other investigators. Both Kaufman andJohnston, and Schwan and Kay, employed atwo-electrode technique. Only the more re-cent work of the latter group was investi-gated in detail.

The present study appears to explain satis-factorily the existing differences in the re-ported resistivities of thoracic tissue with thepossible exception of lung.

MethodsMeasurements of specific resistance of tissue

were carried nut on approximately 50 live, anes-thetized, mongrel dogs weighing from 14 to 30

From the Department of Medicine, Upstate MedicalCenter, and Department of Electrical Engineering,Syracuse University, Syracuse, New York.

Supported by Research Grants H-3241 and H-3949from the National Heart Institute, U. S. PublicHealth Service, and by grants from the Heart Asso-ciation of Onondaga County, New York.

Received for publication July 16, 1962.

40

kilos. The anesthetic was 0.5 cc./kilo of pento-bnrbital initially with additional small doses asneeded. Observations of intact thorax and armresistivities were made on eight human subjects.

The basic technique employed was that of thefour-electrode measurement in which a controlledcurrent was introduced and removed from thespecimen being measured by means of two 'cur-rent' electrodes and a resulting potential differ-ence measured between two points on the specimenwith two additional 'potential' electrodes.

The current electrodes were connected to a cir-cuit shown in figure 1, consisting of a 540 voltbattery in series with a 4 megohm resistor and a.manually operated contact. The contact was closedfor about 0.1 seconds during the measurementthereby generating a pulse waveform at the po-tential electrodes with approximately the samefrequency spectrum as the QRS complex.

A potential difference was measured on thetissue surface by means of two needle electrodes,each connected to an open grid of a cathode fol-lower. The output of the cathode followers sup-plied the differential input of a Sanborn polyvisorecorder which recorded the voltage waveform onheat sensitive paper (fig. 2). The animal wasgrounded to the electrical system at points re-mote from the measuring electrodes.

Three distinct electrode arrangements were re-quired for the various measurements. These willbe designated by the letters A, B, C, as describedin the sequel.

The four-electrode method was chosen primar-ily to provide a means of eliminating the effectsof contact resistance variations on the measure-ments. Such effects were made negligible at thepotential electrodes by the very high input im-pedance of the cathode followers and at the cur-rent electi'odcs by use of a high voltage in serieswith a very high resistance as a. current source.The needles used for all potential electrodes in-sured exact knowledge of their locations on thetissue. The use of a square pulse as the measur-ing signal permitted detection of unusual polari-zation or other effects which might have beenassociated with measurement errors. The entireelectrode array was made small whenever this wasfeasible to minimize the effects of remote tissueson the measurements. Lastly, the same electrodeassemblies devised for isotropic tissues proveduseful for anisotropie measurements.

Electrode set A consisted of four needles whoseCirculation Research, Volume XII, January 19GS

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TISSUE RESISTANCE 41

TABLE 1Mean Resistivity in Ohm-Cm

Tissue

BloodLiverHeart

LungFatSkeletalmuscle(hunuin or dog)Skeletalmuscle(rabbit)Human trunkDog trunkTorso sheath (dog)

Column 1Kaufman and

Johnston

208506216

7442060

648

Column 2ufman and

van Milaan

160

Pi,= 470*P .= 230

415

Column 3Schwan and

Kay

100840965

11201500-5000

965

Column 4Burger andvan Dongen

160

Pu— 675*Pi = 245

p=1800*Pi= 125

Column 5Rush, Abildskov,

and McFee

162J700

Pi,= 563*Pi= 252

21002500

P,,=2300*Pi= 150

4634452 8 1 +

*Pi, and Pi are high and low resistivities of nnisotropic tissue.tData from only two subjects.{Data taken from the literature.

points touched the tissue at four equally spacedpoints along a straight line (fig. 3). Electrodes ofthis typo are commonly used in geophysical ex-plorations where the technique is called theWenner-Gish-Rooney method.5 The needles weremounted on a small plastic bar which in turn wasfixed on a V-shaped steel wire. The electrodeassembly was thus free to move in the verticaland horizontal directions to accommodate themovements of the tissue being measured (fig. 5).

The equation from which the unknown resistiv-ity, p, of the tissue was determined is0

V - (1)

in which 'a' is the electrode spacing, 'I' the cur-rent and VBh the potential difference measuredbetween electrodes 'g' and 'h'. Equation 1 appliesexactly when the electrodes are on the plane sur-face of a homogeneous, isotropic conductor ofinfinite extent which the tissue is assumed toapproximate.

For media which are anisotropic with one direc-tion 'y' of low resistivity, plt parallel to thebounding plane and with two high resistivity, ph,directions V and '-/,', (fig. 4) equation 1 becomes7

v _ VPI.PI I

2™ V c o s - 0 + (Pi/Pn) sin-' 0(2)

0 is the angle the electrode alignment makes withthe V axis. By aligning the electrodes alternatelyCirculation Research, Volume XII, January 1963

along the lines 0 — O, 0 = n/'2 we have fromequation 2

V,Pi,

(3)

From the two expressions in equation 3, ph and p]can be found.

Electrode Set B was devised to find the 'x' and'y' directions on anisotropic tissue and this in-formation was used, in turn, to orient Set A inaccordance with equation 3. Referring to figure3, it was formed by making the spacing e-h ande-f very large and arranging electrode 'g' so thatit could be placed sequentially at eight equallyspaced points on a circle centered at V. Elec-trodes V and were mounted on a commonspring assembly similar to that described Cor SetA. Electrode V pierced the center of a plasticbutton which had eight small holes equally spacedaround a circle of 0.5 cm radius. Electrode 'g'was arranged so that it could be withdrawn froma hole then turned and reinserted into anotherhole without disturbing the positioning of the re-mainder of the electrode assembly (fig. 5).

The equation for V around a circle of radius'a' is, with the exception of a small constantterm, given by equation 3. The constant term de-pends on the location of electrode 'h' and can bemade small by locating it far from the currentelectrodes. The values of V on the circle in anycase will, if plotted on polar coordinate paper,



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42 RUSH, ABILDSKOV, McFEE

FIGURE 1Current circuit for four-electrode measurement.V = 270 volts, R = 2 megohms and 'e' and 'frepresent point-electrodes through which a fixedcurrent passes when key is closed.

CONDUCTING/IMEDIUM

IFIGURE 2

Potential measuring circuit. Vl = 90 volts, Vs= 4") volts, Hh = 0.1 megohms and 'g' and 'h' arepotential measuring electrodes.

have maximum and minimum distances from theorigin at 0 = ir/2 and 0 = 0 respectively. Byrelating these directions to the tissue, the informa-tion required to orient Set A for use with equation3 is obtained.

Electrode Set C was employed to measure cy-lindrical sections such as the arm and thorax. Thetechnique is essentially that described by Burgerand van Milaan.2 Current was introduced andremoved from the specimen through large remoteelectrodes and the potential electrodes were formed

FIGURE 3Arrangement of four point-electrodes for meas-uring the resistivities of a semi-infinite (x > 0 aninsulator) medium.

by needles touching the specimen at points spacedalong a line parallel to the axis of the cylinder.In measurements of the thorax of humans, cur-rent was introduced through three electrodes atthe wrists and neck, and removed through twoelectrodes at the ankles in order to obtain a uni-form distribution in the chest. Similarly placedelectrodes were used for dog thorax measurements.

The electrodes at each end of the body were in-terconnected with 20,000 ohm resistors to minimizethe effects of skin resistance variations on thedistribution. On human subjects, the potentialelectrodes were formed by sterile hypodermicneedles spaced a measured distance apart with thetips placed just under the skin surface and theremainder insulated.

The equation for the mean resistivity of thecylindrical part being measured is

> = *-$-where 'a' is the distance between potential elec-trodes and A is the cross-sectional area of thecylinder. If the cylindrical part is in turn com-posed of 'm' parallel cylinders of different resistivi-ties, acting as resistors in parallel, the mean re-sistivity of equation 4 is given by

n = l P"(5)

in which An is the cross-sectional area of thecylinder of tissue identified by the symbol, n, and

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Set b

Set A

FIGURE 4

Arrangement of four point-electrodes for meas-uring the resistivities of an aiiisotropic, semi-infinte (z > 0 an insulator) conducting medium.

pn is the resistivity of that tissue. The total area,A, is the sum of the individual tissue areas. Equa-tion 5 is applied here to measurements on the armand thorax which are assumed to consist of cy-linders of fat, bone, muscle, etc.

That the electrodes actually performed in ac-cordance with the theoretical predictions of equa-tion 1 was checked by using a standard solutionfor which the resistivity, p, was known precisely.Tlie equation checked to a value well within thepredicted ± 5% construction tolerance of theelectrode array and remained constant for longperiods of time. In addition, during the resistiv-ity measurements, the applicability of the assump-tion of an infinite medium was evaluated for eachtissue. This was done by monitoring the thicknessof the layer being measured as well as the re-sistivity of the underlying layer and checkingthese against theoretical estimates of the effectsof these variables on the measurement.

In practice, the current 'I' and Vgh were notdirectly measured. Instead, at various times dur-ing an experiment, the electrode pairs e-g andh-f were connected to opposite terminals of avariable standard (Shallcross No. 835 Decade Po-tentiometer) resistance. After adjusting the cali-brating resistance, Rc, to give a pen deflectioncomparable to that produced by VRh of the mediumbeing measured, the calibrating potential differ-ence VKh is given by Ohm's Law as

V'Kh = RCI (6)

which combined with equation 1 for example givesVB1, P

Spring

Spring

2ml R,.(7)

FIGURE 5

Electrode Sets A and B showing spring assemblies,needle electrodes, plastic needle holders, and flex-ible wire connections.

The ratio Ysh/VKb is given by the ratio of pendeflections, hence p can be found.

ResultsTISSUE MEASUREMENTS

Unless otherwise noted, tlie data for eachtissue represents measurements on approxi-mately seven animals at one to three differ-ent sites on each animal.

Liver

The liver resistivity was measured usingelectrode Set A. The tissue was exposed byincisions through the abdominal wall or lowerribs depending on the experiment. The resultobtained by this method was 700 olim-t-mwith a per cent standard deviation oi: ± 14%.

Comparing this with the value of S40 ohm-cm given by Schwan and Kay, a differenceof about 18% is seen to exist. By repeatingtheir measurement, i.e., by measuring the re-sistance with a bridge between two electrodesmounted on a catheter-like holder and placedin the tissue, results essentially identical withtheirs were obtained.

The difference in the results given by thefour-electrode and 'catheter' electrode, meas-urements is probably not significant from theviewpoint of electrocardiograph}' but it isconsidered too large to be of a statisticalorigin. Two possible explanations are:

1. Polarization Errors. The method em-ployed by Schwan and Kay may be inaccu-rate because certain unverifiable assumptions

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were involved in deducing the corrections forpolarization. Burger and van Dongen havegiven credence to this possibility by measur-ing the frequency dependence of muscle andfinding none in the range from d-c to 5,000cycles. This is in direct contrast to the strongfrequency dependence for liver, muscle andother tissues reported by Schwan and Kay.If the resistivity of liver is also frequencyindependent in this range, a higher frequencymeasurement with the electrodes of Schwanand Kay should be more representative ofthe true situation since polarization effects(•an be expected to disappear as the frequencyis raised. Schwan and Kay measured a resis-tivity of liver equal to that given by the four-electrode method, 700 ohm-cm, in the vicinityof 5,000 cycles.

2. Boundary Effects. The effects of insulat-ing boundaries on a resistivity measurementwith a catheter electrode of the dimensionsgiven by Schwan and Kay3 were estimated byplacing the electrodes 0.5 cm from the wallof a glass beaker !) cm in diameter containinga solution of known resistivity. An apparentincrease of 15% in the resistivity of thestandard solution was observed. In makingresistivity measurements on liver and heartwith the same electrodes, it proved difficultto place the electrode structure so that theelectrode surfaces were consistently at dis-tances greater than 0.5 cm from the airboundaries. The latter therefore may be acontributing factor to the higher results ob-tained for several tissues with the catheterelectrode.

To summarize, we have obtained a valueof 700 ohm-cm for the resistivity of liverusing the four-electrode method. On the otherhand, using techniques similar to those em-ployed by Schwan and Kay, their publishedvalue of 840 ohm-cm was obtained. Thehigher values of the latter technique may beattributed to polarization and/or boundaryeffects.

HeartThe resistivity of the muscle of the left

ventricular wall of the dog heart was meas-

ured using in sequence electrode Sets B andA. The animal was placed on its right side,artificially l'espirated and the thorax openedat the fifth or sixth intercostal space. Theribs were spread apart, the intervening por-tion of the left lung pushed aside and thepericardium opened to expose the left ven-tricle. Electrode Set B was positioned on theexposed tissue and measurements were takensequentially with the electrode 'g ' at theeight indexed sites equally spaced around acircle centered at current electrode, e. Theresulting curve was plotted and directionsof high and low resistivity marked on thedog's skin. Electrode Set A was then alignedalternately with the marked axes and read-ings taken for use with equation 3. In allcases, the measuring signal was superimposedon the heart's electrical signal; but a largenumber of measurements randomly spacedin time yielded a sufficient number of meas-urement pulses in a relatively quiet and re-fractory portion of the electrical cycle forreadings to be taken. Additional measure-ments not described here, showed that theresistivities in the refractory portion andother parts of the electrical cycle were essen-tially the same. Corrections of the measuredvalues which take account of the effect of thecurved surface and the proximity of theunderlying blood layer were estimated bymathematical analyses. Since these were al-ways less than 20% and in opposite directionsfor the two variables, the net correction re-quired was assumed negligible.

The results of the four-electrode measure-ments showed a slight anisotropy of about2:1 with a high resistivity value of 563 ohm-cm and a low resistivity value of 252 ohm-cm.The per cent standard deviations were ± 15%and ± 30% for the high and low valuesrespectively. These are considerably lowerthan the value of 965 ohm-cm measured bySehwan and Kay. Their results however, wereobtained by measurements following poison-ing of the experimental animal and cessationof all electrical activity in the heart; andtherefore may not be representative of resis-tivity values prior to that time.

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TISSUE EESISTANCE 45

To investigate this question, a catheterelectrode and bridge was again employedwith a visual detection device (ECG pen).Crude balances could readily be obtained inthis fashion without affecting the heart'saction significantly and the mean value at50 cycles was thus determined to be 516 ohm-cm, in addition, upon administration of lethaldoses of barbiturates, a rapid rise in resistiv-ity followed. In two such experiments in-creases of 25% in 15 minutes were observed.

The value 516 ohm-cm obtained by us withthe catheter electrode is to be compared tothe result obtained using electrode Set A.Analytical considerations, based on the poten-tial solution for a sphere in an anisotropicmedium,7 indicates that the catheter elec-trode should measure about 1.13 vW>i- Thus,there is actually a fairly small discrepancybetween the results obtained by the twomethods corresponding to the figures 516 and430 ohm-cm. Again the former quantity isuncorreeted for polarization effects and pos-sible boundary influences both of which tendto give high values. In addition, the elec-trodes are not spherical in shape and theanalysis on this basis may contribute to thedifference.

To summarize, the measurement of themuscle of the left ventricle of the heartshows a resistivity ratio of about 2:1 withPi = 252 and ph = 563 ohm-cm. These valuesare far below that of 965 ohm-cm given bySchwan and Kay whose technique ignored theanisotropy and involved elimination bypoison of the electrical activity of the heart.By omitting the last mentioned step fromthe catheter-electrode procedure, values inreasonable agreement with the theoreticalestimates of such a measurement based onthe p\ and PI, given above, were obtained.

Lung

Electrode Set A, modified slightly to pre-vent piercing of the delicate tissue, was usedto measure the resistivity of lung. The dogwas placed in a crouching position andopened on both sides of the thorax at thefifth and/or sixth intercostal space. To pro-

vide the correct degree of lung inflation, therespirator pressure was monitored by a watermanometer and adjusted to provide a peakpressure equal to the peak pressure normallyexisting between the pleural cavity and thetrachea, i.e., 8 mm of Hg.s The hauncheswere raised 5.5 cm to compensate for theloss of negative intrathoracic pressure therebyminimizing the change in venous return dueto this factor. The electrodes were held inplace manually and resistivity measurementswere taken at the extremes of inflation anddeflation.

The resistivities corresponding to the peakof inflation and maximum deflation duringthe forced breathing cycle, were found to be2,390 and 1,950 ohm-cm respectively, with amean of 2,170 ohm-cm. The per cent standarddeviation of the measurements was ± 17%.

The ratio of lung resistivities as measuredby ourselves and Schwan and Kay can beseen from table 1 to be about 2:1. The meas-urements of the latter group have the advan-tage over ours of being performed in a closedchest. On the other hand, the catheter elec-trode assembly was placed in the bronchi orpulmonary arteries which are conceded tohave an effect on the measurements.3 Themagnitude of this effect was estimated bySchwan and Kay from measurements on ex-cised bronchi. Measurements of excised tis-sues, however, may not yield values repre-sentative of their in situ characteristics. Inaddition, it was not possible to observe theactual situation around the electi'odes withregard to their location, tightness of fit ofthe bronchi about the electrode, collection offluid about the electrodes, proximity to majorblood vessels and possible collapse of thelung about the plugged airway.

In the present study, measurements weremade at a variety of locations with the elec-trodes in view on the outer surface of thelung. Factors which arose from the openchest condition were accounted for as de-scribed. In addition, measurements of thelung made through the pleural membrane inan intercostal space with the chest interiorstill airtight, though too erratic to give quan-

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TABLE 2

Results of 4-Electrode Measurements of Skeletal Muscle

Electrodeconfiguration

A

AAG

Tissue

(longissimus dorsiand spinalis dorsiet cervicismuscles of dog)human arm muscle

Parameter(averagevalue)

Pi,

PI

(PLPI)1/2

PI

Valueohm-cm

1885

205*588itiOt

Per centstandarddeviation

48%

40%10%10%

Number ofmeasurements

14

.14145

*Pi is obtained by combining direct measurements of VPi,/>i and p (see equations 4 and 5).tMeasurenients of arm corrected for bone and fat, but not for deviations of fiber directions

from axis of measurement.

titative results, clearly indicated a resistivitymuch higher than the 1,100 ohm-cm reportedby Schwan and Kay.

Finally, since the measurements discussedwere made in different regions of the lung,one in the interior and the other on theouter portion, it is possible that both arecorrect representations of the conditions intheir respective regions.

To summarize, a mean value of lung tissueresistivity over the breathing cycle has beenmeasured at 2,150 ohm-em. This is in con-trast to a value of 1,120 ohm-cm, reported byScliwan and Kay. The low values of the lat-ter measurements have been attributed to theuncertain conditions around the electrodes,most of which would tend to lower the highvalue we have measured, and/or the fact thatthe interior of the lung around the bronchiand arteries actually may have a lower meanresistivity than the regions nearer the outerlung surfaces.Fat

The resistivity of fat was measured withelectrode Set A on various layers on thechest wall of the animal. The results, table 1,show a value of 2,500 ohm-cm with a largeper cent standard deviation equal to ± 30%.

Sehwan and Kay list a range, 1,500-5,000ohm-cm at 1,000 cycles/sec, as the only re-sistivit3r data on fatty tissue, and these maybe considered in agreement with the resultsof this study. Further discussion of the sub-cutaneous fat layer will be found in the sec-tion on skeletal muscle.

Skeletal MuscleThe resistivity of skeletal muscle was meas-

ured with electrodes Sets A, B, and C. Themarked anisotropy of the muscle presentedspecial difficulties necessitating a fairly com-plicated procedure to obtain both the high andlow resistivity values with satisfactory accu-racy. The final results, table 1, are 2,300 and150 ohm-cm in directions transverse andparallel respectively to the muscle fibers.

Electrode Sets A and B were employed tomeasure the resistivity of the muscles alongthe spine of the dog, (these were selected onthe basis of their thickness) in a fashionsimilar to that used on the heart. Tn thiscase, however, measurements with Set Bindicated that visual observation of the fiberdirections satisfactorily indicated the paralleland transverse directions.

The results of these measurements, table 2,showed \/PIP], = 5SS ohm-cm with a per centstandard deviation of ± 10% and ph = 1,885ohm-cm with a per cent standard deviation of±48%. The combination of these values givesp, = 265 ohm-cm with a per cent standarddeviation of ± 40%. The large spread of themeasurements of pn is attributed primarily tothe extreme sensitivity of this measurementto the electrode orientation. Errors in orienta-tion tend to give lower than true values ofph, equation 2. The calculations of pi reflectthe variability of the p,, measurements. Onthe basis of these results it was concludedthat the measurement of \/PHPI

w a s satisfac-tory but that other procedures described later,were necessary to evaluate ph and p,.

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An independent estimate for Pi was de-duced from the measurements on the humanarm. Electrode Set C was used. Current elec-trodes were located on opposite wrists. Poten-tial electrodes were located on the dorsalsurface of the forearm approximately 5 cmdistal from the elbow. The mean longitudinalresistivity of the arm was computed usingequation 4. This measurement reflects pri-marily the value of p\ but corrections for theeffect of bone, subcutaneous fat, and skewedfiber directions are necessary. The correc-tions for bone and fat are based on equation5.

The bone was taken as a non-conductor asindicated by measurements on the exteriorwall of excised bone and by other investiga-tors.-' u The effect of marrow was neglectedbecause there is no apparent low resistancepath to the bone interior. The area of thebone was taken from an anatomical atlas andwas assumed the same on all subjects.

The skin and subcutaneous fat layer ofthe arm were taken to have the same re-sistivity as the fat measured on the chestwall with a thickness determined as one-half the measured skin-fold dimension. Tosubstantiate this choice of resistivity valuetwo additional considerations were takennote of. First, while attempts to measure theresistivity directly of this layer on the doggave erratic results the minimum estimateso obtained was of the order of 900 ohm-cm.In view of the relatively small cross-sectionalarea of fat relative to the total arm cross-section and the shunting effect of the muscle,even this lowest value would change the fig-ures presented by no more than 6%. Second,statistical considerations indicate that the fatcorrections improve the data. For example,the per cent standard deviation of measure-ments of the arm before fat corrections was± 20% while the same statistic was reducedby the corrections to ± 9%.

These two corrections for inhomogeneity,that is for bone and fat, applied to the valueof 234 ohm-cm for the whole arm, give avalue for the longitudinal resistivity of themuscle of 160 ohm-cm.

The non-parallel orientation of the musclefibers was considered also. For anisotropicmaterials with a high ratio of resistivities,analysis shows that the appropriate correc-tion factor is closely related to the additionallength of the fibers, due to skewed directions,between two planes perpendicular to theaxis. The maximum mean deviation of thefiber directions, as read from an anatomicalatlas, from a direction parallel to the axiswas estimated to be 30°. The correspondingfactor, cos 30° = 0.875, applied to the upperbound of 160 ohm-cm yields a value of 140ohm-cm as a lower bound. The mean of thisrange, i.e., 150 ohm-cm, has been taken asthe best estimate for p\ of skeletal muscle.

Using the value V iPn = 588 ohm-cm ob-tained with electrode Set A and p\ = 150ohm-cm as described above, ph was calculatedto be 2,300 ohm-cm.

Measurements by Burger and van Dongen,table 1, on rabbit muscle yield 125 to 1,800ohm-cm, results which closely approximateours. Their measurements on human armsand legs, however, give results for skeletalmuscle which are lower for ph and higher forPi. If, in computing p\, they had taken intoaccount the subcutaneous fat and the im-perfect alignment of the muscle fibers withthe axes of the arm and leg, their resultsfor this parameter would have been compara-ble to ours. The low values they attributedto ph from measurements transverse to theaxes of the arm and leg may have been dueto the deviations of muscle fiber directionsfrom these axes. Even small deviations ofthis type can be shown to have a very largeeffect on their transverse measurements.

The value presented by Schwan and Kayfor muscle, 965 ohm-cm, represents somekind of mean value of resistivity for aniso-tropic tissue. An analysis similar to thaidescribed in the discussion of the heartindicates that according to our results, thecatheter-electrode should have given valuesbetween 820 and 700 ohm-cm depending onelectrode orientation. As in the measurementsof liver and heart, the two-electrode tech-

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Transverse

direction

Radial direction

Longitudinaldirection

FIGURE 6

Reference directions on torso.

nique gave results about 20% higher thanthe four-electrode measurement.

To summarize, a value of 150 ohm-cm forP\ of skeletal muscle was deduced from var-ious measurements of the whole arm andtissues therein. The geometric mean of theresistivities, y/ptj>i, was obtained from directmeasurements on skeletal muscle with elec-trode .Set A. The combination of results gavethe high resistivity value, ph, as 2,300 ohm-cm.

These numbers agree reasonably with otherdirect measurements on muscle; those ofBurger and van Dongen on rabbit muscleand those of Schwan and Kay on dog mus-cle. In addition, the method of obtainingthese results, i.e., by correcting for the fatlayer, explains how the human arm resistiv-ities given by Burger and van Milaan andBurger and van Dongen are to be reconciledwith the latter group's measurements of p,of rabbit muscle.

Blood

Measurements of human blood resistivitywere not carried out in this study. The litera-ture of four2' *• 9p10 investigations showsagreement within ± 3% of their mean value

which is reported in table 1, i.e., 162 ohm-cm.Further, of these studies, two were madewith a four-electrode technique and two witha two-electrode technique. Correction factorson which there is substantial agreement,were necessary to normalize all the resultsto a common temperature of 37°C.

The value of 100 ohm-cm mentioned bySchwan and Kay3'9 for human blood isbased primarily on measurements of sheepblood.12 It is well known, however, that bloodresistivity is critically dependent on thehematocrit which in turn is a function ofred cell size and count.10 The last mentionedfactors are markedly different for sheep thanfor humans or dogs. By using the data onblood count and serum resistivity given inSchwan's paper and relating the blood countto hematocrit from data on sheep blood countsand hematocrits given by Wintrobe,13 it ispossible to reconcile the 100 ohm-cm valuefor sheep blood quite naturally with thevalues for human blood quoted here.

ThoraxA number of measurements of the human

thorax, dog thorax and of dog thorax minusheart and lungs were made with electrodeSet C. The current electrodes were connectedas described earlier. The potential electrodeswere placed along a line parallel to the spineon the side of the body. They were spaced6 cm apart and centered at the level of thecenter of the heart.

Seven measurements were thus made of theresistivity of the human thorax with a meanof 463 ohm-cm.

On the intact dog thorax, a mean of 445ohm-cm was measured.

To measure the thorax minus heart andlungs, the dog was placed supine and openedalong the sternum. The inferior vena cavaand esophagus were cut and tied and theheart and lungs encased in a plastic bag,after which the measurements were made.The cross-sectional area of the exterior shellwas obtained by moulding a strip of solderaround its perimeter. This mould was latertraced and the area measured with a planim-

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eter. The average of two such measurementsof the shell resistivity was 281 ohm-cm.

The results obtained for the human thoraxwere compared with an alternate estimate ofthe mean thorax resistivity based on theresistivities of the individual tissues, equa-tion 5. The tissue resistivities used were thoseobtained in this study. The tissue cross-sec-tional areas were obtained by averaging theareas shown in Sections 25 and 26 of Eyclesh-ymer and Schoemaker's/l Cross-Section Anat-omj/. In order to treat the highly aniso-tropic muscles of the chest as a single tissuein equation 5, it was necessary to choose arepresentative value for the muscle resistiv-ity in the thorax measurement. Anatomicaldata show the different muscles on the chestalmost randomly distributed over the longi-tudinal and transverse directions (fig. 6).Theoretical considerations, based on randomdirections, give (IR/2) p\ as the appropriatevalue for muscle in the thorax measurement.

The mean value for the thorax based onindividual tissue measurements was thus cal-culated from equation 5 to be 500 ohm-cm;8% higher but substantially in agreementwith the value measured on the trunk ex-terior.

SUMMARY OF RESULTS

The resistivities of lung, fat and liver asmeasured by the four-electrode Set A arecontained in table 1. The per cent standarddeviations of the readings from their meansare 17%, 30% and 14% respectively. Thevalues of resistivity reported for heart mus-cle in table 1 are those obtained by assumingthe heart to be a semi-infinite homogeneousanisotropic medium bounded by a plane sur-face. The per cent standard deviations for ph

and PI are 15% and 30% respectively. Theestimates of pt and ph for skeletal musclereported in table 1 were obtained by combin-ing a variety of measurements as explainedearlier. Eesults of actual measurements withelectrode Sets A and C are reported in table2 for the longissimus dorsi and spinal is dorsiet cervicis muscles along the spine of thedog and for the human arm muscle.

FIGURE 7

Schematics of resistivity models of thorax.

The mean resistivity of the human and dogthorax was measured in a direction parallelto the spine using electrode configuration ' C'.The values given for human blood have beenobtained from the literature. These resultsare also presented in table L

DiscussionIt was necessary to make most individual

tissue measurements (fat, lung, heart muscleand liver) on dogs and to assume that theseare representative of human tissue. The nearequality of the mean thorax resistivities ofhumans and dogs supports this assumption.

That the predicted value of human thoraxresistivity, based on measurements reportedin column 5 of table 1 and anatomical data,is within 8% of the value of the measuredthorax resistivity; lends some support alsoto the measurements on the individual tissues.

The existence of a surface layer of lowresistivity covering the thorax is of signifi-cance in electrocardiograph}7. McFee andParungao10 have reported an anomalous effectin making measurements on lead systemswhich they attribute to this factor.

The work reported here has bearing on themodels used to investigate the nature of elcc-trocardiographic leads. Among such modelspreviously used are (a) the homogeneousthorax, (b) the homogeneous heart-bloodmass with higher resistance exterior,16 and(c) blood cavities of low resistivity sur-rounded by homogeneous tissue of resistivityten times higher.0 The data of this studypresent a more complex picture as can beseen in the schematic drawing of figure 7 inwhich a mean resistivity of 400 ohm-cm forthe outer thorax layer; skin, fat, muscle, andbone has been used,

Circulation Research, Volume XII. January 196$



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SummaryThe resistivity of tissues of the thorax of

dogs has been measured in situ under nearlynormal conditions. Additional data have beenobtained from humans.

Approximate values of tissue resistivityfound are 160 ohm-cm for blood, 2,000 ohm-cm for lung, 2,500 ohm-cm for fat, 700 ohm-cm for liver, 250 and 550 ohm-cm (aniso-tropic) for heart muscle and 150 and 2,500ohm-cm (anisotropic) for skeletal muscle.Reasons for the differences between these andpreviously reported values have been found,and in some cases, verified experimentally.Predictions of whole trunk resistivity basedon anatomical data and these measurementsare within 8% of actual trunk measurements.

References1. KAUFMAN, W., AND JOHNSTON, F. D.t The elec-

trical conductivity of the tissues near theheart and its bearing on the distribution ofcardiac action currents. Am. Heart J. 26:42, 1943.

2. BURGER, H. C, AND VAN MILAAN, J. B.: Measure-

ments of the specific resistance of the humanbody to direct current. Act. Med. Sennd. 114:584, 1943.

3. SCHWAN, H. P., AND KAY, C. F.: Specific resist-

ance of body tissues. Circulation Research 4:664, 1956.

4. BURGER, H. C, AND VAN DONGEN, R.: Specific

electrical resistance of body tissues. Physicsin Medicine and Biology, vol. 5, 4: 431, 196.1.

5. HEILAND, C. A.: Geophysical Exploration. NewYork, Prentice-Hall, 1940, p. 29.

6. HEILAND, C. A.: op. cit., p. 645.

7. BUSH, S.: Methods of measuring the resistivitiesof anisotropie conducting media in situ. Journalof Research of the National Bureau of Stand-ards, Section C: Vol. 66C, No. 3, July-Sep-tember, 1962.

8. FULTON, J. F.: Howell's Textbook of Physiology.loth Ed., Philadelphia, W. B. Saunders Co.,1946, p. 866.

9. SCHWAN, H. P., AND KAY, C. F.: The conduc-

tivity of living tissues. Annals of N. Y. Acad.of Sci., vol. 65, Art. 6: 1007, 1957.

10. HIRSCH, F. G., et al.: The electrical conduc-

tivity of blood, I. Relationship to erythrocytoconcentration. Blood 5: 1017, 1950.

11. ROSENTHAL, R. L., AND TOBIAS, C. W.: Electrical

resistance of human blood. Journal of Lab.and Clin. Med. 33: 1110, 194S.

12. RAJEWSKY, B., AND SCHWAN, H. P.: Uber die

individuelen Schwankungen des spczifischenWidcrstnndos von Blut und Serum. Zeit. f.d.ges. exp. Med. 113: 553, 1944.

.13. WINTROBE, M. M.: Clinical Hematology, 4th Kd.,

Philadelphia, Lea & Fobiger, 1956, p. 1129.

14. EYCLESHYMER, A. C, AND SCHOEMAKER, D. M.:

A Cross-Section Anatomy, New York, Appleton-Century-Crofts, Inc., 1911, pp. 65 and 67.

15. MCFEE, R., AND JOHNSTON, F. I).: Elcctro-

cardiographic leads. Circulation 9: 868, 1954.16. MCFEE, R., AND PARUNGAO, A.: An orthogonal

lead system for clinical electrocardiograph}'.Am. Heart J. 62: 93, 1961.

Circulation Rcucarch, Volume A'//, January 1963



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STANLEY RUSH, J. A. ABILDSKOV and RICHARD MCFEEResistivity of Body Tissues at Low Frequencies

Print ISSN: 0009-7330. Online ISSN: 1524-4571 Copyright © 1963 American Heart Association, Inc. All rights reserved.is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation Research

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