Capacitive Properties of Body Tissues
By HEHMAN P. SCHWAN, P H . D . AND CALVIN F. KAY,
M.D.
The electric capacity of various tissues surrounding the heart has been investigated in living dogs,
using frequency ranges from 10 to 10,000 c.p.s. Electrode polarization, a serious source of error in
such measurements, has been corrected for. Discussion of our results and of resistivity data previously obtained in body tissues proves that the electric properties of body tissues are primarily
resistive ones.
T
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HE electric activity of the heart can be
studied only indirectly by means of the
small fraction of the heart potential that
reaches the body surface. So far it has been
assumed that the electric properties of the
tissues that separate the heart and body surface are purely resistive and establish a homogeneous volume conductor. While the assumption of homogeneity of resistivity has been
found valid1 no investigation of possible nonresistive components of the body tissues has
been conducted in situ. Investigations of the
electric properties of excised muscle tissue
were conducted at low frequencies.2 The ratio
of capacitive to resistive current which we
calculated from these data is shown in table 1
as function of frequency. These ratios, while
small, are indicative of noticeable reactive
current components. Since the capacitive
components had been found to deteriorate
rapidly with time in excised tissue2 the possibility exists that considerably larger values
exist in situ.
If tissue impedance should include a noticeable reactive component, the transfer impedances which are defined by body surface potentials and current generated by the heart would
also be in part reactive. As a consequence, the
various frequency components which in sum
establish the heart signal, would be subjected
not only to attenuation, but also to phase shift
between heart and body surface. As a consequence, it is unlikely that a signal would result
on the body surface which would be identical
with the one to be anticipated if the medium
between heart and body surface were purely
resistive.
This paper considers only the reactive components of various body tissues in situ in order
to provide the necessary information for further discussions of phase shift.
METHODS
Measurement of capacitance in situ requires the
elimination of electrode polarization. The polarization potential, developed between electrodes and
tissue, is proportional to the current passing the
electrode for sufficiently small current density (less
than about 1 ma./cm.2) as always used in our
measurements. Therefore, it may be characterized
by an impedance.
The total capacity (C*), as observed by the
electrode system, can be expressed as a sum of two
components,3
C* = C +
1
(1)
whose first term C is the true capacitance of the
sample and whose second term characterizes the contribution due to electrode polarization (Cp) capacity
of the electrode impedance, R observed resistance,
u/2x frequency). Reduction of the second term may
be accomplished by increasing Cp, by provision of a
heavy coat of platinum black on platinum electrodes
or by use of a sufficiently large electrode area.
Excessive coating with platinum black leads to unstable electrodes for tissue work.1'4 The other
approach of large electrodes also has limitations, due
to the necessity of obtaining meaningful, local
capacitance determinations and the desire of using
an electrode system which can be introduced into
tissue without major operative procedures. The
electrode system and technic previously described1
was used. The polarization contribution l/co2fl2Cp is
compared for a typical experiment with the tissue
sample capacity in table 2. Since l/a>2R.2Cp decreases
rapidly with increasing frequency table 2 shows that
the tissue values for frequencies above 1 Kc. are not
From Electromedical Division, Moore School of
Electrical Engineering, Department of Physical
Medicine, and Robinette Foundation University of
Pennsylvania, Philadelphia, Pa.
These studies were aided by TJ. S. Public Health
Service giants H-339 and H-1253(C2).
Received for publication April 8, 1957.
439
Circulation Research. Volume V, July 1957
440
CAPACITIVE PROPERTIES OF BODY TISSUES
TABLE 1.—Ratio of Capacitive and Resistive Component of Tissue Impedance as Function of Frequency
in Excised Muscle
Frequency (c.p.s.)
RuC
7
10
20
50
100
200
500
1000
0.01
0.01
0.01-0.02
0.02-0.03
0.02-0.03
0.02-0.04
0.03-0.04
0.04-0.05
J
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TABLE 2.—Effect of Electrode Polarization
on Measured Capacitance Values (C*)
Frequency
{c.p.s.)
c*
C
1000
100
10
12
100
2200
11
50
~200
1
50
~2000
affected by polarization. The values below 1 K c ,
however, are affected increasingly. In practice, it has
been found that the polarization component of the
capacity can be obtained with an accuracy of about
10 per cent, as outlined below. This means that from
observed capacitance values C* the true tissue
capacitance could be obtained accurate to 1 per cent
at 1 Kc. and accurate to about 10 per cent at 100
c.p.s. if electrode polarization were the only factor
determining inaccuracy of results. At 10 c.p.s. the
polarization contribution is about 10 times larger
than the sample tissue capacitance itself. At this
frequency, tissue capacitance may be estimated
only within a factor of 2 or 3.
In order to obtain a good estimate of the polarization contribution in equation (1), the polarization
capacity Cp must be known. Unfortunately, Cv depends on the medium in which the electrode system
is immersed. A good estimate of the factor by which
the polarization capacity in tissue is smaller than the
polarization value obtained with a physiologic saline
solution may be obtained as follows: The "masking
factor" which differentiates Cp "in tissue" from
Cp "in saline," is frequency independent. 3 ' 5 The
frequency dependence of the polarization capacitance can be obtained readily from an experiment
in physiologic saline solution, which has negligible
capacitive and known resistive properties. Thus, if
C p in tissue is known at any one frequency, it can
be computed for all the others. Knowledge of Cv in
the tissue is obtained best at 10 c.p.s., since here
polarization is very pronounced in its contribution
to the total capacity. Under the assumption that
tissue capacitance values obtained at 100 c.p.s. may
be extrapolated proportionally down to 10 c.p.s., as
indicated by the dashed line in figure 1, values for
FREQUENCY (Kc)
I
FIG. 1. Frequency dependence of the dielectric
constant of liver tissue in situ in a live dog. Accuracy
of results declines rapidly below 100 c.p.s. (vertical
lines).
tissue capacitance are obtained which are about .10
times smaller than established by polarization. If we
assume an accuracy of the tissue capacitance extrapolation which allows the true capacity to vary
from zero to double the extrapolated value knowledge of the polarization contribution and Cp in
tissue accurate to within 10 per cent is obtained.
The following independent arguments support the
correctness of this procedure:
1. Measurements conducted in excised samples
of tissue where more advanced technics for the
elimination of polarization could be used show
that the capacity increases as frequency decreases
from 100 to 10 c.p.s. by less than a factor of 5.
*
2. Measurements with larger electrodes having
considerably less polarization and applied by the
same technic yield similar results. If the assumption
concerning the frequency behavior which we have
formulated above for tissue were grossly wrong, the
measurements with the bigger electrode would yield
different results. The resultant error would be
greater with the standard electrode system than
with the large electrode system.
3. The values for polarization capacities Cp obtained with our technic permit calculation of
polarization resistance Rp values by use of a relationship formulated by Fricke. 6 Fricke's law has been
checked by us and is found to provide resistance
data in fair agreement with experiments. (Error
smaller than 20 per cent over most of the frequency
range from 10 to 100,000 c.p.s.). The polarization
resistance values obtained in this manner deviate from experimental ones with technics outlined
previously by less than a factor of 1.5.
4. The polarization values obtained by comparison with polarization values in saline provide
reasonable masking factors. If the polarization
capacities in tissue were more than twice as large as
estimated, masking factors far in excess of any
previously discussed factors1 would result.
All measurements were carried out on live dogs
with a bridge described elsewhere.7 The technic of
recording the data is substantially the same as pre-
SCHWAN AND KAY
viously described.1 Resistance measurements were
taken simultaneously in order to permit calculation
of ratio of capacitive to resistive current. Bridge
readings of capacitance were taken in multiples of
1000 nnF, corresponding to multiples of 10,000 in
dielectric constant. Hence, absolute accuracy of the
data declines from 5 per cent at 1 Kc. to about 10-20
per cent at 10 Kc. The absolute accuracy of the data
at frequencies lower than 1 Kc. is completely determined by electrode polarization as discussed above.
RESULTS
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Capacitance data are given for lung, muscle
and liver in table 3 and expressed in terms of
dielectric constants* at the frequencies 100
c.p.s., 1 and 10 Kc. Values at 10 c.p.s. are not
given, since they are inaccurate by a factor of
2. However, it can be stated that they are
between 3 and 10 times larger than the values
at 100 c.p.s.
I t is noted that the variation from sample to
sample within each group of tissue is comparable with the variation between the averages of
various types of tissues as tabulated in table 4.
A possible exception is the fatty material with
its somewhat lower dielectric constant. Therefore, the capacity of all tissues with high water
content recorded here is the same within a
factor of about 1.5 with the exception of lung,
which has lower values. Figure 1 shows that a
very pronounced frequency dependence exists
in a manner which gives increase in capacity
as the frequency decreases. The reasons for a
similar behavior in excised tissue have been
reported elsewhere.2 The variation below and
above the average values are only in part due
to uncertainty in electrode polarization as discussed above. Accuracy of reading established
an additional source of possible error of about
10 per cent.f Hence, true variation in tissue
need be only about 20 or 30 per cent. A sum* The dielectric constant is identical with the
capacitance of a cm.3 tissue, measured in wuF and
multiplied with the factor 3.6 IT.
f The determination of tissue capacitance is much
more difficult than the determination of tissue resistivity due to the fact that tissue has predominantly
resistive character. The RuC products listed in table
2 show that the capacitive current is less than .1 of
the resistive current. Hence, its determination and
consequent determination of capacitance which is
always based on the measurements of this current
are 10 to 100 times more difficult than measurement of
resistive current.
441
T A B L E 3.—Dielectric Constant Values
(X/03) at Three Frequencies
Lung
Muscle
Jver
10 0.1 Kc. 1 Kc. 10 0.1 Kc. 1 Kc. 10
0.1 Kc. 1 Kc. Kc.
Kc.
Kc.
390
500
360
360
390
390
430
290
430
360
1000
720
400
290
200
680
120
]20
100
70
—
70
60
60
60
130
60
60
90
110
60
110
110
30 780
30 650
40 650
20 950
20 520
20 1160
20 530
20 660
20 800
30 530
30 600
30 1120
30 930
40 1590
—
650
30 7S0
30 580
130
140
120
140
130
ISO
110
110
no
110
110
130
130
130
120
160
120
60
60
60
60
SO
SO
40
30
30
—
40
40
40
40
60
90
SO
7S0
7S0
650
650
7S0
1620
1290
1300
1300
1160
1300
1300
930
660
600
930
660
SOO
460
330
270
270
900
450
1200
1030
140
170
140
130
160
140
140
120
170
120
170
140
240
150
150
160
130
150
160
120
90
90
130
140
190
140
60
60
50
50
40
40
40
50
40
50
40
50
70
50
70
50
70
70
50
40
50
60
60
SO
60
20
20
Standard Deviation in Per Cent
40
30 25
35
15 30
40
TABLE 4.—Average Values of Dielectric Constants
(X103) of Total Experimental Material and Equivalent Products RuC
•t/1000
-RuC-
0.1 Kc. 1 Kc. 10 Kc 0.1 Kc.
Lung
Liver
Muscle
Heart muscle..
Fatty tissue. ..
450
900
800
800
150
90
150
130
300
50
30
50
50
100
20
0.02
0.04
0.04
0.04
0.01
1 Kc.
0.05
0.05
0.06
0.15
0.03
10 Kc.
0.13
0.17
0.21
0.32
0.15
mary of all dielectric constants is given in
table 4, together with values of /JoC-products
as calculated from dielectric constant and
simultaneously carried out resistance measurements. It is noticed that theflcoC-valuesare
smaller than 0.1 in the frequency range from
100 to 1000 c.p.s. At 10 Kc. they start to in-
442
CAPACITIVE PROPERTIES OF BODY TISSUES
(X103)for
Human Lung and Dog Lungs
TABLE 5.—Dielectric Constants
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Human lung
(excised)
Dog lung
in situ
(1 hour dead) I
90
90
150
140
90
110
110
110
140
110
110
110
100
150
120
90
90
90
120
130
120
100
100
140
160
100
(110)
(110)
Dog lung
(dead) II
150 T
180
160 1
in
160 situ
140
190
210
260
140
Dog lung
in situ
(dead) III
260
180
110
120
110
110
AR/AC = 2n-/oR2
70 T
70
70 |
excised
190
170
160
160
SO J
(150)
The similarity of the tissue capacitance data
reported with those found in studies with
excised material2 (compare also tables 1 and 4)
suggests that the reason for the frequency
dependence is the same in both cases. The
higher accuracy obtainable in studies with
excised material showed that the change in the
low frequency band between 10 c.p.s. and 100
c.p.s. is explained by an electric relaxation
effect. It was found that the total change in
capacitance (AC) and total change in resistance (AK) throughout the low frequency range
of interest are related by the equation2
(150)
crease. Values for 10 c.p.s. are not given due to
the uncertainty associated with them. However, since resistance increases only slightly
below 100 c.p.s. as frequency decreases1 and
since capacity increases by less than a factor of
10, 72coC-values are certainly smaller at 10
c.p.s. than at 100 c.p.s.
Table 5 brings dielectric constants for lung
tissue obtained from excised human lung and
from 3 different dogs, all dead and either in
situ or excised. Average values are given in
brackets. The frequency is 1 Kc. The measurements reveal no statistically significant difference between in situ and excised dog and
human lungs. By comparison with the "live"
data recorded in tables 2 and 3, it is found that
there is no difference between "live" and
"dead" lung data. Similar results have been
obtained with liver. We conclude, therefore,
that death does not appreciably affect the
capacitance of tissue at least within the first
hour. Previous investigations of the effects of
time on the capacitance of excised tissue2 substantiate this conclusion. A major decrease
occurs after 1 day, especially at the low frequencies.
where / 0 is the frequency for which the capacitance has been reduced from its value at zero
frequency (DC) by a factor of 2. The excised
studies showed that the frequency /o is between
10 and 100 c.p.s. This means that the change
in capacitance below 10 c.p.s. must be smaller
than by a factor of 2. Resistance change, on
the other hand, has been reported to be very
small between 10 to 100 c.p.s.1' 2 Its change
below 10 c.p.s. must likewise be small in view
of the fact that /o, characteristic for both resistance and capacitance change, has been found
to be larger than 10 c.p.s. The combination of
the stated resistance and capacitance changes
to be anticipated below 10 c.p.s results in
RcoC-values which continue to decrease below
10 c.p.s.
Since RoiC values characterize the ratio of
capacitive to resistive current, it can be stated
that the heart produces currents which are at
least 90 per cent resistive in character. However, if capacitance data would have been
larger than recorded by only one order of
magnitude, the assumption of a predominantly
resistive medium around the human heart
would have been grossly in error.
SUMMAHY
The dielectric constant (capacity) of various
tissues, lung, muscle and liver has been investigated with alternating currents in situ in
anesthetized dogs. The frequency range extended from 10 c.p.s. to 10 Kc. The dielectric
constant at 1 Kc. is approximately 100,000.
Lung tissue and especially fatty tissue have a
443
SCHWAN AND KAY
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somewhat lower dielectric constant than liver
and muscular tissue.
The dielectric constant decreases rapidly as
the frequency increases. Values at 100 c.p.s. are
about five times larger than at 1 Kc. and values
at 1 Kc. in turn about three times larger than
values at 10 Kc.
The ratio of the capacitive to the resistive
current component has been determined from
measured capacitance and resistance data and
found to be smaller than 0.1 as long as the
frequency is smaller than 1 Kc. Hence, it is
justified to a good approximation for frequencies up to 1 Kc. to consider body tissues as a
resistive medium.
SUMMARIO IN INTBRLINGUA
Le constante dielectric (capacitate) de varie
tessutos—pulmone, musculo, e hepate—esseva investigate per medio de currentes alternante in sito in canes anesthesiate. Le
frequentias variava inter 10 cyclos per secunda
e 10 Kc. Le constante dielectric a 1 Kc es
approximativemente 100.000. Tessutos pulnionar e specialmente tessutos grasse pote
haber un constante dielectric un pauco plus
basse que tessutos de hepate e musculo.
Le constante dielectric decresce rapidemente
con le elevation del frequentia. A 100 cyclos
per secunda, le valores es approximativemente
5 vices plus grande que a 1 Kc, e le valores a
1 Kc es in torno approximativemente 3 vices
plus grande que le valores a 10 Kc.
Ab le datos mesurate de capacitate e resistentia, le proportion inter le componentes
capacitive e resistive ha essite determinate.
Illo se trova infra 0,1 durante que le frequentia remane infra 1 Kc. Ergo, il es justificate
como un bon approximation—pro frequentias
usque a 1 Kc—considerar le tessutos corporee
como un medio resistive.
REFERENCES
1
H. P. AND KAY, C. F.: Specific resistance
of body tissues. Circulation Research 4: 664,
1956.
2
—: Electrical properties of muscle tissue at low
frequencies. Ztschr. Naturforschung 9b: 245,
1954.
3
—: Electrode polarization and its influence on the
determination of electrical properties of solutions and biological material. Ztschr. Naturforschung 6b: 121, 1951.
4
KAUFMAN, W. AND JOHNSTON, F. D.: The electrical
conductivity of the tissues near the heart and its
bearing on the distribution of cardiac action
currents. Am. Heart J. 26: 42, 1943.
5
SCHWAN, H. P. AND BOTHWELL, T. P.: A method
for the exact determination of volume concentration of non-conducting particles in conducting
solvent. Presented at 6th Annual Conference on
Electronic Instrumentation and Nucleonics in
Medicine, New York, 1953.
0
FRICKE, H.: The theory of electrolytic polarization.
Phil. Mag. 14: 310, 1932.
7
SCHWAN, H. P. AND SITTEL, K.: Wheatstone bridge
for admittance determinations of highly conducting materials at low frequencies. Tr. Am.
Inst. Elec. Engrs. 72: 114, 1953.
SCHWAN,
Capacitive Properties of Body Tissues
HERMAN P. SCHWAN and CALVIN F. KAY
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Circ Res. 1957;5:439-443
doi: 10.1161/01.RES.5.4.439
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Copyright © 1957 American Heart Association, Inc. All rights reserved.
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