Phys. Med. Biol., 1985, Vol. 30, No. 9, 965-973. hinted in Great Britain
Dielectric properties of low-water-content tissues
Susan Rae Smith and Kenneth R Foster
Department of Bioengineering, 220 South 33rd Street, University of Pennsylvania,
Philadelphia, PA 19104, USA
Received 4 December 1984, in final form 5 March 1985
Abstract. The dielectric properties of two low-water-content tissues, bone marrow and
adipose tissue, were measured from1 kHz to 1 GHz. From 1 kHz to 13 MHz, the measure10 MHz to 1 GHz,
ments were performed using a parallel-plate capacitor method. From
areflectioncoefficienttechniqueusing
anopen-endedcoaxialtransmissionlinewas
1 to almost 70% by weight. The dielectric
employed. The tissue water contents ranged from
properties correlate well with the values predicted by mixture theory. Comparison with
previous results from high-water-content tissues suggests that bone marrow and adipose
tissues contain less motionally altered water per unit dry volume than do the previously
of
studied tissues with lower lipid fractions. The high degree of structural heterogeneity
these tissues was reflected in the large scatter of the data, a source of uncertainty that
should be considered in practical applications of the present data.
1. Introduction
The electrical properties of various high-water-content tissues have been well characterised from the audio through
microwave frequency ranges. (For pertinent reviews
seeSchwan(1957),StuchlyandStuchly(1980b)andFosterandSchwan(1985).)
Corresponding data from low-water-content tissues are comparatively
few although
such data are needed for a number
of practical applications. Perhaps the
most extensive
investigation of the dielectric propertiesof fat and marrowwas by Schwan (1958,1960)
who presented results from fatty tissues with varying water contents at 300 MHz and
from samples of red and yellow bone marrow from 100 MHz to 2 GHz. A few other
data have been tabulated by Geddes and Baker (1967).
On a more fundamental level, others have studied the contributions of water to
the dielectric properties of tissues at microwave and UHF frequencies. For example,
Schepps and Foster(1980) studied the dielectric propertiesof a variety of tumour and
normaltissues withvaryingwater
contentsandshowedthattheproperties
were
consistent with the simple Maxwell mixture theory, provided that proper allowance is
made for the fraction of motionally altered water in tissue.
In this paper we consider the electrical properties of twotissues,fat and bone
marrow, over the frequency range of 1 kHz to 1 GHz. The samples exhibit a range of
water contents much lower than that of most of the tissues previously studied by our
group, and their compositionis also quite different. However, the methods of analysis
of the data are similar. This study thus extends our previously reported work.
2. Methods and materials
2.1. Sample preparation
Seven samples of equine and two samplesof canine subcutaneous adiposetissues were
obtained from the pathology laboratory
of the VeterinarySchool and NewBolton
0031-9155/85/090965 +09$02.25
0 1985 The
Institute
Physics
of
965
966
S Rand
Smith
K R Foster
Centerofthe
University of Pennsylvania.Fifteensamples
of bonemarrow were
obtained from the femurs and tibias of a 1 month old calf that had been sacrificed for
anotherstudyattheChildrensHospital
of Philadelphia, All suchsamples were
obtained within 12 h of death and were kept at 4 "C until measurements could be
completed, normally within a day of procuring the tissue. Nine additional samples of
bovine adipose tissue were obtained from a slaughterhouse, for comparison
with the
freshly excised samples.
For the measurements, the adipose and bone marrow
tissues were sectioned into
samples of approximately 1 g each. The region
of the medullary canal (distal third,
centre or proximal third) from which each marrow sample was obtained was noted.
All of the marrow samples contained a mixture of yellow and red marrow that varied
somewhat with the origin of the tissue.
The tissue water contents
were determined by drying each sampleto constantweight
in an oven at 70 "C. The water content of the freshly excised fat samples varied from
8 to 26% of the total weight while that of the marrow samples varied from 26 to 68%
by weight. Fat samples from the slaughterhouse had lower water contents (ranging
from1to
10% by weight) which perhapsarosefrom
drying of thetissue during
processing. Water contents were converted to a volume basis, as required by mixture
theory, by assuming average densities of the lipid and protein fractions to be 0.9 and
1.3 grespectively.
Forsuch estimates, theadipose tissue was assumedtoconsist
of water and lipids, as justified by studies by Baker (1969). The marrow was assumed
to consist of water, lipids and protein with the relative proportion of lipid to water as
given by Dietz (1946) and the remaining material consisting of protein.
For purposes of comparison, the dielectric propertiesof two other tissues were also
measured. The properties of rabbit liver were found at 25 "C using the same techniques
as for the fat and marrow: those of bone (the rat femur in the radial direction) were
measured using techniques reportedby Kosterich et aZ(l983). The bone measurements
had been done at 37 "C, but the variation in dielectric properties with temperature of
this tissue is negligible for the purposes of this study. Since the dielectric properties
of thesetissueshavebeenpreviously
reported, these measurements also
servedas
checks on the overall consistency of the data.
2.2. Measurement techniques
Two techniques were used for the dielectric measurements. From 1 kHz to
13 MHz,
aparallel-platecapacitance
cell was used.From
10 MHzto1GHz,a
reflection
coefficient method using an open-ended coaxial transmission line was employed. All
measurements were performed at 25 "C, except for those on bone as noted above,
Theparallel-plate cell consisted of twoplatinumelectrodes
of 1 cm diameter
mounted in a cylindrical plexiglass sample cell of a slightly larger diameter, in a way
that allowed for variation in sample thickness. A water jacket surrounded the cell for
temperaturecontrol.Electrodes
were electrolyticallycovered with platinumblack
following the methodof Schwan (1966) to reduce electrode polarisation. Measurements
were performed using an impedance analyser (Hewlett-Packard 4192) under computer
control, with the impedance of the empty and short-circuited cell also measured to
allow correction for the series lead inductance and resistance, stray capacitance and
shunt conductance arising within the instrument.
Repeated measurements with different sample thicknesses over the frequency range
5 Hz-l3 MHz allowed examination of electrode polarisation effects. At 5 Hz, electrode
Dielectric properties of low-water-content tissues
967
polarisation obscured the tissue properties but at frequencies
of 1 kHz and higher,
these artefacts could be separated from the tissue data
using correction techniques
outlined by Schwan (1966). Conductivity measurements were accurate to within 3%.
The expected relative errors of the permittivity measurements were typically within
5% but in the worst case (around 1 kHz) were as high as 20%. These figures were
calculated on the basis of measured phase angles of the tissue impedance (average
-0.2", minimum -0.06' at 1 kHz) and measured errorsin the impedance phase angle.
These errors decrease at higher frequencies because tissue phase angles increase.
Over the higher-frequencyrange, we employed an open-ended coaxialtransmission
linetechniquesimilartothatdescribed
by Stuchly and Stuchly(1980a).Theline
(a precision 7 mm airline, model 2653C, Maury Microwave Corporation) was attached
to a computer-controlled impedance analyser (Hewlett-Packard 4191) through a precision flexible arm using precision APC-7 connectors. A water jacket
surrounded the
line for temperature control. A thin (2 mm)Teflon disc was inserted between the inner
and outer conductor at the open end to centre the inner conductor andprevent
to
the
sample from being drawn up into the line. Errors arising from reflections from the
Teflon disc and other instrumental effects were removed by the standard calibration
procedure employing precision short, open and 50 R terminations. After the series of
calibration measurements, the sample was placed against the open end of the line and
the real and imaginary parts of the reflection coefficient were measured with reference
to the plane of the sample-line interface. The termination admittance so obtained had
real and imaginary parts that
were nearlylinearfunctions
of theconductivity and
permittivity of the sample, as determinedby measurements on dioxane-water mixtures
andsalinesolutions
of knowndielectricproperties.Conductivity
and permittivity
measurements were typically accurate to within 3% and 2 dielectric units respectively.
3. Results anddiscussion
3.1. Dielectric properties of tissue as a function of frequency
Dielectric properties of adipose and marrow tissues are shown in figures l ( a ) and ( b ) ,
with those of liver and bone tissues for comparison. The two samples of fat had quite
different water contents (8 and 21%) to illustrate the effect of changing water content
on dielectric properties of the same type of tissue. The dielectric properties of the
bone and liver are in good agreement with previous studies (Stoy et a1 1982, Kosterich
et a1 1983).
For all tissues shown, the permittivity values decrease slowly over four decades of
frequency before approaching alimiting value above 10 MHz. The increasein conductivity, Au, corresponding to this dispersion can be estimated from the
result A u =
25~f~A.s.s~ which applies tosingle
a
time constant relaxation. For the fat tissue of the
lower water content in figure l(b), this is approximately 0.06 mS cm", which is far
smaller than the frequency-independent (ionic) contribution. The pronounced increase
in the conductivity of the liver arises from the short-circuiting of the cell membranes
(the '&dispersion') with a consequent increase in the fraction of the tissue electrolyte
that can carry the current.
This effect is far less pronounced in the fat, the cells of
which principally contain lipids (Sheldon 1964) and are thus poorly conducting at all
frequencies. Curiously, at frequencies below about 100 kHz the conductivity of many
of the fat samples was higher than that of the liver, presumably due to the greater
amount of extracellular fluid in these samples.
968
S R Smith and K R Foster
IO6/
(0)
1
103
io4
io5
10)
loL
io6io5
io7
lo8
io9
io7
lo8
io9
lo6
- 2 - 01
Frequency
I
(Hz)
Figure 1. ( a ) Dielectric permittivity relative to free space and ( b ) electrical conductivity of bone marrow
(+), adipose tissue (0,
+), liver ( X ) and bone (0)as a function of frequency at25 "C, for all tissues except
bone (37 "C). Each symbol represents measurements on two tissue samples, one for high- and one for
low-frequency ranges. The discontinuities in the electrical conductivity data from fat and bone marrow at
10 MHz arise from the heterogeneity of the tissues, as discussed in the text.
The broad dispersions in figure 1( a ) indicate a wide spectrum of relaxation times.
Presumablyin the fat the responsible mechanisms would include remnants
of the
P-dispersion from cell membranes together with ionic polarisation effects. A small
additional dispersion is barely noticeable in the permittivity data from the marrow
with a centre frequency near 1 MHz; this is probably the @-dispersion of the blood
included in the sample (Schwan 1957).
It is interestingtonote that the dispersion
properties of two low-water-content tissues with vastly different structures, bone and
fat, are quite similar.
3.2. Dielectric properties of tissues as a function of tissue water content
The dielectric properties of the various tissues are shown as functionsof water content
in figure 2. The data are either results of single measurements or averages of repeated
measurements on different areas of the same sample, in which case the bars indicate
the spread of values obtained. For comparison, data from canine tumour and normal
tissues (Schepps and Foster 1980) are also shown. These latter data
were adjusted
slightly according to the temperature coefficient given by Schwan (1957) to take into
account the difference in measurement temperature (37 "C compared with 25 "C in the
present study).
Dielectric properties of low-water-content tissues
0.20
0
0.40
0.60
969
1.0
0.80
n
+
,
0
0.20
.
,
.
.
0.40
I
.
.
.
0.60
.
#
.
.
0.80
.
.
1.0
Volume fraction o f water
Figure 2. ( a ) Tissue permittivity normalised by the permittivity of water and ( b ) conductivity plotted against
volume fraction of tissue water at 25 "C. The data represent single measurements, or averages of repeated
measurements on different areas of the same sample and the bars indicate the range of values obtained.
(0)and fat ( + ) . Thefullcurverepresentsvaluespredictedbyequation
(1)
Tissuesarebonemarrow
assuming in ( a ) that the permittivity of the suspended and continuous media are
2.5 and 7.8 respectively
and in ( b ) that the conductivity of the non-water fraction is negligible and that of the tissue electrolyte is
12 mS cm". The data from the tumour and normal tissues from Schepps and Foster (1980) are shown for
of to take into account the different
comparison ( X ) . Their conductivity data were multiplied by a factor 0.8
measurement temperatures (25 "C compared with 37 "C).
ThefullcurvesshowpredictedvaluesbasedontheMaxwellmixtureformula,
which gives the complex permittivity E* of a suspension of spheres of volume fraction
p with permittivity ET in a continuous medium of permittivity E : :
&*
2&f+ET"p(&:-&3
2&:+&T+p(&f-&E:)'
= &f
In the limit that ETCC E : , this can be separated into
two expressions of the form of
equation (1) that apply to the conductivity or permittivity. As applied to tissues, the
excluded volume p would include the protein and lipid, plus whatever water fraction
is presentthathas
lowionicconductivity
or permittivity. Theabove resultis an
excellent approximation for suspensions of low conductivity in a continuous medium
ofmuchgreaterconductivitythat
is notstrongly sensitive to the geometry of the
suspended particles (Chiew and Glandt 1983).
In using equation ( l ) ,the permittivity of the suspended phase (i.e. lipid
or protein)
was chosen to be2.5 which is the permittivity of oleic acid, the predominant fatty acid
970
S R Smith and K R Foster
in lipids. The permittivity of the suspending medium was taken as 78, which is that
of water at 25 "C. The conductivity of the tissue electrolyte was taken to be 12 mS cm"
at 25 "C. This value was obtained by extrapolating the conductivity of the tissues at
100 MHz to zero solid content, and presumably reflects some average conductivity of
the intracellular and extracellular fluids (Schepps and Foster 1980). That the conductivity of the lipid fraction of the fat is negligible at 100 MHz was verified by measurements on samples that had been dehydrated to contain less than 2% water.
In figure 2 the permittivity and conductivity of the high-water-content tissues are
conspicuously below values predicted
by mixture theorywith the assumptions indicated
above. This can be attributed to a water fractionin the tissue that is reduced in mobility
compared to that of the pure liquid, and thus
has a dielectric relaxation frequency
and ionic conductivity lower than those of an electrolyte solution of comparable ionic
strength (Schepps and Foster 1980). This 'bound water' has the effect of increasing
the excluded volume fraction of other proteins in solution by approximately 30% at
microwave frequencies (Pennock and Schwan 1969, Schwan 1957, Grant et a1 1968).
The data from the adipose and marrow tissues are much closer to predictions of the
mixture theory.
These differences presumably reflect a smaller fraction of motionally altered water
in thefatandmarrowcompared
with thehigh-water-contenttumourandnormal
tissues.Lipids
arecomposed primarily of triglycerideswhich arenon-polarand
insoluble in water (Lehninger 1975) and would be expected to be shielded from the
water in marrow and adipose tissues. Thus one would expect less bound water per
unit dry volume than in other tissues. While the present observations are basically
qualitative, it is remarkable that the simple Maxwell theory can lead to a consistent
interpretation of the data from such complex systems.
It is interesting to compare the present
results with earlier data reportedby Schwan
(1960) from human fat samples, which are summarised in figure 3 by empirical curves
that give the trend of several measurements covering a range of water contents from
6-40% by weight. These figures are more useful in predicting the dielectric properties
of such tissues, in that the water content is directly measurable on a weight basis.
3.3. Sample heterogeneity
One pronounced feature of our results is a large scatter in the data. This variability
was studied by means of repeated measurements on samples of adipose tissue from
the same location from one animal using the two techniques at 10 MHz. The results
are summarised in table 1. Measurements on six samples using each technique agree
to within 7%. However, the range of the results was quite large, nearly twofold, which
reflects in part variationsin sample composition. The water contentsof the six samples
studied using the parallel-plate capacitor varied from 19 to 26% water by weight, even
though the tissues were of essentially the same provenance.
It is curious that the variance of the two sets of data in table 1 are similar, even
though the two techniques probe quite different volumes of tissue. The parallel-plate
capacitor cell has a volume of approximately 1 cm3. (In fact, the use of the distance
variation technique to correct for electrode polarisation results in impedance measurements that reflect the contribution of incremental volumes of tissue.) In contrast, the
open-ended coaxial transmission line probes a volume that lies with the fringing field,
or about 0.03 cm3 in the present case. We would expect greater variability using the
transmission line technique, if inhomogeneities in the tissue occur over volumes that
Dielectric properties of low-water-content tissues
97 1
1
0.01
0.1
0.01
0.1
Weightfraction
1.0
10
1.0
of water
Figure 3. ( a ) Permittivity and ( b ) conductivity of bone marrow and adipose tissue at
300 MHz and 25 "C
plotted against fraction by weight of tissue water. The full curve was determined by Schwan (1960) from
results at 300 MHz from numerous samples of human adipose tissue.
Table 1. Results of repeated permittivity measurements on samples of
equineadiposetissuefromthesameregionofthesameanimal,
showing
the
variation
dielectric
in
properties
due
tissue
to
heterogeneity. The measurement techniques are described in the text.
Also shown are the average values and standard deviations for each
series of measurements. Frequency of measurement in both cases is
10 MHz.
Permittivity
Average
*SD
Parallel-plate cell
Coaxial-line cell
32
34
24
15
15
17
15
15
26
33
24
33
22.8
8.6
24.3
8.1
972
S R Smith and K R Foster
are greater than 0.03 but less than 1 cm3. However,thefringing field occursin an
annulus of about 1 cm length. It might be that the heterogeneities in the tissues are
similarwhensampledoverthesetwoquitedifferentvolumesbutsimilarlinear
dimensions. A morequantitativeanalysis of sampleheterogeneity and its effect is
needed.
The marrow samples were visibly heterogeneous, with variations in composition
noticeable even in samples obtained from the same region
of the medullary canal of
the same bone. Moreover, the dielectric properties of marrow tissue varied noticeably
with the origin of the tissue. Bones in the trunk such asribs contain a high percentage
of red marrow, which has less lipid and thus comparatively high conductivity. Limb
bones, especially those in more peripheral locations, contain a larger proportion
of
yellow marrow that has comparatively lower conductivity. Within a single
bone of a
limb, the lipid content is higher at the centre than at either end (Tavassoli and Yoffey
1983). These trends are consistent with the results of the present study. For example,
the average conductivity of marrow from the right femur was 5.3 mS cm" (10 MHz)
while that for the right tibia was 3.6 mS cm". Within a single right femur, the sample
of marrow with the highest conductivity (5.8 mS
cm") was from the proximal end,
while that of the lowest conductivity (4.3 mS cm") was from the centre.
4. Conclusion
This study emphasises once again the strong relationship between the water content
of the tissue and its dielectric properties, and extends the analysis presented in earlier
papers from our group. There is clearly a large variability of the properties of bone
marrow and adipose tissue,thisbeing reflected in their composition and dielectric
properties. A singlevaluecannotbechosen
for the permittivity or conductivity of
these tissues, but instead a range
of values should be used,unless the exact composition
of the tissue is known.
Acknowledgments
Thiswork was supported by Officeof NavalResearch Contract N00014-78-(2-0392
and National Cancer Institute GrantCA26046-05. We acknowledge Professor Herman
P Schwan for many helpfuldiscussions about dielectric properties of tissues and their
measurement.
RBsume
Propriitds diilectriques des tissus B faible teneur en eau.
Les auteurs ont mesuri, entre 1 kHz et 1 GHz, les propriitis diilectriques de deux tissus B faible teneur en
eau, la rnoelle osseuse et le tissu adipeux. De 1 kHz a 13 MHz, les rnesures ont ete rtalistes B I'aide de la
rnethode du condensateura plaques parallkles et, de10 MHz 5 1 GHz, a I'aide d'une technique par coefficient
de rtflexion utilisant une ligne coaxiale ouverte.La teneur rnassique en eau des tissus etudits ttait comprise
entre 1 et environ 70%. I1 est apparu une bonne corrtlation entre les propriitis diilectriques et les valeurs
attendues d'aprks la thtorie des mtlanges. La cornparaison de ces donntes avec des risultats prictdents,
relatifs B des tissus B forte teneur en eau, suggkre que la rnoelle osseuse et
les tissus adipeux contiennent
moins d'eau liie par unite de volume sec que
les tissus ttudits pricidemment et contenant rnoins de lipides.
La grande httiroginiitt de structure ces
de tissus s'est rnanifestie dans la dispersion irnportante des donntes,
source d'incertitudes qui devraititre prise en considirationpour l'utilisation pratique des donntes presentees.
Dielectric properties of low-water-content tissues
973
Zusammenfassung
Dielektrische Eigenschaften von Geweben
mit niedrigem Wassergehalt.
Die dielektrischen Eigenschaften vonzwei Gewebearten mit niedrigem Wassergehalt, namlich Knochenrnark
undFettgewebe,wurdenvon1kHzbis1GHzgernessen.Zwischen1kHzund13MHzwurdendie
Parallel-Platten-Kondensatormethodedurchgefiihrt.Zwischen 10 MHzund
MessungenmitHilfeeiner
1 GHz wurde ein Retlexionskoeffizientenverfahren verwendet, bei dem eine koaxiale Ubertragungsleitung
mit offenem Ende benutzt wird. Der Wassergehalt der Gewebe reicht von 1 bis 70% Gewichtsprozenten.
Die dielektrischen Eigenschaften stimrnen gut mit den nach der Mischungstheorie vorhergesagten Werten
iiberein.EinVergleich mit vorausgegangenenErgebnissenvonGeweben
mit hohemWassergehaltzeigt,
dal3 Knochenmark und Fettgewebe weniger durch Bewegung veranderliches Wasser pro Einheit TrockenvolumenenthaltenalsdievorheruntersuchtenGewebe
mit niedrigeremFettanteil.Dashohe
Mal3 an
struktureller Heterogenitat dieser Gewebe zeigte sich an dergrol3en Streubreite der Daten, eine Fehlerquelle,
die bei der praktischen Anwendung der vorliegenden Werte beriicksichtigt werden sollte.
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