INTRODUCTION
EXPERIMENTAL TECHNIQUES
Techniques
Uncertainties
Materials
RESULTS
Measurements Across The Frequency Range
Comparison Between Species
LITERATURE SURVEY
Review of the Dielectric Properties of Tissues
Presentation of Data
DATA ANALYSIS
Parametric Description of the Dielectric Spectrum
THE DIELECTRIC PROPERTIES BELOW 100 Hz
Electrical properties of Body Tissues
Electrical properties of Body Parts
CONCLUSIONS
REFERENCES
APPENDIX A: Experimental data.
APPENDIX B1: Literature Survey. (Graphs)
APPENDIX B2: Literature Survey. (Data)
APPENDIX C: Modelling the frequency dependence of the dielectric properties to a 4 dispersions spectrum.
APPENDIX D: Tabulation of the experimental data referred to in Appendix C.
Figure 1. Uncorrected values of the permittivity and conductivity of a series of salt solutions.
Figure 2. Comparison between the dielectric properties of tongue muscle from animal and human samples.
Figure 3. Comparison between the dielectric properties of tendon from two anima species.
Figure 4. Comparison between the dielectric properties of small intestine tissue from animal and human samples.
Table 1. Estimates of the conductivity (S/m) of body tissues below 100 Hz at body temperature.
Table 2. Conductivity, in S/m, of the whole and parts of the body obtained by integrating the conductivity values in Table 1 over various parts of the body.
Recent developments in the field of electromagnetic dosimetry have produced high resolution anatomically correct man and animal models from medical imaging data for use in numerical simulation exercises. The level of details is such that over 30 tissue types can be identified. The application of such models require that dielectric properties be allocated to the various tissues at all the frequencies to which the model is exposed. There is, as yet, no consensus on the dielectric data. This project is geared towards this objective. The following has been achieved in the period covered by this report:
The work is briefly described in this report, the data are presented in graphical and tabular format in Appendices A to D.
The dielectric measurements were performed using automatic swept frequency network and
impedance analysers. For the frequency range 10 Hz to 10 MHz, an HP4192A impedance
analyser. An HP 8753C covered the frequency range 300 kHz to 3 GHz and an HP8720 measured
from 130 MHz to 20 GHz. Open ended coaxial probes were used to interface the measuring
equipment with the samples in all cases. The technique used with the HP8700 series network
analysers has been reported in details elsewhere (Gabriel et al 1994) and will not be
discussed further. The techniques used in conjunction with the impedance analyser will be
briefly described. A 50 ohms impedance matched conical coaxial probe was adapted (Gabriel
and Grant 1988) to interface the sample to the HP4192A impedance analyser. The probe is
characterised by a fringing capacitance C and conductance G which are a function of its
physical dimension and can be measured with the impedance analyser. The characteristic
parameters of the probe were calculated from measurements of the impedance components of
the probe in air and in a standard sample (water or salt solution). In principle, the
dielectric properties (permittivity and conductivity
) of an unknown sample can then be calculated from
measurements of the impedance of the probe against an unknown sample using the following
relationships where
is the permittivity of free space
(1)
In practice, the measurement of conductive materials in the frequency range 10 Hz to 10
MHz are not so straightforward. The measurements are affected by two sources of systematic
errors, electrode polarisation and lead inductance errors, which become apparent at the
lower and higher ends of the frequency range under consideration. Electrode polarisation
is a manifestation of molecular charge organisation which occur at the sample-electrode
interface in presence of water molecules and hydrated ions. In its simplest forms the
phenomenon is equivalent to a frequency dependent capacitor in series with a resistor.
Both components can be approximated by negative power functions of frequency, that is
their absolute values decrease with increasing frequency. The effect increases with
increasing sample conductivity and its consequences are more pronounced on the capacitance
than the conductance of ionic solutions as well as biological samples (Schwan 1992). In
the case of biological samples, the poorly conducting cells shield part of the electrode
from the ionic current thus reducing the polarisation effects compared to an ionic
solution equivalent in conductivity to the intracellular fluid. The material of the
electrode plays an important part in determining its polarisation impedance. In the
current study gold plated and sputted platinum electrodes were tested and a choice was
made in favour of the latter. The effect of the rough platinum surface was to shift the
electrode polarisation effect to lower frequencies and thus to reduce its contribution in
the frequency range under consideration. The inductance of the probe and connecting cable
add another series component to the measured impedance. Its value could be determined from
measurements on standard salt solutions and applying an equivalent circuit analysis. For
the present setup the stray inductance is L=2x10-7 henry and the following
equations were used to account for it
(2)
where C and G are the corrected capacitance and conductance expressed in terms of the
measured values Cm and Gm , the lead inductance L and the angular
frequency . The effect of the stray inductance increases with frequency and with sample
conductivity. Figures 1a and b show the effect of electrode polarisation and the stray
inductance on the uncorrected permittivity and conductivity of a series of salt solutions
ranging from zero molar (deionised water) to 0.09 molar. The high permittivity values at
low frequencies are a manifestation of electrode polarisation while negative permittivity
values at high frequency show the effect of the stray inductance. Superimposed on these
data are the uncorrected permittivity and conductivity of a tissue sample (heart tissue).
It can be seen that the low frequency conductivity of the tissue is less than that of 0.01
molar salt solution. It is therefore reasonable to assume that the effect of electrode
polarisation on the tissue is also less than that exhibited by the 0.01 molar salt sample.
A further observation indicates that the errors in the permittivity and conductivity of
the sample are likely to be apparent below 1 kHz and significant below 100 Hz while the
effect of inductance manifests above a few megahertz in the case of tissue samples.
a. Permittivity
b. Conductivity
Figure 1. Uncorrected values of the permittivity and conductivity of a series of salt
solutions.
Also shown are the corrected and uncorrected data for heart tissue at 37oC. To
correct for electrode polarisation and induction errors the capacitance and conductance of
the tissue sample are evaluated in accordance with (2) and normalised to a salt solution
of similar low frequency conductivity. The example in Figures 1a and b was corrected with
reference to a 0.005 molar salt solution, the corrected dielectric properties are shown
for comparison purposes. All impedance analyser tissue measurements were treated in a
similar manner.
The measurement techniques and associated instrumentation used in this study give random reproducibility of about 1% across the frequency range. This statement is based on multiple measurements carried out on standard samples of uniform composition. Biological tissues are inhomogeneous and show considerable variability in structure or composition and hence in dielectric properties. Such variations are natural and may be due to physiological processes or other functional requirements. The spread of values ranges from about +/- 5% above 100 MHz to +/- 15% at the lower end of the frequency scale. Care has been taken to eliminate all known sources of systematic errors, however, in view of the assumptions made in correcting for electrode polarisation it is possible that the dielectric parameters below 1 kHz may be undercorrected. This source of errors may affect the dielectric parameters by up to a factor of two.
Three sources of materials were used:
All animal tissues were used as fresh as possible, mostly within two hours of death, human material was obtained 24 to 48 hours after death. The conical probe used in conjunction with the impedance analyser requires relatively large samples, at least a cube of 5 cm linear dimension. In view of this requirement not all samples could be measured at low frequencies.
Examples of measurements on the three experimental setup, across the frequency range are given in Appendix A (Figures A1 to A11). The agreement between measurements on the three machines was particularly good when the measurements were made on the same sample throughout. To achieve this objective the two network analysers and the impedance analyser were placed in close proximity to each other and interfaced to the same computer. All the measurement procedures were redesigned to operate through LabView(TM), a graphics interface medium from National Instruments running on an Intel Pentium microprocessor. In this arrangement, the measurements could be carried out on all three machines in quick succession. The dielectric properties of muscle are known to be anisotropic. The data reported were obtained by measurement on the paravertebral muscle. The sample was measured twice, first with a transverse section against the probe (Figure A9) and then it was cut along the muscle fibre and re-measured (Figure A10). In view of the radial nature of the fringing field of the coaxial probe these measurements do not represent the true limits of the dielectric properties with the field along and across the fibre. They show, however, the effect of fibre direction and the parts of the spectrum influenced by it. Human material could not be obtained in sufficient quantities for optimum measurements with the conical probe. Under such conditions the measurements on the impedance analyser were consistently lower than those obtained on the network analyser in the same frequency range. Examples of such measurements are given in Figures A12 to A15. Much smaller samples of human material were measured only in the frequency range above 1 MHz on the two impedance analysers. Examples of such measurements are given in Figures A16 to A19.
The differences in the dielectric properties of animal and human species are not
systematic. The variation in tissue properties within a species may well exceed variations
between species. Example of comparative measurements are given in Figures 2 to 4.
Figure 2. Comparison between the dielectric properties of tongue muscle from animal and
human samples.
Figure 3. Comparison between the dielectric properties of tendon from two animal species.
Figure 4. Comparison between the dielectric properties of small intestine tissue from
animal and human samples.
The dielectric properties of tissues have been extracted from the literature of the past five decades and compared to the corresponding data from the current study. The purpose is to provide an objective basis for the evaluation of the experimental data and to reach a broad based consensus on the subject. Reports of dielectric properties of tissues prior to 1950 are difficult to get hold of, they have more historical than practical interest and, with the exception of Osswald (1937), have not been reviewed. The literature in the 1950s and 60s is dominated by the work of H. P. Schwan and his collaborators and has been reviewed and tabulated by Durney et al 1986. Other extensive reviews include Geddes and Baker (1967) who summarised the early reports on the specific resistance of tissues, Stuchly and Stuchly (1980) who tabulated the dielectric properties of tissues in the frequency range 10 kHz to 10 GHz, Foster and Schwan (1989) who provided a wide historical perspective and Duck (1990) who extended their survey by including more recent data. In the current survey, data that correspond more closely to living human tissues were selected in preference to any other. Consequently, human tissue and in vivo measurements were selected in preference to animal tissue and in vitro measurements. For in vitro measurements, data obtained at temperatures closest to that of the body and nearest to the time after death were used when available. Most of the literature data were in graphical rather than table form and in a logarithmic rather than linear format. Such data were retrieved at each decade. When tables were available, a more extensive frequency range was often provided. The data were translated from the various authors' preferred set of parameters and units to relative permittivity and conductivity expressed in S/m. Data obtained at temperature as low as 20oC are included in this survey. It was not considered advisable to translate them to body temperature. The temperature coefficients, for both permittivity and conductivity, are tissue-type and frequency dependent. Information on these coefficients is scarce and not sufficiently robust to warrant generalisation and extrapolation. Moreover, the coefficients are highest (~1-2 %/oC) at low frequencies where the uncertainty and the scatter in the data are of a similar or higher order of magnitude than the differences due to a 10 or 15oC.
The data are presented in Appendix B in tabular as well as graphical formats. Details of the tissue-type, animal species, measurement temperature and the reference are included in the legend. To facilitate the comparison, the same scale was used for all tissues except where the conductivity of the tissue falls below 10-2 S/m. The references from which data were extracted are included in Appendix B.
One of the aims of this project is to derive models for the frequency dependence of the
dielectric properties of the tissues investigated. The basis of the analysis is well known
dispersions in the dielectric spectrum of biological materials and their expression as a
summation of terms corresponding to the main polarisation mechanisms. The spectrum extends
from Hz to GHz and shows 4 dispersion regions. The complexity of the structure and
composition of biological material is such that each dispersion region is broadened by
multiple contributions to it and could be described by a Cole-Cole expression. The model
corresponding to the whole spectrum
(3)
in which, is the permittivity in the terahertz frequency range,
is the
ionic conductivity, for each dispersion region
is the relaxation time and
is the drop in permittivity in
the frequency range corresponding to
. With a choice of parameters appropriate to each tissue, (3) could
be used to predict its dielectric behaviour over the desired frequency range. The
parameters of the model were adjusted to correspond to a close fit between the model and
the most comprehensive data set available for the particular tissue. The 4-Cole-Cole model
describes the frequency dependence of the dielectric properties in the frequency range
from Hz to GHz. It can be used with confidence for frequencies above 1 MHz. At lower
frequencies, where the literature values are scarce and have larger than average
uncertainties, the model should be used with caution in the knowledge that it provides a
'best estimate' based on present knowledge. It is important to stress the limitations of
the model particularly where there are no data at all to support its predictions. The
4-Cole-Cole analysis was carried out on 44 tissue types, the results are presented in a
self explanatory manner in Appendix C, the experimental data are tabulated in Appendix D.
Below 100 Hz the impedance of biological material is mostly resistive. The contribution of the capacitive component is of the order of 10 % in most cases. The literature surveyed in this study shows that there are wide variations in the conductivity values obtained for the same tissue in various studies. The contribution of the tissue permittivity to body current is well within the uncertainty associated with the corresponding tissue conductivity. Therefore, in practice, the estimation of induced current in tissue is based on such conductivity values. Table 1 gives an estimate for conductivity in S/m of the main body tissues below 100 Hz from this study mitigated by literature values. The values tabulated by Duck (1990) are also shown for comparison . Average values were used where appropriate.
The values obtained from this study were used to calculate the conductivity of the
whole and various parts of the body (Table 2). The necessary integration of the
conductivity of tissue to obtain values in table 2 were carried out by allocating the
appropriate values to a voxel anatomical human model developed at The National
Radiological Protection Board (NRPB) to aid dosimetry work. The model known as NORMAN
(normal man) will be described in a future NRPB publication. The results of such an
integration carried out at 10 and 100 kHz has also been included for comparison purposes.
Table 1: Estimates of the conductivity (S/m) of body tissues below
100 Hz at body temperature.
Tissue |
From Duck 1990 |
This study |
---|---|---|
Bladder |
0.2 |
|
Bone -Cancellous |
0.07 |
|
Bone -Marrow |
0.05 |
|
Cartilage |
0.18 |
|
Cerebro Spinal Fluid |
1.81 |
2.0 |
Cornea |
0.4 |
|
Fat |
0.04 |
|
Gall Bladder Bile |
1.6 |
1.4 |
Heart |
0.2 |
0.1 |
Lens |
0.25 |
|
Lung -Deflated |
0.1 |
0.2 |
Muscle |
0.4 |
0.35 |
Pancreas |
0.13 |
0.22 |
Small Intestine |
0.5 |
|
Stomach |
0.5 |
|
Testis |
0.4 |
|
Tongue |
0.3 |
|
Blood |
0.68 |
0.7 |
Bone -Cortical |
0.02 |
0.02 |
Breast |
0.06 |
|
Cerebellum |
0.1 |
|
Colon |
0.1 |
|
Dura |
0.5 |
|
White matter |
0.1 |
0.06 |
Grey Matter |
0.3 |
0.1 |
Kidney |
0.9 |
0.1 |
Liver |
0.12 |
0.07 |
Lung -Inflated |
0.05 |
0.08 |
Nerve |
0.4 |
0.03 |
Skin -Wet |
0.1 |
|
Spleen |
0.1 |
|
Tendon |
0.3 |
|
Urine |
3.3 |
|
Vitreous Humour |
1.5 |
|
Thyroid |
0.5 |
Table 2: Conductivity, in S/m, of the whole and parts of the body
obtained by integrating the conductivity values in Table 1 over various parts of the body
Frequency | Whole body | Head | Torso | Arm | Leg | Neck |
---|---|---|---|---|---|---|
50 Hz | 0.216 | 0.254 | 0.223 | 0.195 | 0.196 | |
10 kHz | 0.276 | 0.285 | 0.256 | 0.238 | 0.222 | |
100 kHz | 0.288 | 0.30 | 0.332 | 0.239 | 0.243 |
The main purpose of this project is to compile a database of dielectric properties of
tissues for use by the scientific community in solving electromagnetic interaction
problems. This has been achieved through measurement in the frequency rang 10 Hz to 20 GHz
and modelling the frequency dependence of the dielectric properties of over 30 body
tissues to parametric expressions for inclusion in numerical solutions.
C Gabriel, T Y A Chan and E H Grant, "Admittance models for open ended coaxial
probes and their place in dielectric spectroscopy", Physics in Medicine and Biology,
39, 12, 2183-2200, 1994.
Gabriel and E.H. Grant, "Dielectric sensors for industrial microwave measurements and
control", Microwellen und HF Magazin, vol 15, pp 643-645, 1989.
P. Schwan, "Linear and nonlinear electrode polarisation and biological
materials" Annals of Biomedical Engineering: 20, 269-288, 1992.
Durney, C.H., Massoudi, H. and Iskander, M.F., 1986, Radiofrequency radiation dosimetry
handbook, Brooks Air Force Base- USAFSAM-TR-85-73 , .
Geddes, L. A. and Barker, L. E., 1967, The specific resistance of biological material - a
compendium of data for the biomedical engineer and physiologist., Medical and Biological
Engineering, 5, 271-293.
Stuchly, M. A. and Stuchly, S. S., 1980, Dielectric properties of biological substances -
tabulated, Journal of Microwave Power, 15, 1, 19-26.
Foster, K. R. and Schwan, H. P., 1989, Dielectric properties of tissues and biological
materials: A critical review, Critical Reviews in Biomedical Engineering, 17, 1, 25-104.
Duck, F. A., 1990, Physical properties of tissue:A comprehensive reference book, Academic
Press, Harcourt Brace Jovanovich, Publishers.
TITLE PAGE: Links and information.
REPORT:
The Dielectric Properties of Body Tissues
APPENDIX
A: Experimental data.
APPENDIX
B1: Literature Survey. (Graphs)
APPENDIX
B2: Literature Survey. (Data)
APPENDIX
C: Modelling the frequency dependence of the dielectric properties to a 4 dispersions
spectrum.
APPENDIX
D: Tabulation of the experimental data referred to in Appendix C.
This is a Department of Defense computer system for authorized use only. DoD computer systems may be monitored for all lawful purposes, including to ensure that their use is authorized, for management of the system, to facilitate against unauthorized access, and to verify security procedures, survivability, and operational security. Using this system constitutes consent to monitoring. All information, including personal information, placed on or sent over this system may be obtained during monitoring. Unauthorized use could result in criminal prosecution.
POC: AFRL/HEDM, (210)536-6816, DSN 240-6816