Parametric Models of Tissue

This page provides the parametric models used to derive the dielectric data. Dielectric properties of WEB Application are calculated using the parametric model provided on this page.

Tissue dielectric properties are expressed as a function of frequency by the following equation [1][3]:

$$\varepsilon_r(f) = \varepsilon'_r(f) - j\varepsilon''_r(f) = \varepsilon_{r,\infty} + {\sigma_S \over j 2 \pi f \varepsilon_0} + \sum_{l=1}^2 {\Delta_l \over 1 + (j{f / f_{r,l}})^{1-\alpha_l}}$$
$$\begin{align} f&: \text{frequency [Hz]} \\ \varepsilon_0&: 8.854 \times 10^{-12} \text{[F/m](Permittivity in vacuum)} \\ \varepsilon_{r,\infty}&: \text{static relative permittivity} \\ \sigma_S&: \text{DC electric conductivity [S/m]} \\ f_{r,l}&: \text{relaxation frequency [Hz]} \\ \Delta_l&: \text{magnitude of }l\text{-th dielectric dispersion} \\ \alpha_l&: \text{distribution parameter of }l\text{-th dielectric dispersion} \\ \end{align}$$

The parameterization for each tissue was derived by applying the parameter fitting technique of [7] to measured data sets in the frequency range of 1 MHz to 100 GHz. Extending the frequency range is not recommended as it may contain unexpected uncertainties in the calculated results.

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Tissue εr,∞ σS Δ1 fr,1 α1 Δ2 fr,2 α2
Adrenal gland 4.68 0.1615 44.57 17684000000.0 0.064 3130.0 1301000.0 0.167
Aorta 5.107 0.1499 41.6 15700000000.0 0.103 9661.0 234150.0 0.157
Bladder 5.265 0.2519 52.05 19299000000.0 0.054 7409.0 810290.0 0.117
Blood 5.662 0.6486 58.79 17737000000.0 0.03 4824.0 1430400.0 0.07
Brain-Cerebellum 4.929 0.1086 39.79 22180000000.0 0.022 2026.0 1863500.0 0.249
Brain-Cerebrospinal fluid 5.331 1.8774 68.5 24558000000.0 0.0 0.0 1.0 0.0
Brain-Hypothalamus 5.161 0.0901 33.03 22647000000.0 0.064 2024.0 1147100.0 0.251
Brain-Pineal gland 4.626 0.093 29.5 18535000000.0 0.082 1637.0 2004600.0 0.222
Brain-Striatum 5.271 0.0852 29.57 23626000000.0 0.03 3223.0 494750.0 0.292
Brain-Brainstem 8.37 0.1138 23.09 20012000000.0 0.104 1504.0 1217000.0 0.251
Brain-Grey matter 5.158 0.1094 35.36 23864000000.0 0.025 3889.0 609170.0 0.274
Brain-Pituitary gland 5.378 0.1825 42.59 18853000000.0 0.053 3266.0 1309400.0 0.183
Brain-Thalamus 5.8 0.1086 28.28 23684000000.0 0.173 1574.0 1241500.0 0.254
Brain-White matter 5.023 0.0685 29.24 22173000000.0 0.095 5807.0 209600.0 0.238
Carotid artery 5.119 0.3217 42.23 16091000000.0 0.098 9592.0 325620.0 0.099
Diaphragm 5.011 0.1444 29.45 14841000000.0 0.106 5502.0 346390.0 0.093
Esophagus 3.416 0.1477 47.12 17448000000.0 0.069 6609.0 892650.0 0.096
Eye-Anterior humor 6.362 1.1776 68.13 19870000000.0 0.007 15844.0 480950.0 0.011
Eye-Cornea 4.326 0.4249 53.22 17595000000.0 0.067 19770.0 352100.0 0.048
Eye-Lens 5.565 0.1419 36.28 16934000000.0 0.061 3294.0 1043000.0 0.143
Eye-Optic nerve 4.514 0.0948 27.67 15873000000.0 0.146 4341.0 300900.0 0.251
Eye-Sclera 5.206 0.4274 43.95 16949000000.0 0.072 17155.0 350600.0 0.074
Eye-Vitreous 5.842 1.0655 68.14 19360000000.0 0.009 11140.0 732160.0 0.021
Fat-Breast 3.789 0.036 9.01 13882000000.0 0.069 10079.0 134550.0 0.037
Fat-Subcutaneous 2.551 0.0016 3.88 12803000000.0 0.199 2464.0 156500.0 0.073
Gallbladder 3.871 0.3568 49.16 16525000000.0 0.137 13375.0 410240.0 0.032
Gallbladder bile 4.804 0.36 60.76 17879000000.0 0.067 66910.0 233650.0 0.018
Genital organ-Epididymis 5.086 0.1836 45.53 16498000000.0 0.076 3922.0 969730.0 0.127
Genital organ-Fallopian tube 5.308 0.1204 47.7 18813000000.0 0.037 3949.0 1250300.0 0.152
Genital organ-Ovary 5.276 0.1655 47.02 19326000000.0 0.005 3009.0 1855700.0 0.166
Genital organ-Testis 5.42 0.1851 43.36 16782000000.0 0.056 4672.0 812700.0 0.169
Genital organ-Uterus 5.706 0.2084 47.39 19658000000.0 0.022 5033.0 1093100.0 0.153
Genital organ-Vagina 5.293 0.0979 47.59 19357000000.0 0.064 13664.0 544800.0 0.094
Intestine-Duodenum 4.794 0.2864 47.24 21629000000.0 0.063 3538.0 1309400.0 0.153
Intestine-Large intestine 3.031 0.153 50.43 21187000000.0 0.098 1715.0 1910800.0 0.09
Intestine-Mesenteric lymph 5.957 0.0993 24.58 16876000000.0 0.023 1393.0 1398500.0 0.167
Intestine-Small intestine 6.427 0.1616 37.81 18937000000.0 0.172 2180.0 1544900.0 0.141
Kidney 4.896 0.1048 38.77 18700000000.0 0.039 4997.0 934460.0 0.182
Liver 5.108 0.094 39.31 18121000000.0 0.062 3735.0 741590.0 0.2
Lung 4.211 0.1361 35.51 18434000000.0 0.093 1507.0 2072000.0 0.159
Mammary gland 5.416 0.0977 37.58 16312000000.0 0.073 40589.0 134720.0 0.081
Medulla oblongata 5.478 0.1052 31.4 21632000000.0 0.069 2371.0 1009900.0 0.239
Muscle-Heart 5.531 0.2158 44.12 17000000000.0 0.053 5409.0 815690.0 0.138
Muscle-Thigh 4.096 0.1882 48.26 17364000000.0 0.09 3578.0 1177000.0 0.121
Nerve (Spinal cord) 5.165 0.0893 25.99 20870000000.0 0.126 3166.0 445100.0 0.216
Pancreas 4.818 0.0 40.65 16722000000.0 0.098 21575.0 192360.0 0.138
Pericardium 5.484 0.1363 25.6 16700000000.0 0.098 1627.0 938820.0 0.055
Skin-Dermis 4.17 0.2049 39.17 13056000000.0 0.141 17201.0 137320.0 0.097
Skin-Epidermis 4.879 0.0199 32.04 19324000000.0 0.102 941.0 4108600.0 0.138
Skin-Epidermis + dermis 5.621 0.0 29.71 20259000000.0 0.085 1326.0 3778500.0 0.147
Skin-Subcutaneous tissue 3.048 0.0561 12.61 16332000000.0 0.092 9638.0 195970.0 0.04
Spleen 4.578 0.1061 41.87 18483000000.0 0.057 2110.0 1677500.0 0.185
Stomach 5.679 0.2358 50.15 19619000000.0 0.029 4318.0 913540.0 0.154
Submandibular gland 3.591 0.0702 28.33 18100000000.0 0.088 2548.0 918840.0 0.192
Tendon 4.159 0.064 49.88 15389000000.0 0.14 39759.0 124910.0 0.059
Thymus 4.939 0.1175 43.58 19400000000.0 0.044 2268.0 2460000.0 0.187
Thyroid 3.773 0.0368 28.69 17024000000.0 0.076 11783.0 235800.0 0.119

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Updated on 30, March, 2023.