Temperature- and frequency-dependent dielectric properties of biological tissues within the temperature and frequency ranges typically used for magnetic resonance imaging-guided focused ultrasound surgery

Figures & data

Table I. Chronological summary of previously published temperature-dependent dielectric properties of various biological tissues.

Tissue type	Frequency range	Temperature range	Reference
Various human autopsy material (see reference)	200 MHz, 400 MHz, 900 MHz	27–42 °C	Schwan and Kam [8]
Biological tissues^a	Microwave^b	Not mentioned	Johnson and Guy [12]
Brain	<0.1 GHz, <2 GHz, 7 GHz	22–25 °C, 37 °C	Foster et al. [9]
Biological tissues^a	Microwave^b	16–36 °C	Schwan and Foster [13]
Myocardium	0.2, 1.1, 2.5, 3.0, 4.0, 5.0, 6.0 GHz	23–37 °C	Semenov et al. [10]
Bovine liver	915 MHz	Above 60 °C	Chin and Sherar [14]
Cow, sheep, and human blood	1 MHz–1 GHz	25–45 °C	Jaspard and Nadi [11]
Bovine and porcine livers	915 MHz	10–90 °C	Stauffer et al. [16]
Rat prostate	915 MHz	45–75 °C	Chin and Sherar [15]
Bovine and porcine livers	500 MHz–20 GHz	Room temperature to 60 °C	Lazebnik et al. [22]
Bovine livers	915 MHz, 2.45 GHz	0–100 °C	Brace [17]

Notes: ^aTissues not specified in the reference.

^bFrequencies not specified in the reference.

Figure 1. Equivalent circuit of the open-ended coaxial probe method. is the equivalent capacitor corresponding to the fringing field in Teflon, is the capacitance accounting for the fringing field in air, and is the complex relative permittivity.

Figure 2. Measured reflection coefficient and reflection coefficient Γ.

Figure 3. Diagram of the measurement system. 1, coaxial line; 2, digital micro-thermometer (used to measure tissue temperature); 3, water bath incubator (used to control water temperature); 4, heater (used to heat water); 5, salver (used to place the tissues); 6, magnet (used to fix the tissues); 7, preservative film (used to pack the tissues); 8, thermometer probe; 9, water.

Figure 4. Smith chart of (A) an open-circuit termination and (B) a short-circuit termination. The reflection coefficients in (B) can be obtained by rotating at an angle of 180° of the reflection coefficients in (A) around the centre point.

Figure 5. Temperature-dependent dielectric properties of porcine tissues at 43 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 6. Temperature-dependent dielectric properties of porcine tissues at 64 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 7. Temperature-dependent dielectric properties of porcine tissues at 128 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 8. Temperature-dependent dielectric properties of porcine tissues at 170 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 9. Temperature-dependent dielectric properties of porcine tissues at 298 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 10. Temperature-dependent dielectric properties of porcine tissues at 400 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Figure 11. Temperature-dependent dielectric properties of porcine tissues at 468 MHz, with mean values and uncertainty margins of the dielectric constant and electric conductivity.

Table II. Maxima of standard uncertainties of the dielectric constant and conductivity of the tissues in this study.

	Standard uncertainties of the dielectric measurements (95% CI)
Tissue	43 MHZ (%)	64 MHz (%)	128 MHz (%)	170 MHz (%)	298 MHz (%)	400 MHz (%)	468 MHz (%)
Uterus
	2.36	2.05	2.53	2.68	3.07	3.07	3.17
(S/m)	6.19	5.63	4.80	4.76	4.41	4.16	4.09
T(°C)	4.65	3.28	4.35	4.43	4.28	4.66	3.43
Liver
	2.75	2.48	1.74	2.91	2.92	2.73	2.73
(S/m)	3.65	3.39	2.96	2.76	2.36	2.12	2.01
T(°C)	4.19	4.63	4.81	4.46	4.21	4.13	4.12
Kidney
	1.68	2.09	1.95	2.08	2.41	2.46	2.53
(S/m)	1.97	1.97	1.70	1.56	3.3	1.84	2.5
T(°C)	3.79	4.63	4.31	4.44	4.12	3.96	3.87
Bladder
	2.73	2.48	2.32	2.35	2.39	2.5	2.33
(S/m)	7.64	7.04	5.85	5.57	4.84	4.44	4.21
T(°C)	4.23	4.31	3.97	4.56	3.78	3.98	4.04
Skeletal muscle
	1.66	1.35	1.77	1.78	1.95	1.96	1.95
(S/m)	2.88	2.87	2.6	2.71	2.12	2.16	2.07
T(°C)	4.45	4.34	4.67	3.97	3.89	3.85	4.21
Fat
	8.35	8.88	9.52	9.52	10.36	11.28	11.05
(S/m)	10	10.62	10.58	10	9.47	10	10.02
T(°C)	4.13	4.28	3.99	4.15	4.47	4.56	4.19

Table III. Range of variation (N = 3) of the dielectric properties at 45 °C, at different discrete frequencies. Mean values of dielectric properties of different tissues at different frequencies can be obtained from Figures 5–11.

	Variability of the dielectric measurements
Tissue	Uterus	Liver	Kidney	Bladder	Muscle	Fat
43 MHz
	96.88–107.28	121.37–124.77	147.87–152.87	117.13–123.13	156.08–161.08	18.36–21.36
(S/m)	1.03–1.06	0.55–0.57	0.83–0.87	0.87–0.88	0.97–1.03	0.17–0.21
64 MHz
	80.46–87.46	94.49–96.79	114.21–117.51	91.84–96.44	114.59–117.49	15.15–18.05
(S/m)	1.06–1.1	0.6–0.62	0.89–0.93	0.9–0.91	1.02–1.08	0.15–0.21
128 MHz
	66.96–71.06	68.45–70.75	78.11–81.71	69.59–72.89	83.73–85.53	11.32–13.82
(S/m)	1.14–1.16	0.7–0.72	0.99–1.03	0.97–0.98	1.09–1.15	0.17–0.22
170 MHz
	60.35–66.05	62.07–64.77	71.92–74.12	65.01–68.11	75.54–77.04	11.39–13.89
(S/m)	1.15–1.19	0.71–0.73	1.02–1.05	0.99–1.01	1.12–1.18	0.19–0.23
298 MHz
	55.68–60.18	53.56–56.36	60.06–63.36	57.9–60.8	67.19–68.39	9.61–12.01
(S/m)	1.19–1.23	0.79–0.81	1.07–1.1	1.03–1.04	1.19–1.23	0.2–0.24
400 MHz
	53.78–58.78	50.29–52.99	57.43–60.43	55.51–58.41	63.51–64.51	9.23–11.53
(S/m)	1.26–1.3	0.83–0.85	1.12–1.14	1.04–1.07	1.21–1.26	0.2–0.24
468 MHz
	53.24–57.44	49.68–51.68	55.71–59.11	54.93–57.73	62.81–64.01	9.03–11.33
(S/m)	1.28–1.32	0.87–0.88	1.13–1.15	1.07–1.09	1.22–1.26	0.21–0.26

Table IV. Comparison of the comparable dielectric constants of the biological tissues between this study and previous studies [6,32].

	Tissue	Dielectric constant (37 °C) at discrete frequency
Uterus
Human^a	MHz	43.36	62.68	131	172.6	300	395.5	475.5
		133	110	81.53	75.37	67.73	65.37	64.2
Porcine	MHz	43	64	128	170	298	400	468
		95.64	82.33	69.9	65.65	61.49	59.72	59.77
Liver
Bovine^a	MHz	43.36	62.68	131	172.6	300	395.5	475.5
		103.2	83.19	62.61	58.15	52.63	50.79	49.89
Porcine	MHz	43	64	128	170	298	400	468
		113.22	89.93	67.83	62.68	55.29	52.74	51.95
Kidney
Bovine^a	MHz	43.36	62.68	131	172.6	300	395.5	475.5
		158	119	78.85	70.4	60.95	58.03	56.65
Porcine	MHz	43	64	128	170	298	400	468
		137.09	107.74	78.16	72.85	63.4	61.26	59.93
Skeletal muscle
Bovine^a	MHz	43.36	62.68	131	172.6	300	395.5	475.5
		97.98	90.2	76.26	72.23	66.71	64.72	63.9
Porcine	MHz	43	64	128	170	298	400	468
		146.98	110.57	83.62	76.04	68.7	65.3	64.94

Note: ^aData from the literature.

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