Electrical and thermal analyses of catheter-based irreversible electroporation of digestive tract

Figures & data

Figure 1. Model of digestive tract and electrode configurations. (A) Geometric parameters of digestive tract model, tumor domain, and normal domain. (B) Schematic drawing of the monopolar model. (C) Schematic drawing of the bipolar model. ML: mucosal layer; SL: submucosal layer; MP: muscularis propria.

Table 1. Electrical and thermal properties of biological tissue and electrode.

Tissue	Muscularis propria	Submucosa layer	Mucosa layer	Electrode
Electrical conductivity (S/m)	0.202	0.251	0.511	3.80×10^7
A	1.5	1.8	1.8	/
Edelta (V/cm)	500	600	600	/
Erange (V/cm)	300	150	150	/
Density (kg/m³)	1090	1027	1088	2700
Heat capacity (J/kg·°C)	3421	2372	3690	910
Thermal conductivity (W/m·°C)	0.49	0.39	0.53	250
Heat transfer rate (ml/min·kg)	37	37	460	/
Heat generation rate (W/kg)	0.91	0.58	7.13	/
References	[22,35–38]	[22,35–38]	[22,35–38]	[35]

Table 2. Base value, range and step length of each parameter.

Parameter	Symbol	Range	Step	Base value
Electrode spacing	d	5–10 mm	1 mm	5 mm
Electrode length	l	5–10 mm	1 mm	5 mm
Voltage	V	0.50–2.00 kV	0.50 kV	0.50 kV
Pulse number	N	0–100	1	0

Figure 2. Effects of electrode length and pulse voltage on the distribution of electric fields in monopolar model. (A) RAR of EEF in digestive tract for different electrode lengths and pulse voltages. (B) RAR of EEF in mucosa for different electrode lengths and pulse voltages. (C) RAR of EEF in submucosa for different electrode lengths and pulse voltages. (D) RAR of EEF in muscularis propria for different electrode lengths and pulse voltages. (E) Distribution of electric fields for different electrode lengths and voltages. EEF: effective electric field; ML: mucosal layer; MP: muscularis propria; SL: submucosal layer; RAR: relative area ratio; V: voltage; l: electrode length.

Figure 3. Effects of electrode length and pulse voltage on the distribution of electric fields for different electrode spacing in bipolar model. (A–F) RAR of EEF in digestive tract for different electrode lengths and pulse voltages (d ranges from 5 to 10 mm). (G) Distribution of electric fields for different electrode lengths (V = 1.00 kV, d = 5 mm). (H) Distribution of electric fields for different pulse voltages (d = 5 mm, l = 5 mm). V: voltage; d: electrode spacing; l: electrode length; EEF: effective electric field; RAR: relative area ratio.

Figure 4. Effects of electrode spacing and pulse voltage on electric field distribution in bipolar model. (A–F) RAR of EEF in digestive tract for different electrode spacing and pulse voltages (l ranges from 5 to 10 mm. (G) RAR of EEF in mucosa for different electrode spacing and pulse voltages. (H) RAR of EEF in submucosa for different electrode spacing and pulse voltages. (I) RAR of EEF in muscularis propria for different electrode spacing and pulse voltages. (J) Distribution of electric fields for different electrode spacing and pulse voltages. V: voltage; d: electrode spacing; l: electrode length; EEF: effective electric field; ML: mucosal layer; SL: submucosal layer; MP: muscularis propria; RAR: relative area ratio.

Figure 5. Effects of electrode length and pulse voltage on electrical and thermal injury by 100 pulses in the tumor tissue of the monopolar model. (A) l = 5 mm. (B) l = 6 mm. (C) l = 7 mm. (D) l = 8 mm. (E) l = 9 mm. (F) l = 10 mm. l: electrode length.

Figure 6. Effects of electrode spacing and pulse voltage on electrical and thermal injury by 100 pulses in the tumor tissue of the bipolar model. (A) d = 5 mm. (B) d = 6 mm. (C) d = 7 mm. (D) d = 8 mm. (E) d = 9 mm. (F) d = 10 mm. d: electrode spacing.

Table 3. Relative area ratio of EI_0.99, TI_0.99, average temperature of tissue and outcomes at N_min in the monopolar model.

V (kV)	l (mm)	Nmin	Tumor tissue			Normal tissue			Protocol outcome
			PTI > 0.99	PEI > 0.99	Average temperature (°C)	PTI > 0.99	PEI > 0.99	Average temperature (°C)
0.50	5.00	100	0.00	0.99	50.78	0.00	0.03	38.28	T-IRE
	6.00	92	0.00	1.00	51.43	0.00	0.04	38.39	T-IRE
	7.00	81	0.00	1.00	51.31	0.00	0.03	38.42	T-IRE
	8.00	75	0.00	1.00	51.42	0.00	0.04	38.57	T-IRE
	9.00	68	0.00	1.00	51.05	0.00	0.04	38.69	T-IRE
	10.00	68	0.00	1.00	51.65	0.00	0.07	39.07	T-IRE
1.00	5.00	81	1.00	1.00	96.62	0.01	0.03	41.20	TI
	6.00	75	1.00	1.00	99.05	0.03	0.04	41.67	TI
	7.00	70	1.00	1.00	H	0.05	0.05	42.27	TI
	8.00	61	1.00	1.00	96.49	0.05	0.05	42.36	TI
	9.00	53	1.00	1.00	91.47	0.06	0.05	42.49	TI
	10.00	51	1.00	1.00	90.66	0.08	0.07	43.42	TI
1.50	5.00	72	1.00	1.00	H	0.12	0.04	46.46	TI
	6.00	64	1.00	1.00	H	0.13	0.04	46.72	TI
	7.00	57	1.00	1.00	H	0.13	0.05	47.18	TI
	8.00	48	1.00	1.00	H	0.12	0.04	46.68	TI
	9.00	41	1.00	1.00	H	0.12	0.05	46.74	TI
	10.00	39	1.00	1.00	H	0.15	0.07	48.70	TI
2.00	5.00	63	1.00	1.00	H	0.18	0.05	54.22	TI
	6.00	56	1.00	1.00	H	0.18	0.05	54.47	TI
	7.00	48	1.00	1.00	H	0.17	0.05	53.65	TI
	8.00	40	1.00	1.00	H	0.16	0.05	52.55	TI
	9.00	33	1.00	1.00	H	0.15	0.05	51.67	TI
	10.00	31	1.00	1.00	H	0.17	0.07	54.90	TI

V: voltage; l: electrode length; N_min: the minimum number of pulses required to reach IRE in the tumor domain; PEI > 0.99, probability of electrical injury > 0.99; PTI > 0.99, probability of thermal injury > 0.99; NT-IRE: nonthermal irreversible electroporation; T-IRE: thermal irreversible electroporation; TI: thermal injury; H: the value is greater than 100 °C.

Table 4. Relative area ratio of EI_0.99, TI_0.99, average temperature of tissue, and outcomes at N_min in the bipolar model.

V (kV)	d (mm)	Nmin	Tumor tissue			Normal tissue			Protocol outcome
			PTI > 0.99	PEI > 0.99	Average temperature (°C)	PTI > 0.99	PEI > 0.99	Average temperature (°C)
0.50	5	100	0.00	0.97	40.93	0.00	0.01	37.59	NT-IRE
	6	100	0.00	0.98	40.04	0.00	0.02	37.48	NT-IRE
	7	100	0.00	0.99	39.30	0.00	0.03	37.39	NT-IRE
	8	96	0.00	1.00	38.65	0.00	0.02	37.30	NT-IRE
	9	93	0.00	1.00	38.23	0.00	0.01	37.24	NT-IRE
	10	92	0.00	1.00	38.04	0.00	0.02	37.22	NT-IRE
1.00	5	82	0.13	1.00	53.64	0.00	0.03	39.00	TI
	6	81	0.00	1.00	50.95	0.00	0.04	38.78	T-IRE
	7	77	0.00	1.00	48.51	0.00	0.02	38.53	T-IRE
	8	76	0.00	1.00	46.98	0.00	0.03	38.43	T-IRE
	9	75	0.00	1.00	45.69	0.00	0.04	38.36	T-IRE
	10	74	0.00	1.00	44.56	0.00	0.05	38.30	T-IRE
1.50	5	74	0.87	1.00	76.03	0.00	0.03	41.20	TI
	6	71	0.73	1.00	68.44	0.00	0.02	40.55	TI
	7	69	0.60	1.00	63.11	0.00	0.03	40.14	TI
	8	67	0.34	1.00	59.03	0.00	0.03	39.85	TI
	9	65	0.05	1.00	55.76	0.00	0.04	39.64	TI
	10	64	0.00	1.00	53.25	0.00	0.04	39.53	T-IRE
2.00	5	68	1.00	1.00	H	0.10	0.04	44.46	TI
	6	65	1.00	1.00	94.99	0.05	0.03	43.04	TI
	7	60	0.95	1.00	81.94	0.01	0.01	41.89	TI
	8	58	0.89	1.00	74.49	0.00	0.02	41.42	TI
	9	56	0.79	1.00	68.41	0.00	0.03	41.06	TI
	10	55	0.59	1.00	63.95	0.00	0.04	40.88	TI

V: voltage; d: electrode spacing; N_min: the minimum number of pulses required to reach IRE in the tumor domain; PEI > 0.99, probability of electrical injury > 0.99; PTI > 0.99, probability of thermal injury > 0.99; NT-IRE: nonthermal irreversible electroporation; T-IRE: thermal irreversible electroporation; TI: thermal injury; H: the value is greater than 100 °C.

Figure 7. Distributions of electrical conductivity, electric fields, temperature and electrical and thermal injury at N_min. (A) MPM V = 0.50 kV, l = 5 mm, N = 100. (B) MPM V = 1.00 kV, l = 5 mm, N = 81. (C) MPM V = 1.50 kV, l = 5 mm, N = 72. (D) MPM V = 2.00 kV, l = 5 mm, N = 63. (E) BPM V = 0.50 kV, d = 5 mm, N = 100. (F) BPM V = 1.00 kV, d = 5 mm, N = 82. (G) BPM V = 1.50 kV, d = 5 mm, N = 74. (H) BPM V = 2.00 kV, d = 5 mm, N = 68. EI: electrical injury; TI: thermal injury; OI: overall injury; V: voltage; l: electrode length; N: pulse number; σ: electrical conductivity; E: electric field; T: temperature.

Figure 8. Distributions of electrical injury and thermal injury at N_min in IRE protocols. (A) BPM V = 0.50 kV, d = 7 mm, N = 100; (B) BPM V = 0.50 kV, d = 8 mm, N = 96; (C) BPM V = 0.50 kV, d = 9 mm, N = 93; (D) BPM V = 0.50 kV, d = 10 mm, N = 92; (E) BPM V = 1.00 kV, d = 7 mm, N = 77; (F) BPM V = 1.00 kV, d = 8 mm, N = 76; (G) BPM V = 1.00 kV, d = 9 mm, N = 75; (H) BPM V = 1.00 kV, d = 10 mm, N = 74; (I) MPM V = 0.50 kV, l = 7 mm, N = 80; (J) MPM V = 0.50 kV, l = 8 mm, N = 75; (K) MPM V = 0.50 kV, l = 9 mm, N = 68; (L) MPM V = 0.50 kV, l = 10 mm, N = 68. V: voltage; d: electrode spacing; N: pulse number; σ: electrical conductivity; E: electric field; T: temperature; EI: electrical injury; TI: thermal injury; OI: overall injury.

Figure 9. Comparison of the monopolar model (l = 5 mm) and bipolar model (d = 6 mm) at a Voltage of 0.50 kV. (A) Changing trend of temperature during one pulse. (B) Distribution of temperature at the end of one pulse in the MPM (upper) and the BPM (bottom). (C) Changing trend of average temperature in the tumor tissue during 100 pulses. (D) RAR of EI_0.99 and TI_0.99 in different layers of the digestive tract for 100 pulses in the MPM (solid line) and the BPM (imaginary line). (E) Distribution of electrical injury at 25, 50, 75 and 100 pulses in the MPM (upper) and the BPM (bottom). (F) Distribution of thermal injury at 25, 50, 75 and 100 pulses in the MPM (upper) and the BPM (bottom). V: voltage; d: electrode spacing; l: electrode length; N: pulse number; MPM: monopolar model; BPM: bipolar model; ML: mucosal layer; SL: submucosal layer; MP: muscularis propria.

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Data availability statement

The data that support the findings of this study are available from the corresponding author R. Wu and Y. Lv upon reasonable request.