Numerical analysis of the relationship between the area of target tissue necrosis and the size of target tissue in liver tumours with pulsed radiofrequency ablation

Figures & data

Figure 1. 2D axis symmetric RFA model and its boundary conditions used in the present study (out of scale, dimension in mm).

Table 1. Thermal and electrical properties of the modelling elements used in the present study.

Modelling element	ρ (kg m^−3)	c (J kg^−1 K^−1)	k (W m^−1 K^−1)	σ (S m^−1)	ω0 (kg m^−3 s^−1)
Healthy liver tissue	1080	3455	0.515^a	0.203^a	17.03^a
Liver tumour	1045	3760	0.60^a	0.50^a	2.09^a
RF electrode	6450	840	18	1.0 × 10^8	–
Insulated shaft	70	1045	0.026	1.0 × 10^−5	–
Blood vessel	1000	4180	0.49	0.667	–

^aEvaluated at 21 °C.

Figure 2. Thermal and electrical conductivities of healthy liver tissue and liver tumour used in the present study.

Table 2. Comparisons of TTN areas from the FEM and in vitro experiment.

Ablation time (s)	TTN area	In vitro experiments#	FEM
360	Dx (mm)	10. 9 ± 0.3	11.2
	Dy (mm)	34.4 ± 0.4	34.6
	Area (mm^2)	295. 6 ± 9.4	325.8
720	Dx (mm)	13.3 ± 0.3	13.6
	Dy (mm)	35.9 ± 0.3	36.1
	Area (mm^2)	374.9 ± 10.4	407.4

#Results of the in vitro experiments were given as mean ± standard deviation.

Figure 3. Two pulsed RF power supply methods: (A) half-square waveform and (B) half-sine waveform.

Figure 4. Finite element models and their mesh modes used in the present study for three sizes of target tissues: (A) 25 mm, (B) 30 mm and (C) 35 mm.

Figure 5. In vitro experimental set-up for the validation of the FEM.

Figure 6. Computational and experimental results for two ablation operations: (A) 360 s, (B) 720 s.

Figure 7. 100 °C isotherm and temperature distribution of the scenario of 47.2 V-720 s at 50 s (A), 442 s (B) and 720 s (C) and the change of the impedance (D).

Figure 8. 100 °C isotherm and temperature distribution of the scenario of 48 V-145 s at 25 s (A), 118 s (B) and 145 s (C) and the change of the impedance (D).

Figure 9. Computational results of TTN areas for target tissues with different sizes: (A) d_x = 25 mm, (B) d_x = 30 mm and (C) d_x = 35 mm.

Table 3. The computational results of TTN area for all PRFA protocols in the present study.

Target tissue (mm)	Pulsed RF waveform	Ablation protocol	D63 (mm)	Complete ablation
dx = 25	Half-square	46 V-720 s	Dx = 19.90, Dy = 40.00	No
		47.2 V-720 s	Dx = 25.00, Dy = 40.00	Yes
		48 V-334 s	Dx = 15.26, Dy = 36.84	No
		51 V-118 s	Dx = 11.16, Dy = 37.36	No
	Half-sine	68 V-720 s	Dx = 18.46, Dy = 36.30	No
		69.9 V-720 s	Dx = 19.18, Dy = 36.48	No
		70 V-682 s	Dx = 18.62, Dy = 35.92	No
		73 V-132 s	Dx = 9.06, Dy = 31.72	No
dx = 30	Half-square	43 V-720 s	Dx = 21.62, Dy = 39.96	No
		44.9 V-720 s	Dx = 25.38, Dy = 40.00	No
		45 V-685 s	Dx = 23.52, Dy = 39.84	No
		48 V-145 s	Dx = 12.90, Dy = 35.00	No
	Half-sine	65 V-720 s	Dx = 19.70, Dy = 36.46	No
		66.5 V-720 s	Dx = 21.60, Dy = 36.50	No
		67 V-457 s	Dx = 17.82, Dy = 35.30	No
		70 V-132 s	Dx = 10.02, Dy = 32.56	No
dx = 35	Half-square	42 V-720 s	Dx = 23.96, Dy = 40.00	No
		43.3 V-720 s	Dx = 25.74, Dy = 40.00	No
		44 V-451 s	Dx = 20.96, Dy = 37.58	No
		47 V-145 s	Dx = 13.54, Dy = 34.98	No
	Half-sine	63 V-720 s	Dx = 21.10, Dy = 35.52	No
		64.4 V-720 s	Dx = 22.64, Dy = 36.38	No
		65 V-432 s	Dx = 19.06, Dy = 35.42	No
		68 V-132 s	Dx = 10.70, Dy = 32.60	No

Figure 10. Target tissue death rate (%) (D63) at its own MVA: (A) d_x = 25 mm, (B) d_x = 30 mm and (C) d_x = 35 mm and the changes of the TTN areas (D).

Figure 11. MVA without the roll-off occurrence for each size of target tissue in the present study.