Study of the relationship between the target tissue necrosis volume and the target tissue size in liver tumours using two-compartment finite element RFA modelling

Figures & data

Figure 1. Dimensions (out of scale and in mm) and boundary conditions of the two-compartment RFA model used in the present study.

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

Modelling element	Material	(kg m^−3)	C (J kg^−1K^−1)	k (W m^−1K^−1)	σ (S m^−1)	(kg m^−3s^−1)
Biological tissue	Healthy liver tissue	1080	3455	Equation 4	Equation 5	17.03
	Liver tumour	1045	3760			2.09
RF electrode	Ni-Ti	6450	840	18	1.0 × 10^8	–
Insulated shaft	Polyurethane	70	1045	0.026	1.0 × 10^−5	–
Blood vessel	Blood	1000	4180	0.49	0.667	–

Figure 2. Placements of the five measured points (out of scale, dimension in mm).

Table 2. Computational results for four target tissue sizes during different RFA protocols.

Target tissue (mm)	Ablation protocol	Maximum temperature (°C)	IT50 (mm)	D63 (mm)	Complete ablation
= 20	35V–720s	105	= 23.445,  = 44.303	= 22.103,  = 42.491	Y
	36.6V–720s	105	= 26.270, Dyz = 44.023	= 23.499,  = 42.792	Y
	37V–490s	106	= 25.257,  = 43.814	= 22.562,  = 42.476	Y
	40V–170s	108	= 22.990,  = 43.165	= 18.312,  = 40.780	Y
= 25	34V–720s	104	= 26.729,  = 43.597	= 25.744,  = 42.050	Y
	35.4V–720s	105	= 27.736,  = 43.997	= 26.785,  = 42.593	Y
	36V–410s	107	= 27.057,  = 43.337	= 25.652,  = 41.611	Y
	38V–200s	108	= 25.419,  = 42.946	= 20.171,  = 40.771	N
= 30	32V–720s	104	= 29.196,  = 42.230	= 27.447,  = 41.772	N
	33.9V–720s	105	= 30.641,  = 43.400	= 29.806,  = 42.576	Y–N
	34V–620s	105	= 30.431,  = 43.208	= 28.340,  = 42.438	Y–N
	37V–185s	106	= 26.322,  = 42.407	= 19.802,  = 39.345	N
= 35	31V–720s	103	= 31.679,  = 41.846	= 29.527,  = 40.831	N
	32.5V–720s	104	= 33.193,  = 42.828	= 30.998,  = 41.282	N
	33V–525s	105	= 32.561,  = 42.818	= 20.431,  = 39.898	N
	35V–245s	107	= 28.893,  = 42.278	= 23.136,  = 40.462	N

Y: yes, N: no

Bold mean that the ablation protocols, which can achieve the largest TTN volume and complete TTN.

Figure 3. TTN volume for each target tissue size at different voltages applied: (A)  = 20 mm, (B)  = 25 mm, (C)  = 30 mm and (D)  = 35 mm.

Figure 4. MVA without the roll-off occurrence for each target tissue size.

Figure 5. Computer simulation results for the TTN of target tissues of different sizes at the MVA (A) 100 °C isotherm, (B) temperature distribution (in °C), (C) tissue death (IT50) and (D) tissue death rate (%) (D63).

Table 3. Volumetric percentage of thermal damage to the healthy liver tissue during different RFA protocols.

Target tissue (mm)	Ablation protocol	(mm^3)	(mm^3)	VP (%)
= 20	35V–720s	934872.2	3093.9	0.33
	36.6V–720s		5416.9	0.58
	37V–490s		3854.1	0.41
	40V–170s		851.5	0.09
= 25	34V–720s	930631.0	1326.3	0.14
	35.4V–720s		2143.3	0.23
	36V–410s		1078.2	0.12
	38V–200s		397	0.04
= 30	32V–720s	925447.1	492	0.05
	33.9V–720s		1031.1	0.11
	34V–620s		861.4	0.09
	37V–185s		168.3	0.02
= 35	31V–720s	919321.0	347.2	0.03
	32.5V–720s		636.1	0.07
	33V–525s		466.5	0.05
	35V–245s		188.6	0.02

Bold mean the two optimal RFA protocols for the 20-mm and 25-mm target tissues, respectively.

Figure 6. Temperature change during the 12-min ablation procedure for each target tissue at its own MVA: (A)  = 20 mm, (B)  = 25 mm, (C)  = 30 mm and (D)  = 35 mm.

Figure 7. Temperature distributions (in °C) obtained with the two-compartment RFA model (A) and the homogenous RFA model (B).