Radiofrequency ablation for liver tumors abutting complex blood vessel structures: treatment protocol optimization using response surface method and computer modeling

Figures & data

Figure 1. The geometric model of RFA for a liver tumor abutting a vascular structure: (a) a 3 D view and (b) X-Z cross-sectional view (with the variables ($x,z,\mathrm{and}\mathrm{ }\theta$) of electrode placement; dimension in mm and out of scale).

Table 1. The velocity and diameter of three vessels in the hepatic vascular system [27].

Vessels	Velocity (cm/s)	Diameter (mm)
Portal vein	19.8 ± 5.1	8–12
Hepatic vein	39.5 ± 12.2	5–9
Hepatic artery	44.3 ± 15.8	2–6

Table 2. Characteristics of the materials used in the theoretical model [32–34].

Modeling element	$\rho$(kg m^-3)	$C$(J kg^-1 K^-1)	$k_0$(W m^-1 K^-1)	$\delta (37)$(S m^-1)	${\omega }_{b0}$(kg m^-3 s^-1)
Liver tissue	1080^a	3455^a	0.515^c	0.203^c	17.03
	370^b	2156^b
Liver tumor	1045^a	3760^a	0.6^c	0.5^c	2.09
	370^b	2156^b
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

^aat temperature below 100 $°C;$ ^bat temperature above 100 $°C;$ ^cassessed at 37 $°C.$

Figure 2. The demonstration of impedance changes along with the energy supply under the impedance-controlled ablation protocol.

Figure 3. The quantification method of vessel thermal damage.

Figure 4. (a) the temperature change at 5, 10, 15, and 20 mm from the center of RF electrode, and (b) the temperature distribution at the ending of RFA treatment.

Table 3. Comparison of the temperature between the proposed RFA computer model and the ex vivo experiments.

Location (mm)	Temperature (°C)		Temperature (°C)
	Simulation	Experiment [27]	Simulation	Experiment* [37]
5	98.9	100.4 ± 1.4	–	–
10	78.3	79.5 ± 4.7	53.5	52 ± 4
15	59.6	57.3 ± 4.2	37.0	33 ± 2
20	45.5	46.2 ± 4.4	30.1	27 ± 1

*An approximate data derived from Figure 4 in [37].

Table 4. Results of ablation and thermal damage for each designed simulation.

No.	Variables				Responses
	t (s)	x (mm)	z (mm)	$\theta$ (°)	$R_a$ (%)	$D_t$ (%)
1	720	60	53.5	0	86.0%	5.2%
2	660	65	53.5	0	88.6%	6.1%
3	720	65	53.5	30	90.3%	5.5%
4	720	65	53.5	−30	39.5%	27.3%
5	780	65	53.5	0	91.6%	8.4%
6	720	70	53.5	0	84.8%	15.0%
7	660	60	58.5	0	97.5%	0.0%
8	720	60	58.5	30	70.8%	0.0%
9	720	60	58.5	−30	70.4%	11.4%
10	780	60	58.5	0	99.3%	0.3%
11	660	65	58.5	30	65.4%	4.2%
12	660	65	58.5	−30	64.2%	21.5%
13	720	65	58.5	0	98.1%	4.1%
14	780	65	58.5	30	67.8%	4.2%
15	780	65	58.5	−30	66.2%	22.2%
16	660	70	58.5	0	96.7%	10.8%
17	720	70	58.5	30	60.7%	14.2%
18	720	70	58.5	−30	60.4%	30.6%
19	780	70	58.5	0	98.3%	11.6%
20	720	60	63.5	0	84.2%	0.0%
21	660	65	63.5	0	89.6%	7.1%
22	720	65	63.5	−30	42.1%	6.5%
23	720	65	63.5	30	90.3%	19.9%
24	780	65	63.5	0	92.5%	7.1%
25	720	70	63.5	0	83.5%	11.9%

Table 5. The value of coefficient in RSM regression model.

	$R_a$	p Value	$D_t$	p Value
${\beta }_0$	0.342	<0.001	0.203	0.003
${\beta }_1$	0.030	0.385	0.002	0.530
${\beta }_2$	0.093	0.143	0.086	<0.001
${\beta }_3$	0.777	0.928	−0.166	0.039
${\beta }_4$	1.660	0.695	−0.516	<0.001
${\beta }_{12}$	−0.002	0.982	0.004	0.910
${\beta }_{13}$	−0.001	0.991	−0.023	0.543
${\beta }_{14}$	0.004	0.964	−0.007	0.854
${\beta }_{23}$	0.005	0.956	0.020	0.594
${\beta }_{24}$	−0.001	0.991	−0.050	0.203
${\beta }_{34}$	−0.990	<0.001	0.084	0.043
${\beta }_{11}$	0.008	0.918	0.018	0.587
${\beta }_{22}$	−0.134	0.105	0.055	0.111
${\beta }_{33}$	−0.282	0.003	0.100	0.009
${\beta }_{44}$	−1.156	<0.001	0.338	<0.001
$R_{\mathit{adj}}^2$	93.61%		95.03%

Figure 5. The multi-objective optimization results of RSM (the red solid line and blue dashed line represent the optimal solutions and predictive results of the regression models, respectively).

Figure 6. The RFA treatment results in X-Z cross-sectional view: (a–c) ablation, thermal damage, and temperature distribution, respectively for the optimized protocol; (d–f) ablation, thermal damage, and temperature distribution, respectively for the reference protocol. (The black line is the contour line of tumor).

Goldberg SN, Stein MC, Gazelle GS, et al. Percutaneous radiofrequency tissue ablation: Optimization of Pulsed-Radiofrequency technique to increase coagulation necrosis. J Vasc Intervent Radiol. 1999;10(7):907–916.

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Haemmerich D. Mathematical modeling of impedance controlled radiofrequency tumor ablation and ex-vivo validation In 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology. IEEE, 2010. p. 1605–1608.

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