Bipolar radiofrequency ablation with 2 × 2 electrodes as a building block for matrix radiofrequency ablation: Ex vivo liver experiments and finite element method modelling

Figures & data

Table 1. Variability of ablation size with commercial RF electrodes in ex vivo bovine liver [33].

Company	Covidien		AngioDynamics		Boston Scientific		Celon		This paper (matrix RFA)
Electrode name	Cool-Tip		Starburst XL		LeVeen		Celon Prosurge		Bipolar 2 x 2 electrodes
Electrode type	Cooled		Expandable		Expandable		Bipolar-cooled		Plain
Electric mode	Monopolar		Monopolar		Monopolar		Bipolar		Bipolar
n electrodes	1	Cluster of 3	1 (9 tines)	1 (9 tines)	1 (12 tines)	1 (12 tines)	2	3	4
Active tip length/
deployment (cm)	3	2,5	3	5	3	5	3	4	3
Duration: mean (min)	12	12	9,36	19,59	4,6	9,15	20,85	40,21	5,30
AD: mean (cm)	4	4,4	3,3	4,5	3,7	4,1	4	5,4	4,15
AD: SD (cm)	0,5	0,5	0,3	0,6	0,6	0,5	0,5	0,5	0,21
AD: CV (%)	13	11	9	13	16	12	13	9	5
TD: mean (cm)	3,75	4,6	3,1	4,05	3,85	5,85	3,7	5,7	3,43
TD: SD (cm)	0,5	0,5	0,6	1	0,7	1	0,6	1,1	0,36
TD: CV (%)	13	11	32	25	18	17	16	19	10

AD = axial diameter = diameter along electrode axis.

TD = transverse diameter = mean of the two orthogonal diameters perpendicular to the electrode axis.

SD = standard deviation.

CV = coefficient of variation = standard deviation/mean diameter.

Figure 1. Matrix radiofrequency ablation. The whole tumour volume is contained within a cage of x × y parallel electrodes. The volume within this cage is the sum of (x − 1) × (y − 1) square blocks, each determined by 2 × 2 electrodes. One cluster of 2 × 2 electrodes is the smallest functional unit of such a matrix of electrodes. Ablation of the whole volume is obtained by activation of the 2 × 2 electrodes around the first block, then rapidly switching to the electrodes around the second block, and so on until impedance rise at all blocks prevents further current flow.

Figure 2. Ex vivo bovine liver experiments. Temperature was monitored with a thermocouple in the centre of the square determined by the tips of the four radiofrequency electrodes.

Figure 3. Ex vivo bovine liver experiments: electric wiring scheme. ◯ = electrode; • = thermocouple. (A) standard ‘row’ pattern: the current flows between the first row of two positive electrodes and the second row of two negative electrodes (B) ‘chessboard’ pattern: the current flows between two positive electrodes which are at the opposite corners of the square and two negative electrodes which are at the other two opposite corners of the square.

Figure 4. (A) Ex vivo bovine liver experiments: influence of power on current (mean ± SD). (B) Ex vivo bovine liver experiments: influence of power on temperature (mean ± SD) measured in the centre of the square determined by the tips of the four radiofrequency electrodes. (C) Ex vivo bovine liver experiments: influence of power on ablation zone in axial and transverse plane and on mean duration until shut-off.

Figure 4. (D) FEM modelling with RAFEM-2: influence of power on temperature distribution in axial and transverse plane at current shut-off.

Figure 5. (A) Ex vivo bovine liver experiments: influence of duration on ablation zone in axial and transverse plane (50 W). (B) FEM modelling with RAFEM-2: influence of duration on temperature distribution in axial and transverse plane (50 W). There are no results for 6 and 10 min because power shut-off in the simulation occurred at 5 min 24 s.

Figure 6. (A) Ex vivo bovine liver experiments: influence of electrode diameter on current. (B) Ex vivo bovine liver experiments: influence of electrode diameter on temperature measured in the centre of the square determined by the tips of the four radiofrequency electrodes. (C) Ex vivo bovine liver experiments: influence of electrode diameter on ablation zone in axial and transverse plane. (D) FEM modelling with ANSYS: influence of electrode diameter on electric field (V/m) at the cross section of the axial and the transverse plane (distances measured from the centre). (E) FEM modelling with ANSYS: influence of electrode diameter on temperature (°C) after 130 s at the cross section of the axial and the transverse plane (distances measured from the centre).

Figure 7. (A) Ex vivo bovine liver experiments: influence of electrode pattern on ablation zone in axial and transverse plane. (B) FEM modelling with RAFEM-2: influence of pattern on electric field (V/m) in axial and transverse plane. (C) FEM modelling with RAFEM-2: influence of pattern on temperature (°C) in axial and transverse plane at current shut-off: 5 min 24 s for row pattern and 3 min 42 s for chessboard pattern.

Figure 8. (A) FEM modelling with RAFEM-2: temperature dependent changes in resistivity during the heating phase are described by a line-circle-line-circle exponential function, Equations 3–7, using parameters given in Table 2. (B) Determination of parameters in Equations 3–7 by fitting ex vivo bovine liver impedance data with RAFEM-2 (power = 50 W, distance between electrodes = 2 cm, diameter of electrode = 1.8 mm, row pattern).

Table 2. Parameters of the resistivity function.

Parameters	Unit	Value	Definition
ω0	Ωm	7.15	Resistivity at 0 °C
T1	°C	85	Temperature at the interception of L1 and L2
T2	°C	121	Temperature at the interception of C2 and Exp
k1	Ωm/°C	−0.065	Slope of L1
k2	Ωm/°C	0.16	Slope of L2
T1b – T1a	°C	15	Temperature span of arc C1
T2 – T2a	°C	5	Temperature span of arc C2
γ	°	80	Slope angle of the exponential curve at T2

Rathke H, Hamm B, Güttler F, Rathke J, Rump J, Teichgräber U, et al. Comparison of four radiofrequency ablation systems at target volumes of 3 and 5 cm in an ex vivo bovine liver model. Diagn Interv Radiol 2014;20:251–8

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