In this section, the results of the experiments performed to validate the models are presented. After model validation, the optimization process to obtain the optimal IRE parameter configuration for bovine liver is also described.

Validation of the models

Finite element model was empirically validated by comparing the model result with the temperature measured in the bovine liver tissue during the IRE experiments. The experimental results are presented in Fig. 3. Three trials of experiments were performed for each combination, where active length and distance between electrode were set to constant at 10 mm.

Fig. 3
figure3

Maximum temperature in the IRE experiment and models simulation in bovine liver tissue with varying a pulse number and b pulse width

Figure 3a presents the temperature achieved by varying the pulse number and the voltage for each experiment. Pulse width was set to constant of 100 μs while combination of pulse number 30, 60, and 90, and input voltage 1000 V, 2000 V, and 3000 V were used. The errors of the temperature measured in the center of the electrode were relatively low, around 3.9 ± 4.2%, except for the last experiment with 3000 V and 90 pulses that achieved error up to 13.2%. Regarding the thermal damage, bovine liver tissue reached maximum temperature more than 50 °C, when the voltage was set to 3000 V and pulse number 60 and 90. Surprisingly, the figure also revealed that with an increase in pulse number and voltage, the maximum temperature in bovine liver was also increased.

The result from the experiment with the pulse width is shown in Fig. 3b. In this experiment, pulse number was set to 90 pulses, while the pulse width and voltage were set to be varied. The error percentage for all the experiment was around 2.9 ± 4.2% for the temperature measurement except for the last experiment with 3000 V and 100 μs combination. Overall, the temperature between the FEM simulation and the ex vivo experiments was quite similar, and it is possible to affirm that the models were validated and can be used for calculating the response of the IRE parameters in the optimization study.

IRE optimization for the treatment on liver tissue

According to Table 1, the experiments will have 162 different possible combinations of parameters. To reduce the number of experiments to be performed without losing significant information, the Taguchi method was used [25]. An L18(21 34) Taguchi design was applied using Minitab 18, resulting 18 combinations of parameters.

After validating the models, the IRE experiment using 18 combination of five IRE parameters was performed by using the FEM analysis. The response of these IRE parameters to the maximum temperature and ablation coverage area (EF > 800 V/m) are presented in Table 5.

Table 5 Ablation area and maximum temperature response on various IRE parameter configuration

RSM was used in Minitab to analyze the result in Table 5. From this method, the relationship between the responses and the variables can be obtained in the form of factorial plots as seen in Fig. 4. Also, the optimal solution of the IRE parameter configuration can be calculated as seen in Fig. 5, to obtain the maximum ablation area between the electrodes without achieving thermal damage in the tissue (temperature lower than 50 °C).

Fig. 4
figure4

Maximum temperature and ablation coverage area (EF > 800 V/s) response to various IRE parameters configuration, including: a active length, b electrode distance, c voltage, d pulse number, and e pulse width

Fig. 5
figure5

Optimization results obtained from RSM. The optimal parameters are presented on the top row, between brackets and in red. The red lines in the graph represent the optimal solutions. The blue dashed lines represent the target values of the objective functions, in this case, the maximum electric field and a temperature of 50 °C

Based on the result in Fig. 4a, b, increasing the active length and the distance of the electrodes is the best option to reduce the maximum temperature while enlarging the ablation area during the treatment. More significant ablation area can be achieved by adjusting the voltage, but it has to be chosen carefully since it also increases the temperature considerably according to Fig. 4c. In term of pulse number (Fig. 4d) and pulse width (Fig. 4e), it is better to use a smaller value to keep the temperature low. Moreover, no significant result can be seen from increasing pulse number and pulse width to the effect of ablation area.

From analysis of variance, the parameter of electrode distance and input voltage has significant effect to the temperature rise in the IRE treatment of bovine liver (P = 0.020 and P = 0.003 respectively). Meanwhile, only the parameter of input voltage significantly affects the ablation area (P < 0.001).

From Fig. 5, the optimal IRE parameter configuration calculated by RSM consists of the insertion of two needle electrodes with an active length of 10 mm and separated by 10 mm, and the delivery of 52.42 pulses with a width of 41.21 µs and amplitude of 3000 V. The number of pulse repetitions was defined as 50 instead of the result of 52.42 calculated by RSM.

The optimal parameters obtained from RSM were inserted in the models to assess the reliability of the method. The ablation area and the maximum temperature achieved at the center point between the electrodes were measured. The outcomes of each response were compared with the ones obtained with RSM by calculating the relative error. The results are shown in Table 6.

Table 6 Comparison of the optimization and simulation results with the optimal IRE parameter configuration for liver tissue

There was a good agreement between the electric field calculated by RSM and by the models. Regarding the temperature, RSM produced an overestimated value. The maximum temperature obtained from the simulation was 45.46 °C, which is less than the threshold for thermal damage (50 °C). Therefore, the error is not significant, since it is less likely that thermal damage occurs in the tissue.

Electric field and temperature distributions for the optimal IRE parameter configuration

Once verified the reliability of the optimization process, the electric field and temperature distributions on liver tissue were calculated using simulations. The graphical representation of the simulation result for the electric field and temperature distribution is displayed in Fig. 6.

Fig. 6
figure6

a Electric field distribution and b temperature distribution in liver tissue when applying the optimal IRE configuration (best view in color)

The electric field distribution between the electrodes seems to be quite homogeneous. However, in Fig. 6a, one can notice that the intensity of the generated electric field is higher near the corners of the electrodes. Electric charges tend to spread as much as possible on the surface of a conductive material, and, therefore, there is a higher concentration of charges in the tips of the electrodes.

The temperature increase is more substantial in the area between the electrodes, and it follows a pattern similar to the electric field distribution as shown in Fig. 6b. Here, the temperature seems to achieve its highest values near the vicinity of the electrodes and then eventually decreases with distance. The increase in temperature outside the area between the electrodes is not significantly high as in between them. Overall, no thermal damage is expected to occur in the tissue when applying the calculated optimal IRE parameter configuration.



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