Use of microwave ablation for thermal treatment of solid tumors with different shapes and sizes-A computational approach

Abstract

Microwave Ablation (MWA) is one of the most recent developments in the field of thermal therapy. This approach is an effective method for thermal tumor ablation by increasing the temperature above the normal physiological threshold to kill cancer cells with minimum side effects to surrounding organs due to rapid heat dispersive tissues. In the present study, the effects of the shape and size of the tumor on MWA are investigated. To obtain the temperature gradient, coupled bio-heat and electromagnetic equations are solved using a three-dimensional finite element method (FEM). To extract cellular response at different temperatures and times, the three-state mathematical model was employed to achieve the ablation zone size. Results show that treatment of larger tumors is more difficult than that of smaller ones. By doubling the diameter of the tumor, the percentage of dead cancer cells is reduced by 20%. For a spherical tumor smaller than 2 cm, applying 50 W input power compared to 25 W has no significant effects on treatment efficiency and only increases the risk of damage to adjacent tissues. However, for tumors larger than 2 cm, it can increase the ablation zone up to 21%. In the spherical and oblate tumors, the mean percentage of dead cells at 6 GHz is nearly 30% higher than that at 2.45GHz, but for prolate tumors, treatment efficacy is reduced by 10% at a higher frequency. Moreover, the distance between two slots in the coaxial double slot antenna is modified based on the best treatment of prolate tumors. The findings of this study can be used to choose the optimum frequency and the best antenna design according to the shape and size of the tumor.

Fig 1. Boundary conditions and the geometry of the present study with different shapes of the tumor.

Since all of the tumors are not necessarily spherical, different shapes of the solid tumors are considered in this study. In all oblate, prolate, and spherical shapes, the volume of the tumors are constant. MWA coaxial antenna is placed at the center of the tumor. Thermal and electrical boundary conditions are applied to the wall of the tissue.

Fig 2. The validation of the current study’s results with the experimental work of Yang et al. [55].

As same as an experimental test, MWA simulated with 75 W input power and frequency of 2.45 GHz. Temperature increment during 150 s MWA is monitored at two point. Our simulation has 3.2% and 6.3% difference with experimental data at 4.5 mm and 7 mm away from the antenna, respectively.

Fig 3. Validation of numerical results with a previously published study.

(A and B) Ablation zone (V+D) calculated by numerical simulation by using the three-state model. (P = 80 W, f = 915 MHz). In the 50 W input power, by increasing frequency to 2.45 GHz, the long and short axis of the ablation zone decreases to 4.65 cm and 1.45 cm, respectively (B). The dimension of the ablation zone has a good agreement with experimental data. (C) Dimensions of the ablation zone calculated by the present numerical simulation and experimental results achieved by Sun et al. [56].

Fig 4. The variation of percentage of cells in tumor radius length.

The three-state mathematical model describes an accurate cell’s response to the temperature during treatment (P = 45 W and f = 2.45 GHz). The fraction of dead cells increases in the tumor by increasing temperature (A) and as expected, fraction of alive cells decreases in the ablation zone (B). Vulnerable is a transient state between alive and dead cells, and some of the cells remain in this state in any treatment time (C).

Fig 5. Effect of change in input power at different tumor sizes.

(A) Mean fraction of dead cells in three tumor sizes. In smaller tumor (r = 0.5 cm and r = 1 cm), all of the cancer cells are ablated as treatment continues, but in the tumor with 1.5 cm, 21% of cancer cells remain alive, even by increasing the input power to 50 W. Treatment efficacies are related to the collateral damage directly, therefore mean fraction of dead cells in normal tissue around the tumor is presented to restrict treatment duration by allowable side effects (B). Due to this issue, the ablation of all parts of the tumor is not possible in all cases. At any treatment time, a fraction of cells remain in a vulnerable state. These cells do not necessarily die after treatment; therefore, the three-state mathematical model helps to estimate treatment efficacy more accurately.

Fig 6. The profile of the ablation zone according to the fraction of dead cells.

The expansion of the ablation zone during the MWA process are shown in different tumor shapes and sizes (A-D) (P = 20 W and f = 2.45 GHz). (E) The average percentage of dead cells in λ = 5 oblate and prolate tumor, all of the tumor will be ablated, but 50% and 58% of normal cells die in prolate and oblate shape, respectively (E and F). Treatment of oblate tumors is more difficult. The ablation and due to the side effects, the whole tumor ablation is not possible. In the case of the prolate shape, if allowable mean percentage of dead cells in healthy tissue considered 10%, 77%, and 68% of the tumor will be ablated in λ = 2 and λ = 5. Therefore, in the same shape, MWA is more difficult by increasing length ratio.

Fig 7. The average percentage of dead cells inside and around the tumor at frequencies of 2.45 GHz and 6 GHz.

By increasing frequency from 2.45 GHz to 6 GHz, the mean fraction of dead cells in the prolate tumor decreased to 11% and 12% at λ = 2 and λ = 5, respectively (A). (B) Mean fraction of dead cells around the prolate tumor; that shows the side effects during MWA. Maximum allowable collateral damage considered 10%, on average. As well as result from Fig 7, the treatment of oblate tumors is more difficult, but by increasing frequency from 2.45 GHz to 6 GHz, the treatment outcome improved by 28% on average (C and D).

Fig 8. Tumor ablation with a single slot antenna and double slot antenna.

MWA applied to the same tumor and the same condition by three different antennas (λ = 5, f = 2.45 GHz, P = 70W). By using a single slot antenna, around 76% of the tumor is ablated, but the ablation zone is expanded to the surrounding healthy tissue(A). In the case of using a double slot antenna, the ablation zone could be further adjusted into the tumor area by optimizing slot to slot distance (B and C).