Numerous liver cancer oncologists suggest bridging therapies to limit cancer growth until donors are available. Interventional radiology including radiofrequency ablation (RFA) is one such bridging therapy. This locoregional therapy aims to produce an optimal amount of heat to kill cancer cells, where the heat is produced by a radiofrequency (RF) needle. Less experienced Interventional Radiologists (IRs) require a software-assisted smart solution to predict the optimal heat distribution as both overkilling and untreated cancer cells are problematic treatments. Therefore, two of the big three partial differential equations, 1) heat equation (Pennes, Journal of Applied Physiology, 1948, 1, 93–122) to predict the heat distribution and 2) Laplace equation (Prakash, Open Biomed. Eng. J., 2010, 4, 27–38) for electric potential along with different cell death models (O’Neill et al., Ann. Biomed. Eng., 2011, 39, 570–579) are widely used in the last three decades. However, solving two differential equations and a cell death model is computationally expensive when the number of finite compact coverings of a liver topological structure increases in millions. Since the heat source from the Joule losses Qr = σ|∇V|2 is obtained from Laplace equation σΔV = 0, it is called the Joule heat model. The traditional Joule heat model can be replaced by a point source model to obtain the heat source term. The idea behind this model is to solve σΔV = δ0 where δ0 is a Dirac-delta function. Therefore, using the fundamental solution of the Laplace equation (Evans, Partial Differential Equations, 2010) we represent the solution of the Joule heat model using an alternative model called the point source model which is given by the Gaussian distribution.Qrx=∑xi∈Ω1K∑icie−|x−xi|22σ2where K and ci are obtained by using needle parameters. This model is employed in one of our software solutions called RFA Guardian (Voglreiter et al., Sci. Rep., 2018, 8, 787) which predicted the treatment outcome very well for more than 100 patients.

Microwave ablation (MWA) is a minimally invasive treatment for cancer that uses electromagnetic waves to kill the tumor cells without significantly damaging the surrounding healthy cells. A three‐state cell death model calculates the thermal damage around the Hepatocellular carcinoma (HCC) tumor in the liver tissue. The temperature profile is simulated for a single‐slot co‐axial antenna with a 1 mm air slot located near the tip of the antenna to produce an adequate amount of heat. The aims of this study are (1) to use the vector/edge finite element method (VFEM) to simulate the electromagnetic wave propagation to obtain the specific absorption rate, which is an input for the bio‐heat equation that predicts the heat distribution in the liver tissue during MWA treatment, and (2) to compare the computational costs of VFEM and the finite element method (FEM) when different types of input powers and dielectric properties are used in the wave propagation equation. This study claims that the accuracy level increases marginally with less computation cost while using VFEM for temperature‐dependent wave propagation equation.