A fundamental solution for radiofrequency heating due to a point electrical current in an infinite spatial domain: Numerical proofs with MATHEMATICA and ANSYS

Abstract

Radiofrequency ablation (RFA) is a minimally invasive therapy widely used for the treatment of tumours. Mathematical modelling of RFA allows medical practitioners to understand the involved electro-thermal transport, thereby helping to improve the effectiveness of prescribed treatments. To this end, we aimed to deduce and numerically prove an analytical transient-time solution for temperature due to a point source of electrical current in an infinite medium. The solution, deduced with the Fourier transform, involves double integrals. The outer integral is a time integral, which was calculated with the trapezoidal rule. The inner integral is a generalised spatial integral with defects, which was computed using the MATHEMATICA command ‘NIntegrate’. For the radius r ≥ 0.088841 m, the computation with NIntegrate was straightforward and the results conformed well to those obtained with ANSYS. For r < 0.088841 m, NIntegrate diverged owing to the strong singularity at the defect. An algorithm was thus implemented to allow approximate calculation of the temperature at any distance from the current source with high precision. The analytical solution and the associated Green's function may be used as fundamental solutions in BEM for RFA modelling. MATHEMATICA notebooks used for calculations are provided as proofs.