Mathematical analysis and numerical simulation of a nonlinear radiofrequency ablation model in cardiac tissue

Abstract

This paper deals with the mathematical analysis and numerical simulation of a new nonlinear ablation system modeling radiofrequency ablation phenomena in cardiac tissue, which incorporates the effects of blood flow on the heat generated when ablation by radiofrequency. The model also considers the effects of viscous energy dissipation. It consists of a coupled thermistor problem and the incompressible Navier–Stokes equations that describe the evolution of temperature, velocity and potential in cardiac tissue. In addition to Faedo–Galerkin method, we use Schauder’s fixed-point theory to prove the existence of the weak solutions in two- and three-dimensional space. Moreover, we prove the uniqueness of the solution under some additional conditions on the data and the solution. Finally, we discuss some numerical results for the validation of the proposed model using the finite element method.