Analytical Solution for the Prediction of Temperature Distributions During Radio-Frequency Ablation of Cardiac Tissue

One of the most effective methods of treatment for cardiac arrhythmias is radio-frequency (RF) ablation. Many studies have shown that the tissue temperature distribution is the key factor influencing lesion shape and size, and that accurate prediction of this distribution is essential to the further improvement of the procedure. Temperature distributions can be obtained by solving the bioheat equation, which has been done in several studies using numerical techniques. This paper describes the development of an analytical solution that can be used as a bench mark for subsequent numerical solutions. Using integral transforms, the bioheat equation is reduced to an ordinary differential equation with time as the independent variable. The solution has the form of a surface integral within another surface integral. An integration routine that extends the trapezoidal method of integration in two dimensions to an analogous method in three dimensions has been developed in order to evaluate the analytical solution. A C program was written to implement this method, and the program was validated using a surface integral with a known analytical solution. The program was then used to generate temperature profiles at various time values and for different convection coefficients.