Analysis under Uncertainty with the Monte Carlo Method Applied to a Bioheat Transfer Problem with Coupled Deep Brain Stimulation Lead

Abstract

This article deals with an analysis of uncertainties applied to a bioheat transfer problem containing a deep brain stimulation lead. The classic two-dimensional bioheat transfer equation in cylindrical coordinates was considered in the mathematical formulation. The electric potential was solved with a Laplace equation to incorporate the DBS lead effects. Thus, the solution for the electric potential was coupled to the temperature problem, considering an external heat transfer rate. The analysis under uncertainties was performed by the Monte Carlo method considering different types of uncertainties for all parameters of the mathematical model. The uncertainties were chosen according to the information available in the literature in order to analyze the problem more realistically. The solutions showed a significant variation in the temperature profile over time when considering the random variations in the parameters.