Towards a Level Set Framework for Infarction Modeling: An Inverse Problem

Abstract

The purpose of this paper is to introduce a level set framework suitable for identifying heart infarctions. We do this by introducing a modified Monodomain model, and an output least squares formulation comparing simulation results with observation data. In this way we obtain a flexible methodology allowing us to approximately determine the characteristics of infarctions with rather complex geometrical properties. Our approach involves a CPU demanding minimization problem. This problem is solved by applying an adjoint equation enabling efficient differentiation of the involved cost-functional. Finally, our theoretical findings are illuminated by a series of numerical experiments.