Article ID: | iaor20114895 |
Volume: | 49 |
Issue: | 1 |
Start Page Number: | 149 |
End Page Number: | 178 |
Publication Date: | May 2011 |
Journal: | Computational Optimization and Applications |
Authors: | Nagaiah Chamakuri, Kunisch Karl, Plank Gernot |
Keywords: | programming: linear, programming: nonlinear, optimization, control, control processes, simulation: applications, simulation: analysis |
The bidomain equations, a continuum approximation of cardiac tissue based on the idea of a functional syncytium, are widely accepted as one of the most complete descriptions of cardiac bioelectric activity at the tissue and organ level. Numerous studies employed bidomain simulations to investigate the formation of cardiac arrhythmias and their therapeutical treatment. They consist of a linear elliptic partial differential equation and a non‐linear parabolic partial differential equation of reaction‐diffusion type, where the reaction term is described by a set of ordinary differential equations. The monodomain equations, although not explicitly accounting for current flow in the extracellular domain and its feedback onto the electrical activity inside the tissue, are popular since they approximate, under many circumstances of practical interest, the bidomain equations quite well at a much lower computational expense, owing to the fact that the elliptic equation can be eliminated when assuming that conductivity tensors of intracellular and extracellular space are related to each other. Optimal control problems suggest themselves quite naturally for this important class of modelling problems and the present paper is a first attempt in this direction. Specifically, we present an optimal control formulation for the monodomain equations with an extra‐cellular current,