Section: New Results

Convergence analysis of a bidomain-bath model

M. Bendahmane and N. Chamakuri performed a convergence analysis for optimal control of a bidomain-bath model by using a finite-element scheme. The bidomain-bath model represents a commonly used experimental setup where a small piece of cardiac tissue is kept alive and studied for some time in a nutrient bath. The bidomain-bath model equations describe the cardiac bioelectric activity in the tissue and bath volumes where the control acts at the boundary of the tissue. The existence of the finite element scheme and convergence to a unique weak solution of the direct problem were established. The convergence proof was based on deriving a series of a-priori estimates and using a general L2-compactness criterion. Moreover, the well-posedness of the adjoint problem and the first order necessary optimality conditions were shown. Comparing to the direct problem, the convergence proof of the adjoint problem is based on using a general L1-compactness criterion. The model was used for a simulation of low-energy defibrillation.