Optimal Sparse Boundary Control of Cardiac Defibrillation

This paper studies the feasibility of optimal sparse boundary control of the bidomain-bath model in cardiac electrophysiology. We incorporated the Luo–Rudy phase I (LR-I) ventricular action potential model, which accounts for more biophysical details of cellular dynamics. The boundary optimal control framework involves a standard quadratic objective functional that is to be minimized and the L1-norm of the control accounting for the sparsity. The existence of the bidomain-bath model using the LR-I is demonstrated, and the derivation of the first-order optimality system is shown. Then we provide the well-posedness and the sparsity of the optimal control problem. The numerical realization of such a boundary control framework for a successful defibrillation study is demonstrated.