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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 L 1 -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. [ABSTRACT FROM AUTHOR]

We present a virtual element method (VEM) for a nonlocal reaction–diffusion system of the cardiac electric field. For this system, we analyze an |$H^1$| -conforming discretization by means of VEM that can make use of general polygonal meshes. Under standard assumptions on the computational domain, we establish the convergence of the discrete solution by considering a series of a priori estimates and by using a general |$L^p$| compactness criterion. Moreover, we obtain optimal order space-time error estimates in the |$L^2$| norm. Finally, we report some numerical tests supporting the theoretical results. [ABSTRACT FROM AUTHOR]