Section: New Results

Optimal control to Bidomain-Bath model

This project is concerned with the study of the convergence analysis for an optimal control of a bidomain-bath model. The bidomain-bath model equations describe the cardiac bioelectric activity at the tissue bath volumes where the control acts at the boundary of the tissue domain. In recent work [13] [44], we established the well-posedeness of the direct bidomain-bath model by a discrete Galerkin approach. The convergence proof is based on deriving a series of a priori estimates and using a general $L2$-compactness criterion. Moreover, the well-posedeness of the adjoint problem and the first order necessary optimality conditions are shown. Comparing to the direct problem, the convergence proof of the adjoint problem is based on using a general $L^1$-compactness criterion. The numerical tests are demonstrated which achieve the successful cardiac defibrillation by utilizing less total current. Finally, the robustness of the Newton optimization algorithm is presented for different finer mesh geometries.