Primal-dual active set strategy for large scale optimization of cardiac defibrillation

In this paper, the feasible study of the optimal control techniques for the cardiac defibrillation on the anatomical three spatial dimensional rabbit ventricle geometry in the presence of bilateral control constraints. The present work addresses the numerical treatment of multiscale and multidomain simulations of bidomain equations, the description of deriving optimality system, the applicability of primal-dual active set methods to treat the bilateral control constraints for solving such large scale optimization of cardiac defibrillation. The numerical results are demonstrated for the successful defibrillation study on 3D rabbit ventricle geometry by utilizing the less total currents, robustness of the optimization algorithm w.r.t to the variations in the model parameters, feasible study of the multiple smaller boundary control support and the numerical convergence of the optimization algorithm on the finer spatial grids. The parallel efficiency is demonstrated for the primal-dual active set optimization algorithm on such finer spatial grid.