Modified Fletcher-Reeves and Dai-Yuan Conjugate Gradient Methods for Solving Optimal Control Problem of Monodomain Model

In this paper, we present the numerical solution for the optimal control problem of monodomain modelwith Rogers-modified FitzHugh-Nagumo ion kinetic. The monodomain model, which is a well-known mathematical model for simulation of cardiac electrical activity, appears as the constraint in our problem. Our control objective is to dampen the excitation wavefront of the transmembrane potential in the observation domain using optimal applied current. Various conjugate gradient methods have been applied by researchers for solving this type of optimal control problem. For the present paper, we adopt the modified Fletcher-Reeves method and modified Dai-Yuan methodfor computing the optimal applied current. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current when the modified Fletcher-Reeves method is used. However, this is not the case when the modified Dai-Yuan method is employed. Numerical results indicate that the modified Dai-Yuan method failed to converge to the optimal solution when the Armijo line search is used.

On the electrophysiology of the atrial fast conduction system:an uncertain quantification study

Cardiac modeling entails the epistemic uncertainty of the input parameters,such as bundles and chambers geometry,electrical conductivities and cell parameters,thus calling for an uncertainty quantification(UQ)analysis.Since the cardiac activation and the subsequent muscular contraction is provided by a complex electrophysiology system made of interconnected conductive media,we focus here on the fast conductivity structures of the atria(internodal pathways)with the aim of identifying which of the uncertain inputs mostly influence the propagation of the depolarization front.Firstly,the distributions of the input parameters are calibrated using data available from the literature taking into account gender differences.The output quantities of interest(Qols)of medical relevance are defined and a set of metamodels(one for each Qol)is then trained according to a polynomial chaos expansion(PCE)in order to run a global sensitivity analysis with non-linear variance-based SoboF indices with confidence intervals evaluated through the bootstrap method.The most sensitive parameters on each Qol are then identified for both genders showing the same order of importance of the model inputs on the electrical activation.Lastly,the probability distributions of the Qols are obtained through a forward sensitivity analysis using the same trained metamodels.It results that several input parameters-including the position of the internodal pathways and the electrical impulse applied at the sinoatrial node一have a little influence on the Qols studied.Vice-versa the electrical activation of the atrial fast conduction system is sensitive on the bundles geometry and electrical conductivities that need to be carefully measured or calibrated in order for the electrophysiology model to be accurate and predictive.