Patient-Specific Cardiac Parametrization from Eikonal Simulations

Simulations in cardiac electrophysiology use the bidomain equations to describe the electrical potential in the heart. If only the electrical activation sequence in the heart is needed, then the full bidomain equations can be substituted by the Eikonal equation which allows much faster responses w.r.t. the changed material parameters in the equation. We use our Eikonal solver optimized for memory usage and parallelization. Patient-specific simulations in cardiac electrophysiology require patient-specific conductivity parameters which are not accurately available in vivo. One chance to improve the given conductivity parameters consists in comparing the computed activation sequence on the heart surface with the measured ECG on the torso mapped onto this surface. By minimizing the squared distance between the measured solution and the Eikonal computed solution we are able to determine the material parameters more accurately. To reduce the number of optimization parameters in this process, we group the material parameters and introduce a specific scaling parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma _k$$\end{document} for each group. The minimization takes place w.r.t. the scaling \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\gamma }$$\end{document}. We solve the minimization problem by the BFGS method and adaptive step size control. The required gradient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla _\gamma f({\gamma })$$\end{document} is computed either via finite differences or algorithmic differentiation using in tangent as well as in adjoint mode. We present convergence behavior as well as runtime and scaling results.