Framework for Modular, Flexible and Efficient Solving the Cardiac Bidomain Equation using PETSc
G. Seemann (Institute of Biomedical Engineering, Universität Karlsruhe [TH], Karlsruhe, Germany), F.B. Sachse (Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, USA ), M. Karl (Institute of Biomedical Engineering and Institute for Applied and Numerical Mathematics, Universität Karlsruhe [TH], Karlsruhe, Germany ), D.L. Weiss (Institute of Biomedical Engineering, Universität Karlsruhe [TH], Karlsruhe, Germany), V. Heuveline (Institute for Applied and Numerical Mathematics, Universität Karlsruhe [TH], Karlsruhe, Germany) and O. Dössel (Institute of Biomedical Engineering, Universität Karlsruhe [TH], Karlsruhe, Germany)
Cardiac electrophysiological modelling gets more quantitative based on new measurements (electrophysiology, heterogeneity, fibre orientation). This implies using whole heart models including ECG simulations based on a modular, flexible and efficient framework.
The framework presented in this work includes the individual calculation of each channel equation for efficiency and to plug channels flexible and modularly. This is done for various tissue classes and any geometry. Arbitrary fibre orientations are considered to account for electrical anisotropies. Individual modules exist to generate system matrices for different methods (eg. FDM, FEM). Just one approach for solving the bidomain equation is implemented based on PETSc. The extracellular field is computed only at significant change. Calculations of one cycle in the complete human heart last less than one hour.