Modeling the Electrical Activity in the Ventricles with Focus on the Purkinje-Myocardial Coupling

The electrical activity in the Purkinje network and the myocardial tissue in the ventricles of the human heart was modeled. The focus was on the Purkinje tree and the coupling of the Purkinje network and the myocardium. Further use of the model could be to look at ventricular arrhythmia. The implementation of the model uses the FEM software FEniCS, goss and gotran, and is written in the Python programming language. The branches in the Purkinje network were modeled with 1D elements (nodes were given 3D coordinates) while the myocardial tissue was modeled with 3D elements. The PRd and Decker et al. cell models (systems of nonlinear ODEs) were used to represent a Purkinje cell and a ventricular myocyte, respectively. These models were coupled to the monodomain equation (nonlinear PDE), which was used as tissue model. The coupling was given particular attention. The Purkinje system and the myocardial tissue are only coupled at the Purkinje-myocardial junctions (PMJs). Different myocardial PMJ areas and different coupling methods were implemented. Two methods gave continuity of membrane potential and conservation of current at the PMJs, while two others ensured conservation of current, but allowed for discontinuous membrane potential. Out of these methods, three used explicit boundary conditions for both the Purkinje and the myocardial problems, while the last method used stimulus currents (in the Decker et al. cell model) for the myocardial problem. This last method was able to give PMJ delay times (but not in the physiological range). The myocardial model does not include fiber directions and assumes isotropy. The mesh is also very coarse. For realistic simulations of the myocardial activity this must be remedied. However, despite these drawbacks, the implemented model is able to reproduce important features such as bidirectional propagation, earliest epicardial breakthrough site in the right anterior-paraseptal region, a general pattern of apex-to-base activation, PMJ delay times in both directions and reasonable total activation times for the Purkinje network and the myocardial tissue