Capacitive coupling between the heart and the tissue and its mathematical representation in forward problem

Objective: To show that if we consider that potential gradient is a source boundary condition in a forward ECG problem, the numerical accuracy is improved. Methods: Employing computational methods based on the boundary element method (BEM) within the SCIRun numerical package, we formulated the forward problem, investigating the relationship between potential on the heart's surface and that on the body's surface. Two boundary conditions, Dirichlet-Neumann and a novel "mix" method approximating Neumann-Neumann, were considered. Results and Conclusion: Computational experiments revealed superior numerical accuracy with the "mix" method, challenging the typical use of Dirichlet-Neumann in ECG modeling. Having analyzed the anatomical evidence concerning the epicardium and the pericardial sac, we assumed capacitive coupling between the heart and surrounding tissue. This assumption imposes no limitation on tissue bulk biopotentials, which can be described using volume conductor theory. Due to capacitive coupling, a non-zero potential gradient at the organ border does not violate the assumption of electroneutrality, which is commonly used as a constraint in inverse procedure. The same applies to the border of the body, at which the normal component of potential gradient does not vanish as well, contrary to what is typically assumed. Significance: The research opens new avenues for understanding the complex interplay of electric potential in the heart and its environment. These findings could improve numerical accuracy in electrophysiological imaging procedures, ultimately enhancing the diagnostic impact of ECG-based approaches and advancing our understanding of cardiac electrophysiology.