Capacitive coupling between the heart and tissue and its mathematical representation in future problems

Objective: The objective of our study was to analyse the physics and mathematics of the coupling of cardiac sources to body volume and the impact of widespread assumptions on solutions of future electrocardiographic problems. Methods: Based on anatomical and physiological knowledge, we discuss the physical reality of the heart boundary and formulate a new way of setting boundary conditions of future problems based on the boundary element method (BEM) within the SCIRun numerical package. This new type of boundary condition – the ”mixed” method approximating Neumann-Neumann, is compared to standard Dirichlet-Neumann conditions. Results: By anatomical and physiological analysis, we show that there is strong evidence that mass transport, particularly charge transport through the pericardium, is negligible. On the physical ground, it should be assumed instead that the ECG signal spreads through the impermeable barrier as a displacement current that which assumes a nonzero normal component of potential gradient on the boundary. The numerical analysis shows that the new conditions give slightly better results than the standard ones. Notably, the quality of calculations is maintained, although the assumptions are different. Conclusions: We claim that there are both physical and numerical arguments that the assumption that the normal component of a potential gradient must be zero at the heart and body border and can should be relaxed. These findings build convergence between the mathematical ideas and the physical reality of the electrolyte-filled human body. We aim to enhance the diagnostic impact of ECG-based approaches and advance our understanding of cardiac electrophysiology.