Abstract
The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process. In the ventricles, electrical activation begins at the insertion points of the Purkinje network in the endocardium. How does the diffusion component of the subsequent excitation wave propagate from the endocardium in a healthy heart wall without creating directional biases? We show that this is a consequence of the particular geometric organization of myocytes in the heart wall. Using a generalized helicoid to model fiber orientation, we treat the myocardium as a curved space via Riemannian geometry, and then use stochastic calculus to model local signal diffusion. Our analysis shows that the helicoidal arrangement of myocytes minimizes the directional biases that could lead to aberrant propagation, thereby explaining how electrophysiological principles are consistent with local measurements of cardiac fiber geometry. We discuss our results in the context of the need to balance electrical and mechanical requirements for heart function.
Highlights
The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process
Because we are interested in the local behavior around the insertion points of the Purkinje network in the endocardium, we focus on the diffusion term and introduce the effect of local fiber geometry via a generalized helicoid model (GHM)
The contraction of myocytes in the heart wall is controlled by current flowing through an elaborate Purkinje network, which raises the question of how current diffuses through the wall around the insertion points
Summary
The mammalian heart must function as an efficient pump while simultaneously conducting electrical signals to drive the contraction process. Our analysis shows that the helicoidal arrangement of myocytes minimizes the directional biases that could lead to aberrant propagation, thereby explaining how electrophysiological principles are consistent with local measurements of cardiac fiber geometry. Analysis methods from differential geometry have shown that the orientations of these fibers approximate a minimal surface in 4, the generalized helicoid model (GHM)[4]. The organization of the cardiomyocytes (i.e. their local orientation) determines a number of essential properties of the heart, including the diffusive propagation of the contraction signal and mechanical efficiency[10]. An important result[17], which we confirm, is that the tissue can be approximated by a manifold with negative scalar curvature This enhances diffusion in abstract manifolds[18,19] and in the walls of the ventricles[17]; it plays a role in models of molecular diffusion[20,21]
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