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Existence and uniqueness for the specialized conduction system/myocardium coupled problem in cardiology

  • Kordoghli, Khouloud
Publication Date
Oct 14, 2020
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The Purkinje network is the rapid conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. From the mathematical viewpoint the model is made up of a degenerate parabolic reaction diffusion system coupled with an ODE system. We derive existence, uniqueness and some regularity results. The excitation of the cardiac cells starts at the sinoatrial node where pacemaker cells generate an electrical current. This current propagates to the right atria then to the left atria through the Bachmann's bundle. The electrical wave does not propagate directly to the ventricle since the interface between the atria and ventricles is insolating. Only the atrioventricular node allows the propagation of this wave to the ventricles. Then the electrical wave follows the His bundle which is a rapid conductive system that ends in the Purkinje fibers directly connected to the ventricular cells. This rapid conduction system is electrically insulated from the heart muscle except at the endpoints that are connected to the myocardium in an area called "Purkinje Muscle Junc-tions" (PMJ). In the present work, we consider the coupling conditions derived in [1] where the myocardium and Purkinje electrical activities are represented by the mon-odomain model and are coupled using source terms and Robin boundary conditions. Our main result in this paper is the existence , uniqueness and some results of regularity of the solution for the coupled problem Purkinje/myocardium.

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