Numerical modeling of 1D arterial networks coupled with a lumped parameters description of the heart

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Abstract
The investigations on the pressure wave propagation along the arterial network and its relationships with vascular physiopathologies can be supported nowadays by numerical simulations. One dimensional (1D) mathematical models, based on systems of two partial differential equations for each arterial segment suitably matched at bifurcations, can be simulated with low computational costs and provide useful insights into the role of wave reflections. Some recent works have indeed moved in this direction. The specific contribution of the present paper is to illustrate a 1D numerical model numerically coupled with a model for the heart action. Typically, the action of the heart on the arterial system is modelled as a boundary condition at the entrance of the aorta. However, the left ventricle (LV) and the vascular network are a strongly coupled single mechanical system. This coupling can be relevant in the numerical description of pressure waves propagation, particularly when dealing with pathological situations. In this work, we propose a simple lumped parameter model for the heart and show how it can be coupled numerically with a 1D model for the arteries. Numerical results actually confirm the relevant impact of the heart-arteries coupling in realistic simulations.