Numerical Modeling of 1D Arterial Networks Coupled with a Lumped Parameters Description of the Heart

MOX 31

Numerical Modeling of 1D Arterial Networks Coupled with a Lumped Parameters Description of the Heart

Friday 27th February 2004

Formaggia, Luca; Lamponi, Daniele; Tuveri, Massimiliano; Veneziani, Alessandro

The investigation on the pressure wave propagation along the arterial network and its relationships with vascular physiopatologies can be supported nowadays by numerical simulation (see e.g. [25]). One dimensional (1D) mathematical models, based on systems of two partial differential equations for each arterial segment suitably matched at bifucations, can be simulated with low computationsl costs and provide useful insights into the role of wave reflections. For instance, those induced by the stiffening of the arterial walls or a vascular endoprothesis, and their influence on the cardiac work. Some recent works have indeed moved in this direction ([19,6,25,24,33]). The specific contribution of the present paper is to illustrate a 1D numerical model in which there is an effective coupling between the heart action and the 1D system. Often, the action of the heart on the arterial system is modelled as a boundary condition at the entrance of the aorta. However, it is well known that the left ventricle and the vascular network are strongly coupled single mechanical system (see [15,25]). This coupling can be relevant in the numerical description of pressure waves propagation particularly when dealing with patological situation. 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.

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Formaggia, L.; Lamponi, D.; Veneziani, A., Tuveri, M., Numerical Modeling of 1D Arterial Networks Coupled with a Lumped Parameters Description of the Heart, Computer Methods in Biomechanics and Biomedical Engineering, 2007, 9, 273-288