Multiscale Modelling of the Circulatory System: a Preliminary Analysis

In this paper we show how numerical solutions of human cardiovascular system may be devised by coupling models having different physical dimensions. One of the aspects of circulatory system is indeed its multiscale nature. Local flow features may have a global effect on circulation. For instance, a stenosis caused by an atherosclerotic plaque may change the overall characteristic of the vessels involved, and consequently have significant influence on the flow in the whole system. Hence, it lays the interest to set up a numerical device that could represent accurately both local and systemic features. For that, it is needed to couple different model scales. From lumped models (which are traditionally described by means of an electrical network analog) to local models based on 2D or 3D Navier-Stokes equations, passing through intermediate 1D models. In this paper, the different assumptions underlying these models, some mathematical issues related to their coupling and preliminary numerical results are presented