Fluid Flow inside Deformable Vessels and in the Left Ventricle*

Abstract. Topics regarding flow inside deformable domains are here considered either for artery and ventricle flows. The theory of finite elasticity is summarised in a perspective of application to fluid-tissue interaction problems. The formulation of a coupled fluid tissue problem is discussed. A linearized technique is then introduced as a model for wall elasticity in artery flow. This simplification transforms the coupled fluid-wall system into a cascade of uncoupled systems on a fixed domain. Computational examples are given in axisymmetric problems, for both finite and infinitesimal deformation cases, to show resonance and stability features of the interactive dynamics. The heart dynamics and the major ventricular diseases are briefly summarised in a mechanical perspective. The formulation of the flow in a model left ventricle is given, and numerical solutions for flow during the left ventricle filling (diastole) is studied and analysed in terms of vorticity dynamics. Results are also presented in relation to the physical phenomena observed in the clinical practice. In connection with this the mitral valve modelling is also introduced. 1. Flow inside Deformable Vessels 1.