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Modelling and simulations in hemodynamics and hemorheology

Blood is a multi-component mixture with complex rheologic characteristics which interacts both mechanically and chemically with vessel walls, giving rise to complex fluid-structure interaction models whose mathematical analysis is still incomplete and which are difficult to simulate numerically in an efficient manner. Experimental investigations over many years show that blood flow exhibits non-Newtonian behaviour such as shear-thinning, viscoelasticity, thixotropy and yield stress and its rheology is influenced by numerous factors including plasma viscosity, rate of shear, hematocrit, level of erythrocytes aggregation and deformability. Hemodynamic analysis of blood flow in vascular beds and prosthetic devices requires the rheological behaviour of blood to be characterized through appropriate constitutive equations relating the stress to deformation and rate of deformation. In this talk we present a short overview of some macroscopic constitutive models that can mathematically characterize the rheology of blood and describe its known phenomenological properties. Some numerical simulations obtained in both idealized and geometrically reconstructed real vessels will be also presented to illustrate the hemodynamic behaviour using Newtonian and non-Newtonian inelastic models under a given set of physiological flow conditions. Moreover we will show preliminary numerical results obtained for a comprehensive model of blood coagulation and clot formation, that integrates physiologic, rheologic and biochemical factors.

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