Fluid Flow inside Deformable Vessels and in the Left Ventricle

Abstract

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.

A computational fluid dynamics study on hemodynamics for different locations of the distal anastomosis of a bypass nearby a collateral vessel in the femoropopliteal area

“…Johnston [15] concludes that a Newtonian model is an adequate approximation in transient simulations at the coronary arteries, even during slow flow periods. Pedrizzetti [16] and Friedman [17] argue that non-Newtonian effects are negligible in large and medium-sized vessels. Lamack [18] found no differences between Newtonian and non-Newtonian fluids on iliac arterial bifurcation.…”

Non‐Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

“…The rheological behavior strongly depends on the properties of the suspended particles (38). Many non-Newtonian mathematical models are presented in order to describe such behavior for blood flow (40)(41)(42). In other words, blood shows a non-Newtonian behavior.…”

“…As there exists a wide range of shear stresses in these microflow fields, it seems necessary to take into account these variations in blood viscosity. Many non-Newtonian mathematical models are presented in order to describe such behavior for blood flow (40)(41)(42). Among these models, the Carreau-Yasuda model is capable of characterizing this shear rate dependency of the viscosity which is called shearthinning phenomenon (33).…”

Effects of highly pulsatile inflow frequency on surface-mounted bluff body wakes

“…of the order of 1000. Cardiovascular flows, human phonation and voiced speech, along with some scales of biolocomotion all exist in or near this range of (Pedrizzetti & Perktold 2003; Liu 2005; Erath & Plesniak 2010).…”