Rocco Michele Lancellotti
Numerical Computations of Deflated Vascular Geometries for Fluid-Structure Interaction in Haemodynamics
Tuesday 28th April 2015
De Rosa, S.
This thesis deals with a computational haemodynamic problem. The purpose is to simulate the prestressed state in human arteries and verify its effectiveness in haemodynamic fluidstructure interaction simulations. In the first part of this work, we describe the vessel wall mechanics in regime of finite deformations with non linear hyperelastic structural models commonly used to describe biological tissue. Subsequently, we implement a parallel algorithm that consists in a simple iterative procedure based on a fixed point method. This algorithm aims at the calculation of deflated vascular geometries starting from three-dimensional vascular geometries reconstructed from radiological images. The idea is to use these deflated geometries as initial reference configurations for fluid-structure interaction simulations, in order to simulate the prestressed state of arteries. Moreover, we have tested the algorithm from a quantitative point of view, using consistency test cases on simple geometries. In the second part of this thesis, we describe the incompressible Navier-Stokes equations in moving domains using the Arbitrary Lagrangian-Eulerian (ALE) formulation, and the fluid-structure coupled problem. Then, we use our algorithm in a parallel partitionated fluidstructure interaction solver and we perform physiological simulations on a patient-specific carotid artery with and without the use of deflated geometries, evaluating the fluid velocity,the fluid pressure, the structure displacement and the wall-shear stress fields in both cases, highlighting the differences. All of the present work is developed within the open source object-oriented library called LifeV, that works on parallel architectures. In particular, LifeV is a finite element library that solves several physical problems, such as fluid dynamics, reaction-diffusion-transport and mechanical problems in a multiphysics contest.