Numerical modelling and simulation for one-dimensional fluid structure interaction in blood flow

Abstract

Fluid structure interaction (FSI) needs to be considered in modeling biofluids because the interaction between blood flow and vessel wall is of great clinical interest. However, the interaction between blood flow and vessel wall make FSI problems complex and challenging. Spurious oscillations were observed from numerical solutions and in the case of Bubnov-Galerkin finite element method, the oscillations occurred at relatively high pressure differences. In this thesis, Streamline-Upwind Petrov Galerkin (SUPG) stabilization scheme was formulated to solve one-dimensional FSI problems in blood flow to eliminate the spurious oscillations and to obtain stable numerical solutions for stenotic vessel. A pressurearea constitutive relation to complement the continuity equation and momentum equation was formulated by adopting the collapsible model. The geometry of stenotic vessel consists of single smooth and single irregular stenosis, multi-smooth and multi-irregular stenosis in this thesis. Numerical results show that there are no vessel collapse phenomena in single smooth stenosis and multi-smooth stenosis cases. Vessel collapse phenomena are observed for single-irregular stenosis with 85% cross sectional area amplitude at distal pressure of 47 mmHg while for multi-irregular stenosis with 60% and 85% cross sectional amplitudes at proximal stenosis and distal stenosis respectively, at distal pressure of 36 mmHg. In addition, paradoxical collapse motion along the time phase cycle is obtained in unsteady cases for single irregular stenosis and multi-irregular stenosis with the distal resistance of 2.73 mmHg/(ml/s) and 2.44 mmHg/(ml/s) respectively when sinusoidal pressure variation is applied at the inlet boundary. In conclusion, numerical results show that vessel collapse phenomena occurs when there is supercritical flow at the minimum cross sectional area of the stenotic vessel which is lower than the minimum cross sectional area at static condition and hence lead to the negative transmural pressure at that position.