Modeling of two-phase blood flow and fluid-structure interactions in cerebral aneurysms

Abstract

This thesis is composed of 7 chapters, each of them dealing with different aspects of numerical tools (e.g., CFD and FSI) for prediction and assessment of cerebral aneurysm rupture. Computation fluid dynamics has been widely used to investigate the effect of single-phase blood model in the risk assessments, but no further application of two-phase blood model and FSI were available. For this reason, the thesis was proposed to evaluate further applications, with the aim of better understanding of the diseases. Rupture risk assessment can be classified as (a) Flow properties (e.g., inflow penetration depth, flow complexity and flow impingement zones) and (b) wall shear stress based hemodynamic indexes (e.g., OSI and TAWSS). Chapter 1 is introductory and reviews the cerebral aneurysms, the mechanisms leading to the disease, and current computational tools in order to predict and assess of aneurysm rupture. Chapter 2 gives a very deep understanding about the mathematical theory behind the single-phase, two-phase flow and FSI. Considering the non-Newtonian nature of blood, two non-Newtonian viscosity models (Casson for single-phase and Carreau– Yasuda for two-phase blood assumption) are discussed here. Then it proceeds with FSI concept where an appraisal of the FSI approach and its implementation, the governing equations regarding the single-phase blood assumption and mechanics of deformable vessel structure are discussed in detail. One of the most important aspects of this thesis is to use open-source solvers for numerical implementations. Regarding the implementation of single-phase and two-phase blood CFD analysis, OpenFOAM is used which is free and open-source software for CFD from the OpenFOAM Foundation. For the implementation of an FSI problem, the preCICE multi-physic coupling toolkit is used in order to couple OpenFOAM (FVM CFD solver) and CALCULIX (FEM structure solver). Furthermore, two wall shear stress based hemodynamic indexes (TAWSS and OSI) are introduced which can be used in order to make a bridge from numerical results to rupture risk assessments. Two patient-specific cerebral aneurysms are given in chapter 3 where the first patient was a female of 41 years old, who had anterior communicating artery aneurysm with concomitant subarachnoid hemorrhage and left frontobasal hematoma, and the second patient was a female of 62 years old, who had dolichoectatic carotid and vertebral arteries. The 3D images in digital imaging and communications in medicine format were anatomically remodeled into patient-specific 3D geometries in the STL format. The FVM mesh, boundary conditions and numerical implementations used for CFD and FSI analysis of two aneurysms are discussed in detail in this chapter. Chapter 4 investigates the blood transport in the cerebral aneurysm using single-phase and two-phase models. In two-phase Euler-Euler approach, the blood is represented by two interpenetrating continua where the dispersed red blood cells of non-Newtonian characteristics are suspended in the continuous Newtonian plasma. The results of two phase model, where the RBCs phase is assumed to be Carreau–Yasuda fluid, are validated against the experimental data. Furthermore, comparative analyses were performed in two patient-specific aneurysms, which indicated that for a given pulsatile flow rate, the two-phase blood approach has vitally advantageous over the single-phase assumption, and revealed a deeper inflow penetration, more complex flow structures and denser flow diversion zones in the aneurysm sac. It was obvious that the high OSI values calculated by the two-phase model covered much wider regions than the single phase predicted. It was equally crucial that these regions coincided with the TAWSS values lower than the threshold that the single-phase approach can predict. Apparently, the single-phase model failed to spot sites of high rupture risk. The results were further exploited to identify the RBCs aggregation regions as, for example, the concave structures and narrow paths in the saccular aneurysms, for their possible use as the precursors of the thrombus formation. Chapter 5 investigates the effect of variations in the haematocrit level on the blood flow in two cerebral aneurysms using the two-phase Euler-Euler approach and the Carreau–Yasuda viscosity model. The results showed that the maximum inflow jet penetration was achieved at the lowest haematocrit level, and this accompanied with strong flow impingements at the narrow corners deep inside the aneurysm sac and undesired complex flow patterns spreading from entrance to the aneurysm dome. The decrease in H level also changed the characteristics of the velocity profile inside the dome from a single- to a double-peak profile, which increased the likelihood of a daughter aneurysm formation. Furthermore, the TAWSS and OSI indicators showed that lowering the H values could change an initially low-risk case into a very high rupture risk situation. The two-phase Euler-Euler approach was used to enlighten the effect of variations in the haematocrit level to cure the blood flow issue in two cerebral aneurysms. A comprehensive description of the two-phase Euler-Euler approach and the relevant viscosity specifications were described in the previous chapter. The same patient specific aneurysms and the numerical implementations of the two-phase model discussed before were used here. However, this chapter presents an appraisal of the approach and interpretations of the flow complexity, features of the inflow diversion zone, penetration depths and the shear stress parameters based on varying Hematocrit values. Chapter 6 investigates dynamics of the wall movements of a patient-specific aneurysm dome using the interactions of the non-Newtonian blood flow and the deformable vessels. The patient under consideration had an anterior communicating artery aneurysm with a concomitant subarachnoid hemorrhage and left frontonasal hematoma. A finite volume CFD solver was used with a 3D mesh of roughly 300000 cells and three boundary patches; the inlet, deformable walls and outlets. A linear elastic material model was considered for the deformation of the aneurysm wall and, in the structural computations, a finite element solver was employed with a solid domain of approximately 12000 elements. An open-source code was exploited for the coupling between the CFD and finite element solvers. Results showed that at the peak systole, the vortical structure of the flow in the aneurysm dome was complicated. Furthermore, the instabilities in the flow field produced intense shear forces, due to which a possible weakening of the wall material will certainly lead to an increase in the risk of the rupture and bleeding. The non-uniformity of the flow field acquired large values of the von Mises stresses, resulting in prominent wall displacements, which also matched to the high OSI and low TAWSS values. The maximum displacements exhibited a non-stationery movement everywhere in the dome though mostly remained in the region of the impingement. And finally, chapter 7 covers conclusions and remarks respectively.