ARTICLE | doi:10.20944/preprints202303.0271.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: Fluid-Structure Interaction (FSI), cerebral aneurysms, Finite Element Method, hyperelastic materials, Arbitrary Lagrangian-Eulerian, hydrodynamic forces, hemodynamic phenomena.
Online: 15 March 2023 (08:36:23 CET)
In recent years, there has been a growing interest in the preoperative modeling of fluid-structure interaction in the treatment of cerebral aneurysms. In this study, we investigate two cases involving laminar incompressible fluid flow interacting with hyperelastic materials (a vertical flap and aneurysm walls) under the effect of fluid flow. We present a finite element method (FEM) for these prototypical two-dimensional ($2D$) configurations, taking into account the complex flows and deformation of the variant's structure models. We use an Arbitrary Lagrangian-Eulerian (ALE) formulation in a continuum, fully monolithic coupled way, and discretize the fluid and solid domains using the quadratic LBB stable $P_2P_1$ finite element pair to approximate the displacement, velocity, and pressure spaces independently. The resulting discretized form of the nonlinear algebraic system is linearized using a variant of Newton's procedure, and the Jacobian matrices are approximated via the divided difference method. The resulting linear systems are solved using a direct solver MUMPS. We evaluate hydrodynamic forces such as drag and lift coefficients for nonlinear elastic material models, including Saint-Venant Kirchoff, Neo-Hookean, and Mooney-Rivlin (2 parameters) separately. To gain more physical insight into the problem, we verify the computed results by comparing the velocity, viscosity, and pressure fields. Our aim is to qualitatively analyze the changes in the mechanics of the wall behavior of the elasticity of the flap vs. the complexity of deformation, interface, details for prototypical flow situations, corresponding displacement, and deformation. We also provide a physical interpretation of blood flow magnitude and basic hemodynamic phenomena of wall shear stresses (WSS) in aneurysma and the range of deformation. Overall, this study presents a comprehensive approach to modeling fluid-structure interaction in cerebral aneurysms, which could help in the development of more effective treatment strategies.
ARTICLE | doi:10.20944/preprints202303.0127.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: inite element method; Stenosis; Bifurcation; Wall shear stress; Elastic walls
Online: 7 March 2023 (07:32:27 CET)
The buildup of plaque in the arteries characterizes atherosclerosis, which causes the walls of the arteries to thicken, the lumen to narrow, and the wall to thin in certain areas. These changes can lead to alterations in blood flow, potentially resulting in aneurysms and heart attacks if left untreated. This paper presents a phenomenological model to explain the mechanics of plaque rupture in stenosed bifurcated elastic arteries. The model considers the interaction between the plaque and artery wall, blood flow, mechanical properties of the artery wall and plaque, and hemodynamic forces in the system. Using the Navier-Stokes equations to describe blood flow and elastic properties of artery walls, our study shows that blood flow can become turbulent, leading to backflow, vortices, and possible stagnation. Certain regions can become highly vulnerable and result in elevated heat transfer between blood and arterial walls, which can lead to the rupture of the plaque cap. The study focuses on blood flow features such as velocity profiles and wall displacement on fluid-structure interaction, which are consistent with the literature. Finally, we calculate the wall shear stress (WSS) for minimum and maximum times while considering elastic walls. Our findings may provide valuable insights into the mechanisms of plaque rupture and inform the development of improved diagnostic and therapeutic approaches.
ARTICLE | doi:10.20944/preprints202303.0117.v1
Subject: Computer Science And Mathematics, Computational Mathematics Keywords: Bifurcation; Elastic walls; Finite element method; Stenosis; Wall shear stress; Mag-netic field
Online: 7 March 2023 (02:03:46 CET)
To investigate the impact of a magnetic field on plaque development in a stenotic bifurcated artery, a finite element method is utilized. The blood flow is modelled as a stable, incompressible, Newtonian, biomagnetic, and laminar fluid. Furthermore, the arterial wall is assumed to be linear elastic. The Arbitrary Lagrangian Eulerian (ALE) method is employed to describe the hemodynamic flow in a bifurcated artery under the influence of an asymmetric magnetic field, taking into account two-way fluid-structure interaction coupling. A stable $P_2P_1$ finite element pair discretizes a nonlinear system of partial differential equations that requires a solution. The Newton-Raphson method is utilized to find a solution to the resulting nonlinear algebraic equation system. Numerical modelling is used to simulate the presence of magnetic fields, and the resulting displacement, velocity magnitude, pressure, and wall shear stresses are shown for a range of Reynolds numbers ($Re = 500$, $1000$, $1500$, and $2000$). The results of the numerical analysis demonstrate that the presence of a magnetic field has a significant effect not only on the magnitude of displacement but also on the velocity of the flow. The application of a magnetic field reduces flow separation, extends the recirculation area near the stenosis, and increases wall shear stress.