Hafez Asgharzadeh

Platelet activation of mechanical versus bioprosthetic heart valves during systole

Thrombus formation is a major concern for recipients of mechanical heart valves (MHVs), which requires them to take anticoagulant drugs for the rest of their lives. Bioprosthetic heart valves (BHVs) do not require life-long anticoagulant therapy but deteriorate after 10-15years. The thrombus formation is initiated by the platelet activation which is thought to be mainly generated in MHVs by the flow through the hinge and the leakage flow during the diastole. However, our results show that the activation in the bulk flow during the systole phase might play an essential role as well. This is based on our results obtained by comparing the thrombogenic performance of a MHV and a BHV (as control) in terms of shear induced platelet activation under exactly the same conditions. Three different mathematical activation models including linear level of activation, damage accumulation, and Soares model are tested to quantify the platelet activation during systole using the previous simulations of the flow through MHV and BHV in a straight aorta under the same physiologic flow conditions. Results indicate that the platelet activation in the MHV at the beginning of the systole phase is slightly less than the BHV. However, at the end of the systole phase the platelet activation by the bulk flow for the MHV is several folds (1.41, 5.12, and 2.81 for linear level of activation, damage accumulation, and Soares model, respectively) higher than the BHV for all tested platelet activation models.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Effects of Reynolds and Womersley Numbers on the Hemodynamics of Intracranial Aneurysms

The effects of Reynolds and Womersley numbers on the hemodynamics of two simplified intracranial aneurysms (IAs), that is, sidewall and bifurcation IAs, and a patient-specific IA are investigated using computational fluid dynamics. For this purpose, we carried out three numerical experiments for each IA with various Reynolds (Re = 145.45 to 378.79) and Womersley (Wo = 7.4 to 9.96) numbers. Although the dominant flow feature, which is the vortex ring formation, is similar for all test cases here, the propagation of the vortex ring is controlled by both Re and Wo in both simplified IAs (bifurcation and sidewall) and the patient-specific IA. The location of the vortex ring in all tested IAs is shown to be proportional to Re/Wo2 which is in agreement with empirical formulations for the location of a vortex ring in a tank. In sidewall IAs, the oscillatory shear index is shown to increase with Wo and 1/Re because the vortex reached the distal wall later in the cycle (higher resident time). However, this trend was not observed in the bifurcation IA because the stresses were dominated by particle trapping structures, which were absent at low Re = 151.51 in contrast to higher Re = 378.79.

Vortex Generation in Two Intracranial Aneurysms

Three-dimensional numerical simulations, using the sharp-interface immersed boundary method, are carried out to investigate the effect of aneurysm shape on the hemodynamics of intracranial aneurysm. In our previous work [1] only a single geometry of an aneurysm was tested, but here two three-dimensional geometries are tested by reconstruction from three-dimensional rotational angiography of a human subject [2]. The results support our previous hypothesis [1], i.e., when the vortex formation time scale at the parent artery is smaller than the transportation time scale across the aneurysm neck, the flow aneurysm dome is dominated by a dynamic, unsteady vortex formation.Copyright