Hyoungsu Baek

Flow instability and wall shear stress variation in intracranial aneurysms

We investigate the flow dynamics and oscillatory behaviour of wall shear stress (WSS) vectors in intracranial aneurysms using high resolution numerical simulations. We analyse three representative patient-specific internal carotid arteries laden with aneurysms of different characteristics: (i) a wide-necked saccular aneurysm, (ii) a narrower-necked saccular aneurysm, and (iii) a case with two adjacent saccular aneurysms. Our simulations show that the pulsatile flow in aneurysms can be subject to a hydrodynamic instability during the decelerating systolic phase resulting in a high-frequency oscillation in the range of 20–50 Hz, even when the blood flow rate in the parent vessel is as low as 150 and 250 ml min−1 for cases (iii) and (i), respectively. The flow returns to its original laminar pulsatile state near the end of diastole. When the aneurysmal flow becomes unstable, both the magnitude and the directions of WSS vectors fluctuate at the aforementioned high frequencies. In particular, the WSS vectors around the flow impingement region exhibit significant spatio-temporal changes in direction as well as in magnitude.

A convergence study of a new partitioned fluid-structure interaction algorithm based on fictitious mass and damping

We develop, analyze and validate a new method for simulating fluid-structure interactions (FSIs), which is based on fictitious mass and fictitious damping in the structure equation. We employ a partitioned method for the fluid and structure motions in conjunction with sub-iteration and Aitken relaxation. In particular, the use of such fictitious parameters requires sub-iterations in order to reduce the induced error in addition to the local temporal truncation error. To this end, proper levels of tolerance for terminating the sub-iteration procedure have been obtained in order to recover the formal order of temporal accuracy. For the coupled FSI problem, these fictitious terms have a significant effect, leading to better convergence rate and hence substantially smaller number of sub-iterations. Through analysis we identify the proper range of these parameters, which we then verify by corresponding numerical tests. We implement the method in the context of spectral element discretization, which is more sensitive than low-order methods to numerical instabilities arising in the explicit FSI coupling. However, the method we present here is simple and general and hence applicable to FSI based on any other discretization. We demonstrate the effectiveness of the method in applications involving 2D vortex-induced vibrations (VIV) and in 3D flexible arteries with structural density close to blood density. We also present 3D results for a patient-specific aneurysmal flow under pulsatile flow conditions examining, in particular, the sensitivity of the results on different values of the fictitious parameters.

Generalized fictitious methods for fluid–structure interactions: Analysis and simulations

We present a new fictitious pressure method for fluid–structure interaction (FSI) problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in [1]. The fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver. We analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor (convergence rate index) at the FSI interface [2]. This analysis also demonstrates an apparent similarity of fictitious methods to the FSI approach based on Robin boundary conditions, which have been found to be very effective in FSI problems. We implement all methods, including the semi-implicit Robin based coupling method, in the context of spectral element discretization, which is more sensitive to temporal instabilities than low-order methods. However, the methods we present here are simple and general, and hence applicable to FSI based on any other spatial discretization. In numerical tests, we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex-induced vibrations (VIV) even at zero mass ratio (“for-ever-resonance”). We also develop an empirical a posteriori analysis for complex geometries and apply it to 3D patient-specific flexible brain arteries with aneurysms for very large deformations. We demonstrate that the fictitious pressure method enhances stability and convergence, and is comparable or better in most cases to the Robin approach or the other fictitious methods.

Modeling of blood flow in arterial trees.

Advances in computational methods and medical imaging techniques have enabled accurate simulations of subject‐specific blood flows at the level of individual blood cell and in complex arterial networks. While in the past, we were limited to simulations with one arterial bifurcation, the current state‐of‐the‐art is simulations of arterial networks consisting of hundreds of arteries. In this paper, we review the advances in methods for vascular flow simulations in large arterial trees. We discuss alternative approaches and validity of various assumptions often made to simplify the modeling. To highlight the similarities and discrepancies of data computed with different models, computationally intensive three‐dimensional (3D) and inexpensive one‐dimensional (1D) flow simulations in very large arterial networks are employed. Finally, we discuss the possibilities, challenges, and limitations of the computational methods for predicting outcomes of therapeutic interventions for individual patients. Copyright

Sub-iteration leads to accuracy and stability enhancements of semi-implicit schemes for the Navier-Stokes equations

We present an iterative semi-implicit scheme for the incompressible Navier-Stokes equations, which is stable at CFL numbers well above the nominal limit. We have implemented this scheme in conjunction with spectral discretizations, which suffer from serious time step limitations at very high resolution. However, the approach we present is general and can be adopted with finite element and finite difference discretizations as well. Specifically, at each time level, the nonlinear convective term and the pressure boundary condition - both of which are treated explicitly in time - are updated using fixed-point iteration and Aitken relaxation. Eigenvalue analysis shows that this scheme is unconditionally stable for Stokes flows while numerical results suggest that the same is true for steady Navier-Stokes flows as well. This finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters. In unsteady flows, second- and third-order temporal accuracy is obtained for the velocity field at CFL number 5-14 using analytical solutions. Systematic accuracy, stability, and cost comparisons are presented against the standard semi-implicit method and a recently proposed fully-implicit scheme that does not require Newtons iterations. In addition to its enhanced accuracy and stability, the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully-implicit schemes.

Distribution of WSS on the Internal Carotid Artery With an Aneurysm: A CFD Sensitivity Study

Intracranial blood flow simulations for studying brain aneurysms are based on many assumptions including the Womersley profile for the inlet boundary condition. Moreover, computational domains seem to be more or less arbitrarily chosen. Previous studies have shown that long inlet vessels lead to more realistic flow just upstream of the aneurysm. In order to guide our studies of cerebral aneurysms, using the high-order spectral/hp element method, we systematically investigated the geometric sensitivity of wall shear stress (WSS) on aneurysms; specifically, the effect of parent vessel geometry on the WSS in aneurysms was considered. Using datasets of two patients with different type of aneurysms, five different geometric models were generated. With the aneurysm geometries fixed, the length or turning angles of inlet parent vessel were varied one at a time. This study demonstrates that the turning angle of upstream blood vessel, the type of aneurysm, and its location with respect to the parent vessel affect the distribution of WSS in the aneurysm. In the fusiform aneurysm with sharp turns, the inlet length makes a substantial difference on impinging location, magnitude, and direction of WSS. On the other hand, the saccular type aneurysm with a smoother parent vessel does not show any significant change. Therefore, the computational domain should be determined based on the geometry of parent vessels and the type of aneurysm.Copyright

Numerical investigation of non-linear deflections of an infinite beam on non-linear and discontinuous elastic foundation

ABSTRACT The analysis of static deflections of an infinite beam resting on a non-linear and discontinuous foundation is not trivial. We apply a recently proposed iterative non-linear procedure to the analysis. Mathematical models of the elastic foundation are incorporated into the governing non-linear fourth-order differential equation of the system and then the differential equation is transformed into an equivalent non-linear integral equation using Greens functions. Numerical solutions of the integral equation clearly demonstrate herein that our non-linear iterative numerical method is simple and straightforward for approximate solutions of the static deflection of an infinite beam on a non-linear elastic foundation. Iterative numerical solutions converge fast to corresponding analytic solutions. However, numerical errors are observed in a narrow neighbourhood of material discontinuities of foundations.

CFD Challenge: Solutions Using the Spectral Element Solver NEKTAR

Flow problems in cardiovascular mechanics involve complex geometries and pulsatile flow that may give rise to instabilities, especially in pathological cases. High-order methods are particularly suitable for resolving such unsteady phenomena whereas low-order methods may exhibit excessive dissipation and hence suppress any such physical instabilities. This, for example, is the case for certain type of cerebral aneurysms, see [1], for which we have demonstrated that shear layer instabilities may be triggered even at physiological flow rates, giving rise to audible frequencies in the range of 10Hz to 50 Hz. Similar phenomena may be present in stenotic arteries, where a jet type flow may develop that is also susceptible to temporal instabilities, especially during the decelerating systole.Copyright

Wall Shear Stress Fluctuations due to Flow Instability in Intracranial Aneurysms

Experimental studies of an impingement area inside aneurysms showed that loss of smooth muscle cells and degenerative remodeling of vessel walls occur at the region of high wall shear stress (WSS) and WSS gradient where the flow accelerates [1]. Also, a more sensitive response of endothelial cells to turbulent oscillatory shear rather than to laminar and steady shear has been demonstrated experimentally [2]. Therefore, it seems imperative to understand the spatio-temporal behavior of WSS vectors in the impingement (stagnation) locations. To this end, we investigate systematically the oscillatory behavior of WSS vectors inside aneurysms and the flow instability due to the presence of an aneurysm in the internal carotid arteries (ICA), more specifically, at the posterior communicating artery (PCoA) origin.Copyright

Temporal variation of wall shear stress on the aneurysms in the supraclinoid internal carotid artery

We investigate temporal and spatial variation of wall shear stress (WSS) vectors in aneurysms in the supraclinoid internal carotid artery (ICA). This study shows that contrary to our expectation, WSS vectors do not change their directions significantly over the cycle, especially when the WSS magnitude is larger that 5 N/m2. However, the direction-change may increase as high as 100 degrees when the WSS magnitude is small or hydrodynamic instability exists inside the aneurysms or when the swirling motion in the ICA segment is strong. Minimum WSS and maximum WSS magnitude on a patch demonstrate a linear relationship.