Volumetric lattice Boltzmann method for wall stresses of image-based pulsatile flows.

Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems.

Two-dimensional Finite Element Model of Breast Cancer Cell Motion Through a Microfluidic Channel.

A two-dimensional model for red blood cell motion is adapted to consider the dynamics of breast cancer cells in a microfluidic channel. Adjusting parameters to make the membrane stiffer, as is the case with breast cancer cells compared with red blood cells, allows the model to produce reasonable estimates of breast cancer cell trajectories through the channel. In addition, the model produces estimates of quantities not as easily obtained from experiment such as velocity and stress field information throughout the fluid and on the cell membrane. This includes locations of maximum stress along the membrane wall. A sensitivity analysis shows that the model is capable of producing useful insights into various systems involving breast cancer cells. Current results suggest that dynamics taking place when cells are near other objects are most sensitive to membrane and cytoplasm elasticity, dynamics taking place when cells are not near other objects are most sensitive to cytoplasm viscosity, and dynamics are significantly affected by low membrane bending elasticity. These results suggest that continued calibration and application of this model can yield useful predictions in other similar systems.

Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels.

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier-Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid-structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis.

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Reconfiguration and the reduction of vortex-induced vibrations in broad leaves.

Flexible plants, fungi and sessile animals reconfigure in wind and water to reduce the drag acting upon them. In strong winds and flood waters, for example, leaves roll up into cone shapes that reduce drag compared with rigid objects of similar surface area. Less understood is how a leaf attached to a flexible leaf stalk will roll up stably in an unsteady flow. Previous mathematical and physical models have only considered the case of a flexible sheet attached to a rigid tether in steady flow. In this paper, the dynamics of the flow around the leaf of the wild ginger Hexastylis arifolia and the wild violet Viola papilionacea are described using particle image velocimetry. The flows around the leaves are compared with those of simplified physical and numerical models of flexible sheets attached to both rigid and flexible beams. In the actual leaf, a stable recirculation zone is formed within the wake of the reconfigured cone. In the physical model, a similar recirculation zone is observed within sheets constructed to roll up into cones with both rigid and flexible tethers. Numerical simulations and experiments show that flexible rectangular sheets that reconfigure into U-shapes, however, are less stable when attached to flexible tethers. In these cases, larger forces and oscillations due to strong vortex shedding are measured. These results suggest that the three-dimensional cone structure in addition to flexibility is significant to both the reduction of vortex-induced vibrations and the forces experienced by the leaf.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments.

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Interaction between a flexible filament and a downstream rigid body.

A filament flapping in the bow wake of a rigid body is considered in order to study the hydrodynamic interaction between flexible and rigid bodies in tandem arrangement. Both numerical and experimental methods are adopted to analyze the motion of the filament, and the drag force on both bodies is computed. It is shown that the results largely depend on the gap between the two objects and the Reynolds number. The flexible body may have larger vibration amplitude but meanwhile experience a reduced drag force. On the other hand, the trailing rigid body enjoys a drag reduction. The qualitative behavior of the filament is independent of the filament's length and mass ratio or the shape of the rigid body for the parameter regime considered. The result is in contrast with the interaction between two rigid or two flexible objects in tandem arrangement, and it may provide a physical insight into the understanding of the aquatic animals swimming in the bow wake of ships or staying in the bow wake of stationary structures.

Effects of stent sizing on endothelial and vessel wall stress: potential mechanisms for in-stent restenosis.

Stent sizing and apposition have been shown to be important determinants of clinical outcome. This study evaluates the mechanical effects of undersizing and oversizing of stents on endothelial wall shear stress (WSS) and vessel wall stress to determine a possible biomechanical mechanism of in-stent restenosis and thrombosis. Three-dimensional computational models of stents, artery, and internal fluid were created in a computer-assisted design package, meshed, and solved in finite element and computational fluid dynamic packages. The simulation results show that the effects of various degrees of undersizing on WSS, WSS gradient, and oscillatory shear index were highly nonlinear. As the degree of undersizing increased, the heterogeneity of WSS became smaller. The WSS distribution for the 20% undersizing was smooth and uniform, whereas the 5% case was very heterogeneous. The combination of lower WSS and higher WSS gradient and oscillatory shear index in the 5% undersized case may induce neointimal hyperplasia or thrombosis. Additionally, the oversizing simulation results show that the maximum intramural wall stress of the 20% oversizing case is significantly larger than the maximum stress for the 10% and zero oversizing cases. Edge stress concentration was observed, consistent with the restenosis typically observed in this region. This study demonstrates that proper sizing of stent is important for reducing the hemodynamic and mechanical disturbances to the vessel wall. Furthermore, the present findings may be used to improve stent design to reduce endothelial flow disturbances and intramural wall stress concentrations.