Volumetric Lattice Boltzmann Method for Wall Stresses of Image-based Pulsatile Flows

Abstract

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 technique to compute wall stresses in image-based pulsatile flows using the lattice Boltzmann method (LBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and CFD, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the LBM and then conduct an application study 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 agreement with Womersley solutions for laminar flows and concurrent laboratory measurements for turbulent flows. This technique is being used to study (1) the hemodynamic wall stresses in inner choroid endothelium, (2) the drag force in sand flows, and (3) effects of waste streams on ion exchange kinetics in porous media.

A new noninvasive and patient‐specific hemodynamic index for the severity of renal stenosis and outcome of interventional treatment

“…The aortorenal arterial system is represented by the volumetric parameter field , defined in the following sections In this work, we use Materialize Mimics, for the convenience to deal with the parametric deterioration of the RAS (described in Section 2.2), to extract the anatomical geometry of the aortorenal arterial system from patient's CTA and save the image segment in STL format. Then we calculate the field using our in‐house Matlab code 39 …”

“…Equation (1) consists of three operations: (1) collision taking into account the momentum exchange between the willfully moving boundary and the flow, (2) streaming accompanying a volumetric bounce‐back procedure in boundary cells, and (3) boundary‐induced volumetric fluid migration moving the residual fluid particles into the flow domain when the boundary swipes over a boundary cell toward a solid cell. The detailed formulae are found in the publications 34,39 . In this work, we treat static arterial walls thus no momentum exchange between the arterial wall and the blood flow is accounted for.…”

“…We use InVascular to compute the TPI based on imaging data. The detailed methods of InVascular including image segmentation, VLBM solver, inlet and outlet boundary conditions, and GPU parallelization are referred to references [34,37,39,40]. Here we consolidate the major components for the completion of this presentation.…”

“…Then we calculate the P x ð Þ field using our in-house Matlab code. 39 The VLBM 34 is a volumetric representation of the lattice Boltzmann method. In VLBM, fluid particles are uniformly distributed in lattice cells as opposed to sitting at lattice nodes in the conventional lattice Boltzmann method.…”

“…The detailed formulae are found in the publications. 34,39 In this work, we treat static arterial walls thus no momentum exchange between the arterial wall and the blood flow is accounted for. The VLBM can handle arbitrary oriented boundaries with or without motion, and it satisfies mass conservation strictly.…”