Efficient viscosity contrast calculation for blood flow simulations using the lattice Boltzmann method

Abstract

The lattice Boltzmann method (LBM) combined with the immersed boundary method is a common tool to simulate the movement of red blood cel ls (RBCs) through blood vessels. With very few exceptions, such simulations neglect the difference in viscosities between the hemoglobin solution inside the cells and the blood plasma outside, although it is well known that this viscosity contrast can severely affect cell deformation. While it is easy to change the local viscosity in LBM, the challenge is to distinguish whether a given lattice point is inside or outside the RBC at each time step. Here, we present a fast algorithm to solve this issue by tracking the membrane motion and computing the scalar product between the local surface normal and the distance vector between the closest LBM lattice point and the surface. This approach is much faster than, for example, the ray-casting method. With the domain tracking applied, we investigate the shape transition of a RBC in a microchannel for different viscosity contrast and validate our method by comparing with boundary-integral simulations.

A hyperelastic model for simulating cells in flow

“…To obtain (approximately) the limit of a purely elastic particle, we exploit a recently developed method by Lehmann et al. ( 2020 ) to discriminate between the cell interior and exterior during the simulation. Using this technique, we can tune the ratio between inner and outer viscosity with representing a purely elastic particle.…”

Predicting cell stress and strain during extrusion bioprinting

“…In addition to the elastic stress, we compute the viscous contribution resulting from the fluid motion enclosed by the cell volume. This quantity is extracted from the Lattice-Boltzmann strain rate tensor field [41, 66] inside the cell using our method from [67] and averaging over the cell volume. In figure S-2 we show that the agreement of the numerically obtained viscous cell stress with Roscoe theory is equally good as for the elastic component.…”

Lattice-Boltzmann Modelling for Inertial Particle Microfluidics Applications — A Tutorial Review

“…Different strategies have been suggested, such as simple ray-casting [259] and the Hoshen-Kopelman algorithm [260]. More recently, a fast tracking algorithm has been proposed by computing the scalar product of area-weighted surface normals and local distance vectors in the vicinity of the membrane [261]. Once each lattice node knows its viscosity µ(x), the local lattice-Boltzmann relaxation time is calculated via Eq.…”