An Efficient Red Blood Cell Model in the Frame of Ib-LBM and Its Application

Abstract

A two-dimensional red blood cell (RBC) membrane model based on elastic and Euler–Bernoulli beam theories is introduced in the frame of immersed boundary-lattice Boltzmann method (IB-LBM). The effect of the flexible membrane is handled by the immersed boundary method in which the stress exerted by the RBC on the ambient fluid is spread onto the collocated grid points near the boundary. The fluid dynamics is obtained by solving the discrete lattice Boltzmann equation. A "ghost shape", to which the RBC returns when restoring, is introduced by prescribing a bending force along the boundary. Numerical examples involving tumbling, tank-treading and RBC aggregation in shear flow and deformation and restoration in poiseuille flow are presented to verify the method and illustrate its efficiency. As an application of the present method, a ten-RBC colony being compressed through a stenotic microvessel is studied focusing the cell–cell interaction strength. Quantitative comparisons of the pressure and velocity on specified microvessel interfaces are made between each aggregation case. It reveals that the stronger aggregation may lead to more resistance against blood flow and result in higher pressure difference at the stenosis.

A Numerical Simulation of Cell Separation by Simplified Asymmetric Pinched Flow Fractionation

“…U ( s , t ) is the membrane velocity and u ( x , t ) is the fluid velocity. d x is the lattice side length; Ω is the nearby area of the membrane defined by the Delta function D ( x − X ) [33–35]:$\begin{array}{c}T1D\left(\mathbf{x}-\mathbf{X}\right)=\underset{i=\mathrm{normal1}}{\overset{n}{{\displaystyle false\prod }}}\delta \left({\mathbf{x}}_i-{\mathbf{X}}_i\right),\end{array}$where…”

“…The fluid-structure-interaction is enforced by the following equation [27, 32, 33, 36]:$\begin{array}{c}T1\mathbf{f}\left(\mathbf{x},t\right)={{\displaystyle false\int }}_{\mathrm{normal\Gamma }}\mathbf{F}\left(s,t\right)D\left(\mathbf{x}-\mathbf{X}\left(s,t\right)\right)ds,\end{array}$where F ( s , t ) is Lagrangian force acting on the ambient fluid by the cell membrane. In the present study, the cell model is proposed as$\begin{array}{c}T1\mathbf{F}={\mathbf{F}}_l-{\mathbf{F}}_b+{\mathbf{F}}_s+{\mathbf{F}}_e,\end{array}$where F l is the tensile force, F b is the bending force, F s is the normal force on the membrane which controls the cell incompressibility, and F e is the membrane-wall extrusion acting on the cell.…”

“…In the present study, the cell model is proposed as$\begin{array}{c}T1\mathbf{F}={\mathbf{F}}_l-{\mathbf{F}}_b+{\mathbf{F}}_s+{\mathbf{F}}_e,\end{array}$where F l is the tensile force, F b is the bending force, F s is the normal force on the membrane which controls the cell incompressibility, and F e is the membrane-wall extrusion acting on the cell. The four force components are [33, 37–39]$\begin{array}{c}T17{\mathbf{F}}_l=\frac{\partial }{\partial s}\left[K_l\left(\left|\frac{\partial \mathbf{X}\left(s,t\right)}{\partial s}\right|-\mathrm{1}\right)\frac{\partial \mathbf{X}\left(s,t\right)}{\partial s}\right],\\ \end{array}$ $\begin{array}{c}{\mathbf{F}}_b=K_b\frac{{\partial }^{\mathrm{4}}\mathbf{X}\left(s,t\right)}{\partial s^{\mathrm{4}}},\\ \end{array}$ $\begin{array}{c}{\mathbf{F}}_s=K_s\frac{S-S_{\mathrm{0}}}{S_{\mathrm{0}}}\mathbf{n},\\ \end{array}$ $\begin{array}{c}{\mathbf{F}}_e=\left\{\begin{array}{c}{K}_e\frac{\mathrm{boldX}\left(s,t\right)-{\mathrm{boldX}}_w}{{\left(\right)}^{}}\hfill \end{array}\right.\end{array}$…”

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

“…(2) and (3). Compared to ALE [53] and Cartesian mesh based methods [35,[54][55][56][57][58][59], this method does not apply interpolation when moving mesh is involved, and thus, has high accuracy and efficiency. This method has been extensively described in the references cited above.…”

Deformation of a Capsule in a Power-Law Shear Flow

“…The synthetic microcapsules with polymerized interfaces are designed for drug delivery, cosmetic production, and other technical usages [11, 12]. Therefore, great effort has been made to study this problem (e.g., [1, 4, 6, 8, 10, 12–14]).…”