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TECHNICAL PAPERS: Cell

Computational Fluid Dynamic Simulation of Aggregation of Deformable Cells in a Shear Flow

[+] Author and Article Information
Prosenjit Bagchi

Department of Mechanical & Aerospace Engineering, Rutgers,  The State University of New Jersey, 98 Brett Road, Piscataway, NJ 08854

Paul C. Johnson

Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093

Aleksander S. Popel

Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, 720 Rutland Avenue, 611 Traylor Bldg., Baltimore, MD 21205

J Biomech Eng 127(7), 1070-1080 (Aug 15, 2005) (11 pages) doi:10.1115/1.2112907 History: Received November 12, 2004; Revised July 27, 2005; Accepted August 15, 2005

We present computational fluid dynamic (CFD) simulation of aggregation of two deformable cells in a shear flow. This work is motivated by an attempt to develop computational models of aggregation of red blood cells (RBCs). Aggregation of RBCs is a major determinant of blood viscosity in microcirculation under physiological and pathological conditions. Deformability of the RBCs plays a major role in determining their aggregability. Deformability depends on the viscosity of the cytoplasmic fluid and on the rigidity of the cell membrane, in a macroscopic sense. This paper presents a computational study of RBC aggregation that takes into account the rheology of the cells as well as cell-cell adhesion kinetics. The simulation technique considered here is two dimensional and based on the front tracking/immersed boundary method for multiple fluids. Results presented here are on the dynamic events of aggregate formation between two cells, and its subsequent motion, rolling, deformation, and breakage. We show that the rheological properties of the cells have significant effects on the dynamics of the aggregate. A stable aggregate is formed at higher cytoplasmic viscosity and membrane rigidity. We also show that the bonds formed between the cells change in a cyclic manner as the aggregate rolls in a shear flow. The cyclic behavior is related to the rolling orientation of the aggregate. The frequency and amplitude of oscillation in the number of bonds also depend on the rheological properties.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 6

Explanation of oscillations in the total number of bonds as the aggregate rolls in shear flow. The shape and orientation of the aggregate are shown at a few time instants.

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Figure 7

(a) Angular orientation and (b) velocity of an aggregate at γ̇=75s−1. The dash line is Jeffery’s (37) solution. -●- Kb=0.875,λ=5; -◻- Kb=0.875,λ=1; -엯- Kb=3,λ=1.

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Figure 5

Evolution of the number of bonds with time. (A) Effect of spring constant Kb. Curves (a) to (e) represent Kb=0.175, 0.875, 1.0, 2.0, and 3.0. (B) Effect of viscosity ratio λ. The four curves are for (a) Kb=0.175,λ=1, (b) Kb=0.875,λ=1, (c) Kb=0.175,λ=5, (d) Kb=0.875,λ=5. (C) Effect of varying shear rate (a), (b), and (c) in the plot) and varying membrane rigidity (b), (d), and (e). (a) γ̇=225s−1, (b) γ̇=75s−1, and (c) γ̇=25s−1. (b) E*=0.096, (d) E*=0.5, and (e) E*=0.02.

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Figure 4

Fluid velocity vectors and color contours showing the fluid velocity component in the x direction during aggregate rolling

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Figure 3

Simulation of aggregate formation between two cells. (a) Evolution of cell shape under the no-flow condition. Three time instants are tγ̇=0, 50, and 97. (b) γ̇=75s−1,Kb=2,λ=1. The four instants are approximately at equal time interval during a rotation of the aggregate. (c) Effect of reduced bond strength at Kb=0.875,λ=1,γ̇=75s−1. (d) Kb=0.175,λ=1,γ̇=75s−1. (e) Effect of cell viscosity: Kb=0.875,λ=5,E*=0.096,γ̇=75s−1.

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Figure 1

Computational domain and grids

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Figure 8

Effect of membrane viscoelasticity on the instantaneous shape of the rolling aggregate. (a) Viscoelasticity included. Four different time instants are shown: tγ̇=42, 48, 53, and 58. (b) Viscoelasticity not included. Shapes at tγ̇=42 and 48 are shown.

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Figure 9

Relaxation of an initially elliptic (left) cell and a biconcave (right) cell toward their resting circular shape under the action of bending resistance at EB∕(a2Es)=0.003,λ=1

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Figure 10

Effect of bending resistance and biconcave shape on the shape evolution of an aggregate. Both elliptic and biconcave cells are considered. Figures at left and right show the formation of the aggregate under static and rolling conditions, respectively. In (a), the solid line is for bending moment included, and the dash line is without bending moment.

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Figure 11

Effect of viscoelasticity and bending resistance on the number of bonds. Bold line is for elliptic cells without bending resistance and viscoelasticity. …, viscoelastic membrane; —, elliptic cell with bending resistance; –––––, biconcave discoid cell with bending resistance.

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