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 Computational Fluid Dynamic Simulation of Aggregation of Deformable Cells in a Shear Flow We present computational fluid dynamic (CFD) simulation of aggregation of two deform- able 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 deter- minant of blood viscosity in microcirculation under physiological and pathological con- ditions. 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 pre- sented 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. DOI: 10.1115/1.2112907 1 Introduction Aggregation of cells plays a key role in many important bio- logical processes. In the blood of humans and many other mam- mals, red blood cells RBCs aggregate at low shear rates forming a linear or fractal-like structure called “rouleaux.” During me- tastasis, cancer cells often flow through the blood stream as ag- gregates. Platelets form aggregates to prevent blood clotting. The present work is primarily motivated by an attempt to develop computational models and simulations of aggregation of RBCs in a shear flow. RBCs under normal conditions are highly deform- able. Under pathological conditions, such as sickle cell anemia and bacterial infections, deformability of RBCs is greatly reduced. Clinical studies have shown that under such conditions aggrega- bility of RBCs is also increased 1,2. It is however not estab- lished whether there is a connection between reduced deformabil- ity and increased aggregability of RBCs. We hypothesize that deformability of cells, and hence their rheological property, plays a key role in determining their aggregability. To that end, we develop a computational fluid dynamic simulation to study aggre- gation of deformable cells. The simulations considered here are two dimensional2D, though the methodology can be extended to 3D. This is a simulation of aggregation of cells that takes into account cell rheology. The methodology is general and can be applied to any deformable cell, though the specific rheological values used here correspond to RBCs. The mechanism of RBC aggregation in blood flow is as fol- lows. RBCs are randomly drawn close to each other by the flow of plasma. If the shearing forces by fluid motion are small, the cells adhere to each other and form aggregates. Currently there are two theories that describe the mechanism of aggregation: bridging be- tween cells by cross-linking molecules 3, and osmotic force gen- erated by the depletion of molecules in the intercellular space 4. RBC aggregation leads to increased blood viscosity, and hence elevated resistance to blood flow. Aggregation is common in pa- tients with peripheral vascular disease. Elevated aggregation is often associated with a higher risk of cardiovascular disease. RBC aggregation is elevated after myocardial infarction, ischemic brain infarcts, in diabetes, and during sepsis. Thus, understanding the mechanics of RBC aggregation may lead to a better understanding of cardiovascular diseases and the pathology of blood. Studies on the effect of RBC aggregation in microcirculation are summarized in recent reviews 1,5. Theoretical approaches to the study of aggregation can be broadly classified into two categories. The first one is the quasi- steady approach which predicts the equilibrium shape of the RBCs forming the aggregate through a balance between the adhe- sive surface energy and the elastic energy stored in the RBC mem- brane 6,7. The motion and breakage of an aggregate in a fluid flow cannot be modeled in this approach. The second approach is based on the theory of kinetic modeling of colloidal suspension 8–10. In the kinetic approach deformation of a cell is not con- sidered. Further, the details of the flow pattern around each de- formable cell and aggregate are also neglected which can have a significant effect on the stability and motion of the aggregate. It has been shown earlier by in vitro 11, and recently by in vivo experiments that aggregation has a significant effect on the veloc- ity profiles in microvessels 12–15. Clearly, a theoretical/computational model of cell aggregation that would take into account deformability of the cells and their dynamic motion in a flow is lacking. Aggregation is a multiscale process. At the nanoscale the molecular bridging between adjacent cells initiates aggregation. At the microscale, deformability of in- dividual cells dictates the process. At the macroscale, the flow of plasma imparts a shear force causing the rolling and breakage of the aggregates. Here we present a computational fluid dynamic model that combines the three scales of the problem. Specifically we study the effect of cell deformation, strength of the adhesion molecule, and the shear rate of the bulk flow on the motion and Contributed by the Bioengineering Division of ASME for publication in the JOUR- NAL OF BIOMECHANICAL ENGINEERING. Manuscript received November 12, 2004; revi- sion received July 27, 2005. Review conducted by: C. Ross Ethier. Technical Editor: Frank Yin. Approved August 15, 2005. 1070 / Vol. 127, DECEMBER 2005 Copyright © 2005 by ASME Transactions of the ASME