## Computational Hydrodynamics of Capsules and Biological Cells

### C Pozrikidis (Editor)

### Taylor & Francis, 2010

## Chapters

1 | C. Pozrikidis | Flow-induced deformation of two-dimensional biconcave capsules |

2 |
D. Barthes-Biesel
J. Walter A.-V. Salsac |
Flow-induced deformation of artificial capsules |

3 |
J. B. Freund Hong Zhao |
A high-resolution fast boundary-integral method for multiple interacting blood cells |

4 |
J. Zhang P. C. Johnson A. S. Popel |
Simulating microscopic hemodynamics and hemorheology |

5 | Prosenjit Bagchi | Front-tracking methods for capsules, vesicles and blood cells |

6 |
D. A. Fedosov B. Caswell G. E. Karniadakis |
Dissipative particle dynamics modeling of red blood cells |

7 | T. W. Secomb | Simulation of red blood cell motion in microvessels and bifurcations |

8 |
N. A. Mody
M. R. King |
Multiscale modelling
of transport and
receptor-mediated
adhesion
of platelets in the bloodstream |

## Preface

Computational biofluiddynamics addresses a diverse family of problems involving fluid flow inside and around living organisms, organs and tissue, biological cells, and other biological materials. Numerical methods combine aspects of computational mechanics, fluid dynamics, computational physics, computational chemistry and biophysics into an integrated framework that couples a broad range of scales. The goal of this edited volume is to provide a comprehensive, rigorous, and current introduction into the fundamental concepts, mathematical formulation, alternative approaches, and predictions of computational hydrodynamics of capsules and biological cells. The book is meant to serve both as a research reference and as a teaching resource.The numerical methods discussed in the following eight chapters cover a broad range of possible formulations for simulating the motion of rigid particles (platelets) and the flow-induced deformation of liquid capsules and cells enclosed by viscoelastic membranes. Although some of the physical problems discussed in different chapters are similar or identical, the repetition is desirable in that solutions produced by different numerical approaches can be compared and the efficiency of alternative formulations can be assessed. The consistency of the results validates the procedures and offers several alternatives.

The first three chapters present boundary-integral formulations. In Chapter 1, the editor of this volume discusses a boundary-element method for computing the flow-induced deformation of idealized two-dimensional red blood cells in Stokes flow and provides a pertinent matlab code. In Chapter 2, Barthes-Biesel, Walter & Salsac discuss highly accurate boundary-element methods for simulating capsules with spherical unstressed shapes based on direct and variational formulations. Their work delineates the occurrence of membrane wrinkling due to local compression. In Chapter 3, Freund & Zhao present an advanced boundary-integral formulation based on Fourier expansions and discuss the results of simulations for cellular flow in domains with complex geometry. A snapshot of their simulations with thirty periodically repeated cells is featured on the cover of this volume. In the past, such depictions have been possible only by artist rendition or schematic illustration.

Chapters 4 and 5 present immersed-boundary methods. In Chapter 4, Zhang, Johnson & Popel discuss an immersed-boundary -- lattice-Boltzmann formulation that takes into consideration cell aggregation. Results are presented for a broad range of conditions illustrating, among other effects, the significance of rouleaux formation. In Chapter 5, Bagchi discusses immersed-boundary -- front-tracking methods for computing the deformation of capsules and cells in dilute and dense suspensions. Combining the basic algorithm with a coarse-grain Monte-Carlo method for intermolecular forces allows the simulation of leukocyte rolling on an adhesive substrate under the influence of a shear flow.

In Chapter 6, Fedosov, Caswell & Kardiadakis present a discrete membrane model where a surface network of viscoelastic links emulates the spectrin network of the cytoskeleton. The motion of the internal and external fluids is computed by the method of dissipative particle dynamics. One strength of this approach is that the network potential can be adjusted to exhibit desired macroscopic properties without ad-hoc adjustment. The surface discretization scheme can be used as a module in other problems involving membrane--flow interaction.

In Chapter 7, Secomb discusses a two-dimensional model of red and white blood cell motion. A novel feature of his approach is that a cell is modeled as a network of membrane and interior viscoelastic elements mediating elastic response and viscous dissipation. Coupled with a finite-element formulation for the ambient plasma flow, the formulation yields a powerful technique for simulating cell motion in dilute and concentrated suspensions.

In Chapter 8, Mody & King discuss the numerical simulation of platelet motion near a wall representing injured tissue. The computational model is based on the boundary-integral formulation for Stokes flow containing rigid particles with arbitrary shapes. Brownian motion and adhesive forces between platelets and substrate are implemented in terms of surface bonds. The simulations furnish a wealth of information on microstructural platelet dynamics near an injured vascular wall.

The subject of computational cellular mechanics and biofluiddynamics has emerged as an eminent topic, bridging biological, mathematical, computational, and engineering sciences. The authors of this volume conclude their chapters by pointing out venues for further work in the mathematical formulation and numerical implementation, and by identifying physiological problems to be addressed in future work. Their comments serve as a roadmap for students and researchers who wish to contribute to these efforts.