Computational Hydrodynamics of Capsules and Biological Cells: 1st Edition (Paperback) book cover

Computational Hydrodynamics of Capsules and Biological Cells

1st Edition

Edited by Constantine Pozrikidis

CRC Press

327 pages | 114 B/W Illus.

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Spanning biological, mathematical, computational, and engineering sciences, computational biofluiddynamics addresses a diverse family of problems involving fluid flow inside and around living organisms, organs, tissue, biological cells, and other biological materials. Computational Hydrodynamics of Capsules and Biological Cells provides a comprehensive, rigorous, and current introduction to the fundamental concepts, mathematical formulation, alternative approaches, and predictions of this evolving field.

In the first several chapters on boundary-element, boundary-integral, and immersed-boundary methods, the book covers the flow-induced deformation of idealized two-dimensional red blood cells in Stokes flow, capsules with spherical unstressed shapes based on direct and variational formulations, and cellular flow in domains with complex geometry. It also presents simulations of microscopic hemodynamics and hemorheology as well as results on the deformation of capsules and cells in dilute and dense suspensions. The book then describes a discrete membrane model where a surface network of viscoelastic links emulates the spectrin network of the cytoskeleton, before presenting a novel two-dimensional model of red and white blood cell motion. The final chapter discusses the numerical simulation of platelet motion near a wall representing injured tissue.

This volume provides a roadmap to the current state of the art in computational cellular mechanics and biofluiddynamics. It also indicates areas for further work on mathematical formulation and numerical implementation and identifies physiological problems that need to be addressed in future research. MATLAB® code and other data are available at


"The two books edited by Constantine Pozrikidis [see also Modeling and Simulation of Capsules and Biological Cells] deal primarily with mathematical evaluations and in silico investigations (modeling and simulations) of particles in motion. … they complement each other in that information provided in one book is either absent, described in more detail, or expanded upon in the other. … Both books contain a collection of chapters contributed by investigators from around the world who provide their expert experiences in fields such as biology and physiology, mathematics, mechanical and chemical engineering, as well as computer and information science. … well written and structured, and the sequence of topics presented in the chapters is appropriate. … Both books are fascinating … a welcome addition to the growing number of publications in the fast-advancing field of biological dynamics."

—Christian T.K.-H. Stadtländer, Journal of Biological Dynamics, Vol. 7, 2013

"This book gives a quite extensive overview of different possible formulations for the motion of rigid or deforming particles and for the solution of flow-induced deformations. A wide range of numerical and methodological approaches are illustrated … The presence of many numerical examples allows one to appreciate the capabilities of the approaches proposed and provides useful reference material. … this book is a highly valuable reference for any graduate student or researcher interested in cellular mechanics, bio-fluid dynamics, bio-rheology or, in general, applications involving the transport of micro-capsules or cells by a fluid. It is accompanied by an Internet site where some additional material, including MATLAB code, may be found."

—Luca Formaggia, Mathematical Reviews, Issue 2012a

Table of Contents

Flow-Induced Deformation of Two-Dimensional Biconcave Capsules, C. Pozrikidis


Mathematical framework

Numerical method

Cell shapes and dimensionless numbers

Capsule deformation in infinite shear flow

Capsule motion near a wall


Flow-Induced Deformation of Artificial Capsules, D. Barthès-Biesel, J. Walter, and A.-V. Salsac


Membrane mechanics

Capsule dynamics in flow

B-spline projection

Coupling finite elements and boundary integrals

Capsule deformation in linear shear flow


A High-Resolution Fast Boundary-Integral Method for Multiple Interacting Blood Cells, Jonathan B. Freund and Hong Zhao


Mathematical framework

Fast summation in boundary-integral computations

Membrane mechanics

Numerical fidelity


Summary and outlook

Simulating Microscopic Hemodynamics and Hemorheology with the Immersed-Boundary Lattice-Boltzmann Method, J. Zhang, P. C. Johnson, and A.S. Popel


The lattice-Boltzmann method

The immersed-boundary method

Fluid property updating

Models of RBC mechanics and aggregation

Single cells and groups of cells

Cell suspension flow in microvessels

Summary and discussion

Front-Tracking Methods for Capsules, Vesicles, and Blood Cells, Prosenjit Bagchi


Numerical method

Capsule deformation in simple shear flow

Capsule interception

Capsule motion near a wall

Suspension flow in a channel

Rolling on an adhesive substrate


Dissipative Particle Dynamics Modeling of Red Blood Cells, D.A. Fedosov, B. Caswell, and G.E. Karniadakis


Mathematical framework

Membrane mechanical properties

Membrane-solvent interfacial conditions

Numerical and physical scaling

Membrane mechanics

Membrane rheology from twisting torque cytometry

Cell deformation in shear flow

Tube flow


Simulation of Red Blood Cell Motion in Microvessels and Bifurcations, T.W. Secomb


Axisymmetric models for single-file RBC motion

Two-dimensional models for RBC motion

Tank-treading in simple shear flow

Channel flow

Motion through diverging bifurcations

Motion of multiple cells


Multiscale Modeling of Transport and Receptor-Mediated Adhesion of Platelets in the Bloodstream, N.A. Mody and M.R. King


Mathematical framework

Motion of an oblate spheroid near a wall in shear flow

Brownian motion

Shape and wall effects on hydrodynamic collision

Transient aggregation of two platelets near a wall

Conclusions and future directions


About the Editor

C. Pozrikidis is a professor in the Department of Chemical Engineering at the University of Massachusetts, Amherst.

About the Series

Chapman & Hall/CRC Mathematical and Computational Biology

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MEDICAL / Biotechnology
SCIENCE / Physics