Computational Hydrodynamics of Capsules and Biological Cells  book cover
1st Edition

Computational Hydrodynamics of Capsules and Biological Cells

ISBN 9781138374263
Published October 18, 2019 by CRC Press
327 Pages 114 B/W Illustrations

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Book Description

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

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


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


"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