Computational Hydrodynamics of Capsules and

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.

Preface	p. xi
About the Editor	p. xv
Flow-induced deformation of two-dimensional biconcave capsules	p. 1
Introduction	p. 1
Mathematical framework	p. 4
Membrane mechanics	p. 5
Boundary-integral formulation	p. 7
Numerical method	p. 9
Solution of the integral equation	p. 10
MATLAB“ code rbc_2d	p. 12
Cell shapes and dimensionless numbers	p. 13
Capsule deformation in infinite shear flow	p. 15
Capsule motion near a wall	p. 25
Discussion	p. 30
Flow-induced deformation of artificial capsules	p. 35
Introduction	p. 35
Membrane mechanics	p. 38
Membrane deformation	p. 38
Membrane constitutive laws and equilibrium	p. 40
Osmotic effects and prestress	p. 42
Capsule dynamics in flow	p. 43
Instability due to compression	p. 45
Numerical procedure	p. 46
B-spline projection	p. 46
Computation of boundary integrals	p. 50
Two-grid method	p. 51
Coupling finite elements and boundary elements	p. 52
Isoparametric interpolation	p. 52
Mesh generation	p. 53
Membrane finite-element formulation	p. 54
Computation of boundary integrals	p. 57
Capsule deformation in linear shear flow	p. 57
Simple shear flow	p. 57
Flane hyperbolic flow	p. 63
Discussion	p. 65
A high-resolution fast boundary-integral method for multiple interacting blood cells	p. 71
Introduction	p. 72
Fast summation methods	p. 75
Boundary conditions	p. 76
Membrane constitutive equations	p. 76
Preamble	p. 77
Mathematical framework	p. 77
Integral formulation	p. 78
Time advancement	p. 82
Flow specification	p. 82
Fast summation in boundary-integral computations	p. 83
Short-range component evaluation	p. 84
Smooth component evaluation	p. 84
Particle-particle/particle-mesh method (PPPM)	p. 85
Membrane mechanics	p. 87
Spectral basis functions	p. 87
Constitutive equations	p. 88
Equilibrium equations	p. 89
Numerical fidelity	p. 90
Truncation errors, convergence and resolution	p. 90
Aliasing errors, nonlinear instability and dealiasing	p. 92
Simulations	p. 96
Resolution and dealiasing	p. 97
Effective viscosity	p. 100
Leukocyte transport	p. 101
Complex geometries	p. 102
Summary and outlook	p. 104
Pros	p. 104
Cons	p. 105
Simulating microscopic hemodynamics and hemorheology with the immersed-boundary lattice-Boltzmann method	p. 113
Introduction	p. 114
The lattice-Boltzmann method	p. 116
General algorithm	p. 116
Boundary conditions	p. 119
The immersed-boundary method	p. 121
Fluid property updating	p. 123
Models of RBC mechanics and aggregation	p. 124
RBC geometry and fluid viscosity	p. 124
Single cells and groups of cells	p. 126
Deformation of a single cell in shear flow	p. 127
Channel flow	p. 129
Rouleaux formation	p. 130
Rouleaux dissociation in shear flow	p. 130
Cell suspension flow in microvessels	p. 134
Cell-free layers	p. 136
RBC distribution and velocity profile	p. 137
Effect of cell deformability and aggregation	p. 139
Effect of the channel width	p. 141
Summary and discussion	p. 142
Front-tracking methods for capsules, vesicles and blood cells	p. 149
Introduction	p. 149
Numerical method	p. 153
Navier-Stokes solver	p. 154
Computation of the interfacial force	p. 156
Membrane discretization	p. 157
Capsule deformation in simple shear flow	p. 157
Spherical capsules	p. 158
Ellipsoidal capsules	p. 159
Vesicles	p. 162
Red blood cells	p. 164
Capsule interception	p. 164
Capsule motion near a wall	p. 167
Suspension flow in a channel	p. 168
Rolling on an adhesive substrate	p. 170
Summary	p. 173
Dissipative particle dynamics modeling of red blood cells	p. 183
Introduction	p. 184
Mathematical framework	p. 185
Dissipative particle dynamics	p. 185
Mesoscopic viscoelastic membrane model	p. 187
Triangulation	p. 189
Membrane mechanical properties	p. 190
Shear modulus	p. 191
Compression modulus	p. 192
Bending rigidity	p. 193
Membrane viscosity	p. 194
Membrane-solvent interfacial conditions	p. 196
Numerical and physical scaling	p. 197
Membrane mechanics	p. 198
Equilibrium shape and the stress-free model	p. 199
Membrane rheology from twisting torque cytometry	p. 202
Cell deformation in shear flow	p. 204
Tube flow	p. 209
Summary	p. 212
Simulation of red blood cell motion in microvessels and bifurcations	p. 219
Introduction	p. 219
Axisymmetric models for single-file RBC motion	p. 222
Two-dimensional models for RBC motion	p. 225
Element cell model	p. 226
Governing equations and numerical method	p. 228
Tank-treading in simple shear flow	p. 229
Channel flow	p. 231
Motion through diverging bifurcations	p. 232
Motion of multiple cells	p. 235
Discussion	p. 239
Multiscale modelling of transport and receptor-mediated adhesion of platelets in the bloodstream	p. 245
Introduction	p. 246
Role of shear flow in platelet transport and function	p. 247
Models of transport, deposition, and aggregation	p. 249
Motion of oblate spheroids in semi-infinite shear flow	p. 250
Preamble	p. 252
Mathematical framework	p. 253
The CDL-BIEM method	p. 254
Repulsive contact force	p. 256
Numerical implementation	p. 257
Validation of half-space CDL-BIEM for oblate spheroid motion	p. 258
Motion of an oblate spheroid near a wall in shear flow	p. 258
Regime I: Modified Jeffery orbits	p. 259
Regime II: Pole vaulting and periodic tumbling	p. 259
Regime III: Wobble flow	p. 261
Chaotic motion	p. 264
Oblate spheroids with aspect ratio 0.3-0.5	p. 265
Brownian motion	p. 266
Brownian motion near a wall in a quiescent fluid	p. 267
Convective and diffusive transport	p. 269
Influence on surface adhesive dynamics	p. 272
Shape and wall effects on hydrodynamic collision	p. 274
Collision mechanisms	p. 275
Collision frequency	p. 275
Transient aggregation of two platelets near a wall	p. 283
Adhesive dynamics model	p. 285
Binding efficiency for GPIb_¿-vWF kinetics	p. 289
Effect of interplatelet binding on collision	p. 290
Force mechanics of bond rupture	p. 292
Conclusions and future directions	p. 294
Index	p. 309
Table of Contents provided by Ingram. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Computational Hydrodynamics of Capsules and Biological Cells

Summary

Table of Contents

Supplemental Materials