Table Of ContentModeling of Mass
Transport Processes in
Biological Media
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Modeling of Mass
Transport Processes in
Biological Media
Edited by
Sid Becker
Department ofMechanical Engineering, University of Canterbury, Christchurch,New Zealand
Andrey V. Kuznetsov
Department ofMechanical& AerospaceEngineering, North Carolina State University,
Raleigh,NC, United States
Filippo de Monte
Department ofIndustrial and Information Engineering and Economics, University ofL’Aquila,
L’Aquila, Italy
Giuseppe Pontrelli
Institute ofAppliedMathematics- CNR, Rome, Italy
Dan Zhao
Department ofMechanical Engineering, University of Canterbury, Christchurch,New Zealand
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Contents
Contributors.........................................................................................................................................xv
Preface................................................................................................................................................xxi
CHAPTER 1 Applications of porous media in biological
transport modeling......................................................................1
KhalilKhanafer andKambiz Vafai
1.1 Introduction................................................................................................................1
1.2 Applications ofporous media inmodeling inmodeling transport
phenomena in arteries................................................................................................1
1.3 Fluid–structure interaction inbiomedical applications..............................................5
1.4 Brain aneurysms.........................................................................................................6
1.5 Magnetic resonance imaging (MRI)........................................................................10
1.6 Concluding remarks.................................................................................................11
References................................................................................................................12
CHAPTER 2 Metabolic consumption of microorganisms.................................17
Peter Vadasz and Alisa S. Vadasz
2.1 Introduction..............................................................................................................17
2.2 Model formulation andmetabolic mass transfer.....................................................20
2.3 Analysis of the equation governing monotonic growth..........................................21
2.3.1 Dimensionlessform ofthe governing equation............................................21
2.3.2 Conditionfor alogarithmic inflectionpoint (LIP)........................................22
2.3.3 Representation of the solutions on phase diagrams and LAG......................23
2.4 Closed form analyticalsolution of the monotonic growth......................................24
2.5 Results and discussion..............................................................................................26
2.6 Conclusions..............................................................................................................27
References................................................................................................................30
Further reading.........................................................................................................32
CHAPTER 3 Numerical simulation of deformability cytometry: Transport of
a biological cell through a microfluidic channel.........................33
LucasDanielWittwer,FelixReichel,and Sebastian Aland
3.1 Introduction..............................................................................................................33
3.2 Modelingbiological cells inan RT-DC channel.....................................................35
3.2.1 Themeasurementbuffer asa non-Newtonian fluid......................................35
3.2.2 Thecellasa viscoelastic solid material........................................................36
3.2.3 Boundaryconditions andfluid-solidcoupling..............................................37
3.2.4 Finite-element implementation......................................................................37
v
vi Contents
3.3 Hydrodynamicstresseson the cell surface..............................................................39
3.3.1 Fluidflowinthe microfluidic chip...............................................................39
3.3.2 Deformedcells inthe region ofinterest........................................................40
3.4 Cell shapesand cell deformation.............................................................................42
3.4.1 Deformation of highly viscous cells at the outflow......................................46
3.4.2 Inertiaratio andFourier transcriptors............................................................46
3.5 Extraction of the cell viscosity................................................................................47
3.6 Approximationerrorofthe cell volume over the channel......................................50
3.7 Conclusions..............................................................................................................52
Appendix Derivation of the deformation measure from cell contours...................53
Fourier shape descriptors....................................................................................54
Acknowledgments....................................................................................................54
References................................................................................................................54
CHAPTER 4 Computation of organelle age during axonal transport.................57
Ivan A. Kuznetsov and Andrey V. Kuznetsov
4.1 Introduction..............................................................................................................57
4.2 Governing equations.................................................................................................59
4.3 Simulation ofthe DCV concentration inthe axon..................................................62
4.4 Age distributionmodelof DCVs andmeanage ofDCVsin boutons....................63
4.5 Parameter value estimation......................................................................................66
4.5.1 Two groups of parameters.............................................................................66
4.5.2 Estimation ofsaturated concentrations ofDCVs inthe resident
state inboutons..............................................................................................67
4.5.3 Estimation ofthe masstransfer coefficients and the saturated
concentrations ofDCVsin boutons...............................................................68
4.6 Numerical approach.................................................................................................69
4.7 Results......................................................................................................................69
4.7.1 Assumption about the fate ofDCVs captured into the resident
state inboutons..............................................................................................69
4.7.2 Verification ofthe valuestowhichconcentrations converge
as t!∞..........................................................................................................69
4.7.3 Investigating sensitivity ofthe mean age ofDCVsinboutons
to various parameters.....................................................................................73
4.7.4 Verifying the accuracy ofcomputations........................................................76
4.7.5 Effect ofparameter ε onanterograde andretrograde fluxes between
the boutons.....................................................................................................76
4.8 Discussion, modelconstraints,and future directions..............................................77
Acknowledgments....................................................................................................83
References................................................................................................................83
Contents vii
CHAPTER 5 Continuum models of drug transport to multiple cell-type
population................................................................................87
Filippode Monte, Giampaolo D’Alessandro, SidBecker,
and Giuseppe Pontrelli
5.1 Introduction..............................................................................................................88
5.1.1 Transmembrane transport..............................................................................90
5.1.2 Reaction terms andbinding models..............................................................91
5.1.3 Extensionto multiple cell-type populations..................................................93
5.2 Formulation of the problem.....................................................................................95
5.2.1 Concentrations andvolume-averaged variables............................................96
5.2.2 Governing equations......................................................................................98
5.3 Method ofsolution.................................................................................................100
5.3.1 Uncouplingprocedure..................................................................................100
5.3.2 Transformed mass balance equationfor the extracellular space................105
5.3.3 Physical interpretation: The dual-phase-lag model.....................................105
5.3.4 Concentration distribution ofthe k-thtype of cell......................................107
5.4 Casestudy:A3D rectangular biological tissue.....................................................107
5.4.1 One-dimensional governing equations........................................................108
5.4.2 Exact analyticalsolution..............................................................................110
5.4.3 Concentration solution indimensionless form............................................115
5.4.4 Convergence ofthe series-solution..............................................................117
5.4.5 Computationofthe eigenvalues..................................................................120
5.5 Results and discussion............................................................................................121
5.6 Conclusions............................................................................................................124
5.A Appendix A............................................................................................................124
5.B Appendix B.............................................................................................................127
5.C Appendix C.............................................................................................................128
5.D AppendixD............................................................................................................129
5.D.1 Convergence criteria...................................................................................130
5.E AppendixE.............................................................................................................132
5.E.1 Convergence criteria....................................................................................133
References..............................................................................................................135
CHAPTER 6 Computational investigation of the role of low-density
lipoprotein and oxygen transport in atherosclerotic arteries......139
Anna Corti, Monika Colombo, Giuseppe De Nisco, Jose Felix
Rodriguez Matas,FrancescoMigliavacca,and Claudio Chiastra
6.1 Introduction: Atherosclerosis and the role ofmasstransport................................139
6.2 Mass transfer oflow-densitylipoproteins andoxygeninarteries:
Theoretical background..........................................................................................141
viii Contents
6.2.1 Transport mechanisms.................................................................................141
6.2.2 Role ofhemodynamics................................................................................143
6.2.3 Mathematicalformulationand modeling strategies....................................147
6.3 Mass transferof low-densitylipoproteins inarteries:
Computational modeling........................................................................................151
6.3.1 Introduction..................................................................................................151
6.3.2 Wall-free models..........................................................................................151
6.3.3 Fluid-wall models........................................................................................159
6.3.4 Multilayer models........................................................................................172
6.4 Mass transferof oxygen inarteries:Computational modeling.............................181
6.4.1 Introduction..................................................................................................181
6.4.2 Wall-free models..........................................................................................181
6.4.3 Fluid-wall models........................................................................................194
6.5 Limitations of the current models andfuture directions.......................................199
6.6 Conclusions............................................................................................................202
Acknowledgment...................................................................................................203
References..............................................................................................................203
CHAPTER 7 Fluid dynamics and mass transport in lower limb vessels:
Effects on restenosis...............................................................215
MonikaColombo, Anna Corti,Sean McGinty,Francesco Migliavacca,
and Claudio Chiastra
7.1 Introduction............................................................................................................215
7.2 Lowerlimb vessels: Anatomy, physiopathology,treatment options,
and their failure......................................................................................................216
7.2.1 Anatomy andpathophysiology oflower limb vessels................................216
7.2.2 Treatments oflower limb vessels andtheir failure.....................................218
7.3 Modelingthe hemodynamics oftreatedlower limb vessels.................................221
7.3.1 Introduction..................................................................................................221
7.3.2 Computational models oflower limb hemodynamics.................................222
7.3.3 In-stentrestenosis.........................................................................................230
7.3.4 Restenosis invein grafts..............................................................................234
7.3.5 Limitations of the current CFD models.......................................................236
7.4 State-of-the-artcomputational masstransportmodels oflower limb vessels......237
7.4.1 Introduction..................................................................................................237
7.4.2 Modelingmass transportinlower limb vessels..........................................239
7.4.3 Modelingthe transportofdrugs delivered from drug-coated
balloons........................................................................................................242
7.4.4 Limitations of the current models ofmass transportinlower
limb vessels..................................................................................................245
7.4.5 Futureremarks ondrug transportindiseased lower limb vessels..............247
Contents ix
7.5 Conclusionsand future directions..........................................................................251
Acknowledgment...................................................................................................252
References..............................................................................................................252
CHAPTER 8 Numerical modeling in support of locoregional drug delivery
during transarterial therapies for liver cancer...........................259
Charlotte Debbaut and Tim Bomberna
8.1 Introduction............................................................................................................259
8.1.1 Clinical context............................................................................................260
8.1.2 Transarterialtherapies..................................................................................260
8.1.3 Chemoembolization versus radioembolization............................................260
8.1.4 Clinical microspheres...................................................................................262
8.1.5 Clinical catheter types..................................................................................262
8.1.6 Theroleof numerical modeling..................................................................263
8.2 Stateof the art ofcomputational techniques.........................................................264
8.2.1 Hepatic arterial geometry.............................................................................264
8.2.2 Dimensionality.............................................................................................266
8.2.3 Multiphasephysics.......................................................................................267
8.2.4 Flow pulsatility............................................................................................270
8.2.5 Fluid–structure interaction...........................................................................270
8.2.6 Boundaryconditions....................................................................................271
8.3 Clinical parameters.................................................................................................274
8.3.1 Cross-sectional injection location................................................................274
8.3.2 Axial injectionlocation................................................................................275
8.3.3 Microsphere types andcharacteristics.........................................................277
8.3.4 Catheter type, distal direction, and tiporientation......................................278
8.3.5 Catheter injection flow rate.........................................................................279
8.4 Stateof the art ofexperimental techniques...........................................................281
8.4.1 Invitro techniques........................................................................................281
8.4.2 Invivo techniques........................................................................................283
8.5 Closing remarks......................................................................................................283
Acknowledgment...................................................................................................284
Funding...................................................................................................................284
References..............................................................................................................284
CHAPTER 9 Active gel: A continuum physics perspective............................287
LucianoTeresi, Michele Curatolo, and Paola Nardinocchi
9.1 Introduction............................................................................................................287
9.2 A short insight into active gel physics...................................................................287
