Contributors |
|
xv | |
Preface |
|
xxi | |
|
Chapter 1 Applications of porous media in biological transport modeling |
|
|
1 | (16) |
|
|
|
|
1 | (1) |
|
1.2 Applications of porous media in modeling in modeling transport phenomena in arteries |
|
|
1 | (4) |
|
1.3 Fluid-structure interaction in biomedical applications |
|
|
5 | (1) |
|
|
6 | (4) |
|
1.5 Magnetic resonance imaging (MRI) |
|
|
10 | (1) |
|
|
11 | (1) |
|
|
12 | (5) |
|
Chapter 2 Metabolic consumption of microorganisms |
|
|
17 | (16) |
|
|
|
|
17 | (3) |
|
2.2 Model formulation and metabolic mass transfer |
|
|
20 | (1) |
|
2.3 Analysis of the equation governing monotonic growth |
|
|
21 | (3) |
|
2.3.1 Dimensionless form of the governing equation |
|
|
21 | (1) |
|
2.3.2 Condition for a logarithmic inflection point (LIP) |
|
|
22 | (1) |
|
2.3.3 Representation of the solutions on phase diagrams and LAG |
|
|
23 | (1) |
|
2.4 Closed form analytical solution of the monotonic growth |
|
|
24 | (2) |
|
2.5 Results and discussion |
|
|
26 | (1) |
|
|
27 | (3) |
|
|
30 | (2) |
|
|
32 | (1) |
|
Chapter 3 Numerical simulation of deformability cytometry: Transport of a biological cell through a microfluidic channel |
|
|
33 | (24) |
|
|
|
|
|
33 | (2) |
|
3.2 Modeling biological cells in an RT-DC channel |
|
|
35 | (4) |
|
3.2.1 The measurement buffer as a non-Newtonian fluid |
|
|
35 | (1) |
|
3.2.2 The cell as a viscoelastic solid material |
|
|
36 | (1) |
|
3.2.3 Boundary conditions and fluid-solid coupling |
|
|
37 | (1) |
|
3.2.4 Finite-element implementation |
|
|
37 | (2) |
|
3.3 Hydrodynamic stresses on the cell surface |
|
|
39 | (3) |
|
3.3.1 Fluid flow in the microfluidic chip |
|
|
39 | (1) |
|
3.3.2 Deformed cells in the region of interest |
|
|
40 | (2) |
|
3.4 Cell shapes and cell deformation |
|
|
42 | (5) |
|
3.4.1 Deformation of highly viscous cells at the outflow |
|
|
46 | (1) |
|
3.4.2 Inertia ratio and Fourier transcriptors |
|
|
46 | (1) |
|
3.5 Extraction of the cell viscosity |
|
|
47 | (3) |
|
3.6 Approximation error of the cell volume over the channel |
|
|
50 | (2) |
|
|
52 | (1) |
|
Appendix Derivation of the deformation measure from cell contours |
|
|
53 | (1) |
|
Fourier shape descriptors |
|
|
54 | (1) |
|
|
54 | (1) |
|
|
54 | (3) |
|
Chapter 4 Computation of organelle age during axonal transport |
|
|
57 | (30) |
|
|
|
|
57 | (2) |
|
|
59 | (3) |
|
4.3 Simulation of the DCV concentration in the axon |
|
|
62 | (1) |
|
4.4 Age distribution model of DCVs and mean age of DCVs in boutons |
|
|
63 | (3) |
|
4.5 Parameter value estimation |
|
|
66 | (3) |
|
4.5.1 Two groups of parameters |
|
|
66 | (1) |
|
4.5.2 Estimation of saturated concentrations of DCVs in the resident state in boutons |
|
|
67 | (1) |
|
4.5.3 Estimation of the mass transfer coefficients and the saturated concentrations of DCVs in boutons |
|
|
68 | (1) |
|
|
69 | (1) |
|
|
69 | (8) |
|
4.7.1 Assumption about the fate of DCVs captured into the resident state in boutons |
|
|
69 | (1) |
|
4.7.2 Verification of the values to which concentrations converge as t → ∞ |
|
|
69 | (4) |
|
4.7.3 Investigating sensitivity of the mean age of DCVs in boutons to various parameters |
|
|
73 | (3) |
|
4.7.4 Verifying the accuracy of computations |
|
|
76 | (1) |
|
4.7.5 Effect of parameter e on anterograde and retrograde fluxes between the boutons |
|
|
76 | (1) |
|
4.8 Discussion, model constraints, and future directions |
|
|
77 | (6) |
|
|
83 | (1) |
|
|
83 | (4) |
|
Chapter 5 Continuum models of drug transport to multiple cell-type population |
|
|
87 | (52) |
|
|
|
|
|
|
88 | (7) |
|
5.1.1 Transmembrane transport |
|
|
90 | (1) |
|
5.1.2 Reaction terms and binding models |
|
|
91 | (2) |
|
5.1.3 Extension to multiple cell-type populations |
|
|
93 | (2) |
|
5.2 Formulation of the problem |
|
|
95 | (5) |
|
5.2.1 Concentrations and volume-averaged variables |
|
|
96 | (2) |
|
5.2.2 Governing equations |
|
|
98 | (2) |
|
|
100 | (7) |
|
5.3.1 Uncoupling procedure |
|
|
100 | (5) |
|
5.3.2 Transformed mass balance equation for the extracellular space |
|
|
105 | (1) |
|
5.3.3 Physical interpretation: The dual-phase-lag model |
|
|
105 | (2) |
|
5.3.4 Concentration distribution of the k-th type of cell |
|
|
107 | (1) |
|
5.4 Case study: A 3D rectangular biological tissue |
|
|
107 | (14) |
|
5.4.1 One-dimensional governing equations |
|
|
108 | (2) |
|
5.4.2 Exact analytical solution |
|
|
110 | (5) |
|
5.4.3 Concentration solution in dimensionless form |
|
|
115 | (2) |
|
5.4.4 Convergence of the series-solution |
|
|
117 | (3) |
|
5.4.5 Computation of the eigenvalues |
|
|
120 | (1) |
|
5.5 Results and discussion |
|
|
121 | (3) |
|
|
124 | (1) |
|
|
124 | (3) |
|
|
127 | (1) |
|
|
128 | (1) |
|
|
129 | (3) |
|
5.D.1 Convergence criteria |
|
|
130 | (2) |
|
|
132 | (7) |
|
5.E.1 Convergence criteria |
|
|
133 | (2) |
|
|
135 | (4) |
|
Chapter 6 Computational investigation of the role of low-density lipoprotein and oxygen transport in atherosclerotic arteries |
|
|
139 | (76) |
|
|
|
|
Jose Felix Rodriguez Matas |
|
|
|
|
6.1 Introduction: Atherosclerosis and the role of mass transport |
|
|
139 | (2) |
|
6.2 Mass transfer of low-density lipoproteins and oxygen in arteries: Theoretical background |
|
|
141 | (10) |
|
6.2.1 Transport mechanisms |
|
|
141 | (2) |
|
6.2.2 Role of hemodynamics |
|
|
143 | (4) |
|
6.2.3 Mathematical formulation and modeling strategies |
|
|
147 | (4) |
|
6.3 Mass transfer of low-density lipoproteins in arteries: Computational modeling |
|
|
151 | (30) |
|
|
151 | (1) |
|
|
151 | (8) |
|
|
159 | (13) |
|
|
172 | (9) |
|
6.4 Mass transfer of oxygen in arteries: Computational modeling |
|
|
181 | (18) |
|
|
181 | (1) |
|
|
181 | (13) |
|
|
194 | (5) |
|
6.5 Limitations of the current models and future directions |
|
|
199 | (3) |
|
|
202 | (1) |
|
|
203 | (1) |
|
|
203 | (12) |
|
Chapter 7 Fluid dynamics and mass transport in lower limb vessels: Effects on restenosis |
|
|
215 | (44) |
|
|
|
|
|
|
|
215 | (1) |
|
7.2 Lower limb vessels: Anatomy, physiopathology, treatment options, and their failure |
|
|
216 | (5) |
|
7.2.1 Anatomy and pathophysiology of lower limb vessels |
|
|
216 | (2) |
|
7.2.2 Treatments of lower limb vessels and their failure |
|
|
218 | (3) |
|
7.3 Modeling the hemodynamics of treated lower limb vessels |
|
|
221 | (16) |
|
|
221 | (1) |
|
7.3.2 Computational models of lower limb hemodynamics |
|
|
222 | (8) |
|
7.3.3 In-stent restenosis |
|
|
230 | (4) |
|
7.3.4 Restenosis in vein grafts |
|
|
234 | (2) |
|
7.3.5 Limitations of the current CFD models |
|
|
236 | (1) |
|
7.4 State-of-the-art computational mass transport models of lower limb vessels |
|
|
237 | (14) |
|
|
237 | (2) |
|
7.4.2 Modeling mass transport in lower limb vessels |
|
|
239 | (3) |
|
7.4.3 Modeling the transport of drugs delivered from drug-coated balloons |
|
|
242 | (3) |
|
7.4.4 Limitations of the current models of mass transport in lower limb vessels |
|
|
245 | (2) |
|
7.4.5 Future remarks on drug transport in diseased lower limb vessels |
|
|
247 | (4) |
|
7.5 Conclusions and future directions |
|
|
251 | (1) |
|
|
252 | (1) |
|
|
252 | (7) |
|
Chapter 8 Numerical modeling in support of locoregional drug delivery during transarterial therapies for liver cancer |
|
|
259 | (28) |
|
|
|
|
259 | (5) |
|
|
260 | (1) |
|
8.1.2 Transarterial therapies |
|
|
260 | (1) |
|
8.1.3 Chemoembolization versus radioembolization |
|
|
260 | (2) |
|
8.1.4 Clinical microspheres |
|
|
262 | (1) |
|
8.1.5 Clinical catheter types |
|
|
262 | (1) |
|
8.1.6 The role of numerical modeling |
|
|
263 | (1) |
|
8.2 State of the art of computational techniques |
|
|
264 | (10) |
|
8.2.1 Hepatic arterial geometry |
|
|
264 | (2) |
|
|
266 | (1) |
|
|
267 | (3) |
|
|
270 | (1) |
|
8.2.5 Fluid--structure interaction |
|
|
270 | (1) |
|
8.2.6 Boundary conditions |
|
|
271 | (3) |
|
|
274 | (7) |
|
8.3.1 Cross-sectional injection location |
|
|
274 | (1) |
|
8.3.2 Axial injection location |
|
|
275 | (2) |
|
8.3.3 Microsphere types and characteristics |
|
|
277 | (1) |
|
8.3.4 Catheter type, distal direction, and tip orientation |
|
|
278 | (1) |
|
8.3.5 Catheter injection flow rate |
|
|
279 | (2) |
|
8.4 State of the art of experimental techniques |
|
|
281 | (2) |
|
8.4.1 In vitro techniques |
|
|
281 | (2) |
|
|
283 | (1) |
|
|
283 | (1) |
|
|
284 | (1) |
|
|
284 | (1) |
|
|
284 | (3) |
|
Chapter 9 Active gel: A continuum physics perspective |
|
|
287 | (24) |
|
|
|
|
|
287 | (1) |
|
9.2 A short insight into active gel physics |
|
|
287 | (3) |
|
9.3 A continuum model of active gels |
|
|
290 | (9) |
|
9.3.1 Chemo-mechanical states |
|
|
290 | (2) |
|
|
292 | (1) |
|
9.3.3 Constitutive theory |
|
|
293 | (4) |
|
9.3.4 Remodeling and diffusion evolution laws |
|
|
297 | (1) |
|
9.3.5 Simple solutions and steady states |
|
|
298 | (1) |
|
|
299 | (6) |
|
9.4.1 Bulk contraction in homogeneous active gels |
|
|
300 | (2) |
|
9.4.2 Driving liquid migration by bulk contraction |
|
|
302 | (3) |
|
9.5 Conclusions and future challenges |
|
|
305 | (1) |
|
Appendix Cylindrical coordinates |
|
|
305 | (3) |
|
|
308 | (1) |
|
|
308 | (3) |
|
Chapter 10 Modeling nasal spray droplet deposition and translocation in nasal airway for olfactory delivery |
|
|
311 | (24) |
|
|
|
|
311 | (2) |
|
10.2 Materials and methods |
|
|
313 | (6) |
|
|
313 | (1) |
|
10.2.2 Nasal airway model |
|
|
314 | (2) |
|
10.2.3 Spray release model |
|
|
316 | (1) |
|
10.2.4 Airflow and droplet transport models |
|
|
317 | (1) |
|
10.2.5 Eulerian wall film model |
|
|
317 | (1) |
|
|
318 | (1) |
|
|
319 | (9) |
|
10.3.1 Airflow and wall shear |
|
|
319 | (1) |
|
10.3.2 Initial deposition of nasal droplets |
|
|
320 | (5) |
|
10.3.3 Wall film migration |
|
|
325 | (3) |
|
10.4 Discussions and conclusion |
|
|
328 | (2) |
|
|
330 | (1) |
|
|
330 | (5) |
|
Chapter 11 Drug delivery and in vivo absorption |
|
|
335 | (56) |
|
|
|
|
|
|
|
|
|
|
335 | (18) |
|
|
335 | (2) |
|
11.1.2 Modern age: Second millennium |
|
|
337 | (2) |
|
11.1.3 Modern age: Third millennium |
|
|
339 | (12) |
|
11.1.4 Mathematical modeling |
|
|
351 | (2) |
|
|
353 | (22) |
|
11.2.1 Drug delivery models |
|
|
353 | (16) |
|
11.2.2 PK and PBPK models |
|
|
369 | (4) |
|
|
373 | (2) |
|
|
375 | (7) |
|
|
382 | (1) |
|
|
382 | (9) |
|
Chapter 12 Modeling the physiological phenomena and the effects of therapy on the dynamics of tumor growth |
|
|
391 | (14) |
|
|
|
|
391 | (1) |
|
12.2 Formal reaction kinetics |
|
|
392 | (3) |
|
12.3 Creating tumor model with formal reaction kinetics |
|
|
395 | (7) |
|
|
402 | (1) |
|
|
402 | (3) |
|
Chapter 13 Mathematical models of water transport across ocular epithelial layers |
|
|
405 | (30) |
|
|
|
|
|
13.1 Introduction to fluid transport in the eye |
|
|
405 | (3) |
|
13.1.1 Brief description of the anatomy and physiology of the eye |
|
|
405 | (2) |
|
13.1.2 General characteristics of ocular epithelial layers |
|
|
407 | (1) |
|
13.2 Formulation of the problem of water and solute transport |
|
|
408 | (3) |
|
13.2.1 Governing equations |
|
|
408 | (1) |
|
13.2.2 Ion transport across the cell membrane |
|
|
409 | (2) |
|
13.3 Mechanisms involved in water transport across cell layers |
|
|
411 | (9) |
|
13.3.1 Mechanical pressure difference |
|
|
411 | (1) |
|
13.3.2 Oncotic and osmotic pressures |
|
|
412 | (1) |
|
|
412 | (3) |
|
|
415 | (4) |
|
13.3.5 Cotransporter as a possible means of water transport |
|
|
419 | (1) |
|
13.4 Aqueous humor production at the ciliary processes |
|
|
420 | (4) |
|
13.4.1 Importance of aqueous humor production for ocular homeostasis |
|
|
420 | (1) |
|
13.4.2 Mechanisms of aqueous humor formation |
|
|
421 | (1) |
|
13.4.3 Models of aqueous formation |
|
|
422 | (2) |
|
13.5 Transport across the corneal endothelium |
|
|
424 | (4) |
|
13.5.1 Structure of the cornea and corneal endothelium |
|
|
424 | (1) |
|
13.5.2 Importance of corneal endothelium to prevent corneal swelling |
|
|
425 | (1) |
|
13.5.3 Proposed mechanisms of fluid transport across the corneal endothelium |
|
|
425 | (1) |
|
13.5.4 A model of electroosmotic transport across the corneal endothelium |
|
|
426 | (2) |
|
13.6 Transport across the retinal pigment epithelium |
|
|
428 | (2) |
|
13.6.1 Structure of the retinal pigment epithelium and its function in regulating fluid flow across the retina |
|
|
428 | (1) |
|
13.6.2 A mathematical model of ion and fluid transport across the RPE |
|
|
428 | (2) |
|
|
430 | (1) |
|
|
431 | (4) |
|
Chapter 14 Multidimensional modeling of solid tumor proliferation following drug treatment: Toward computational prognosis as a tool to support oncology |
|
|
435 | (20) |
|
|
|
|
|
|
435 | (3) |
|
14.1.1 Cancer proliferation and current understanding |
|
|
435 | (1) |
|
14.1.2 Improved prognoses via cancer modeling |
|
|
436 | (1) |
|
14.1.3 The proposed framework for solid tumor prognosis |
|
|
436 | (2) |
|
14.2 The workflow of the simulation framework |
|
|
438 | (3) |
|
14.3 Mathematical formulation |
|
|
441 | (4) |
|
14.3.1 Tumor progression phases |
|
|
441 | (2) |
|
14.3.2 The administered therapy |
|
|
443 | (1) |
|
14.3.3 The biological conversion mechanism |
|
|
443 | (1) |
|
14.3.4 Governing equations |
|
|
443 | (1) |
|
14.3.5 Initial and boundary conditions, proliferation, and therapy onset |
|
|
444 | (1) |
|
14.3.6 Numerical treatment |
|
|
445 | (1) |
|
|
445 | (7) |
|
14.4.1 A new interpretation of DLBCL proliferation and therapy effect |
|
|
445 | (3) |
|
14.4.2 Same-IPI patients, with different tumor progressions |
|
|
448 | (1) |
|
14.4.3 Virtual therapy testing |
|
|
448 | (1) |
|
14.4.4 Virtual tumor malignancy testing |
|
|
448 | (1) |
|
|
448 | (4) |
|
|
452 | (1) |
|
|
452 | (3) |
|
Chapter 15 Modeling LDL accumulation within an arterial wall |
|
|
455 | (38) |
|
|
|
|
|
|
|
455 | (4) |
|
15.1.1 The relationship between low-density lipoprotein and cardiovascular diseases (CVDs) |
|
|
455 | (2) |
|
15.1.2 Anatomy of an artery |
|
|
457 | (1) |
|
15.1.3 Summary of the present chapter |
|
|
458 | (1) |
|
15.2 Wall-free and single-layer models |
|
|
459 | (3) |
|
|
459 | (1) |
|
15.2.2 Single-layer models |
|
|
460 | (2) |
|
|
462 | (11) |
|
|
462 | (2) |
|
15.3.2 Governing equations |
|
|
464 | (2) |
|
15.3.3 Transport properties |
|
|
466 | (7) |
|
15.4 Published results of multilayer models |
|
|
473 | (13) |
|
15.4.1 Straight idealized arteries |
|
|
473 | (6) |
|
15.4.2 Stenosed idealized arteries |
|
|
479 | (4) |
|
15.4.3 Bifurcations, patient-specific, and curved geometries |
|
|
483 | (3) |
|
15.5 Conclusions and future developments |
|
|
486 | (2) |
|
|
488 | (5) |
|
Chapter 16 Modeling transport of soluble proteins and metabolites in the brain |
|
|
493 | (16) |
|
|
|
|
|
|
493 | (3) |
|
|
496 | (2) |
|
16.2.1 Flow across the BBB |
|
|
496 | (2) |
|
16.3 Flow through the parenchyma |
|
|
498 | (6) |
|
16.3.1 Illustrative example |
|
|
498 | (2) |
|
|
500 | (4) |
|
|
504 | (1) |
|
|
504 | (1) |
|
|
505 | (4) |
|
Chapter 17 Hybrid-dimensional models for blood flow and mass transport: Sequential and embedded 3D-1D models |
|
|
509 | (28) |
|
|
|
|
509 | (5) |
|
17.1.1 Multiscale modeling of the cardiovascular system |
|
|
510 | (4) |
|
17.2 3D-1D geometric sequential multiscale models |
|
|
514 | (4) |
|
17.2.1 1D models for larger deformable vessels |
|
|
514 | (1) |
|
17.2.2 Conditions at the boundaries and at the junctions |
|
|
515 | (1) |
|
17.2.3 Compartmental (0D) models |
|
|
516 | (1) |
|
17.2.4 1D models for blood solutes |
|
|
517 | (1) |
|
17.2.5 Sequential coupling of 3D and 1D models |
|
|
517 | (1) |
|
17.3 3D-1D geometric embedded multiscale models |
|
|
518 | (15) |
|
17.3.1 1D models for rigid vessels |
|
|
520 | (4) |
|
17.3.2 More complex geometries, vascular networks |
|
|
524 | (2) |
|
17.3.3 The embedded coupling conditions |
|
|
526 | (3) |
|
17.3.4 A 3D-1D embedded model for mass transport |
|
|
529 | (2) |
|
17.3.5 Numerical simulations of oxygen transport |
|
|
531 | (2) |
|
|
533 | (1) |
|
|
534 | (3) |
|
Chapter 18 Chemical thermodynamic principles and computational modeling of NOX2-mediated ROS production on cell membrane |
|
|
537 | (44) |
|
|
|
|
|
|
|
537 | (3) |
|
18.2 Thermodynamic principles for biochemical systems modeling |
|
|
540 | (5) |
|
18.2.1 Thermodynamics of biochemical reactions |
|
|
540 | (2) |
|
18.2.2 Thermodynamics of oxidation-reduction reactions |
|
|
542 | (3) |
|
18.3 Mathematical modeling of NOX2 enzyme function |
|
|
545 | (13) |
|
18.3.1 Mechanistic computational modeling of NOX2 assembly and activation |
|
|
547 | (4) |
|
18.3.2 Thermodynamically constrained computational modeling of NOX2 complex-mediated electron transfer, superoxide production, and regulation by pH |
|
|
551 | (7) |
|
18.3.3 Calculation of apparent enzyme kinetic parameters |
|
|
558 | (1) |
|
18.4 Data analysis and estimation of unknown model parameters |
|
|
558 | (6) |
|
18.4.1 Key experimental data for model parameterization and validation |
|
|
558 | (2) |
|
18.4.2 Estimation of unknown model parameters by fitting model solutions to experimental data |
|
|
560 | (4) |
|
18.5 Biological insights into NOX2 enzyme function |
|
|
564 | (6) |
|
18.5.1 Kinetic mechanisms of NOX2 assembly, activation, and regulation by guanine nucleotides and mutual binding enhancements between cytosolic subunits |
|
|
564 | (1) |
|
18.5.2 Kinetic mechanisms of NOX2 complex-mediated electron transfer and superoxide production, and regulation by pH |
|
|
565 | (1) |
|
18.5.3 Model corroborations and simulations of key emergent properties of NOX2 enzyme system and crosstalk between NOX2 assembly and activation with NOX2 complex-mediated electron transfer and superoxide production |
|
|
566 | (4) |
|
18.6 Summary and conclusion |
|
|
570 | (3) |
|
18.7 Model limitations and future directions |
|
|
573 | (3) |
|
|
576 | (1) |
|
|
576 | (5) |
Index |
|
581 | |