Modeling of Mass Transport Processes in Biological Media

Front Cover
Modeling of Mass Transport Processes in Biological Media
Copyright
Contents
Contributors
Preface
Chapter 1: Applications of porous media in biological transport modeling
1.1. Introduction
1.2. Applications of porous media in modeling in modeling transport phenomena in arteries
1.3. Fluid-structure interaction in biomedical applications
1.4. Brain aneurysms
1.5. Magnetic resonance imaging (MRI)
1.6. Concluding remarks
References
Chapter 2: Metabolic consumption of microorganisms
2.1. Introduction
2.2. Model formulation and metabolic mass transfer
2.3. Analysis of the equation governing monotonic growth
2.3.1. Dimensionless form of the governing equation
2.3.2. Condition for a logarithmic inflection point (LIP)
2.3.3. Representation of the solutions on phase diagrams and LAG
2.4. Closed form analytical solution of the monotonic growth
2.5. Results and discussion
2.6. Conclusions
References
Further reading
Chapter 3: Numerical simulation of deformability cytometry: Transport of a biological cell through a microfluidic channel
3.1. Introduction
3.2. Modeling biological cells in an RT-DC channel
3.2.1. The measurement buffer as a non-Newtonian fluid
3.2.2. The cell as a viscoelastic solid material
3.2.3. Boundary conditions and fluid-solid coupling
3.2.4. Finite-element implementation
3.3. Hydrodynamic stresses on the cell surface
3.3.1. Fluid flow in the microfluidic chip
3.3.2. Deformed cells in the region of interest
3.4. Cell shapes and cell deformation
3.4.1. Deformation of highly viscous cells at the outflow
3.4.2. Inertia ratio and Fourier transcriptors
3.5. Extraction of the cell viscosity
3.6. Approximation error of the cell volume over the channel
3.7. Conclusions
Appendix. Derivation of the deformation measure from cell contours
Fourier shape descriptors
Acknowledgments
References
Chapter 4: Computation of organelle age during axonal transport
4.1. Introduction
4.2. Governing equations
4.3. Simulation of the DCV concentration in the axon
4.4. Age distribution model of DCVs and mean age of DCVs in boutons
4.5. Parameter value estimation
4.5.1. Two groups of parameters
4.5.2. Estimation of saturated concentrations of DCVs in the resident state in boutons
4.5.3. Estimation of the mass transfer coefficients and the saturated concentrations of DCVs in boutons
4.6. Numerical approach
4.7. Results
4.7.1. Assumption about the fate of DCVs captured into the resident state in boutons
4.7.2. Verification of the values to which concentrations converge as t
4.7.3. Investigating sensitivity of the mean age of DCVs in boutons to various parameters
4.7.4. Verifying the accuracy of computations
4.7.5. Effect of parameter ε on anterograde and retrograde fluxes between the boutons
4.8. Discussion, model constraints, and future directions
Acknowledgments
References
Chapter 5: Continuum models of drug transport to multiple cell-type population
5.1. Introduction
5.1.1. Transmembrane transport
5.1.1.1. Diffusion-based transmembrane transport models
5.1.1.2. Facilitated diffusion transmembrane transport models
5.1.1.3. Rapid transmembrane transport approximation
5.1.2. Reaction terms and binding models
5.1.2.1. Nonreversible first-order drug target binding model
5.1.2.2. Slow reversible nonlinear drug-target-binding models
5.1.2.3. Mathematical expressions of drug administration
5.1.3. Extension to multiple cell-type populations
5.2. Formulation of the problem
5.2.1. Concentrations and volume-averaged variables
5.2.2. Governing equations
5.3. Method of solution
5.3.1. Uncoupling procedure
5.3.1.1. First step: Elimination of C1
5.3.1.2. Second step: Elimination of C2
5.3.1.3. Third step: Elimination of C3
5.3.2. Transformed mass balance equation for the extracellular space
5.3.3. Physical interpretation: The dual-phase-lag model
5.3.4. Concentration distribution of the k-th type of cell
5.4. Case study: A 3D rectangular biological tissue
5.4.1. One-dimensional governing equations
5.4.2. Exact analytical solution
5.4.2.1. Extracellular space solution
5.4.2.2. Solution of the Fick-type diffusive equation
5.4.2.3. Fourier series-based solution
5.4.2.4. Special case: Boundary condition of the first kind
5.4.2.5. Cell concentration solution
5.4.3. Concentration solution in dimensionless form
5.4.4. Convergence of the series-solution
5.4.5. Computation of the eigenvalues
5.5. Results and discussion
5.6. Conclusions
5.A. Appendix A
5.B. Appendix B
5.C. Appendix C
5.D. Appendix D
5.D.1. Convergence criteria
5.E. Appendix E
5.E.1. Convergence criteria
References
Chapter 6: Computational investigation of the role of low-density lipoprotein and oxygen transport in atherosc
6.1. Introduction: Atherosclerosis and the role of mass transport
6.2. Mass transfer of low-density lipoproteins and oxygen in arteries: Theoretical background
6.2.1. Transport mechanisms
6.2.2. Role of hemodynamics
6.2.2.1. Hemodynamic effect on passive transport
6.2.2.2. Hemodynamic effect on active transport
6.2.3. Mathematical formulation and modeling strategies
6.3. Mass transfer of low-density lipoproteins in arteries: Computational modeling
6.3.1. Introduction
6.3.2. Wall-free models
6.3.3. Fluid-wall models
6.3.4. Multilayer models
6.4. Mass transfer of oxygen in arteries: Computational modeling
6.4.1. Introduction
6.4.2. Wall-free models
6.4.3. Fluid-wall models
6.5. Limitations of the current models and future directions
6.6. Conclusions
Acknowledgment
References
Chapter 7: Fluid dynamics and mass transport in lower limb vessels: Effects on restenosis
7.1. Introduction
7.2. Lower limb vessels: Anatomy, physiopathology, treatment options, and their failure
7.2.1. Anatomy and pathophysiology of lower limb vessels
7.2.2. Treatments of lower limb vessels and their failure
7.2.2.1. Surgical treatment: Bypass
7.2.2.2. Endovascular treatment: Angioplasty, stent, and drug-coated balloons
7.2.2.3. Comparison of treatments
7.2.2.4. Failure of PAD treatments: Restenosis
7.3. Modeling the hemodynamics of treated lower limb vessels
7.3.1. Introduction
7.3.2. Computational models of lower limb hemodynamics
7.3.3. In-stent restenosis
7.3.4. Restenosis in vein grafts
7.3.5. Limitations of the current CFD models
7.4. State-of-the-art computational mass transport models of lower limb vessels
7.4.1. Introduction
7.4.2. Modeling mass transport in lower limb vessels
7.4.3. Modeling the transport of drugs delivered from drug-coated balloons
7.4.4. Limitations of the current models of mass transport in lower limb vessels
7.4.5. Future remarks on drug transport in diseased lower limb vessels
7.4.5.1. Mass transport model of a diseased SFA treated with a DCB
7.4.5.2. Investigated clinical scenarios
7.5. Conclusions and future directions
Acknowledgment
References
Chapter 8: Numerical modeling in support of locoregional drug delivery during transarterial therapies for liver cancer
8.1. Introduction
8.1.1. Clinical context
8.1.2. Transarterial therapies
8.1.3. Chemoembolization versus radioembolization
8.1.4. Clinical microspheres
8.1.5. Clinical catheter types
8.1.6. The role of numerical modeling
8.2. State of the art of computational techniques
8.2.1. Hepatic arterial geometry
8.2.2. Dimensionality
8.2.3. Multiphase physics
8.2.3.1. Modeling of the fluid phase
8.2.3.2. Modeling of the discrete phase
8.2.3.3. Coupling between the discrete and fluid phases
8.2.4. Flow pulsatility
8.2.5. Fluid-structure interaction
8.2.6. Boundary conditions
8.3. Clinical parameters
8.3.1. Cross-sectional injection location
8.3.2. Axial injection location
8.3.3. Microsphere types and characteristics
8.3.4. Catheter type, distal direction, and tip orientation
8.3.5. Catheter injection flow rate
8.4. State of the art of experimental techniques
8.4.1. In vitro techniques
8.4.2. In vivo techniques
8.5. Closing remarks
Acknowledgment
References
Chapter 9: Active gel: A continuum physics perspective
9.1. Introduction
9.2. A short insight into active gel physics
9.3. A continuum model of active gels
9.3.1. Chemo-mechanical states
9.3.2. The balance laws
9.3.3. Constitutive theory
9.3.4. Remodeling and diffusion evolution laws
9.3.5. Simple solutions and steady states
9.3.5.1. Steady states
9.4. Worked examples
9.4.1. Bulk contraction in homogeneous active gels
9.4.1.1. Dry and initial states
9.4.1.2. Dynamics
9.4.2. Driving liquid migration by bulk contraction
9.4.2.1. Dry and initial states
9.4.2.2. Dynamics
9.5. Conclusions and future challenges
Appendix. Cylindrical coordinates
Acknowledgments
References
Chapter 10: Modeling nasal spray droplet deposition and translocation in nasal airway for olfactory delivery
10.1. Introduction
10.2. Materials and methods
10.2.1. Study design
10.2.2. Nasal airway model
10.2.3. Spray release model
10.2.4. Airflow and droplet transport models
10.2.5. Eulerian wall film model
10.2.6. Numerical methods
10.3. Results
10.3.1. Airflow and wall shear
10.3.2. Initial deposition of nasal droplets
10.3.2.1. Spray release position effect
10.3.2.2. Nasal spray application angle (α) effect
10.3.2.3. Effects of nasal spray properties
10.3.2.4. Identifying the optimal delivery system
10.3.3. Wall film migration
10.3.3.1. Wall film intranasal distribution at a 0.1-mL dose
10.3.3.2. Wall film intranasal distributions at increased doses (0.2-0.8mL)
10.3.3.3. Wall film intranasal distributions with the baseline delivery system
10.4. Discussions and conclusion
Acknowledgment
References
Chapter 11: Drug delivery and in vivo absorption
11.1. Drug delivery
11.1.1. History
11.1.2. Modern age: Second millennium
11.1.3. Modern age: Third millennium
11.1.4. Mathematical modeling
11.2. State of the art
11.2.1. Drug delivery models
11.2.1.1. Diffusion
11.2.1.2. Swelling
11.2.1.3. Erosion
11.2.1.4. Drug dissolution
11.2.1.5. Drug-DS interactions
11.2.1.6. Initial drug distribution inside DS
11.2.1.7. Osmotic DS
11.2.1.8. Poly-dispersed DS
11.2.2. PK and PBPK models
11.2.3. IVIV correlations
11.3. Oral administration
11.4. Conclusions
References
Chapter 12: Modeling the physiological phenomena and the effects of therapy on the dynamics of tumor growth
12.1. Introduction
12.2. Formal reaction kinetics
12.3. Creating tumor model with formal reaction kinetics
12.4. Concluding remarks
References
Chapter 13: Mathematical models of water transport across ocular epithelial layers
13.1. Introduction to fluid transport in the eye
13.1.1. Brief description of the anatomy and physiology of the eye
13.1.2. General characteristics of ocular epithelial layers
13.1.2.1. Introduction to epithelial types
13.1.2.2. Features of a secretory epithelium
13.2. Formulation of the problem of water and solute transport
13.2.1. Governing equations
13.2.2. Ion transport across the cell membrane
13.3. Mechanisms involved in water transport across cell layers
13.3.1. Mechanical pressure difference
13.3.2. Oncotic and osmotic pressures
13.3.3. Local osmosis
13.3.4. Electroosmosis
13.3.4.1. A simple model of electroosmosis
13.3.5. Cotransporter as a possible means of water transport
13.4. Aqueous humor production at the ciliary processes
13.4.1. Importance of aqueous humor production for ocular homeostasis
13.4.2. Mechanisms of aqueous humor formation
13.4.3. Models of aqueous formation
13.5. Transport across the corneal endothelium
13.5.1. Structure of the cornea and corneal endothelium
13.5.2. Importance of corneal endothelium to prevent corneal swelling
13.5.3. Proposed mechanisms of fluid transport across the corneal endothelium
13.5.3.1. Cotransport with lactate
13.5.3.2. Electroosmosis
13.5.4. A model of electroosmotic transport across the corneal endothelium
13.6. Transport across the retinal pigment epithelium
13.6.1. Structure of the retinal pigment epithelium and its function in regulating fluid flow across the retina
13.6.2. A mathematical model of ion and fluid transport across the RPE
13.7. Conclusions
References
Chapter 14: Multidimensional modeling of solid tumor proliferation following drug treatment: Toward computational prognos ...
14.1. Introduction
14.1.1. Cancer proliferation and current understanding
14.1.2. Improved prognoses via cancer modeling
14.1.3. The proposed framework for solid tumor prognosis
14.2. The workflow of the simulation framework
14.3. Mathematical formulation
14.3.1. Tumor progression phases
14.3.2. The administered therapy
14.3.3. The biological conversion mechanism
14.3.4. Governing equations
14.3.5. Initial and boundary conditions, proliferation, and therapy onset
14.3.6. Numerical treatment
14.4. Results
14.4.1. A new interpretation of DLBCL proliferation and therapy effect
14.4.2. Same-IPI patients, with different tumor progressions
14.4.3. Virtual therapy testing
14.4.4. Virtual tumor malignancy testing
14.4.5. Model assumptions
14.5. Conclusions
References
Chapter 15: Modeling LDL accumulation within an arterial wall
15.1. Introduction
15.1.1. The relationship between low-density lipoprotein and cardiovascular diseases (CVDs)
15.1.2. Anatomy of an artery
15.1.3. Summary of the present chapter
15.2. Wall-free and single-layer models
15.2.1. Wall-free models
15.2.2. Single-layer models
15.3. Multilayer modeling
15.3.1. Introduction
15.3.2. Governing equations
15.3.3. Transport properties
15.4. Published results of multilayer models
15.4.1. Straight idealized arteries
15.4.2. Stenosed idealized arteries
15.4.3. Bifurcations, patient-specific, and curved geometries
15.5. Conclusions and future developments
References
Chapter 16: Modeling transport of soluble proteins and metabolites in the brain
16.1. Introduction
16.2. Blood-brain barrier
16.2.1. Flow across the BBB
16.3. Flow through the parenchyma
16.3.1. Illustrative example
16.3.2. Paravascular flow
16.3.2.1. Mechanics of the flow
16.4. Conclusions
Acknowledgments
References
Chapter 17: Hybrid-dimensional models for blood flow and mass transport: Sequential and embedded 3D-1D models
17.1. Introduction
17.1.1. Multiscale modeling of the cardiovascular system
17.2. 3D-1D geometric sequential multiscale models
17.2.1. 1D models for larger deformable vessels
17.2.2. Conditions at the boundaries and at the junctions
17.2.3. Compartmental (0D) models
17.2.4. 1D models for blood solutes
17.2.5. Sequential coupling of 3D and 1D models
17.3. 3D-1D geometric embedded multiscale models
17.3.1. 1D models for rigid vessels
17.3.1.1. 1D model for steady flow in a curved cylinder
17.3.2. More complex geometries, vascular networks
17.3.2.1. Weak formulation of the vascular network problem
17.3.3. The embedded coupling conditions
17.3.4. A 3D-1D embedded model for mass transport
17.3.5. Numerical simulations of oxygen transport
17.4. Conclusions
References
Chapter 18: Chemical thermodynamic principles and computational modeling of NOX2-mediated ROS production on cell membrane
18.1. Introduction
18.2. Thermodynamic principles for biochemical systems modeling
18.2.1. Thermodynamics of biochemical reactions
18.2.2. Thermodynamics of oxidation-reduction reactions
18.3. Mathematical modeling of NOX2 enzyme function
18.3.1. Mechanistic computational modeling of NOX2 assembly and activation
18.3.2. Thermodynamically constrained computational modeling of NOX2 complex-mediated electron transfer, superoxide produ ...
18.3.2.1. Postulated mechanism of NOX2 complex-mediated electron transfer and superoxide production
18.3.2.2. Thermodynamics of NOX2 electron transfer reactions and regulation by pH
18.3.2.3. Derivation of NOX2 reaction flux expression for superoxide production
18.3.2.4. Simplified NOX2 flux expression in the absence of reaction products
18.3.3. Calculation of apparent enzyme kinetic parameters
18.4. Data analysis and estimation of unknown model parameters
18.4.1. Key experimental data for model parameterization and validation
18.4.2. Estimation of unknown model parameters by fitting model solutions to experimental data
18.5. Biological insights into NOX2 enzyme function
18.5.1. Kinetic mechanisms of NOX2 assembly, activation, and regulation by guanine nucleotides and mutual binding enhance ...
18.5.2. Kinetic mechanisms of NOX2 complex-mediated electron transfer and superoxide production, and regulation by pH
18.5.3. Model corroborations and simulations of key emergent properties of NOX2 enzyme system and crosstalk between NOX2 ...
18.6. Summary and conclusion
18.7. Model limitations and future directions
Acknowledgment
References
Index
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