Modeling of Mass Transport Processes in Biological Media

Description

Modeling of Mass Transport Processes in Biological Media focuses on applications of mass transfer relevant to biomedical processes and technology―fields that require quantitative mechanistic descriptions of the delivery of molecules and drugs. This book features recent advances and developments in biomedical therapies with a focus on the associated theoretical and mathematical techniques necessary to predict mass transfer in biological systems. The book is authored by over 50 established researchers who are internationally recognized as leaders in their fields. Each chapter contains a comprehensive introductory section for those new to the field, followed by recent modeling developments motivated by empirical experimental observation. Offering a unique opportunity for the reader to access recent developments from technical, theoretical, and engineering perspectives, this book is ideal for graduate and postdoctoral researchers in academia as well as experienced researchers in biomedical industries. 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 Back Cover