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Transport Phenomnea in Biological, Biophysical, and Physiological SystemsTime & Place: TBD
Instructor:
Jun Ni, Ph.D., Associate Professor
Department of Radiology, Carver College of Medicine,
Department of Biomedical Engineering, College of Engineering
Department of Mechanical Engineering, College of Engineering
Department of Computer Science, College of Liberal Arts
The University of Iowa, Iowa City, IA, USA
Tel: (319) 335-9490
E-mail: jun-ni@uiowa.eduOffice Hours and Place:
Textbook:
George A. Truskey, Fan Yuan, David F. Katz , "Transport Phenomena in Biological System ," Second Edition, Pearson Prentice Hall, 2008.
Class Lecture Notes:
Additional notes or handouts may be available in classroom.Course Description: this course addresses the issues of transport phenomena in biological and physiological systems. It presents engineering fundamentals and biological applications, and helps biomedical students learn how to develop and critically analyze models of biological transport and reaction processes. It course covers topics in fluid mechanics, mass transport, and biochemical interactions, with engineering concepts motivated by specific biological and physiological problems. The course is designed for graduate level biomedical students, and thermal science students who are interested in modeling and simulations of transport phenomena in biomedical systems.
Pre-requisites: TBD
Course Contents:
1. Introduction (Lecture I, 1st Week)Part I. Introduction to Physiological Fluid Mechanics1.1. The Role of Transport Processes in Biological Systems
1.2. Definition of Transport Processes
1.2.1. Diffusion
1.2.2. Convection
1.2.3. Transport by Binding Interactions
1.3. Relative Importance of Convection and Diffusion
1.4. Transport Within Cells
1.4.1. Transport Across the Cell Membrane
1.4.2. Transport Within the Cell
1.5. Transcellular Transport
1.5.1. Junctions Between Cells
1.5.2. Epithelial Cells
1.5.3. Endothelial Cells
1.6. Physiological Transport Systems
1.6.1. Cardiovascular System
1.6.2. Respiratory System
1.6.3. Gastrointestinal Tract
1.6.4. Liver
1.6.5. Kidneys
1.6.6. Integrated Organ Function1.7. Application of Transport Processes in Disease Pathology, Treatment, and Device Development
1.7.1. Transport Processes and Atherosclerosis
1.7.2. Transport Processes and Cancer Treatment
1.7.3. Transport Processes, Artificial Organs, and Tissue Engineering
1.8. Relative Importance of Transport and Reaction Processes
2. Conservation Relations and Momentum Balances (Lecture 200, Second Week)
3. Conservation Relations for Fluid Transport, Dimensional Analysis, and Scaling (Lecture 300, Third Week)2.1. Introduction
2.2. Fluid Kinematics
2.2.1. Control Volumes2.3. Conservation Relations and Boundary Conditions
2.2.2. Velocity Field
2.2.3. Flow Rate
2.2.4. Acceleration
2.2.5. Fluid Streamlines
2.3.1. Conservation of Mass2.4. Fluid Statics
2.3.2. Momentum Balances
2.3.3. Forces
2.3.4. Boundary Conditions
2.4.1. Static Equilibrium2.5. Constitutive Relations
2.4.2. Surface Tension
2.4.3. Membrane and Cortical Tension
2.5.1. Newton’s Law of Viscosity2.6. Laminar and Turbulent Flow
2.5.2. Non-Newtonian Rheology
2.5.3. Time-Dependent Viscoelastic Behavior
2.7. Application of Momentum Balances
2.7.1. Flow Induced by a Sliding Plate2.8. Rheology and Flow of Blood
2.7.2. Pressure-Driven Flow Through a Narrow Rectangular Channel
2.7.3. Pressure-Driven Flow Through a Cylindrical Tube
2.7.4. Pressure-Driven Flow of a Power Law Fluid in a Cylindrical Tube
2.7.5. Flow Between Rotating Cylinders
2.8.1. Measurement of Blood Viscosity
2.8.2. Rheology of Blood Flow in Large Vessels
2.8.3. Blood Flow in Small Tubes
2.8.4. Blood Flow in Capillaries
2.8.5. Regulation of Blood Flow
3.1. Introduction4. Approximate Methods for the Analysis of Complex Physiological Flow (Lecture 400, Fourth Week)
3.2. Differential Form of the Equation of Conservation of Mass in Three Dimensions
3.2.1. General Form of the Equation of Conservation of Mass3.3. Differential Form of the Conservation of Linear Momentum and the Navier–Stokes Equations in Three Dimensions
3.2.2. Conservation of Mass for Incompressible Fluids
3.3.1. General Form of the Equation of Conservation of Linear Momentum3.4. Fluid Motion with More Than One Dependent Variable
3.3.2. The Navier–Stokes Equation for an Incompressible Newtonian Fluid
3.4.1. Two-Dimensional Flow in a Channel3.5. Dimensional Analysis and Dimensionless Groups
3.4.2. Time Required to Establish a Steady Flow in a Rectangular Channel
3.5.1. Dimensional Analysis3.6. Low-Reynolds-Number Flow
3.5.2. Dimensionless Form of the Navier–Stokes Equation
3.5.3. Dimensional Analysis and Dynamic Similarity
3.6.1. Conservation Relations for Low-Reynolds-Number Flow
3.6.2. Low-Reynolds-Number Flow Around a Sphere
4.1. Introduction5. Fluid Flow in the Circulation and Tissues (Lecture500, Fifth Week)
4.2. Integral Form of the Equation of Conservation of Mass
4.3. Integral Form of the Equation of Conservation of Linear Momentum
4.4. Bernoulli’s Equation
4.4.1. Bernoulli’s Equation Applied to Stenotic Heart Valves4.5. Boundary Layer Theory
4.4.2. The Engineering Bernoulli Equation: The Effects of Viscous Losses and Time-Dependent Energy Changes
4.5.1. Background to Boundary Layer Theory4.6. Flow Separation
4.5.2. Derivation of the Boundary Layer Equations
4.5.3. Integral Momentum Equations for Boundary Layer Flows
4.7. Lubrication Theory
4.8. Peristaltic Pumping
5.1. Introduction
5.2. Oscillating Flow in a Cylindrical Tube
5.3. Entrance Lengths
5.4. Flow in Curved Vessels
5.5. Flow in Branching Vessels
5.6. Flow in Specific Arteries
5.6.1. Carotid Artery5.7. Arterial Fluid Dynamics and Atherosclerosis
5.6.2. Aorta
5.6.3. Effect of Vessel Wall Elasticity
5.6.4. Coronary Arteries
5.7.1. Hemodynamic Variables Associated with Atherosclerosis5.8. Heart-Valve Hemodynamics
5.7.2. Effect of Hemodynamics upon Endothelial Cell Function
5.8.1. Artificial Heart Valves5.9. Fluid Dynamic Effects of Reconstructive Surgery for Congenital Heart Defects
5.8.2. Turbulent Flow Around Heart Valves
Midterm I
Part II. Fundamentals and Applications of Mass Transport in Biological Systems
6. Mass Transport in Biological Systems (Lecture600, Sixth Week)
6.1. Introduction7. Diffusion with Convection or Electrical Potentials (Lecture700, Seventh Week)
6.2. Solute Fluxes in Mixtures
6.2.1. The Dilute-Solution Assumption6.3. Conservation Relations
6.3.1. Equation of Conservation of Mass for a Mixture6.4. Constitutive Relations
6.3.2. Boundary Conditions
6.4.1. Fick’s Law of Diffusion for Dilute Solutions6.5. Diffusion as a Random Walk
6.4.2. Diffusion in Concentrated Solutions
6.6. Estimation of Diffusion Coefficients in Solution
6.6.1. Transport Properties of Proteins6.7. Steady-State Diffusion in One Dimension
6.6.2. The Stokes–Einstein Equation
6.6.3. Estimation of Frictional Drag Coefficients
6.6.4. The Effects of Actual Surface Shape and Hydration
6.6.5. Correlations
6.7.1. Diffusion in Rectangular Coordinates6.8. Unsteady Diffusion in One Dimension
6.7.2. Radial Diffusion in Cylindrical Coordinates
6.7.3. Radial Diffusion in Spherical Coordinates
6.8.1. One-Dimensional Diffusion in a Semi-Infinite Medium6.9. Diffusion-Limited Reactions
6.8.2. One-Dimensional Unsteady Diffusion in a Finite Medium
6.8.3. Model of Diffusion of a Solute into a Sphere from a Well-Stirred Bath
6.8.4. Quasi-Steady Transport Across Membranes
6.9.1. Diffusion-Limited Binding and Dissociation in Solution6.10. A Thermodynamic Derivation of the Stokes–Einstein Equation
6.9.2. Diffusion-Limited Binding Between a Cell Surface Protein and a Solute
6.9.3. Diffusion-Limited Binding on a Cell Surface
7.1. Introduction8. Transport in Porous Media (Lecture800, Eighth Week)
7.2. Fick’s Law of Diffusion and Solute Flux
7.3. Conservation of Mass for Dilute Solutions
7.3.1. Transport in Multicomponent Mixtures7.4. Dimensional Analysis
7.5. Electrolyte Transport
7.5.1. Nernst–Planck Equation7.6. Diffusion and Convection
7.5.2. Electrolyte Transport Across Membranes
7.6.1. Release from the Walls of a Channel: A Short-Contact-Time Solution7.7. Macroscopic Form of Conservation Relations for Dilute Solutions
7.6.2. Momentum and Concentration Boundary Layers
7.8. Mass Transfer Coefficients
7.9. Mass Transfer Across Membranes: Application to Hemodialysis
7.9.1. Cocurrent Exchange
7.9.2. Countercurrent Exchange
8.1. Introduction9. Transvascular Transport (Lecture900, Ninth Week)
8.2. Porosity, Tortuosity, and Available Volume Fraction
8.3. Fluid Flow in Porous Media
8.3.1. Darcy’s Law8.4. Solute Transport in Porous Media
8.3.2. Brinkman Equation
8.3.3. Squeeze Flow
8.4.1. General Considerations8.5. Fluid Transport in Poroelastic Materials
8.4.2. Effective Diffusion Coefficient in Hydrogels
8.4.3. Effective Diffusion Coefficient in a Liquid-Filled Pore
8.4.4. Effective Diffusion Coefficient in Biological Tissues
9.1. Introduction
9.2. Pathways for Transendothelial Transport
9.2.1. Continuous Capillaries9.3. Rates of Transvascular Transport
9.2.2. Fenestrated Capillaries
9.2.3. Discontinuous Capillaries
9.3.1. Osmotic Pressure9.4. Phenomenological Constants in the Analysis of Transvascular Transport
9.3.2. Rate of Fluid Flow and Starling’s Law of Filtration
9.3.3. Rate of Solute Transport and the Kedem–Katchalsky Equation
9.5. A Limitation of Starling’s Law
9.5.1. Fluid Filtration in the Steady State
9.5.2. A New View of Starling’s LawMidterm II
Part III. The Effect of Mass Transport Upon Biochemical Interactions
10. Mass Transport and Biochemical Interactions (Lecture1000, Tenth Week)10.1. Introduction11. Cell-Surface Ligand–Receptor Kinetics and Molecular Transport Within Cells (Lecture1100, Eleventh Week)
10.2. Chemical Kinetics and Reaction Mechanisms
10.2.1. Reaction Rates10.3. Sequential Reactions and the Quasi–Steady-State Assumption
10.2.2. Reaction Mechanisms
10.2.3. First-Order Reactions
10.2.4. Second-Order Irreversible Reactions
10.2.5. Reversible Reactions
10.4. Enzyme Kinetics
10.4.1. Derivation of Michaelis–Menten Kinetics10.5. Regulation of Enzyme Activity
10.4.2. Application of the Quasi–Steady-State Assumption to Enzyme Kinetics
10.4.3. Determination of K_m and R_{max}
10.5.1. Competitive Inhibition10.6. Effect of Diffusion and Convection on Chemical Reactions
10.5.2. Uncompetitive and Noncompetitive Inhibition
10.5.3. Substrate Inhibition
10.6.1. Reaction and Diffusion in Solution
10.6.2. Interphase Mass Transfer and Reaction
10.6.3. Intraphase Chemical Reactions
10.6.4. Interphase and Intraphase Diffusion and Reaction
10.6.5. Observable Quantities and the Effectiveness Factor
10.6.6. Transport Effects on Enzymatic Reactions
11.1. Introduction12. Cell Adhesion (Lecture1200, Twelve Week)
11.2. Receptor–Ligand Binding Kinetics
11.3. Determination of Rate Constants for Receptor–Ligand Binding
11.4. Deviations from Simple Bimolecular Kinetics11.4.1. Ligand Depletion11.5. Receptor-Mediated Endocytosis
11.4.2. Two or More Receptor Populations
11.4.3. Interconverting Receptor Subpopulations11.5.1. A Kinetic Model for LDL Receptor-Mediated Endocytosis11.7. Signal Transduction
11.5.2. Receptor Interaction with Coated Pits
11.6. Receptor Regulation During Receptor-Mediated Endocytosis
11.7.1. Qualitative Aspects of Signal Transduction11.8. Regulation of Gene Expression
11.7.2. Quantitative Aspects of Signal Transduction
11.8.1. Simplified Model for Gene Induction and Expression
12.1. Introduction, 582
12.2. Effect of Force on Bond Association and Dissociation
12.2.1. The Influence of Energy Barriers on Molecular Interactions12.3. Cell–Matrix Adhesion
12.2.2. Bond Disruption in the Presence of an Applied Force
12.2.3. Bond Formation in the Presence of an Applied Force
12.2.4. The Effect of Loading Rates on Bond Forces
12.3.1. Cell Attachment12.4. Biophysics of Leukocyte Rolling and Adhesion
12.3.2. Cell Detachment
12.4.1. Overview12.5. Stochastic Effects on Chemical Interactions
12.4.2. Modeling Leukocyte–Endothelial Cell Interactions
12.4.3. Effect of Cell Deformation on Leukocyte Adhesion to Endothelium
12.5.1. Kinetic Analysis of Stochastic Chemical Reactions
12.5.2. Monte Carlo Analysis of Stochastic Chemical Reactions
Part IV. Transport in Organs
13. Transport of Gases Between Blood and Tissues (Lecture1300, Thirteenth Week)
13.1. Introduction14. Transport in the Kidneys (Lecture1400, Fourth Week)
13.2. Oxygen–Hemoglobin Equilibria, 626
13.3. Oxygen–Hemoglobin Binding Kinetics, 631
13.4. Dynamics of Oxygenation of Blood in Lung Capillaries, 632
13.5. Oxygen Delivery to Tissues, 637
13.5.1. The Krogh Cylinder Model of Oxygen Transport in Tissues13.6. Nitric Oxide Production and Transport in Tissues
13.5.2. Analysis of Assumptions Used in the Krogh Model13.6.1. NO Formation and Reaction
13.6.2. NO Formation, Diffusion, and Reaction in Tissues14.1. Introduction15. Drug Transport in Solid Tumors (Lecture1500, Fifteenth Week)
14.2. Mechanisms of Transmembrane Transport
14.2.1. Direct Diffusion14.3. Renal Physiology
14.2.2. Facilitated Transport
14.2.3. Active Transport
14.3.1. Renal Blood Flow14.4. Quantitative Analysis of Glomerular Filtration
14.3.2. Urine Formation
14.4.1. Hydraulic Conductivity of Glomerular Capillaries14.5. Quantitative Analysis of Tubular Reabsorption
14.4.2. Solute Transport Across Glomerular Capillaries
14.5.1. Mass Balance Equations14.6. A Whole-Organ Approach to Renal Modeling
14.5.2. Fluxes of Passive Diffusion and Convection
14.5.3. Goldman–Hodgkin–Katz Equation for Ion Channels
14.5.4. Mathematical Modeling of Carrier-Mediated Transport
14.5.5. A Mathematical Model of Na+/K+ ATPase
14.6.1. Filtration
14.6.2. Reabsorption
14.6.3. Secretion15.1. Introduction16. Transport in Organs and Organisms (Lecture1600, Sixteen Week)
15.1.1. Drug Delivery in Cancer Treatment15.2. Quantitative Analysis of Transvascular Transport
15.1.2. Routes of Drug Administration
15.1.3. Drug Transport Within Solid Tumors
15.3. Quantitative Analysis of Interstitial Fluid Transport
15.3.1. Governing Equations15.4. Interstitial Hypertension in Solid Tumors
15.3.2. Unidirectional Flow of Fluid at Steady State
15.3.3. Unsteady State Fluid Transport
15.4.1. Effects of Interstitial Hypertension on Drug and Gene Delivery15.5. Quantitative Analysis of Interstitial Transport of Solutes
15.4.2. Etiology of Interstitial Hypertension
15.4.3. Strategies for Reducing Interstitial Fluid Pressure
15.5.1. Governing Equations
15.5.2. Unidirectional Transport in a Solid Tumor
15.5.3. Unidirectional Transport in the Krogh Cylinder16.1. Introduction, 736
16.2. General Considerations in Pharmacokinetic Analysis
16.3. Simple Compartment Models in Pharmacokinetic Analysis
16.3.1. One-Compartment Model
16.3.2. Two-Compartment Model
16.4. Physiologically Based Pharmacokinetic Models
16.4.1. Transport in Individual Organs
16.4.2. Physiologically Based Pharmacokinetic Analysis of Methotrexate
16.5. Allometric Scaling Law and Its Application to Transport Properties
16.5.1. Scaling Laws
16.5.2. Applications of the Allometric Scaling Law in Pharmacokinetic Analysis
Part V. Energy and Bioheat Transfer
17. Energy Transport in Biological Systems (Lecture1700, Seventeenth Week)
17.1. Introduction
17.2. First Law of Thermodynamics and Metabolism
17.2.1. Conservation Relations17.3. Steady and Unsteady Heat Conduction
17.2.2. Differential Forms of the Conservation of Energy
17.2.3. Constitutive Relation and Boundary Conditions
17.2.4. Dimensionless Form of the Conservation Relations
17.3.1. Insulation and Heat Conduction Through Layers of Different Thermal Conductivity17.4. Convective Heat Transfer
17.3.2. Steady State Conduction and Metabolic Energy Production
17.3.3. Unsteady Heat Conduction
17.3.4. Unsteady Heat Conduction with a Phase Change
17.4.1. Correlations for Forced Convection17.5. Energy Transfer Due to Evaporation
17.4.2. Natural Convection
17.6. Metabolism and Regulation of Body Temperature
17.6.1. Basal Metabolic Rate and Efficiency
17.6.2. Regulation of Body Temperature
17.6.3. Macroscopic Balance for Energy Transfer in Biological Systems
17.7. The Bioheat-Transfer Equation
17.8. CryopreservationFinal Project (Eighteenth Week)
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