Biotransport: Principles and Applications

Transcription

1 Biotransport: Principles and Applications

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3 Robert J. Roselli l Kenneth R. Diller Biotransport: Principles and Applications

4 Robert J. Roselli, Ph.D. Vanderbilt University Dept. Biomedical Engineering Nashville, Tennessee USA Kenneth R. Diller, Sc.D. University of Texas, Austin Dept. Biomedical Engineering Austin, Texas USA ISBN e-isbn DOI / Springer New York Dordrecht Heidelberg London Library of Congress Control Number: # Springer ScienceþBusiness Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Foreword The science of biotransport embraces the application of a large body of classical engineering knowledge of transport processes to the solution of problems in living systems covering a broad range of phenomena that are essential to homeostasis, and are encountered in routine experiences of human life, or in traumatic, diagnostic, or therapeutic contexts. Analyses of the transport of fluid, heat, and mass have been taught as fundamental components of engineering curricula for many decades, primarily with a focus on applications in industrial processes and design of various types of high-performance devices. The knowledge base that underpins this discipline derives from extensive high-quality, fundamental research conducted over the past century. Consequently, there have been hundreds of textbooks written for the instruction of undergraduates and graduates on the subject of transport processes. In relatively recent times, a new arena of application for transport analysis has arisen dealing with processes in living systems. Although the fundamental physics of the governing transport phenomena remains unchanged, living systems tend to have constitutive properties that are quite distinct from those of typical inanimate systems, including anisotropy, complex geometries, composite materials, nonlinear dependence on state properties, and coupling across multiple energy domains. Therefore, it is important that bioengineering students be able to understand and appreciate the principles and subtleties of transport phenomena in the context of the types of problems that arise in their own field. The subject of biotransport is now widely accepted including the basics of fundamental transport science and the unique challenges that are encountered in dealing with biological cells, tissues, and organisms. A number of excellent texts have been published during the past decade that address various aspects of biotransport as a defined field of study. The present text derives its genesis from a novel synthesis of cross-disciplinary intellect, that being the National Science Foundation sponsored Engineering Research Center (ERC) in Bioengineering Educational Technologies. This ERC was a multi-institutional consortium among Vanderbilt, Northwestern, Texas, and Harvard/MIT Universities (VaNTH) based on a collaboration among bioengineers, learning scientists, and learning technologists. It has the objective of developing state-of-the-art learning materials for students in bioengineering. One major outcome from this collaboration has been a refinement and application of the How People Learn (HPL) framework of student learning to higher education in the field of v

6 vi Foreword bioengineering. The HPL framework is explained in Part I of the text. The team of learning scientists and bioengineers has devised a set of materials designed to guide students into an experience of adaptive learning in which they gain expertise in both the core knowledge taxonomy of the subject material and the creative ability to innovatively apply the appropriate components of knowledge to solutions for problems presented in novel contexts. This book is designed for use in either a traditional didactic style of course or in a learning environment achieved through a nontraditional course organization based on the HPL framework in which students are presented with a series of open-ended challenge problems. The suite of challenges is structured to drive learning through targeted components of the knowledge taxonomy while developing innovative problem definition and solving skills. HPL provides a learning context in which students can receive constructive formative feedback from instructors in both the knowledge and the innovation dimensions. It is important that the suite of challenge problems used for an entire course be constructed and choreographed to provide a logical progression through the knowledge taxonomy, although it is not at all necessary that the progression be linear in the traditional style of textbook organization. The authors have accrued experience in teaching biotransport in the HPL format as a required core curriculum course in their home institutions over several years, and for an accrued total of more than 70 years. Extensive data have been gathered on student learning of the subject knowledge and on development of innovative analysis skills, and the data have been compared with control groups presented with the same subject material in a conventional didactic format. The results show the expected acquisition of knowledge along with a significant increase in innovative ability. Furthermore, surveys of student attitudes show that over the period of the course the students gained an understanding of the novel approach and an appreciation of how it helped them learn and prepare for their future careers, including lifelong learning. Further information on this research is presented in Chap. 1. The text has been developed with dual objectives: to provide a coherent and concise pedagogical exposition of biotransport that includes the domains of fluid, heat and mass flows, and to present a guide for teaching and studying a core engineering subject in the HPL framework, with appropriate supporting materials for students and teachers. It is the authors understanding that there is no other text that meets the latter objective. The text is organized differently than standard transport textbooks. It is not designed to be a handbook of biotransport, where all aspects of a given topic are grouped together in sections or chapters. Instead, we have attempted to organize the text around principles for more effective learning. In Part I, we provide an extensive orientation for both instructors and students to the HPL framework. This provides a basis for understanding and appreciating the advantages of an active learning environment. The main portion of the text consists of an exposition of the taxonomy of knowledge in the field of biotransport. Part II presents enduring concepts and analogies that form the foundations of biotransport. In Parts III V, these fundamentals are expanded in a progressive manner for momentum, heat, and mass transport. Each transport-specific section is further subdivided into four chapters.

7 Foreword vii The first chapter contains an expanded treatment of the fundamentals underlying the transport phenomena under consideration and treats topics unique to that transport mode (e.g., non-newtonian fluids, radiation heat transfer, chemical reactions). The second chapter in each section deals with steady and unsteady-state transport in systems treated using a macroscopic approach, in which the focus of interest is on overall transport in a system, rather than on local property variations. Application of conservation principles in these problems leads to solutions involving algebraic equations or transient ordinary differential equations. We believe the first two chapters in each section will be of value not only to bioengineers, but also to those in the medical and life sciences. The third chapter deals with steady and unsteady-state transport in a single direction. For each problem, conservation principles are applied to a differential control volume. Steady-state solutions lead to ordinary differential equations or systems of ordinary differential equations. Unsteady-state applications lead to more complex partial differential equations that are first order in time and second order in position. The last chapter in each section of the text develops the general multidimensional microscopic transport equation(s) for that area. Our focus in these chapters is to identify situations when this more complex analysis is appropriate, how these general expressions can be simplified, how appropriate initial and boundary conditions can be specified, and how a limited number of important applications can be solved. These chapters also form the basis for more advanced studies in biotransport. In summary, the fundamental enduring concepts presented in Part II are reinforced in each transport-specific section, and are presented in an order that allows students to progressively analyze problems that are increasingly more difficult. Learning is further promoted by repeating this process for analogous aspects of momentum, heat, and mass transport. A major objective of this text is to assist instructors in freeing up some of the time spent on classroom didactic lectures, thus allowing more teacher student classroom contact opportunities for formative feedback, modeling problem definition and solution strategies, answering specific questions, and explaining difficult or subtle concepts. Therefore, we have endeavored to provide clear and complete explanations of the subject materials in the text along with numerous example problems with numerical solutions to help students learn effectively during selfstudy. We have included all intermediate steps in derivations to make it easier for students to follow along. Important equations have been highlighted to distinguish them from intermediate steps. We have avoided the use of tensors, which often are confusing for students who study introductory transport. The text includes extensive examples of various learning challenges that have been written by the authors for use in their own biotransport courses. The authors introduce physiological principles and data only to the extent that it is a requisite for learning the relevant biotransport principles. Likewise, they limit the coverage and depth of transport to the fundamentals necessary to achieve an integrated, working overview of the subject. There are numerous treatises that address both a broad physiological background and more comprehensive transport analysis. The focus of this text is to cover the basics of biotransport sufficient for a standalone course on the subject in an undergraduate curriculum in the context of

8 viii Foreword introducing and explaining an approach for students to learn the subject in the HPL framework. There is more material in this text that can be adequately covered in a single semester or quarter. Different institutions combine biotransport topics differently in their introductory courses. Some combine all three domains in a single course, others teach bioheat and biomass together with a separate course in biofluids, and others combine biofluids and biomass transfer. We have included enough material so that the text could be used for introductory semester courses in biofluid, biomass, and bioheat transfer. Some materials in the latter sections of the last two chapters of each section can be skipped in shorter courses. It is our hope that using this text would enable students to move more quickly and effectively along the pathway to becoming adaptive experts and productive practicing engineers. We expect that when students have completed a course using this text and learning method they will be able to demonstrate a breadth of knowledge across all three domains of biotransport and be able to sort and appropriately apply that knowledge to understand and solve problems in biotransport they have not encountered previously. The text is also organized in a format that we hope will enable new adopters to move to the HPL framework with little required added investment of time beyond that associated with using any new teaching materials. We appreciate that there may be an upfront acculturation to understand HPL, but, based on our own experiences, this transition should lead to a teaching process that is no more demanding on a teacher s time than traditional pedagogical methods. The text should serve as a clear and effective resource for students to learn the basic components of the knowledge taxonomy for the subject so that a larger component of the faculty student interaction can be focused on developing skills in adaptive thinking and solving open-ended problems. The authors realize that many potential users of this text may not be ready to adopt the HPL framework for a complete course. In this context, we have tested many of the challenges as individual modules in both undergraduate and graduate courses. Colleagues at other institutions have done likewise. Our experience is that the challenges can be useful learning tools when used individually, and many faculty may find them to be quite helpful this way. Furthermore, this partial or progressive approach to adoption may provide a gradual pathway to using the HPL framework more fully. We have found that there is a considerable shift in the learning culture in which instructor and student mutually engage in this learning environment. In particular, for the HPL method to be effective, there needs to be an established level of trust and confidence of the students toward the teacher since the expectations for learning differ from the more traditional approach with which they are likely familiar that is more oriented toward memorization and repetition. Such a shift is not necessarily easy to effect in a step-wise manner. However, our experience is that the HPL framework can provide a much richer level of instructional interaction between faculty and students and that the level of enthusiasm exuded by the students in realizing a rapid learning curve toward adaptive expertise is rewarding for both student and teacher.

9 Foreword ix Developing a text that is compatible with learning in the HPL framework represents somewhat of a pioneering effort. We have tested and evolved the methodology with our own students and courses plus with some beta-phase adopters at sister institutions. It is certain that this approach will continue to be refined and improved; in that process, we hope that students will be enabled to learn with an enriched depth of understanding and perspective and that faculty will be stimulated to engage students in a community of learners and to acquire new and exciting dimensions in their careers as educators. We realize that the process of understanding the HPL methods and its implementation in higher education is an ongoing process requiring continuous improvement. Thus, we anticipate and request feedback on the structure and utility of this text. We are most happy to acknowledge with a tremendous level of appreciation and gratitude our learning science colleagues, Professors Sean Brophy of Purdue University, Taylor Martin and Tony Petrosino of the University of Texas at Austin, and John Bransford of the University of Washington, for guiding us along the pathway of learning about the principles of HPL and applying these principles to our own teaching in biomedical engineering. We also thank Professor Jack Patzer at the University of Pittsburgh, Robby Sanders at Tennessee Tech University and Valerie Guenst at Vanderbilt University for their valuable assistance in reviewing the text, and Professor Todd Giorgio at Vanderbilt University for providing some end-of-chapter problems. Our colleague Thomas R. Harris of Vanderbilt University as leader of the VaNTH ERC has been a continual inspiration for us to engage in this endeavor. We have educated about 1,000 of our own students using early versions of this text and materials. The feedback and enthusiasm of these students has been highly motivational to us. Most importantly, we thank our wives Kathleen and JoAnn for their patient endurance, encouragement, and proofreading during the writing process over the past five years. And finally, we appreciate the continuing support of the editorial staff of the Springer Press. March, 2011 Robert J. Roselli Vanderbilt University Kenneth R. Diller The University of Texas at Austin

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11 Contents Part I Fundamentals of How People Learn (HPL) 1 Introduction to HPL Methodology Introduction Adaptive Expertise Learning for Adaptive Expertise Principles of Effective Learning Challenge-Based Instruction STAR.Legacy (SL) Cycle for Inquiry Learning Developing Innovation How to Use the Generate Ideas Model How to Use This Textbook to Develop Innovation Learning to Gain Understanding References Part II Fundamental Concepts in Biotransport 2 Fundamental Concepts in Biotransport Introduction The System and Its Environment Transport Scales in Time and Space Continuum Concepts Conservation Principles Transport Mechanisms Molecular Transport Mechanisms Convective Transport Mechanisms Macroscopic Transport Coefficients Interphase Transport Transport in Biological Systems: Some Unique Aspects Summary of Key Concepts Questions Problems xi

12 xii Contents 2.12 Challenges References Modeling and Solving Biotransport Problems Introduction Theoretical Approach Geometric Considerations Governing Equations Solution Procedures Presentation of Results Scaling: Identification of Important Dimensionless Parameters Examples of the Theoretical Approach Empirical Approach The Buckingham Pi Theorem: Dimensional Analysis Summary of Key Concepts Questions Problems Challenges References Part III Biofluid Transport 4 Rheology of Biological Fluids Introduction Solids and Fluids Flow Regimes: Laminar and Turbulent Flow Boundary Conditions Viscous Properties of Fluids Viscous Momentum Flux and Shear Stress Viscometers Newtonian and Non-Newtonian Fluid Models Newtonian Fluid Model Non-Newtonian Fluid Models Identification of Constitutive Model Equations Rheology of Biological Fluids Rheological Properties of Extravascular Body Fluids Blood Rheology Biorheology and Disease Summary of Key Concepts Questions Problems Challenges References

13 Contents xiii 5 Macroscopic Approach for Biofluid Transport Introduction Conservation of Mass Conservation of Momentum Conservation of Energy Engineering Bernoulli Equation Friction Loss in Conduits Friction Loss Factors, Flow Through Fittings Laminar Flow and Flow Resistance in Noncircular Conduits Flow in Packed Beds External Flow: Drag and Lift Blood Flow in Microvessels Steady Flow Through a Network of Rigid Conduits Compliance and Resistance of Flexible Conduits Flow in Collapsible Tubes Fluid Inertia Blood Flow in Organs Osmotic Pressure and Flow Summary of Key Concepts Questions Problems Challenges References Shell Balance Approach for One-Dimensional Biofluid Transport Introduction General Approach Selecting an Appropriate Shell Fluid Mass Balance Fluid Momentum Balance Application of the Fluid Constitutive Relation to Find Fluid Velocity Examining and Applying Solutions for Shear Stress and Velocity Additional Shell Balances in Rectangular Coordinates One-Dimensional Shell Balances in Cylindrical Coordinates Flow of a Newtonian Fluid Through a Circular Cylinder Flow of a Newtonian Fluid in an Annulus with Inner Wall Moving Flow Through an Inclined Tube or Annulus Flow of a Casson Fluid Through a Circular Cylinder Osmotic Pressure and Flow in a Cylindrical Pore Unsteady-State 1-D Shell Balances Summary of Key Concepts

14 xiv Contents 6.6 Questions Problems Challenges References General Microscopic Approach for Biofluid Transport Introduction Conservation of Mass Conservation of Linear Momentum Moment Equations General Constitutive Relationship for a Newtonian Fluid Substantial Derivative Modified Pressure, Equations of Motion for Newtonian Fluids The Stream Function and Streamlines for Two-Dimensional Incompressible Flow Use of Navier Stokes Equations in Rectangular Coordinates Hydrostatics Reduction of the Equations of Motion Navier Stokes Equations in Cylindrical and Spherical Coordinate Systems Use of Navier Stokes Equations in Cylindrical and Spherical Coordinates Scaling the Navier Stokes Equation General Momentum Equations for Use with Non-Newtonian Fluids Constitutive Relationships for Non-Newtonian Fluids Power Law Fluid Bingham Fluid Casson Fluid Herschel Bulkley Fluid Setting Up and Solving Non-Newtonian Problems Summary of Key Concepts Questions Problems Challenges References Part IV Bioheat Transport 8 Heat Transfer Fundamentals Introduction Conduction Thermal Resistance in Conduction

15 Contents xv 8.3 Convection Four Principle Characteristics of Convective Processes Fundamentals of Convective Processes Forced Convection Analysis Free Convection Processes Thermal Resistance in Convection Biot Number Thermal Radiation Three Governing Characteristics of Thermal Radiation Processes The Role of Surface Temperature in Thermal Radiation The Role of Surface Properties in Thermal Radiation The Role of Geometric Sizes, Shapes, Separation, and Orientation in Thermal Radiation Electrical Resistance Model for Radiation Common Heat Transfer Boundary Conditions Summary of Key Concepts Questions Problems Challenges References Macroscopic Approach to Bioheat Transport Introduction General Macroscopic Energy Relation Steady-State Applications of the Macroscopic Energy Balance Thermal Resistances Heat Transfer Coefficients Convective Heat Transport Biomedical Applications of Thermal Radiation Heat Transfer with Phase Change Unsteady-State Macroscopic Heat Transfer Applications Lumped Parameter Analysis of Transient Diffusion with Convection Thermal Compartmental Analysis Multiple System Interactions Convection: Multiple Well-Mixed Compartments Combined Conduction and Convection Radiation: Flame Burn Injury Human Thermoregulation Summary of Key Concepts Questions Problems

16 xvi Contents 9.9 Challenges References Shell Balance Approach for One-Dimensional Bioheat Transport Introduction General Approach Steady-State Conduction with Heat Generation Steady-State Conduction with Heat Generation in a Slab Steady-State Conduction with Heat Generation in a Cylinder Steady-State Conduction with Heat Generation in a Sphere Steady-State One-dimensional Problems Involving Convection Internal Flow Convection with a Constant Temperature Boundary Condition Internal Flow Convection with a Constant Heat Flux Boundary Condition Heat Exchangers One-Dimensional Steady-State Heat Conduction Heat Conduction with Convection or Radiation at Extended Surfaces Heat Exchange in Tissue: Transient and Steady-State Pennes Equation Transient Diffusion Processes with Internal Thermal Gradients Symmetric Geometries: Exact and Approximate Solutions for Negligible Heat Generation Semi-Infinite Geometry Graphical Methods Summary of Key Concepts Questions Problems Challenges References General Microscopic Approach for Bioheat Transport General Microscopic Formulation of Conservation of Energy Derivation of Conservation of Energy for Combined Conduction and Convection Simplifying the General Microscopic Energy Equation

17 Contents xvii 11.2 Numerical Methods for Transient Conduction: Finite Difference Analysis Forward Finite Difference Method Backward Finite Difference Method Thermal Injury Mechanisms and Analysis Burn Injury Therapeutic Applications of Hyperthermia Laser Irradiation of Tissue Distributed Energy Absorption Time Constant Analysis of the Transient Temperature Field Surface Cooling During Irradiation Summary of Key Concepts Questions Problems Challenges References Part V Biological Mass Transport 12 Mass Transfer Fundamentals Average and Local Mass and Molar Concentrations Phase Equilibrium Liquid Gas Equilibrium Liquid Liquid, Gas Solid, Liquid Solid, Solid Solid Equilibrium Species Transport Between Phases Species Transport Within a Single Phase Species Fluxes and Velocities Diffusion Fluxes and Velocities Convective and Diffusive Transport Total Mass and Molar Fluxes Molecular Diffusion and Fick s Law of Diffusion Mass Transfer Coefficients Experimental Approach to Determining Mass Transfer Coefficients Relation Between Individual and Overall Mass Transfer Coefficients Permeability of Nonporous Materials Membrane Permeability Vessel or Hollow Fiber Permeability Comparison of Internal and External Resistances to Mass Transfer Transport of Electrically Charged Species

18 xviii Contents 12.8 Chemical Reactions Hemoglobin and Blood Oxygen Transport Blood CO 2 Transport and ph Enzyme Kinetics Ligand Receptor Binding Kinetics Cellular Transport Mechanisms Carrier-Mediated Transport Active Transport Mass Transfer Boundary Conditions Mass or Molar Concentration Specified at a Boundary Mass or Molar Flux Specified at a Boundary No-Flux Boundary Condition Concentration and Flux at an Interface Heterogeneous Reaction at a Surface Summary of Key Concepts Questions Problems Challenges References Macroscopic Approach to Biomass Transport Introduction Species Conservation Compartmental Analysis Single Compartment Two Compartments Multiple Compartments Indicator Dilution Methods Stewart Hamilton Relation for Measuring Flow Through a System Volume Measurements Permeability-Surface Area Measurements Chemical Reactions and Bioreactors Homogeneous Chemical Reactions Heterogeneous Reactions Pharmacokinetics Renal Excretion Drug Delivery to Tissue, Two Compartment Model More Complex Pharmacokinetics Models Mass Transfer Coefficient Applications Solute Flow Through Pores in Capillary Walls Small Solute Transport Large Solute Transport Through Pores

19 Contents xix 13.9 Summary of Key Concepts Questions Problems Challenges References Shell Balance Approach for One-Dimensional Biomass Transport Introduction Microscopic Species Conservation One-Dimensional Steady-State Diffusion Through a Membrane D Diffusion with Homogeneous Chemical Reaction Zeroth Order Reaction First-Order Reaction Michaelis Menten Kinetics Diffusion and Reaction in a Porous Particle Containing Immobilized Enzymes Convection and Diffusion Conduits with Constant Wall Concentration Hollow Fiber Devices Capillary Exchange of Non-Reacting Solutes Convection, Diffusion, and Chemical Reaction Transcapillary Exchange of O 2 and CO Tissue Solute Exchange, Krogh Cylinder Bioreactors One-Dimensional Unsteady-State Shell Balance Applications Diffusion to Tissue Unsteady-State 1D Convection and Diffusion Summary of Key Concepts Questions Problems Challenges References General Microscopic Approach for Biomass Transport Introduction D, Unsteady-State Species Conservation Comparison of the General Species Continuity Equation and the One-Dimensional Shell Balance Approach Diffusion Steady-State, Multidimensional Diffusion Steady-State Diffusion and Superposition

20 xx Contents Unsteady-State, Multidimensional Diffusion Diffusion and Chemical Reaction Convection and Diffusion Steady-State, Multidimensional Convection and Diffusion Convection, Diffusion, and Chemical Reaction Blood Oxygenation in a Hollow Fiber Summary of Key Concepts Questions Problems Challenges References Appendix A Nomenclature Appendix B.1 Physical Constants Appendix B.2 Prefixes and Multipliers for SI units Appendix B.3 Conversion Factors Appendix C Transport Properties Appendix D Charts for Unsteady Conduction and Diffusion Index