Biotransport: Fluid Biotransport: Fluid Mechanics, Mechanics,

Heat and Mass TransferHeat and Mass Transfer

Dr. Portonovo S. AyyaswamyDr. Portonovo S. Ayyaswamy

Department of Mechanical Department of Mechanical Engineering and Applied Engineering and Applied

MechanicsMechanics

University of PennsylvaniaUniversity of Pennsylvania

There is an important need for comprehensive There is an important need for comprehensive courses related to Biotransport to be offered at the courses related to Biotransport to be offered at the undergraduate and graduate levels in US undergraduate and graduate levels in US Universities.Universities.

These courses must emphasize both theory and These courses must emphasize both theory and applications, motivating students to carry out applications, motivating students to carry out careful experimentation which will validate what careful experimentation which will validate what they have learned in theory.they have learned in theory.

At present, although there are many different At present, although there are many different descriptions of courses related to biotransport that descriptions of courses related to biotransport that are available in catalogues of various departments, are available in catalogues of various departments, it is clear that a systematic approach is needed to it is clear that a systematic approach is needed to develop a formally comprehensive set of guidelines develop a formally comprehensive set of guidelines and course material descriptions that will be useful and course material descriptions that will be useful for the student body at large.for the student body at large.

AbstractAbstract

As a part of this discussion, a comprehensive As a part of this discussion, a comprehensive model course description is displayed in the model course description is displayed in the following.following.

This model will apply to undergraduate and This model will apply to undergraduate and graduate level courses; the degree of detail, graduate level courses; the degree of detail, rigor, and emphasis will vary depending on the rigor, and emphasis will vary depending on the level at which the course is offered.level at which the course is offered.

Abstract (cont’d)Abstract (cont’d)

Introduction to BiotransportIntroduction to Biotransport

The role of transport processes in biological The role of transport processes in biological systems; biological system description must systems; biological system description must include precise concepts both from biology include precise concepts both from biology and from engineering. What constitutes a and from engineering. What constitutes a biological system model must be addressed.biological system model must be addressed.

Multiphase (both on the basis of material Multiphase (both on the basis of material composition and thermodynamically distinct composition and thermodynamically distinct phases) are common in biotransport.phases) are common in biotransport.

Diffusion, convection, binding interactions, Diffusion, convection, binding interactions, and cellular transport are the most common and cellular transport are the most common types and must be clearly discussed.types and must be clearly discussed.

Introduction to Biotransport Introduction to Biotransport (cont’d)(cont’d)

Transport within cells and across membranesTransport within cells and across membranes

Physiological transport systems: Consideration Physiological transport systems: Consideration may be limited to the cardiovascular system may be limited to the cardiovascular system and the respiratory system since they are well and the respiratory system since they are well understood.understood.

Review of Fundamentals of Review of Fundamentals of Fluid MechanicsFluid Mechanics

Review of fluid properties and their ranges as Review of fluid properties and their ranges as functions of pressure and temperaturefunctions of pressure and temperature

Newtonian and non-Newtonian fluids: limits Newtonian and non-Newtonian fluids: limits where fluids may be considered Newtonian to where fluids may be considered Newtonian to an excellent approximationan excellent approximation

Fluid statics, fluid kinematics; relevance to Fluid statics, fluid kinematics; relevance to transport phenomenatransport phenomena

Laminar and turbulent flows as illustrated by Laminar and turbulent flows as illustrated by examples taken from systemsexamples taken from systems

Review of Fundamentals of Review of Fundamentals of Fluid Mechanics (cont’d)Fluid Mechanics (cont’d)

Lagrangian and Eulerian view points of fluid Lagrangian and Eulerian view points of fluid flow; why are these important and where such flow; why are these important and where such descriptions are suitabledescriptions are suitable

Compressible and incompressible flows; Compressible and incompressible flows; examples of systems where this distinction is examples of systems where this distinction is criticalcritical

Inviscid and Irrotational Flows; Bernoulli and Inviscid and Irrotational Flows; Bernoulli and Euler equations; examples in systems where Euler equations; examples in systems where these offer suitable descriptionsthese offer suitable descriptions

Review of Conservation Review of Conservation Relations in Integral and Relations in Integral and

Differential FormsDifferential Forms Control volume; fixed and moving; frames of Control volume; fixed and moving; frames of

referencereference

Basic equations in integral form, Reynolds Basic equations in integral form, Reynolds transport equationtransport equation

Applicable boundary (interface) and initial Applicable boundary (interface) and initial conditionsconditions

Review of differential forms of the equation of Review of differential forms of the equation of conservation of mass, linear momentum and conservation of mass, linear momentum and Navier-Stokes equationNavier-Stokes equation

Fluid motion with more than one dependent Fluid motion with more than one dependent variablevariable

Low, intermediate and high Reynolds-number Low, intermediate and high Reynolds-number flowsflows

Blood Rheology: Blood Rheology: Properties of Flowing BloodProperties of Flowing Blood

Blood composition, viscosity, yield stress, Blood composition, viscosity, yield stress, Fahraeus-Lindqvist effectFahraeus-Lindqvist effect

Power-law model, Casson model, Carreau-Power-law model, Casson model, Carreau-Yasuda modelYasuda model

Usefulness and shortcomings of existing Usefulness and shortcomings of existing modelsmodels

Blood vessel structureBlood vessel structure

Circulatory Biofluid MechanicsCirculatory Biofluid Mechanics

Systemic and Pulmonary circulationsSystemic and Pulmonary circulations

Inviscid approximations; viscous flows and Inviscid approximations; viscous flows and boundary layer theoryboundary layer theory

Flow separation; examples from systemsFlow separation; examples from systems

Lubrication theory; limits of applicabilityLubrication theory; limits of applicability

Peristaltic pumpingPeristaltic pumping

Fluid Flow in the Circulation Fluid Flow in the Circulation and Tissuesand Tissues

IntroductionIntroduction

Oscillating flow in a cylindrical tubeOscillating flow in a cylindrical tube

Entrance lengthsEntrance lengths

Flow in curved vesselsFlow in curved vessels

Flow in branching vesselsFlow in branching vessels

Fluid Flow in the Circulation Fluid Flow in the Circulation and Tissues (cont’d)and Tissues (cont’d)

Flow in arteriesFlow in arteries

Flow in collapsible tubesFlow in collapsible tubes

Heart-valve HemodynamicsHeart-valve Hemodynamics

Introduction to non-Newtonian flows in tubesIntroduction to non-Newtonian flows in tubes

Use of models in flow descriptions, arterial Use of models in flow descriptions, arterial fluid dynamicsfluid dynamics

Mass Transport in Biological Mass Transport in Biological SystemsSystems

IntroductionIntroduction

Solute fluxes in mixturesSolute fluxes in mixtures

Conservation relations, Fick’s lawsConservation relations, Fick’s laws

Steady and unsteady diffusionSteady and unsteady diffusion

Diffusion-limited reactions, equimolar counter Diffusion-limited reactions, equimolar counter diffusiondiffusion

Lumped parameter techniques; Lumped parameter techniques; Compartmental models with pharmokineticsCompartmental models with pharmokinetics

Mass Transport in Biological Mass Transport in Biological systems (cont’d)systems (cont’d)

Transport across membranesTransport across membranes

Conservation of mass for dilute solutionsConservation of mass for dilute solutions

Dimensional analysisDimensional analysis

Electrolyte transport, diffusion and convectionElectrolyte transport, diffusion and convection

Mass transfer coefficientsMass transfer coefficients

Mass transfer across membranesMass transfer across membranes

Transport in Porous MediaTransport in Porous Media

IntroductionIntroduction

PorosityPorosity

Toruosity, and available volume fractionToruosity, and available volume fraction

Fluid flow in porous mediaFluid flow in porous media

Solute transport in porous mediaSolute transport in porous media

Fluid transport in poroelastic materialsFluid transport in poroelastic materials

Introduction to Molecular Introduction to Molecular Transport Within CellsTransport Within Cells

Receptors and LigandsReceptors and Ligands

Binding kinetics, rate constants, endocytosis, Binding kinetics, rate constants, endocytosis, signal transduction, gene expressionsignal transduction, gene expression

Cell attachment and detachmentCell attachment and detachment

Rolling and adhesionRolling and adhesion

Introduction to Bio Heat Introduction to Bio Heat TransferTransfer

Basic conceptsBasic concepts

Conservation of energy equation; thermal Conservation of energy equation; thermal effects; role of Prandtl numbereffects; role of Prandtl number

Heat transfer to blood vesselsHeat transfer to blood vessels

Equilibration lengthsEquilibration lengths

Models of perfused tissues, continuum models, Models of perfused tissues, continuum models, Pennes heat sink model, directed perfusion Pennes heat sink model, directed perfusion model, effective conductivity model, model, effective conductivity model, combination modelscombination models

Parameter valuesParameter values

Solutions of continuum modelsSolutions of continuum models

Treatment of boundary conditionsTreatment of boundary conditions

Vascular geometry generating algorithmsVascular geometry generating algorithms

Solution of coupled tissue-vascular modelsSolution of coupled tissue-vascular models

Statistical interpretationStatistical interpretation

Introduction to Bio Heat Introduction to Bio Heat Transfer (cont’d)Transfer (cont’d)

Applications of Theory Applications of Theory Elasticity in BiomechanicsElasticity in Biomechanics

ExtensionExtension

CompressionCompression

Simple shear of soft tissueSimple shear of soft tissue

Extension and torsion of a papillary muscleExtension and torsion of a papillary muscle

Analysis of stress, strain and deformationAnalysis of stress, strain and deformation

Recommended BooksRecommended Books

(1) Transport Phenomena in Biological Systems by (1) Transport Phenomena in Biological Systems by G.A. Truskey, F. Yuan and D. F. Katz, Pearson G.A. Truskey, F. Yuan and D. F. Katz, Pearson Prentice Hall, 2004.Prentice Hall, 2004.

(2) Biofluid Mechanics—The Human Circulation by (2) Biofluid Mechanics—The Human Circulation by K.B. Chandran, A.P. Yoganathan, and S.E. Rittgers, K.B. Chandran, A.P. Yoganathan, and S.E. Rittgers, Taylor & Francis, 2007.Taylor & Francis, 2007.

(3) Biomechanics: Mechanical Properties of Living (3) Biomechanics: Mechanical Properties of Living Tissues by Y.C. Fung, Second Edition, Springer, Tissues by Y.C. Fung, Second Edition, Springer, 1993.1993.

(4) Biomechanics: Circulation by Y.C. Fung, Second (4) Biomechanics: Circulation by Y.C. Fung, Second Edition, Springer, 1997.Edition, Springer, 1997.

(5) Biofluid Dynamics: Principles and Selected (5) Biofluid Dynamics: Principles and Selected Applications by C. Kleinstreuer, Taylor and Applications by C. Kleinstreuer, Taylor and Francis, 2006. Francis, 2006.

(6) Biofluid Mechanics by J.N. Mazumdar, World (6) Biofluid Mechanics by J.N. Mazumdar, World Scientific, 2004.Scientific, 2004.

Recommended Books (cont’d)Recommended Books (cont’d)

(7) The Fluid Mechanics of Large Blood Vessels by (7) The Fluid Mechanics of Large Blood Vessels by T.J. Pedley, Cambridge Univ. Press, 1980.T.J. Pedley, Cambridge Univ. Press, 1980.

(8) Introduction to Bioengineering by S.A. Berger, W. (8) Introduction to Bioengineering by S.A. Berger, W. Goldsmith and E.R. Lewis, Oxford, 1996.Goldsmith and E.R. Lewis, Oxford, 1996.

(9) Nonlinear theory of elasticity: Applications in (9) Nonlinear theory of elasticity: Applications in biomechanics by L.A. Taber, World Scientific, biomechanics by L.A. Taber, World Scientific, 2004.2004.

(10) Basic Transport Phenomena in Biomedical (10) Basic Transport Phenomena in Biomedical Engineering by R.L. Fournier, Taylor and Francis, Engineering by R.L. Fournier, Taylor and Francis, 2007. 2007.

(11) Introduction to Biofluid Mechanics by P.S. (11) Introduction to Biofluid Mechanics by P.S. Ayyaswamy, Chapter 17 in Fluid Mechanics by P.K. Ayyaswamy, Chapter 17 in Fluid Mechanics by P.K. Kundu and I.M. Cohen, Elsevier, 2008.Kundu and I.M. Cohen, Elsevier, 2008.

(12) Analysis of Transport Phenomena by William M. (12) Analysis of Transport Phenomena by William M. Deen, Oxford, 1998.Deen, Oxford, 1998.