Fall 2007; BME 495
Biomedical Mass Transfer













































Instructor:  Morris  (Link to homepage)
 Phone 274 1802 email: emorris@iupui.edu


Second Instuctor:  Ji
email: jji@iupui.edu












































TA Normandin
email mnormand@iupui.edu












































Room
 SL 216
 Time
 TR, 1:30-2:45pm















































Weekly homework problems:   analytical and numerical
(e.g., with Matlab)



Exams Midterm and final
(dates to be arranged)



Quizes Short, periodic
(announced and  unannounced)



Paper  Short analysis of a scientific paper
that covers biomedical transport and
 uses a mathematical model





Grading: Homework 25%; Exams 2 X 25%;
Paper: 10%; Quizes 5%;
Class Participation: 10%








Primary Texts















































Basic transport in Biomedical
Engineering

 Fournier
 Taylor & Francis













































Partial Differential Eqns for
 Scientists and Engineers

 Farlow
 Dover













































Transport Phenomena In Biological
Systems

 Truskey
 Pearson
 errata.doc
(right click to
download)












































Supplemental Texts















































Mathematical Models in Biology

 Edelstein-Keshet
 SIAM
 errata.pdf





























































































Link to BME 595 syllabus


Link to (some) Transport papers



     
Date   Lecture topics
 Subtopics Reading More reading Homework
23-Aug 0 What is diffusion?  Diffusion as random walk.  Derivation of diffusion in 1D from concept of random walk
 Edelstein-Keshet p450; Truskey p 266-270

Edelstein-Keshet chapt 9, p404-5; Truskey ch 6.5
   derive diffusion equation from ramndom walk in 3dimensions. What is D (diffusivity) in terms of tau and deltaX?

HW1 details
  1 What is mass transfer. Why is heat transfer similar?   Examples of (biomedical) mass transfer: transport through artery wall, through other tissue, modeling of microdialysis proble; design of artifical kidney Middleman M&H Chap 1
Truskey Chap 1
  
  28-Aug
 2 Mathematical warmup - Continuous models (ODEs) growth of microorganisms, bacterial growth in a chemostat, formulating a model, dimensional analysis of the equations Edelstein-Keshet chap 4-4.5   HW 2: read Fournier Chap 1, and do problems 10, 12 from Chap 1
  30-Aug
 3 Math warmup (cont) Solving engineering problems, Material Balances Species balances, mass balances Fournier chap 1.4  
  4-Sept
 4 Introduction to Diffusion Derivation of conservation equation, conservation of mass, ID diffusion, anisotropic media Middleman M&H Chap 2; Crank ch 1  
  4-Sept
 5 Mathematical intro to PDEs and the diffusion equation
Farlow lesson 1 & 2  
  6-Sept
 6 1-D diffusion with variable cross-section Fick's law in 1D, 2, 3. Gradient, DIvergence Edelstein-Keshet chap 9
Truskey 6.7.2
   HW 3. Extend derivation of diffusion in varying cross section to explain RADIAL diffusion in spherical coordinates
 11-Sept
 7 Review Fournier HW
Boundary conditions
Heat/mass anaologies

  Dirichlet condition, Neuman condition

 Farlow lesson 1 & 2

  
  13-Sept
 8 Derivation of heat equation, conservation of heat
Incropera?  
  9 Separation of Variables, transforming nonhomgeneous BCs into homogeneous ones   Farlow lesson 5, 6  
  10 Diffusion-reaction equations Danckwert's transformation Crank chap 14;   
  11 Diffusion-convection, attraction chemotaxis Edelstein-Keshet 9.8, 9.9  Laufenbuger ch 6 p302-318  
  12 More math: how to transform a diffusion-convection equation into the diffusion eqn   Farlow lesson 8  
  13 Laplace transforms   Farlow lesson 13  
  14 Applications: mass transfer in the artery, design of artificial kidney   Patel Ch 10; Middleman chap 3.3  
  15 Transport through a membrane; properties of cell membranes quasi-steady approximation Truskey p 317; Fournier chap 3  
  16 Michaelis-Menten kinetics  another use of the quasi-steady approximation Edelstein-Keshet ch 7.2  
  17 Unsteady state mass transfer sustained release drug delivery Middleman M&H chap 4  
  18 Diffusion with laminar convection 1 artificial kidney    
  19 Diffusion with laminar convection 2      
  20 Diffusion with laminar convection 3      
  21 Diffusive-convective systems
 modeling arterial wall  transport of proteins Truskey chap 7.1-7.3
   Tedgui and Lever Circ Res. 1985

Guide for reading paper
  22 Model of capillary transport; flow and exchange in the capllary bed Krogh cyllinder' Fournier chap 5; Jacquez chap 10; Truskey ch 13.5  
  23 Transport of Ions Nernst-Planck equation Keyner and Sneyd p52-56, 83-89  
  24 Compartmental models   Truskey chap 16  
  25 Physiologically based pharmacokinetic models   Truskey chap 16  
  26 Numerical Methods Dynamic systems of ODEs, Euler, Runge-Kutta Dunn chap 7, Farlow Lessons 37-40  
  27 Numerical Methods 2 Numerical Stability Dunn chap 7, Farlow Lessons 37-40  
  28 Numerical Methods 3 Systems of PDEs, Finite Differences, computational models, implicit, explicit methods Dunn chap 8  
  29 Special Topics 1 - Chemotaxis
 TBA TBA   Lee, Saidel, Penn Paper

Study Guide for Lee et al.
  30 Special Topics 2 TBA TBA  
  31 Special Topics 3 TBA TBA  
  32 Special Topics 4 TBA TBA  
  33        
  34        

35

36

37


site updated by EDM 6:30pm Sept 6.