L1

Introduction/Summary

Examples

(PDF)

Handouts

Overheads (PDF - 1.6 MB)

I. Chemical Subsystem

L2

Continuity of Chemical Species, Flux, Reaction Rates, Boundary Conditions

(PDF)

L3

Diffusion

Begin Reaction

Damkohler #

Scaling and Approximations

(PDF)

L4

Example Problems: Separation of Variables Method

(PDF)

Handouts

Overheads on IGF-I Transport (PDF)

L5

Example Problems: Separation of Variables Method (cont.)

Case Study: IGF Problem from Lecture L1 using Matrix Continuum Distribution of IGF Binding Proteins

Numerical Considerations (if time)

(PDF)

L6

Diffusion/Reaction (cont. from Lecture L3)

plus Add Cell Related (Receptor) Binding

(PDF)

Handouts

Derivation of Michaelis-Menten Kinetics (PDF)

Green's Functions
a)  Section 13-12, "Nonhomogeneous Boundary-Value Problems." In Ritger, P. D., and N. J. Rose. Differential Equations with Applications. Mineola, NY: Dover Publications, 2000. [reprint of 1967 edition]. ISBN: 9780486411545.

b)  Hildebrand, F. B. Problems 56-59 in Advanced Calculus for Applications. Upper Saddle River, NJ: Prentice-Hall, 1976. ISBN: 9780130111890.

L7

Diffusion/Reaction (cont.)

Examples of Numerical Approaches to Nonlinear Problems

(PDF)

II. Electrical Subsystem

L8

IGF + E-field and Transport

Maxwell's Equations

(PDF)

L9

Define Potential, Conservation of Charge

Electroquasistatics

(PDF)

L10

Laplacian Solutions via Separation of Variables

Electrical Boundary Conditions, Ohmic Transport and Electrochemical Systems

(PDF)

L11

Charge Relaxation

Electrical Double Layers

Poisson Boltzmann

(PDF)

L12

Donnan Equilibrium in Tissues, Gels, Polyelectrolyte Networks

(PDF)

L13

Charge Group Ionization and Electro-diffusion Reaction in Molecular Networks

(PDF)

III. Cellular Applications

L14

Experimental Methods

L15

Ligand Binding to Cell Receptors

(PDF)

L16

Diffusion in Heterogeneous Media

(PDF)

Handouts

PI3K Activation Diagram (PDF)

III. Mechanical Subsystem; Electromechanical Case Studies

L17

Conservation of Mass and Momentum in Fluids

(PDF)

L18

Newtonian, Fully Developed Low Reynold's Number Flows

Examples

(PDF)

L19

Capillary Electroosmosis-Electrophoresis in MEMs and Microfluidics

(PDF)

L20

Streaming Potentials

Begin Electrophoresis

(PDF)

IV. Mechanical, Electrical and Physicochemical Interactions: Integrative Case Studies

L21

Convective Solute Transport

(PDF)

L22

Hindered Transport in Membranes and Tissues

(PDF)

L23

Coupled Fluid and Electrical Shear Stresses: Cell/Molecular Electrophoresis

(PDF)

L24

Convective and Charge Relaxation Effects in Double Layers: Electrokinetics

(PDF)

L25

DLVO Theory - Double Layer Repulsion and Molecular Interactions (Proteins, DNA, GAGs)

(PDF)

L26

Tissue/Molecular Swelling Stresses: Donnan (Macro) vs. Poisson Boltzmann (Nano)

(PDF)

R1

Molecular Transport and Mass Transport (PDF)

R2

Linear Operator Theory and Eigenfunction Expansion (PDF)

R3

Green's Functions (PDF)

R4

Electro-Quasi-Statics (EQS) (PDF)

R5

Electrochemical Subsystem (PDF)

R6

Urinary Tract Infection Problem (PDF)

Urinary Tract Infection Answer Summary (PDF)

Final Review 2003 (PDF)

Final Review 2004 (PDF)

Homework 1 (PDF)

Hints (PDF)

(PDF)

Homework 2 (PDF)

(PDF)

Homework 3 (PDF)

(PDF - 1.1 MB)

Homework 4 (PDF)

(PDF)

Homework 5 (PDF)

(PDF)

Homework 6 (PDF)

(PDF)

Homework 7 (PDF)

(PDF)