| 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: 0486411540.
b) Hildebrand, F. B. Problems 56-59 in Advanced Calculus for Applications. East Rutherford, NJ: Prentice-Hall, 1976. ISBN: 0130111899. |
| 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) |