Lecture Notes

ses # TOPICS lecture notes
L1 Introduction/Summary



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
L4 Example Problems: Separation of Variables Method (PDF)


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)
L6 Diffusion/Reaction (cont. from Lecture L3)

plus Add Cell Related (Receptor) Binding


Derivation of Michaelis-Menten Kinetics (PDF)

Green's Functions
a) Amazon logo 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) Amazon logo 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
II. Electrical Subsystem
L8 IGF + E-field and Transport

Maxwell's Equations
L9 Define Potential, Conservation of Charge

L10 Laplacian Solutions via Separation of Variables

Electrical Boundary Conditions, Ohmic Transport and Electrochemical Systems
L11 Charge Relaxation

Electrical Double Layers

Poisson Boltzmann
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)


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

L19 Capillary Electroosmosis-Electrophoresis in MEMs and Microfluidics (PDF)
L20 Streaming Potentials

Begin Electrophoresis
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)