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6.561

Fields, Forces, and Flows in Biological Systems

Graduate · Historical course

Fall 2015

Topics

  • Course introduction, overview, and objectives
  • Introduction to random processes; Boltzmann distribution and statistical thermodynamics
  • Diffusion as a random walk; Stokes-Einstein relation for diffusion coefficient
  • Constitutive equations for diffusion (Fick’s Laws); Conservation of mass for a control volume; Differential form; Steady diffusion (1D); Boundary conditions
  • Diffusion and reaction; Reaction rates, order, molecularity and mechanisms; Scaling and the Damköhler number; Solution procedures
  • Examples of diffusion-reaction: Diffusion of a ligand through tissue with cell receptor-ligand interactions; Diffusion-reaction kinetics
  • Case study: IGF-1 diffusion-reaction within tissues and cell seeded scaffolds; binding to IGF binding proteins & cell surface receptors; experimental methods
  • E-fields and transport; Maxwell’s equations
  • Define electrical potential; conservation of charge; Electro-quasistatics
  • Laplacian solutions via Separation of Variables; Electric field boundary conditions; Ohmic transport; Charge Relaxation; Electrical migration vs. chemical diffusive fluxes
  • Electrochemical coupling; Electrical double layers; Poisson–Boltzmann Equation
  • Donnan equilibrium in tissues, gels, polyelectrolyte networks
  • Charge group ionization & electro-diffusion-reaction in molecular networks
  • Case study: Charged protein transport in charged tissues & gels; Donnan partitioning, diffusion-reaction in extracellular matrix; experimental methods
  • Conservation of mass and momentum in fluids; convective solute transfer
  • Viscous stress-strain rate relations; Navier–Stokes equations
  • Low Reynolds number flows; Stokes equation; Scaling and dimensional analysis
  • Newtonian, fully developed low Reynolds number flows
  • Diffusion and convection; The Peclet number; Convection-diffusion-reaction and boundary layers
  • Concentration boundary layers: Fully-developed flow and transport
  • Capillary electroosmosis: Theory and experiments
  • MEMs, microfluidics + electrokinetics, cells and hydrogels; (with guest lecture)
  • Electrophoresis, chromatography and extracellular matrix biochemistry
  • DLVO theory: Double layer repulsion and molecular interactions (proteins, DNA, GAGs)
  • Porous media flows: Extracellular and intracellular
  • Cell / molecular electrokinetics; review of term paper project

Readings

Sources