Actions

• 2007-01-21: make a quick report of everything I've done relevant to the project so far.
• 2007-01-21: sent Natalia an email
• 2007-01-23: waiting for a reply from Natalia
• --: change the code so that there is no speed penalty for forward euler methods
• --: put the IM cod in memfem
• --: do a literature search for the paper
• --: fill out ResearchChecklist for this project.

Reference

I have a code that can solve the ionic models

Ran some 0D simulations to get the differences in running times between the two codes. Haven't compared the old code forward euler to the new code forwark euler in an actual simulation.

Ran some psuedo 2D simulations to study the effects of shocks on the new ionic model solvers.

Havent' tested adaptive integration routines.

Prepared graph illustrating poor conditioning of problem from the eigenvalues. Havent' analized conditioning after removal of the gating equations.

Haven't convinced myself that the substitution we do on the gating variables is valid, nor have I verified stability regions.

Havent' tested predictor corrector.

Havent' tried converting calcium dynamics into differential equations, comparing those equations

Haven't fixed that one second differentiation into the rest of the system.

Things still left to do:

• recieve email from Ed about accuracy of ionic models.
• run 0D simulations, study the effects.
• run 2D shock, study stability, conduction velocity, etc.
• clean up slides on CEPTalk, make them relevant to our simulation.
• graph jacobian over time, prepare figure.
• add Slava's calcium changes to aLRd, see if they have any effect.
• use operator splitting for the differential variables, see if that improves the conditioning of the system.
• test with lookup tables.

Format of final project:

• introduction to cardiac electrophysiology
• ODE system and complexity
• description of equations
• why DAE isn't applicable.
• conditioning of the equations
  • figure of stiffness here
• convergence studies of explicit methods:
  • Euler's method
  • RK2
  • RK4
• implicit methods
• automatic differentiation - what and why
• Backwards Euler
• Trapezoid
• Simulation results in actual shock experiments

-- RobBlake - 08 Dec 2006