- Introduction (Nancy Griffeth)
- The Secret Life of Chaos (video)
- Excitable Systems (Flavio Fenton)

- Spiral Waves and Modeling Action Potentials (Flavio Fenton)
- Saline Density Oscillator (Rupinder Singh)
- Pictures of the Saline Oscillator in the Lab

- Simplified Models of Cardiac Action Potentials (Flavio Fenton)
- Pictures of Oscillations in Fluids in the Lab

- More Complex Cardiac Models (Flavio Fenton)
- Robert Gilmour Lecture

- The 3V and 4V Models (Flavio Fenton)
- Pictures of whiteboard

- Modeling (Nancy Griffeth)
- Octave (Nancy Griffeth)
- Reference Card
- Fitzhugh-Nagumo code (Monday's class exercise)
- Comments on code

- Differential Equations (ppt) (Terri Grosso)
- Differential Equations (pdf) (Terri Grosso)
- Numerical Integration (Kai Zhao)
- Numerical Integration Tutorial

Snow-day reading (if necessary):

- Wikipedia Article on Parallel Computing: This article gives a lot of motivational information and information about various approaches to parallel computing. It touches on the CUDA architecture briefly in its discussion of GPGPU, in the section on Specialized Parallel Computers (section 3.2.4). The hardware that we'll use is GPGPU.
- A good simple tutorial on parallel programming: Takes you from basic organization, through parallel computing, including some terminology that should help when the folks that do a lot of parallel computing start talking.
- Basic tutorial for cuda (start with supercomputing for the masses part 2): This is how your introductory lecturer, Joshua Rogers, learned about CUDA.
- In-workshop introduction to GPGPU and CUDA (Joshua Rogers)
- Performance of Parallel Systems (Ezio Bartocci)

- A CUDA performance demonstration: We modified the program you played with today in class to run through a range of matrix and block sizes and output the result in a .csv file.
- The 4V Model (Ezio Bartocci)
- A Matlab/Octave version of the 4V model: You will also need the Heaviside function

- CUDA files observing a cable of cells (unzip to edit and compile; aligned and not_aligned must be run on a CUDA computer)

Octave application for plotting data from above file- The first parameter is the path to the data file. The second parameter is the number of cells in the cable (nx=1024). The third is the time (between 1 and sim_time=10000).

or this one.

- Look at Applets at theVirtualHeart.org
- Cell Dynamics

Fitzhugh-Nagumo: http://thevirtualheart.org/java/fhn25.html

See what alpha, beta, gamma do - 2D Dynamics

Fitzhugh-Nagumo: http://thevirtualheart.org/java/2dfhn.html

To get a spiral, "Start" then "Reset h"

Change parameters very slowly to see what happens

For example, change eps from 0.01 to 0.011 or 0.009

Too much of a change will not render a continuous spiral wave - What are the potential tip trajectory shapes and names of shapes
- Review the relationships between parameters and shapes in the file below:
- Some results for spiral tip trajectories when changing parameters
- Also, a note from Flavio: Below is a very nice paper, a bit mathematical but shows very nicely how two parameters can set a large variety of spiral trajectories and explains using the two frequencies what is happening to the system.
- http://chaos.utexas.edu/manuscripts/1064255172.pdf

- The hybrid automaton and parameter values
- The above figures are from a recent paper by Grosu, Fenton, Glimm, Smolka, Bartocci, and others.

- Instructions for storing data on flash drives
- Parameters for each group to test

- Creating spiral wave tip trajectories on our CUDA supercomputers ("David" and "Goliath")

- Student presentations on tip trajectories
- Model checking (Scott Smolka)