1. Hybrid Automata as a Unifying Framework for Modeling Excitable Cells
Radu Grosu Computer Science SUNY at Stony Brook
Aaa
Group: S.A. Smolka (CS), E. Entcheva (BME), P. Ye (CS) and M. True (CS)

2. Background
Excitable cells: neurons, cardiac myocytes, skeletal muscle cells.
Traditionally modeled by complex systems of nonlinear ODEs/PDEs.
Highly accurate but highly compute-intensive.
The other extreme are cellular automata.
Highly efficient, purely discrete models but fail to capture essential cell characteristics.

3. Research Goals & Results
Hybrid automata are a mixture of discrete and continuous systems.
Our results show that HA can be used to efficiently model excitable cell types while preserving essential characteristics (AP morphology, response to pacing.)
HA model exhibits nearly 10-fold speedup in simulation of 400 x 400 cell network.
HA models amenable to formal analysis.

4. Mathematical Models Hodgkin-Huxley (HH) model Luo-Rudy (LRd) model
Membrane potential for squid giant axon
Developed in 1952
Framework for the following models
Luo-Rudy (LRd) model
Model for cardiac cells of guinea pig
Developed in 1991
Neo-Natal Rat (NNR) model
Under development by E. Entcheva et al. (Stony Brook)

5. Action Potential & HA Template
Stimulated
Caused by ion fluxes:
- inward: Na+, Ca2+,
- outward: K+

6. HA for NNR Model

7. Simulation for NNR Model
Single cell, single AP
3 APs on a 2*2 cell array

8. Large-Scale Spatial Simulation for NNR Model
Re-entry on a 400*400 cell array

9. Performance Comparison
Run on a Pentium® 4 CPU 3.00GHz, 1G Memory machine