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Efficient Modeling of Excitable Cells Using Hybrid Automata Radu Grosu SUNY at Stony Brook

Efficient Modeling of Excitable Cells Using Hybrid Automata Radu Grosu SUNY at Stony Brook. Joint work with Pei Ye, Emilia Entcheva and Scott A. Smolka. Background. Excitable cells Neuron Cardiac Cells Different concentrations of ions inside and outside of cells form:

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Efficient Modeling of Excitable Cells Using Hybrid Automata Radu Grosu SUNY at Stony Brook

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  1. Efficient Modeling of Excitable Cells Using Hybrid AutomataRadu GrosuSUNY at Stony Brook Joint work with Pei Ye, Emilia Entcheva and Scott A. Smolka

  2. Background • Excitable cells • Neuron • Cardiac Cells • Different concentrations of ions inside and outside of cells form: • Trans-membrane potential • Ion currents through channels across the cell membrane

  3. Na+ Na+ Ca2+ K+ Na+ K+ Ca2+ Ca2+ K+ Na+ K+ Na+ Na+ Na+ K+ Ca2+ Ions and Channels of Excitable Cells Cell channel Cell

  4. Caused by positive ions moving in and then out of the cell membrane. 5 stages Resting Upstroke Early Repolarization Plateau Final Repolarization Action Potential (AP)

  5. Restitution Property • Excitable cells respond to different frequency stimuli. • Each cycle is composed of: • Action Potential Duration (APD) • Diastolic Interval (DI) • Longer DI, longer APD

  6. Restitution Property

  7. Mathematical Models • Hodgkin-Huxley (HH) model • Membrane potential forsquid giant axon • Developed in 1952 • Framework for the following models • Luo-Rudy (LRd) model • Model forcardiac cells of guinea pig • Developed in 1991 • Neo-Natal Rat (NNR) model • Being developed in Stony Brook University by Emilia Entcheva et al.

  8. Hodgkin-Huxley Model • C: Cell capacitance • V: Trans-membrane voltage • gna, gk, gL: Maximum channel conductance • Ena, Ek, EL: Reversal potential • m, n, h: Ion channel gate variables • Ist: Stimulation current

  9. Circuit for Hodgkin-Huxley Model C gna gK gL V EK EL Ena

  10. Hybrid Automata (HA) • Variables • Control Graph • Modes • Switches • Init, Inv and flow • Jumps and Actions • Events

  11. Two Ways of Abstraction • Rational method: derive the flow functions from the differential equations in the original model • Empirical method: use curve-fitting techniques to get the flow functions with the form chosen (here we use the form ).

  12. General HA Template • 4 control modes: • Resting and Final repolarization (FR) • Stimulated • Upstroke • Early repolarization (ER) and Plateau • Threshold voltage monitoring mode switches • Vo, VT and VR • Event VS represents the presence of stimulus

  13. HA for HH Model

  14. Simulation of HH Model

  15. New Features of HA for LRd and NNR Model • Adding vz to enrich modeling ability • Using vn to remember the current voltage when the next stimulus is coming. • Define , , determines the time cell stays in mode ER and plateau • Thus, APD will change withDI • For NNR model, define and , thus the threshold voltages are also influenced by DI.

  16. HA for LRd Model

  17. HA for NNR Model

  18. Simulation for LRd Model

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

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

  21. Performance Comparison

  22. Future Work • Using Optimization techniques to derive the parameters for HA model automatically. • Develop simpler spatial model to further improve efficiency.

  23. Thank you 04/05/2005

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