Epilepsy as a dynamic disease: Musings by a clinical computationalist

1. Epilepsy as a dynamic disease: Musings by a clinical computationalist John Milton, MD, PhD William R. Kenan, Jr. Chair Computational Neuroscience The Claremont Colleges

2. Computational neuroscience?

3. Variables as a function of time

4. Differential equations = hypothesis = “Prediction”

5. Variables versus parameters • Variable: Anything that can be measured • Parameter: A variable which in comparison to other variables changes so slowly that it can be regarded to be constant.

6. Math/computer modeling Make better predictions Make better comparisons between observation and prediction In other words, essential scientific tools to enable science to “mature” Scientific Method

7. Inputs and outputs • Measure outputs in response to inputs to figure out “what is inside the black box”

8. Linear black boxes

9. Linear aspects Graded potentials at axonal hillock sum linearly Nonlinear aspects Action potential Problem Cannot solve nonlinear problem with paper and pencil Qualitative methods Neurons behave both as linear and nonlinear black boxes

10. Qualitative theory of differential equations • Consider system at equilibrium or steady state • Assume for very small perturbations systems behaves linearly • “If all you have is a hammer, then everything looks like a nail”

11. Qualitative theory: pictorial approach • Potential, F(x), where

12. Potential surfaces and stability

13. Cubic nonlinearity: Bistability

14. Success story of computational neuroscience

15. Ionic pore behaves as RC circuit • Membrane resistance • Value intermediate between ionic solution and lipid bilayer • Value was variable • Membrane noise • “shot noise”

16. Dynamics of RC circuit

17. Hodgkin-Huxley equations

18. HH equations (continued) • “Linear” membrane hypothesis • So equation looks like • Problem: g is a variable not a parameter

19. Hypothesis Ion channel dynamics

20. HH equations • Continuing in this way we obtain

21. Still too complicated:Fitzhugh-Nagumo equations

22. V nullcline W nullcline Graphical method: Nullcline

23. Neuron: Excitability

24. Neuron: Bistability

25. Neuron: Periodic spiking

26. Neuron: Starting & stopping oscillations

27. Dynamics change as parameters change Not a continuous relationship Bifurcation: Abrupt qualitative change in dynamics as parameter passes through a bifurcation point Dynamics and parameters

28. The challenge …..

29. A -> B -> C -> D -> ?

30. Is the anatomy important?

31. What should we be modeling?

32. Physical Science Neurodynamics Neurons are “pulse-coupled” Such models meet requirement for low spiking frequency Models are not based on differential equations but instead focus on spike timing Are differential equations appropriate?

33. Models Measurements Fundamental problem

34. Questions like these can only be answered using scientific method Epilepsy physicians are the only investigators who legally can investigate the brain of patient’s with epilepsy Need for interdisciplinary teams