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Epilepsy as a dynamic disease: Musings by a clinical computationalist

Join Dr. John Milton, a computational neuroscience expert, as he explores the dynamic nature of epilepsy through the lens of clinical research. From the use of differential equations to model variables and parameters to the challenges of understanding neuron dynamics, this thought-provoking discussion sheds light on the complexities of epilepsy and the need for interdisciplinary teamwork.

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Epilepsy as a dynamic disease: Musings by a clinical computationalist

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  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

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