Epilepsy as a dynamic disease: Musings by a clinical computationalist

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Epilepsy as a dynamic disease Musings by a
clinical computationalist

• John Milton, MD, PhD
• William R. Kenan, Jr. Chair
• Computational Neuroscience
• The Claremont Colleges

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Computational neuroscience?
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Variables as a function of time
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Differential equations

• hypothesis
• Prediction

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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.

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Scientific Method

• Math/computer modeling
• Make better predictions
• Make better comparisons between observation and
  prediction
• In other words, essential scientific tools to
  enable science to mature

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Inputs and outputs

• Measure outputs in response to inputs to figure
  out what is inside the black box

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Linear black boxes
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Neurons behave both as linear and nonlinear black
boxes

• Linear aspects
• Graded potentials at axonal hillock sum linearly
• Nonlinear aspects
• Action potential
• Problem
• Cannot solve nonlinear problem with paper and
  pencil
• Qualitative methods

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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

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Qualitative theory pictorial approach

• Potential, F(x), where

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Potential surfaces and stability
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Cubic nonlinearity Bistability
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Success story of computational neuroscience
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Ionic pore behaves as RC circuit

• Membrane resistance
• Value intermediate between ionic solution and
  lipid bilayer
• Value was variable
• Membrane noise
• shot noise

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Dynamics of RC circuit
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Hodgkin-Huxley equations
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HH equations (continued)

• Linear membrane hypothesis
• So equation looks like
• Problem g is a variable not a parameter

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Ion channel dynamics

• Hypothesis

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HH equations

• Continuing in this way we obtain

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Still too complicatedFitzhugh-Nagumo equations
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Graphical method Nullcline

• V nullcline
• W nullcline

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Neuron Excitability
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Neuron Bistability
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Neuron Periodic spiking
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Neuron Starting stopping oscillations
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Dynamics and parameters

• Dynamics change as parameters change
• Not a continuous relationship
• Bifurcation Abrupt qualitative change in
  dynamics as parameter passes through a
  bifurcation point

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The challenge ..
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A -gt B -gt C -gt D -gt ?
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Is the anatomy important?
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What should we be modeling?
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Are differential equations appropriate?

• 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

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Fundamental problem

• Models

• Measurements

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Need for interdisciplinary teams

• Questions like these can only be answered using
  scientific method
• Epilepsy physicians are the only investigators
  who legally can investigate the brain of
  patients with epilepsy