Mark Kramer, Boston University “Multi-scale Seizure...
Transcript of Mark Kramer, Boston University “Multi-scale Seizure...
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Mark Kramer,Boston University
“Multi-scale Seizure Dynamics”Pre-Seminar Talk
Ariana MinotMarch 15, 2013
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• Building brain functional networks
• Bridging multiscale brain activity
• Neuronal dynamics & mathematics
Research
http://math.bu.edu/people/mak/research.html
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Seizure Terminology• What is a seizure? Disruption of the brains’s electrical activity
• epileptic
• non-epileptic
• What are stages of a seizure?
• ictal: in seizure, postictal: right after a seizure
• How do we detect/measure seizures?
• EEG: electroencephalography
• Brain activity is very active during a seizure
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Critical Transitions• Critical point is parameter at which a system changes behavior. Bifurcation is
a qualitative change that occurs in the nature of a solution when a parameter passes through a critical point.
• Cute example from math
• εx5- x +1 = 0
• lim ε➝0: x ~ -1, ε1/411/4
• (3 real roots, 2 imaginary)
• lim ε➝∞: x ~ ε1/5(-1)1/5
• (1 real roots, 4 imaginary)
• ∃ ε* dividing these two regimes. This is the critical point.
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What properties of a network cause it to have tipping points?
• Positive feedback mechanism
• heterogeneity & connectivity of components
• types of interactions between components
Driven by environment (more) robust ... till pushed to critical
point
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How can we tell if a network is near a critical point?
1. Critical slowing down
• Critical slowing down near tipping points: the rate at which a system recovers from small perturbations becomes very slow
• Slowing down can be inferred indirectly from increased variance and higher lag-1 autocorrelation slow recovery ratefast recovery rate
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How can we tell if a network is near a critical point?2. Flickering
• Useful for indicating highly stochastic systems near critical point
• flickering: noise causes bistable system to oscillate between two alternative attractors
• Detect flickering via increase in variance
• Study how distribution of states taken on by system changes with time to infer potential landscape
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Challenges, Conclusions, & Open Questions
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• By crossing a bifurcation causing the system to shift to an alternative attractive regime
• Evidence?
• 1. Measurements of electrical activity in brain demonstrates signature of impending critical transistion - critical slowing down and flickering.
• 2. Simulation using computational model with ictal and postictal as alternative stable attractors reproduce this behavior.
How do seizures spontaneously terminate?
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I. Evidence of critical transitions behavior from measurements
• Collect data using various different techniques to measure brain electrical activity in different parts of the brain and at different scales
• Population results vs MUA data
• MUA data at smallest spatial scale
Slowing/chirp?
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I. Evidence of critical transitions behavior from simulation
• mean-field model: simulate population of neurons rather than a single neuron
• What’s a neuron?
• biomechanical mechanism: strengthening of excitatory synapses
• dynamic mechanism: strengthening connectivity
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Thanks!
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References
• http://en.wikipedia.org/wiki/Electroencephalography
• http://en.wikipedia.org/wiki/Ictal
• http://hopf.chem.brandeis.edu/yanglingfa/pattern/rd/LN_Bifurcation.pdf
• http://isites.harvard.edu/fs/docs/icb.topic984197.files/