Mark Kramer, Boston University “Multi-scale Seizure Dynamics”iacs-courses.seas.harvard.edu/.../kramer...31513.pdf · Mark Kramer, Boston University “Multi-scale Seizure Dynamics”

Mark Kramer,Boston University

“Multi-scale Seizure Dynamics”Pre-Seminar Talk

Ariana MinotMarch 15, 2013

• Building brain functional networks

• Bridging multiscale brain activity

• Neuronal dynamics & mathematics

Research

http://math.bu.edu/people/mak/research.html

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

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.

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

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

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

Challenges, Conclusions, & Open Questions

• 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?

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?

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

Thanks!

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/