Multiscale Modeling of Brain Dynamics

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Multiscale Modeling of Brain Dynamics

• Peter Robinson
• School of Physics, University of Sydney
• Brain Dynamics Center, Westmead Hospital
• University of Sydney
• Faculty of Medicine, University of Sydney
• Supported by the ARC and NHMRC.

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Kevin AquinoHomi Bahramali Matt Barton Lindsay
Botha Paul Bourke Michael BreakspearParry Chen
Po-Chia Chen Alan Chiang Jonathon Clearwater
Nick CooperTim Cooper Peter DrysdaleBen
FulcherCandy FungBiljana Germanoska Evian
Gordon Stuart GrieveRon Grunstein
Collaborators
Alex Guinaudeau Rebecca Hamilton James
Henderson Hal Henke Jackie Huber Kim
Kaufmann Cliff Kerr Jong-Won Kim Krzysztof Kozak
Anthony Krensel Andrew Layden Belinda Liddle
Peter Loxley Neil Mahant Elie Matar Suzanne
OConnor Andrew Phillips Rebecca Powles
Chris Rennie Michelle Rigozzi Peter Riley James
Roberts Naomi Rogers Donald Rowe Sacha van
Albada Helena van der Merwe Rebecca
Whitehouse Lea Williams Keith Wong Jim
Wright Hui-Ying Wu
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The Big Picture
behavioral outputs
stimuli
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Measurement what, why, how?
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Integration
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A First-Cut Model Working Brain

• Responds to stimuli, diurnal,
• circadian drives. Arousable.
• Reproduces EEG, fMRI, etc.
• Incorporates neuromodulation
• and simple behavioral
• feedbacks.
• Starting point for further
• development.
• Framework for integration
• unification.

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Modeling

• We use a continuum model at scales of 0.1 mm to
  whole brain
• Retains key anatomy and physiology at multiple
  scales.
• Cortex approximated as 2D.
• Include corticothalamic connections (plus others
  later).
• Average over scales below about 0.1 mm (1000
  neurons).
• Seek partial differential equations for
  continuum fields.
• Such models date from 1950s on Beurle, Nunez,
  Wilson, Cowan, Lopes da Silva,
• Freeman, Wright, Liley, Jirsa, Haken,
  Steyn-Ross, Sydney group, Coombes, others.

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Neurons

• Excitatory (e) neurons excite others.
• Inhibitory (i) neurons suppress others.
• Inputs thru synapses on dendrites.
• Firing triggered at axonal hillock.
• Outputs via axon synaptic terminals.
• e.g., Cortex contains
• Long-range (several cm) excitatory neurons.
• Mid-range (several mm) excitatory neurons.
• Short-range (lt 1 mm) excitatory neurons.
• Short-range (lt 1 mm) inhibitory neurons.

Axonal hillock
Kandel, Schwartz, Jessell (2000)
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Synapses and Dendrites

• Incident neurons transmit chemical
• signals to dendrites at synapses.
• Chemical neurotransmitters are
• released into the synaptic cleft, changing
  postsynaptic potential.
• Synaptic dynamics and dendritic
• propagation smear signals over
• 1-100 ms at the cell body.

Nolte (2002)
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Cell Body

• Cell body potentials Va approximately obey
• ?ab mean activity from neural type b.
• sab mean strength of connections.
• Nab mean number of connections.

• Single cell response has a nonlinear
• threshold firing rate behavior.
• Sigmoidal when averaged over a
• population
• Qa (Va) Sa(Va).

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Axonal Propagation

• Activity spreads in a wavelike fashion with
  velocity vab and mean range rab.
• Approximate using a damped wave equation
• ? ab vab / rab damping rate.

• The propagator ?ab(0)(r,t) is the solution to
• this equation for a ?-function input.
• Spatial part (effectively nonlocal)

Braitenberg Shüz (1998)
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The Model

• Our equations form a closed nonlinear set,
  parametrized
• physiologically

Activity fields ?ab
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Steady States, Response Properties

• Setting gives uniform
  nonlinearly determined steady states.
• 2 stable steady states low-?e (normal) and
  high- ?e (seizure).
• Only the seizure state survives at high
  stimulation levels.
• Linear perturbations yield EEG spectra and ERPs.
• Clarify links to physiology.

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Coherence, Time Series, Stability
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Brain Resource International Database

• Brain Resource Ltd.
• Spinoff 2001, ASX listed.
• Approx. 40M market cap.
• Database of circa 30 000 subjects, aged 6-80.
• Approx. 50 functional measures per subject MRI.
• Excellent statistics.
• Customers and labs in circa 10 countries.
• 1st fully standardized international brain
  function database.
• Access via BRAINnet.

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Inversion

• Fitting predictions to data yields best estimates
  of parameters for individuals

• Can map parameters and combine consistently with
  other measures

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Absence Seizures
Fz (µV)
?e (s-1)

• Linear instability at 3 Hz.
• Ramping ?se up and down yields start and end of
  spike and wave oscillations via supercritical
  Hopf bifurcation.

Time (s)
Time (s)
Frequency (Hz)
Frequency (Hz)
Time (s)
Time (s)
Fz (µV)
?e (s-1)
Time (s)
Time (s)
2
?e (s-1)
Fz (µV)
1
?e (s-1)
?se
Time (s)
Time (s)
?(t-t)
?(t-t)
?(t)
?(t-2t)
?(t-2t)
?(t)
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Ocular Dominance and Orientation Preference

• Orientation preference (OP) varies with
• position in each OD band.
• Singularities, or pinwheels, occur mostly
• near OD band centers.
• V1 is tessellated into hypercolumns
• boundaries nonunique.
• Each hypercolumn corresponds to
• a visual field (VF).

Kandel, Schwartz, Jessell (1995)
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Gamma Oscillations, Binding

• Scenes are analyzed via several
  feature-sensitive paths.
• How are these aspects bound into one percept?
• Firing of simultaneously stimulated cells in the
  visual
• cortex is highly correlated over many mm.
• Correlation functions (CFs) usually peak at T0,
  even
• when large conduction delays exist.
• CFs are highest for nearby cells with similar
  feature
• preference.
• Do gamma oscillations reflect or mediate
• binding, or are they epiphenomena?

Engel, Konig, Kreiter, Schillen, Singer (1992)
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Gamma Resonances from Patchy Propagators

• Use of patchy propagators yields new transfer
  functions and spectra.
• Waves obey Schroedinger equation.
• Resonances at and gamma
• frequencies.

P(k,?)
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Gamma Correlations

• Peak at T0. Spatial and temporal extents
• consistent with data.
• 1 long bar crossing different VFs produces a
• stronger correlation than 2 separate short bars.
• Consistent with summation over stimuli and
• infill of missing contours

Dworetzky (1994)
Engel, Konig, Kreiter, Schillen, Singer (1992)
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Scene Segmentation
S1S2

• Conflicting stimuli presented to 4 sites
• 1 and 2 have vertical OP.
• 3 and 4 have horizontal OP.
• Correlations segment the scene into objects.
• Correlations between groups destroyed.
• Theory explains this effect via superposition

S1
S2
S3
Engel, Konig, Singer (2002)
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Arousal Dynamics

• How does the brain move between arousal states?
• Develop and apply a quantitative,
  physiologically-based model of arousal dynamics,
  with parameters from experiment.
• Brainstem ascending arousal system must be
  integrated, plus circadian oscillations.
• Physiological Modeling and Parameter Constraints

• Diffusely projecting brainstem nuclei
• control sleep-wake cycle
• MA (monoaminergic)
• ACh (cholinergic)
• Circadian (C) and Homeostatic (H)
• drives integrated in VLPO
• Mutual MA-VLPO inhibition gives
• flip-flop behavior
• Mean ACh and ORX inputs included

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Model Dynamics

• Neuronal population modeling
• predicts mean voltages Vi and
• firing rates Qi.

• Physiology dynamics constrain parameters via a
  few experiments.
• Dynamics accords with experiment

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Orexin, Narcolepsy, and Modafinil

• Orexin group has input to the MA group.
• Reducing this results in smaller hysteresis
  loop age, narcolepsy.

• Stability of wake and sleep states reduced.
• Modafinil pharmacokinetics imply stronger MA
  input
• This restores hysteresis loop antinarcoleptic.

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A First-Cut Model Working Brain

• Responds to stimuli, diurnal,
• circadian drives. Arousable.
• Reproduces the range of
• results discussed others.
• Incorporates neuromodulation,
• simple behavioral feedback.
• Starting point for further
• development, detailed analysis
• of subsystems.
• Framework for integration
• unification.
• Basal ganglia being incorporated.

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fast
slow
macro
imaging intracellular
micro
basic features
fine detail
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Summary

• Our continuum model tractably includes many
  features of neurophysiology, anatomy,
  measurement, and behavior from the microscale up.
• Unifies many phenomena across scales.
• Provides an approximate framework for
  interrelating observations.
• Parameters lie in physiological ranges.
• Many successful predictions including
• Steady states, stability, spectra, coherence,
  correlations, seizures
• EEGs, ERPs, SSEPs, ECoGs, fMRI connections.
• Gamma phenomena in perception.
• Arousal Dynamics normal, abnormal, drugs.
• Parameter space structure of states, parameter
  mapping.
• Ongoing basal ganglia, parkinsons, gamma-theta
  correlations, development, network connections,
  pharmacology,
• Future attention, learning, plasticity, memory,
  pharmacology, cerebellum,

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