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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 Aquino Homi Bahramali Matt Barton Lindsay Botha Paul Bourke Michael Breakspear Parry Chen Po-Chia Chen Alan Chiang Jonathon Clearwater Nick Cooper Tim Cooper Peter Drysdale Ben Fulcher Candy Fung Biljana Germanoska Evian Gordon Stuart Grieve Ron Grunstein 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 Collaborators: 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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stimuli behavioral outputs manipulations observations measurements PROCESSES The Big Picture

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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 (< 1 mm) excitatory neurons. Short-range (< 1 mm) inhibitory neurons. Kandel, Schwartz, & Jessell (2000) Axonal hillock

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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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Single cell response has a nonlinear threshold firing rate behavior. Sigmoidal when averaged over a population: Q a (V a ) = S a (V a ). Cell body potentials V a approximately obey ab = mean activity from neural type b. s ab = mean strength of connections. N ab = mean number of connections. Cell Body

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Activity spreads in a wavelike fashion with velocity v ab and mean range r ab. Approximate using a damped wave equation: ab = v ab / r ab = damping rate. The propagator ab (0) (r,t) is the solution to this equation for a -function input. Spatial part (effectively nonlocal): Axonal Propagation Braitenberg & Shüz (1998)

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The Model Our equations form a closed nonlinear set, parametrized physiologically: Activity fields ab V a Cell-body potentials Q a Firing rates PropagationSynaptic/dendritic dynamics Nonlinear threshold response t0t0 Corticothalamic loop delay Synaptodendritic response rates G ab Gains r ab Axonal ranges v ab Axonal velocities Q a,max Maximum firing rate SymbolQuantity

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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. Steady States, Response Properties

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Coherence, Time Series, Stability Theory Data Eyes open Eyes closed Normal sleep Deep sleep

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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. 1 st 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 Linear instability at 3 Hz. Ramping se up and down yields start and end of spike and wave oscillations via supercritical Hopf bifurcation. υ se e (s -1 ) 1 2 Time (s) e (s -1 ) Time (s) Frequency (Hz) Time (s) e (s -1 ) Time (s) e (s -1 ) (t) (t-τ) (t-2τ) Time (s) Fz (µV) Time (s) Frequency (Hz) Time (s) Fz (µV) (t) (t-τ) (t-2τ)

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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 T=0, 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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Use of patchy propagators yields new transfer functions and spectra. Waves obey Schroedinger equation. Resonances at and gamma frequencies. Gamma Resonances from Patchy Propagators P(k,ω)P(k,ω)

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Peak at T=0. 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: Engel, Konig, Kreiter, Schillen, & Singer (1992) Gamma Correlations Dworetzky (1994)

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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: Scene Segmentation Engel, Konig, & Singer (2002) S1 S2 S3 S1+S2

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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 Arousal Dynamics 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 V i and firing rates Q i. 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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macro micro fast slow imaging intracellular basic featuresfine 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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