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.
Mar 29, 2015
Multiscale Modeling of Brain Dynamics
Peter RobinsonSchool of Physics, University of Sydney
Brain Dynamics Center, Westmead Hospital
& University of Sydney
Faculty of Medicine, University of SydneySupported by the ARC and NHMRC.
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
Alex Guinaudeau Rebecca Hamilton James Henderson Hal Henke Jackie HuberKim KaufmannCliff KerrJong-Won KimKrzysztof Kozak Anthony KrenselAndrew LaydenBelinda Liddle Peter LoxleyNeil Mahant Elie MatarSuzanne O’Connor Andrew Phillips Rebecca Powles
Collaborators: Chris Rennie Michelle RigozziPeter RileyJames Roberts Naomi RogersDonald RoweSacha van Albada Helena van der Merwe Rebecca WhitehouseLea Williams Keith Wong Jim WrightHui-Ying Wu
stimuli behavioral outputsmanipulations
observations
measurementsPROCESSES
The Big Picture
Measurement: what, why, how?
Integration
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.
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.
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
Synapses and Dendrites
• Incident neurons transmit chemicalsignals to dendrites at synapses.• Chemical neurotransmitters are
released into the synaptic cleft, changing postsynaptic potential.
• Synaptic dynamics and dendriticpropagation smear signals over ~ 1-100 ms at the cell body.
Nolte (2002)
• Single cell response has a nonlinearthreshold firing rate behavior.
• Sigmoidal when averaged over apopulation:
Qa (Va) = Sa(Va).
• Cell body potentials Va approximately obey
• ab = mean activity from neural type b.• sab = mean strength of connections.• Nab= mean number of connections.
/)(max
1)(
Ve
QVS
Cell Body
. 1111
2
2
babababa sNV
dt
d
dt
d
• 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):
. rr ),(),(121 22
2
2
2tQtr
tt babababab
Axonal Propagation
. rr rrr
arrabab etdt /)0(
0
)0( ~),(2)(2
Braitenberg & Shüz (1998)
The Model
• Our equations form a closed nonlinear set, parametrized physiologically:
Activity fields
ab
Va Cell-body potentials
Qa Firing rates
Propagation Synaptic/dendritic dynamics
Nonlinear thresholdresponse
t0Corticothalamic loop delay
Synaptodendritic response rates
GabGains
rabAxonal ranges
vabAxonal velocities
Qa,maxMaximum firing rate
SymbolQuantity
• 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.
0,0
xt
Steady States, Response Properties
Coherence, Time Series, Stability
Theory DataEyes open
Eyes closed
Normalsleep
Deep sleep
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.
Inversion• Fitting predictions to data yields best estimates of parameters for individuals
• Can map parameters and combine consistently with other measures:
2040
60
2040
60800
10
20
30
40
50
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.
υse
e (s
-1)
1
2
Time (s)
e (s
-1)
Time (s)
Fre
quen
cy (
Hz)
Time (s)
e (s
-1)
Time (s)
e (s
-1)
(t)
(t-
τ)
(t-2τ)
Time (s)
Fz
(µV
)
Time (s)
Fre
quen
cy (
Hz)
Time (s)
Time (s)
Fz
(µV
)F
z (µ
V)
(t)
(t-
τ)
(t-2τ)
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)
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)
• 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)
Kk
• 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)
• 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
• 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
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:
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.
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.
macro
micro
fast slow
imaging
intracellular
basic features fine detail
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, parkinson’s, gamma-theta correlations, development, network connections, pharmacology, …• Future: attention, learning, plasticity, memory, pharmacology, cerebellum, …