Carilion Research Institute Bradley Department of Electrical amp Computer Engineering Department of Psychiatry amp Behavioral Medicine Virginia Tech Carilion School of Medicine SPM Course MEEG Queen Square May 1618 ID: 934720
Download Presentation The PPT/PDF document "l Rosalyn Moran Virginia Tech" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
l
Rosalyn Moran
Virginia Tech
Carilion Research InstituteBradley Department of Electrical & Computer EngineeringDepartment of Psychiatry & Behavioral Medicine, Virginia Tech Carilion School of Medicine SPM Course M/EEG, Queen Square, May 16-18th 2016
Dynamic causal models for
Steady State Responses
Slide2Milliseconds: M/EEG
Connectivity from EEG/LFP Data: Dynamic Causal Models
mV
time
Event related potentials & Oscillations of different frequencies
Implicated in specific cognitive tasks/regions
Eg
. Hippocampal Theta (4 – 8 Hz) &
Sensory
Gamma (30 – 60 Hz)
Slide3Dynamic Causal
Modeling: Generic Framework
simple neuronal model(slow time scale)
fMRIdetailed neuronal model(synaptic time scales)EEG/MEG
Neural state equation:
Hemodynamic
forward model:
neural
activity BOLD
Time Domain
Data
Resting State Data
Electromagnetic
forward model:
neural
activity EEG
MEG
LFP
Time Domain ERP Data
Phase Domain Data
Time Frequency Data
Spectral Data
Frequency (Hz)
Power
(mV
2
)
“theta”
A Neural Mass Model
Slide4Macro and
meso
-scales: The Neural Mass Model
internal granular
layer
internal pyramidal
layer
external pyramidal
layer
external granular
layer
macro-scale
meso-scale
micro-scale
The state of a neuron comprises a number of attributes, membrane potentials,
conductances
etc. Modelling these states can become intractable.
Mean field approximations
summarise the states in terms of their ensemble density.
Neural mass models
consider only point densities and describe the interaction of the means in the ensemble
Slide5M
eso
-
scale dynamics
internal granular
layer
internal pyramidal
layer
external pyramidal
layer
external granular
layer
AP generation zone
synapses
AP generation zone
Slide6Convolution Based Neural Mass Models
Slide7Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Take one spiny stellate cell…..
Slide8Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Heaviside function
P(Action Potential)
Depolarization
Take a population
of spiny stellate
cells & assume either:
Unimodal
distribution over firing thresholds
Unimodal
distribution over population
Membrane
depolarizations
Slide9Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Heaviside function
Sigmoidal
Presynaptic Firing Function
P(Action Potential)
Depolarization
Average Firing Rate
Depolarization
Ensemble Synchronicity/Gain
Slide10Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Sigmoidal
Presynaptic Firing Function
Average Firing Rate
Depolarization
Postsynaptic Kernel
Time (
msec
)
Depends on postsynaptic receptor
activated by particular neurotransmitter
Slide11Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Sigmoidal
Presynaptic Firing Function
Average Firing Rate
Depolarization
Postsynaptic Kernel
Time (
msec
)
E.g. Glutamate from SS to AMPA receptor
+depolarization
time constant ~ 15msec
Slide12Convolution-Based Neural Mass Models in DCM
Inhibitory interneuron
Pyramidal cells
Sigmoidal
Presynaptic Firing Function
Average Firing Rate
Depolarization
E.g. GABA from inhibitory interneuron to
GABAa
receptor
Postsynaptic Kernel
Time (
msec
)
-hyperpolarization
time constant ~ 8msec
Slide13Convolution-Based Neural Mass Models in DCM
Spiny
stellate cells
Pyramidal cells
Sigmoidal
Presynaptic Firing Function
Average Firing Rate
Depolarization
Postsynaptic Kernel
Time (
msec
)
Connectivity?
Maximum
Postsynaptic
Potential
Time constant
connectivity
gain
Slide14Convolution to ODEs
Spiny
stellate cells
Pyramidal cells
By parts twice
Convolution Equation
Second Order Differential Equation
2 Coupled First Order Differential
For each transmitter receptor pair
.
Slide15Multilaminar
NMMS
Spiny
stellate cellsPyramidal cellsInhibitory interneuron
Assume glutamate from
p
yramidal cells & spiny
stellate cells activate AMPA receptors
Assume GABA from inhibitory interneurons activate
GABAa
receptors
Then construct
interlaminar
connectivity
5 connections giving 5x2 coupled first
order differential equations
Slide16Spiny
stellate cells
Pyramidal cells
Inhibitory interneuron
5
g
Excitatory spiny cells
being granular layers
Excitatory pyramidal
cells
in
extragranular
layers
Inhibitory cells in
extragranular
layers
One region: 12 equations 10 + 2 difference
Slide17Spiny
stellate cells
Pyramidal cells
Inhibitory interneuron
5
g
Exogenous Input
Excitatory spiny cells
being granular layers
Excitatory pyramidal
cells
in
extragranular
layers
Inhibitory cells in
extragranular
layers
Measured
response:
One region: 12 equations 10 + 2 difference
Dipole
(t)
Slide18Conductance Based Neural Mass Models
Slide19Current in =
Conductance
X Potential Difference
-
=
)
(
V
V
g
V
C
rev
&
Conductance-Based Neural Mass Models in DCM
Ohm’s Law V = IR
Ohm’s Law for a Capacitor I = C dv/
dt
Glutamate
G
aba
Slide20Conductance-Based Neural Mass Models in DCM
Ohm’s Law V = IR
Ohm’s Law for a Capacitor I = C
dv/
dt
Dynamic Conductance
Glutamate
G
aba
Current in =
Conductance
X Potential Difference
=
-
=
(
)
(
g
V
V
g
V
C
aff
rev
g
k
&
&
-
g
)
Slide21Connectivity driven by
different
neurotransmitters and receptors
State equations & parameters
Conductance-Based Neural Mass Models in DCM
Slide22Spiny
stellate cells
Pyramidal cells
Inhibitory interneuron
Exogenous input
Excitatory spiny cells in granular layers
Excitatory pyramidal cells in
extragranular
layers
Inhibitory cells in
extragranular
layers
Measured response
Conductance-Based Neural
Mass Models in DCM
Slide23A selection of intrinsic architectures in SPM
A suite of neuronal population models including neural masses, fields and conductance-based models…expressed in terms of sets of differential equations
Slide24Spiny
stellate
Pyramidal cells
Inhibitory interneuron
Extrinsic Output
GABA Receptors
AMPA Receptors
NMDA
Receptors
Predictive coding-based
Neural
Mass
Models in DCM
Spiny
stellate
Superficial pyramidal
Inhibitory interneuron
Deep pyramidal
4-subpopulation
Canonical Microcircuit
Backward
Extrinsic Output
Forward
Extrinsic Output
Moran et al. 2011,
Neuroimage
Slide25Inference on models
Model Inversion & Inference
Bayesian Inversion
Bayes’ rules:
Model 1
Model 2
Model 1
Free Energy:
max
Inference on parameters
Model comparison via Bayes factor:
accounts for
both
accuracy and complexity of the model
allows for inference about structure (generalisability) of the model
Slide26Data & Hypotheses
data
y
Model
1
Model
2
...
Model
n
Model selection:
best?
STG
STG
A1
A1
STG
A1
A1
Event-Related Potentials
Channels
Time
Slide27Data & Hypotheses
Model
1
Model
2
...
Model
n
Model selection:
best?
STG
STG
A1
A1
STG
A1
A1
Cross-Spectral
Responses
1
1
2
2
3
3
4
4
Slide28Inversion in the real & complex domain
0
10
20
30
40
50
0
0.5
1
1.5
2
2.5
3
3.5
Frequency (Hz
)
real
prediction and response: E-Step: 32
0
10
20
30
40
50
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Frequency (Hz)
imaginary
prediction and response: E-Step: 32
0
10
20
30
40
50
60
70
80
-2
-1.5
-1
-0.5
0
0.5
1
1.5
parameter
conditional [minus prior] expectation
Slide29Interconnected
Neural mass models
Lead Field
Empirical Observations
(
eg
Sensor Level)
Forward Model: Neural
Mass
Models in DCM
Slide30Event-Related Potentials
Neural Mass Models in DCM for ERPs
Interconnected
Neural mass modelsLead Field
data
y
Channels
Time
Slide31mV
State
equations from time to spectral domain
Time Differential Equations
Linearise
Analytic Transfer Function in the Frequency domain
White/Pink Noise
Slide32DCM for SSR/CSD Examples
Slide33Connectivity changes underlying
spectral EEG changes during propofol-induced loss of consciousness.
Wake
Mild Sedation: Responsive to command
Deep Sedation: Loss of Consciousness
Boly, Moran, Murphy,
Boveroux
, Bruno,
Noirhomme
,
Ledoux
,
Bonhomme
,
Brichant
,
Tononi
,
Laureys
,
Friston
, J Neuroscience, 2012
Slide34Propofol
-induced loss of consciousnessWake
Mild Sedation: Responsive to command
Deep Sedation: Loss of ConsciousnessAnterior Cingulate/mPFCPrecuneus/Posterior Cingulate
Slide35Wake
Mild Sedation: Responsive to commandDeep Sedation: Loss of Consciousness
Increased gamma power in
Propofol vs WakeIncreased low frequency power when consiousness is lostMurphy et al. 2011
Propofol
-induced loss
of consciousness
Anterior
Cingulate/
mPFC
Precuneus
/Posterior
Cingulate
Slide36Bayesian Model Selection
WakeMild SedationDeep Sedation
Propofol
-induced loss of consciousness
ACC
PCC
ACC
PCC
ACC
PCC
Thalamus
Thalami
Slide37Wake
Mild SedationDeep Sedation
Propofol
-induced loss of consciousness
ACC
PCC
ACC
PCC
ACC
PCC
Thalamus
Thalami
Slide38Wake
Propofol
-induced loss of consciousness
Parameters of Winning Model
ACC
PCC
Thalamus
Slide39Wake
Mild Sedation
:Increase in thalamic excitability
Propofol-induced loss of consciousness
ACC
PCC
Thalamus
ACC
PCC
Thalamus
Slide40Wake
Mild Sedation
:Increase in thalamic excitability
Propofol-induced loss of consciousness
ACC
PCC
Thalamus
ACC
PCC
Thalamus
Loss of Consciousness
:Breakdown
in
Cortical Backward
Connections
ACC
PCC
Thalamus
Slide41Propofol
-induced loss
of consciousness
Loss of Consciousness:Breakdown in Cortical Backward Connections
ACC
PCC
Thalamus
Boly, Moran, Murphy,
Boveroux
, Bruno,
Noirhomme
,
Ledoux
,
Bonhomme
,
Brichant
,
Tononi
,
Laureys
,
Friston
, J Neuroscience, 2012
Slide42The Ketamine Model of Psychosis & Schizophrenia
Noncompetitive NMDA-r antagonistDissociative anaesthetic
: "... a peculiar anaesthetic state in which marked sensory loss and analgesia as well as amnesia is not accompanied by actual loss of consciousness.” (Bonta
, 2004)Subanaesthetic Doses:Model of psychosis in animals, producing hyperlocomotion and disruption of PPIReproduces in humans both positive and negative symptoms of schizophrenia along with associated cognitive deficits.
Slide43The Ketamine Model of Psychosis
& SchizophreniaWith Matthew Jones, University of Bristol
Hippocampal & Prefrontal Recordings
5 mins of recordings from freely moving rat: tetrodes in dCA1 & mPFCBowers et al. 2010Ketamine Dose: 0, 2, 4, 8, 30 mgkg-1
Slide44Effects
on Oscillations: Theta reduction in the hippocampus and Gamma enhancement in hippocampus and neocortex. Antipsychotic drugs (D2 antagonists) acutely reduce cortical gamma oscillations in rats (Jones et al. 2011).Aberrant beta and gamma synchrony observed in patient populations (
Uhlhaas et al. 2008).Reduced or enhanced gamma depending on state late/prodromal ( Sun et al. 2011).
BehaviourConnectivityReceptor Neurochemistry
The Ketamine Model of Psychosis & Schizophrenia
Slide45Behavioural Phenotype
mean ± std
Speed of movement
Hyper-locomotion
0
4
6
8
10
12
14
16
18
20
2
4
8
Mg
Ketamine
/kg
**
**
Slide46p < 0.005 **p < 0.05 *
0
10
20
30
40
50
60
70
80
0
5
10
15
20
25
30
35
40
**
0
10
20
30
40
50
60
70
80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
*
0
10
20
30
40
50
60
70
80
0
5
10
15
Veh
(13)
2mg (8)
4mg (8)
8mg (13)
30 mg (5)
Recorded
HPC-HPC
HPC-PFC
PFC-PFC
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Power
a.u
.
Power
a.u
.
Power
a.u
.
*
*
5 minutes : freely moving
Oscillatory Characteristics
Slide47Hippocampal & Prefrontal Recordings
5 mins of recordings from freely moving rat: tetrodes in dCA1 & mPFC
Ketamine Dose:
0, 2, 4, 8, 30 mgkg-1Hypothesis, Data & Model-based analysis:DopamineGammaGabaNMDAFrontal Regions
Temporal Cortex
Glutamate &
NMDA Receptor
Glutamate &
AMPA Receptor
“Bottom-up”
Slide48p < 0.005 **p < 0.05 *
0
10
20
30
40
50
60
70
80
0
5
10
15
20
25
30
35
40
**
0
10
20
30
40
50
60
70
80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
*
0
10
20
30
40
50
60
70
80
0
5
10
15
Veh
(13)
2mg (8)
4mg (8)
8mg (13)
30 mg (5)
Recorded
HPC-HPC
HPC-PFC
PFC-PFC
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Power
a.u
.
Power
a.u
.
Power
a.u
.
*
*
5 minutes : freely moving
What
Cortico
-Limbic Connectivity Changes are responsible for theta and gamma changes under ketamine?
What
Intrinsic Connectivity
Changes are responsible for theta and gamma changes?
What
Receptors are involved at these extrinsic & intrinsic synapses?
Hypothesis, Data & Model-based analysis:
Slide49Proposed Architecture
CA1
mPFC
Pyramidal Cells
Inhibitory Interneurons
AMPA Receptor
NMDA Receptor
GABA
A
Receptor
HPC
mPFC
CA1
CA3
iis
SPys
D
Pys
Slide50Model Comparison
Ketamine doses parametrically modulate:All extrinsic connections,
Intrinsic NMDA andInhibitory / Modulatory processes
HPC
mPFC
+
B
ket
Slide51Model Comparison
Ketamine doses parametrically modulate:All extrinsic connections,
Intrinsic NMDA andInhibitory / Modulatory processes
HPC
mPFC
Model 1
Model 1
+
B
ket
Slide52Model Comparison
Ketamine modulates:All extrinsic connections,
Intrinsic NMDA andInhibitory / Modulatory
processes
HPC
mPFC
Model 2
Model 2
Slide53HPC
mPFC
Model 3
Model 3
Ketamine modulates:
A
ll extrinsic connections,
I
ntrinsic NMDA and
Inhibitory / Modulatory
processes
Model Comparison
Slide54Model Comparison
HPC
mPFC
Model 4
Model 4
Ketamine modulates:
A
ll extrinsic connections,
I
ntrinsic NMDA and
Inhibitory / Modulatory
processes
Slide55HPC
mPFC
Model 5
Model 5
Ketamine modulates:
A
ll extrinsic connections,
I
ntrinsic NMDA and
Inhibitory / Modulatory
processes
Model Comparison
Slide561
2
3
4
5
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Log-evidence (relative)
Models
Bayesian Model Selection: FFX
Pyramidal Cells
Inhibitory Interneurons
Tetrode
Placement
AMPA Receptor
NMDA Receptor
GABA
A
Receptor
Extrinsic Input
Extrinsic Output
mPFC
CA3
CA1
HPC
SPy
DPy
Model 2
Model 1
Model 4
Model 5
Model 3
Model Comparison
Slide57Model Fits
predicted: saline vehicle
observed: saline vehicle
predicted: 2
mgkg
-1
observed: 2
mgkg
-1
predicted: 4
mgkg
-1
observed: 4
mgkg
-1
observed: 8
mgkg
-1
predicted: 30
mgkg
-1
observed: 30
mgkg
-1
observed: 8
mgkg
-1
frequency (Hz)
40
45
50
55
60
65
70
75
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
40
45
50
55
60
65
70
75
0
0.01
0.02
0.03
0.04
0.05
0.06
Gamma in
mPFC
40
45
50
55
60
65
70
75
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
frequency (Hz)
Gamma in
dCA1-mPFC
Gamma in dCA1
Spectral density
(modulus)
2
4
6
8
10
0.2
0.4
0.6
0.8
1
1.2
1.4
Theta in dCA1
frequency (Hz)
2
4
6
8
10
0
0.05
0.1
0.15
Theta in dCA1-mPFC
2
4
6
8
10
0.05
0.1
0.15
0.2
0.25
Theta in
mPFC
frequency
(
Hz)
Spectral density
(modulus)
0
0
Slide58Extrinsic Connectivity Changes
under Ketamine
0
24
Ketamine Dose
0
2
4
Ketamine Dose
8
30
Theta Model
Gamma Model
dCA1
mPFC
0
50
100
strength (%)
NMDA-mediated input to PFC from dCA1
0
50
100
0
50
100
150
200
strength (%)
0
50
100
150
200
AMPA-mediated input to PFC from dCA1
0
50
100
strength (%)
NMDA-mediated input to HPC from
mPFC
0
50
100
Slide59Intrinsic Connectivity
Changes under KetamineTheta ModelGamma Model
0
50
100
strength (%)
NMDA-mediated excitation
of hippocampal
Interneurons
0
50
100
1/Signal to Noise Ratio in the Hippocampus
0
2
4
Ketamine Dose
0
2
4
Ketamine Dose
8
30
0
500
1000
1500
2000
strength (%)
0
100
200
300
400
dCA1
Confirmed by MUA in CA1:
High but uncorrelated unit activity
Slide60Losing Control Under Ketamine
Enhanced Gamma
With AMPA
Reduced ThetaWithout NMDAFrontal RegionsTemporal Cortex
Reduced
Cortico
-Limbic Control mediated by NMDA
Enhanced Limbic-
Cortico
Drive via AMPA:
Runaway
bottom-up
sensory-driven processing :
disorganised
cognition & environmental interactions
Large difference in intrinsic processing: early dopaminergic D2 problem in schizophrenia?
Slide61Why these models?
Slide62DCM for SSR/CSD
Why I think these models are useful:Models of Synaptic Activity using invasive and non-invasive electrophysiological time series from large neuronal populations.Useful models of pharmacological effects – where are the drug’s effects most prominent, are other receptors affected?
Useful link to predictive coding: top-down vs. bottom up and their belief mappings.Potential to scale to clinical settings: could patients be stratified based on endogenous connectivity profiles?
Slide63DCM for SSR/CSD
Why these models can be more than mildly irritating :Local Minima (not the model’s fault)
Slide64Thank You
VTCRI
Jessica Gilbert
Jian LiWynn LegonSarah AdamsSteven PunzellEhsan DowlattiKarl Friston, UCLMatt Jones, University of BristolRick Adams, UCLKlaas Stephan, University of Zurich