Moran Virginia Tech Carilion Research Institute Dynamic Causal Modelling for Cross Spectral Densities Outline DCM amp Spectral Data Features the Basics DCM for CSD vs DCM for SSR ID: 621205
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Slide1
Rosalyn
Moran
Virginia Tech
Carilion Research Institute
Dynamic Causal Modelling for Cross Spectral DensitiesSlide2
Outline
DCM & Spectral Data Features (the Basics)DCM for CSD vs DCM for SSR
DCM for CSD ExampleSlide3
Outline
DCM & Spectral Data Features (the Basics)DCM for CSD vs DCM for SSR
DCM for CSD ExampleSlide4
Dynamic Causal
Modelling
: Generic Framework
simple neuronal model
Slow time scale
fMRI
complicated neuronal model
Fast time scale
EEG/MEG
Neural state equation:
Hemodynamic
forward model:
neural
activity BOLD
Time Domain Data
Electromagnetic
forward model:
neural
activity EEG
MEG
LFP
Time Domain ERP Data
Phase Domain Data
Time Frequency Data
Steady State Frequency Data
Cross Spectral Densities (Frequency Domain) Slide5
Dynamic Causal
Modelling
: Generic Framework
simple neuronal model
Slow time scale
fMRI
complicated neuronal model
Fast time scale
EEG/MEG
Neural state equation:
Electromagnetic
forward model:
neural
activity EEG
MEG
LFP
CSDs
Hemodynamic
forward model:
neural
activity BOLD
Time Domain Data
Frequency (Hz)
Power (mV
2
)
“theta”Slide6
Dynamic Causal
Modelling: Framework
simple neuronal model
fMRI
complicated neuronal model
EEG/MEG
Neural state equation:
Electromagnetic
forward model:
Hemodynamic
forward model:
Generative Model
Bayesian Inversion
Empirical Data
Model Structure/ Model ParametersSlide7
Inference on models
Dynamic Causal Modelling
: Framework
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 modelSlide8
Inference on models
Inference on parameters
Dynamic Causal Modelling
: Framework
Bayesian Inversion
Model comparison via Bayes factor:
Bayes’ rules:
accounts for
both
accuracy and complexity of the model
allows for inference about structure (generalisability) of the model
Model 1
Model 2
Model 1
Free Energy:
maxSlide9
Dynamic Causal
Modelling
: Neural Mass Model
neuronal (source) model
State equationsExtrinsic Connections
spiny stellate cells
inhibitory interneurons
Pyramidal
Cells
Intrinsic Connections
Internal Parameters
EEG/MEG/LFP
signal
Properties of tens of thousands of neurons approximated by their average responseSlide10
Dynamic equations mimic physiology and produce electrophysiological responses
A Neural
Mass
Model (6) layer cortical regions)
State equations: A dynamical systems
description
of anatomy and physiology
Extrinsic
Connections
spiny
stellate
cells
Supragranular
Pyramidal Cells + inhibitory
interneurons
Deep Pyramidal
Cells + inhibitory
interneurons
Intrinsic
Connections
Internal
Parameters
Eg
.
Time constants of Sodium ion channels
GABAa
receptors
AMPA receptors
Neurotransmitters:
Glu
/GABASlide11
Dynamics mimicked at AMPA and GABA receptors
AP generation zone
synapses
Cortico
-cortical connection
GABAa
receptors
AMPA receptors
Neurotransmitters:
Glu
/GABA
AP generation zone
Intrinsic Connection
Cortico
-cortical connection
Granular
Layer:
Excitatory Cells
Supragranular
Layer:
Inhibitory Cells
Infragranular
Layer:
Pyramidal
CellsSlide12
Parameters quantify
contributions at AMPA and GABA receptors
synapses
Cortico
-cortical connection
GABAa
receptors
AMPA receptors
Neurotransmitters:
Glu
/GABA
AP generation zone
Intrinsic Connection
Granular
Layer:
Excitatory Cells
Supragranular
Layer:
Inhibitory Cells
Infragranular
Layer:
Pyramidal
CellsSlide13
Extrinsic
forward connections
Extrinsic backward connections
Intrinsic connections
Extrinsic lateral connections
spiny
stellate
cells
inhibitory
interneurons
pyramidal cells
State
equations in a 6 layer cortical modelSlide14
Time Differential
Equations
State Space
Characterisation
Transfer Function
Frequency Domain
Linearise
mV
State
equations to Spectra
Moran
,
Kiebel, Stephan, Reilly, Daunizeau, Friston (2007)
A neural mass model of spectral responses in electrophysiology.
NeuroImageSlide15
Predicted response
(Pyramidal Cell Depolarization)
Given an empirical recording: estimate parameters of the model
4
g
3
g
2
g
1
2
4
9
1
4
4
1
2
)
)
(
(
x
x
u
a
x
s
H
x
x
x
e
e
e
e
k
k
g
k
-
-
+
-
=
=
&
&
Excitatory spiny cells in granular layers
3
g
1
g
2
g
5
g
AMPA receptor density
GABAa
receptor density
Glutamate
release
0
2
4
6
8
10
12
14
16
18
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
800
2
4
6
8
10
12
14
16
Frequency (Hz)
Frequency (Hz)
Normalised Power (a.u.)
L-Dopa
Placebo
Frequency (Hz)
Normalised Power (
a.u
.)
0
6
11
16
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Measurement
AMPA time constant
GABA
release
Bayesian Inversion
Increased activity at GABA
r
eceptors
i
n
supragranular
layers
Superficial layers
Granular
layers
Deep layers
GABAa
TC
Moran, Stephan, Seidenbecher, Pape, Dolan, Friston (2009)
Dynamic Causal Model of Steady State Responses.
NeuroImage
Friston, Bastos, Litvak, Stephan, Fries, Moran (2012)
DCM for complex data: cross-spectra, coherence and phase-delays.
NeuroImage Slide16
Neuromodulators
: Acetylcholine/Dopamine
f
Mg
=
Superficial layers
Granular
layers
Deep layers
Sodium Channel
Chloride Channel
Potassium Channel
Depolarization dependent
Calcium Channel
NMDA mediated switch
Neurotransmitters:
Glu
/GABA
A conductance
m
odel offers more biological plausibility
Moran, Stephan, Dolan, Friston (2011)
Consistent Spectral Predictors for Dynamic Causal Models of Steady State Responses
.
NeuroImage
0
2
4
6
8
10
12
14
16
18
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
800
2
4
6
8
Frequency (Hz)
Frequency (Hz)
Normalised Power (a.u.)
Frequency (Hz)
Normalised Power (
a.u
.)
AMPA/NMDA Ratio higher in Prefrontal Regions
t
han Parietal Regions
0
6
11
16
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4Slide17
Roadmap
Specify model
Extract Data Features
Maximise the model evidence (~
-F)Test models or MAP parameters
Find your experimental dataSlide18
Prediction
Prediction
Prediction
Summary:DCM for Steady State Responses
Cortical
Macrocolumns
and free parameters
dx/dt
=
Ax
+ B
| H
1
(
ω
) . H
1
*
(
ω
) |
| H
1
(
ω
) . H
2
*
(
ω
) |
| H
2
(
ω
) . H
2
*
(
ω
) |
Generative ModelSlide19
Cortical
Macrocolumns
and free parameters
dx/dt
=
Ax
+ B
| H
1
(
ω
) . H
1
*
(
ω
) |
| H
1
(
ω
) . H
2
*
(
ω
) |
| H
2
(
ω
) . H
2
*
(
ω
) |
Model Inversion
Summary:
DCM for Steady
State ResponsesSlide20
Outline
DCM & Spectral Data Features (the Basics)DCM for CSD vs
DCM for SSRDCM for CSD ExampleSlide21
Time to Frequency Domain
Linearise
around a stable fixed point or LC
DCM for SSRDCM for CSDSlide22
Prediction
Prediction
Prediction
DCM for Cross Spectral Densities
Cortical
Macrocolumns
and free parameters
dx/dt
=
Ax
+ B
H
1
(
ω
) . H
2
*
(
ω
)
Generative Model
Spectra and Phase lag
Coherence
Cross Correlations
H
1
(
ω
) . H
1
*
(
ω
)
H
2
(
ω
) . H
2
*
(
ω
)Slide23
Cortical
Macrocolumns
and free parameters
dx/dt
=
Ax
+ B
Model Inversion using
full complex signal
Spectra and Phase lag
Coherence
Cross Correlations
H
1
(
ω
) . H
2
*
(
ω
)
H
2
(
ω
) . H
2
*
(
ω
)
H
1
(
ω
) . H
1
*
(
ω
)
DCM for
Cross Spectral
Densities
Prediction
Prediction
PredictionSlide24
Accommodating Imaginary Numbers
F
E:
M:
Real and imaginary
errors
Real and imaginary
derivatives
wrt
fx
, GSlide25
Interface Additions
New CSD routines, similar to SSR
SPM_NLSI_GN accommodates
imag numbers, slopes, curvatures A host of new results features, in channel and source space!RoadmapSpecify model
Extract Data Features
Maximise the model evidence (~
-F
)
Test models or MAP parameters
Find your experimental data
And also report phase lags coherence & delays
In channel or source spaceSlide26
PFC
Hipp
Conditional Estimates:
Spectral Power
10
20
30
40
0
2
4
6
8
10
12
14
16
18
mode 1 to 1
frequency Hz
10
20
30
40
0
2
4
6
8
10
12
14
16
18
mode 2 to 1
frequency Hz
10
20
30
40
0
5
10
15
Spectral density over modes
(in channel-space)
frequency (Hz)
abs(CSD)
10
20
30
40
0
2
4
6
8
10
12
14
16
18
mode 2 to 2
frequency Hz
predicted: trial 1
observed: trial 1
predicted: mode 1
observed: mode 1
predicted: mode 2
observed: mode 2
Abs(H
1
(
ω
) . H
1
*
(
ω
)) Abs(H
1
(
ω) .
H
2
*(
ω))
Abs(
H
2
(
ω
) . H
1
*
(
ω
))
Abs(
H
2
(
ω) .
H
2
*(
ω))
PowerSlide27
PFC
Hipp
0
10
20
30
40
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Channels: 2 to 1
frequency Hz
predicted: trial 1
observed: trial 1
0
10
20
30
40
50
1
1
1
1
1
1
1
1
Coh
:
pfc
to
hipp
frequency Hz
Conditional Estimates:
Coherence
|(H
1
(
ω
).H
2
*
(
ω
))|
2
______________________
{(H
1
(
ω).
H
1
*(
ω))
+ (H
2
(
ω).
H
2
*(
ω))
}Slide28
PFC
Hipp
F
-1
(H
1
(
ω
).H
1
*
(
ω
))
F
-1
(H
1
(
ω
).
H
2
*
(
ω
))
F
-1
(
H
2
(
ω
).
H
1
*
(
ω
)
)
F
-1
(H
2
(
ω
).
H
2
*
(
ω
))
-100
-50
0
50
100
-0.05
0
0.05
0.1
0.15
0.2
mode 1 to 1
lag (ms)
-100
-50
0
50
100
-0.05
0
0.05
0.1
0.15
0.2
mode 2 to 1
lag (ms)
-100
-50
0
50
100
-0.05
0
0.05
0.1
0.15
0.2
Auto-covariance
(in channel-space)
Lag (ms)
auto-covariance
-100
-50
0
50
100
-0.05
0
0.05
0.1
0.15
0.2
mode 2 to 2
lag (ms)
trial 1
channel 1
channel 2
Conditional Estimates:
CovarianceSlide29
PFC
Hipp
arg
(H
1
(
ω
).H
2
*
(
ω
))
____________
ω
0
10
20
30
40
50
-25
-20
-15
-10
-5
0
5
Delay (ms) 2 to 1
frequency Hz
predicted: trial 1
observed: trial 1
0
10
20
30
40
50
-25
-20
-15
-10
-5
0
5
10
Delay (ms)
PfC
to
Hipp
Frequency Hz
trial 1
Conditional Estimates:
DelaysSlide30
Outline
DCM & Spectral Data Features (the Basics)DCM for CSD
vs DCM for SSRDCM for CSD ExamplesSlide31
Pharmacological Manipulation of Glutamate and GABA
4 levels of anaesthesia: each successively decreasing glutamate and increasing GABA
(Larsen
et al Brain Research 1994; Lingamaneni et al
Anesthesiology 2001; Caraiscos et al J Neurosci 2004 ; de Sousa
et al
Anesthesiology
2000 )
LFP recordings from primary
auditory cortex (A1) & posterior auditory field (PAF)
White
noise
stimulus & Silence
-
0.06
0
0.06
0.12
mV
A2
LFP
-
0.06
0
0.06
0.12
mV
-
0.06
0
0.06
0.12
mV
-
0.06
0
0.06
0.12
mV
A1
1.4 %
Isoflurane
1.8 %
Isoflurane
2.4 %
Isoflurane
2.8 %
IsofluraneSlide32
Summary
DCM for CSD:Suitable for long time series with trial-specific spectral features eg pronounced betaFits complex s
pectral data featuresOffers similar connectivity estimates to DCM for ERPsWith estimates of frequency specific delays
and coherenceCan be used with all biophysical, Neural Mass Models (CMC, LFP etc.) Slide33
Thank You
The FIL Methods Group
Karl
FristonDimitris PinotsisMarco LeiteVladimir
LitvakJean DaunizeauStephan KiebelWill Penny
Klaas
Stephan
Andre
Bastos
Pascal Fries
Acknowledgments