x - wellcome trust centre for neuroimaging
TRANSCRIPT
Slide 1in Parkinson's Disease
Wellcome Trust Centre for Neuroimaging
University College London
(DCM)
responses (SSR)
parkinsonian networks
• functional connectivity = statistical dependencies between regional time series
• effective connectivity = directed influences between neurons or neuronal populations
Sporns 2007, Scholarpedia
Some models of effective connectivity
• Structural Equation Modelling (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000
• regression models
• Volterra kernels Friston & Büchel 2000
• Time series models (e.g. MAR/VAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003
• Dynamic Causal Modelling (DCM) fMRI: Friston et al. 2003; MEEG: David et al. 2006
6
Data
best?
p(y|m) become maximal?
Which model represents the
best balance between model
fit and model complexity?
Pitt & Miyung (2002) TICS
log p(y |m)
F = log p(y |q,m) q -KL q q( ), p q |m( )éë ùû
balance between fit and complexity = accuracy - complexity
KLLaplace = 1
The negative free energy approximation
Bayes factors
For a given dataset, to compare two models, we compare
their evidences.
150 99% Very strong
or their log evidences
• Gaussian assumptions about the posterior distributions of the parameters
• posterior probability that a certain parameter (or contrast of parameters cT ηθ|y) is above a chosen threshold γ:
• By default, γ is chosen as zero ("does the effect exist?").
Inference about DCM parameters
simple neuronal model complicated forward model
complicated neuronal model simple forward model
fMRI EEG/MEG
fMRI
EEG/MEG
Steady State Frequency Data
“beta”
Hemodynamic
Inference on models
-2 -1 0 1 2 3 4 5 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
),()( mypq
accounts for both accuracy and complexity of the model
allows for inference about structure (generalisability) of the model
Stephan, Penny, Daunizeau, Moran, Friston (2009)
Dynamical Causal Modelling: Generic Framework
Granular
Layer:
attributes, membrane potentials, conductances
intractable. Mean field approximations
density. Neural mass models consider only
point densities and describe the interaction of
the means in the ensemble
One Source
x x
&
&
4
3
1
2
Inhibitory cells in agranular layers
),( uxfx &
11812
10
2
1112511
1110
7
2
8938
87
2)(
2)()(
xxx
xxxSHx
xx
xxxSAAHx
xx
iiii
ee
LB
ee
Neural Mass Model
x x
&
&
4
3
1
2
Inhibitory cells in agranular layers
),( uxfx &
1
2
4914
41
Neural Mass Model
time p o
g r
a te
x x
&
&
Intrinsic connections
Inhibitory cells in agranular layers
),( uxfx &
11812
10
2
1112511
1110
7
2
8938
87
2)(
2)()(
xxx
xxxSHx
xx
xxxSAAHx
xx
iiii
ee
LB
ee
hrv
• Parkinson’s disease (PD) is associated with abnormally synchronized oscillations in
the beta frequency band in the cortical-basal ganglia-thalamocortical network.
Amplitude changes in these oscillations correlate with variations in motor
impairment.
• To study effective connectivity in this network, we use a dynamic causal model
(DCM) of steady-state responses (SSR), which summarizes electrophysiological data
in terms of their cross-spectral density. These spectral features are generated by
biologically plausible, neural-mass models of coupled electromagnetic sources.
• Our ultimate goal is to use such models, once validated, to identify novel
therapeutic targets in patients with PD.
Beta synchrony in parkinsonian networks
Traditional theory of negative
unbalance in the striatal outputs of
direct ( ) /indirect ( ) pathways
synchrony: STN
20 Hz
Pathologic Beta Rythm in Parkinson`s
A B
Cortico-basal ganglia-thalamocortical
depletion of Parkinson's disease (PD),
leading to pathologically exaggerated beta
oscillations.
connectivity underlying these spectral
striatum, GPe and STN.
Time (sec)
F re
H z )
4. Subthalamic Nucleus (STN)
4. Subthalamic Nucleus (STN)
5. Entopedencular Nuclues (EPN)
Even with reduced circuit model & LFP recordings with EEG we have at least 2 hidden sources
Rat Limited network
sampling in rodents
Frequency (Hz)
0 20 40
0 20 40
exacerbate the problem oscillation?
d peak
What leads to an increase in beta overall when particular synapses are perturbed?
Contribution Analysis
exacerbate the problem oscillation?
exacerbate the problem oscillation?
4
6
8
10
12
14
16
2
4
6
8
10
12
4
6
8
10
12
14
exacerbate the problem oscillation?
4
6
8
10
12
14
16
2
4
6
8
10
12
4
6
8
10
12
14
Glutamatergic stellate cells
4. Subthalamic Nucleus (STN)
5. Internal globus pallidus (GPi)
Even with reduced circuit model & DBS recordings with EEG we have at least 3 hidden sources
Human Limited network
sampling in patients
Glutamatergic stellate cells
4. Subthalamic Nucleus (STN)
The problem: limited network sampling in patients
Even with reduced circuit model & DBS recordings with EEG we have at least 3 hidden sources
Human Human
Levedopa
OFF
ON
CTX-CTX
Levedopa
OFF
ON
0 20 40 0
5 Auto-Ctx
5 Auto-STN
5 Auto-GPi
5 Ctx-STN
5 Ctx-GPi
5 STN-GPi
5 Auto-Ctx
5 Auto-STN
5 Auto-GPi
5 Ctx-STN
5 Ctx-GPi
5 STN-GPi
OFF ON
4. Subthalamic Nucleus (STN)
-8%
4. Subthalamic Nucleus (STN)
-0.27
1 2 3 4 5 6 7 8 9 -1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 -100
-80
-60
-40
-20
0
20
40
60
80
100
10
20
30
40
50
60
70
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
(modulation connectivity measures) where,
connections 1 and 2
parameters
Bayesian Model Comparison
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
Model 1 Model 3 Model 2 Model 4
Bayesian Model Comparison
500
1000
1500
2000
2500
3000
3500
4000
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
4. Subthalamic Nucleus (STN)
STN source
0
2
4
6
8
10
12
14
Hz
-7
-6
-5
-4
-3
-2
-1
0
4. Subthalamic Nucleus (STN)
Lesioning connections to STN
10 20 30 40
10 20 30 40
10 20 30 40
10 20 30 40
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
healthy to lesioned in rodents
Ctx-STN strengthened
STN-GPi strengthened
in rodents
Ctx-STN increased
GPe-STN increased
STN-GPe increased
STN-GPi increased
Striatum-GPe increased
GPe-STN increased
pathway in the Parkinsonian state and increased beta
promoting potency in the GPe to STN pathway.
Comparison between PD patients with 6OHDA midbrain lesion rodents
• Our results indicate that one can use DCM for SSR to estimate network connection strengths
within network models of Rat and Human PD, using LFPs.
• Using real data, we found good agreement on optimal model architecture and connectivity
parameter estimation when compared with previous studies in human and rat.
• This model was further validated through the prediction of the effects of standard
therapeutic procedures aimed at the STN.
• We are able to explore the effects of candidate therapeutic interventions through safe, cheap
and valid simulations.
Wellcome Trust Centre for Neuroimaging
University College London
(DCM)
responses (SSR)
parkinsonian networks
• functional connectivity = statistical dependencies between regional time series
• effective connectivity = directed influences between neurons or neuronal populations
Sporns 2007, Scholarpedia
Some models of effective connectivity
• Structural Equation Modelling (SEM) McIntosh et al. 1991, 1994; Büchel & Friston 1997; Bullmore et al. 2000
• regression models
• Volterra kernels Friston & Büchel 2000
• Time series models (e.g. MAR/VAR, Granger causality) Harrison et al. 2003, Goebel et al. 2003
• Dynamic Causal Modelling (DCM) fMRI: Friston et al. 2003; MEEG: David et al. 2006
6
Data
best?
p(y|m) become maximal?
Which model represents the
best balance between model
fit and model complexity?
Pitt & Miyung (2002) TICS
log p(y |m)
F = log p(y |q,m) q -KL q q( ), p q |m( )éë ùû
balance between fit and complexity = accuracy - complexity
KLLaplace = 1
The negative free energy approximation
Bayes factors
For a given dataset, to compare two models, we compare
their evidences.
150 99% Very strong
or their log evidences
• Gaussian assumptions about the posterior distributions of the parameters
• posterior probability that a certain parameter (or contrast of parameters cT ηθ|y) is above a chosen threshold γ:
• By default, γ is chosen as zero ("does the effect exist?").
Inference about DCM parameters
simple neuronal model complicated forward model
complicated neuronal model simple forward model
fMRI EEG/MEG
fMRI
EEG/MEG
Steady State Frequency Data
“beta”
Hemodynamic
Inference on models
-2 -1 0 1 2 3 4 5 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
),()( mypq
accounts for both accuracy and complexity of the model
allows for inference about structure (generalisability) of the model
Stephan, Penny, Daunizeau, Moran, Friston (2009)
Dynamical Causal Modelling: Generic Framework
Granular
Layer:
attributes, membrane potentials, conductances
intractable. Mean field approximations
density. Neural mass models consider only
point densities and describe the interaction of
the means in the ensemble
One Source
x x
&
&
4
3
1
2
Inhibitory cells in agranular layers
),( uxfx &
11812
10
2
1112511
1110
7
2
8938
87
2)(
2)()(
xxx
xxxSHx
xx
xxxSAAHx
xx
iiii
ee
LB
ee
Neural Mass Model
x x
&
&
4
3
1
2
Inhibitory cells in agranular layers
),( uxfx &
1
2
4914
41
Neural Mass Model
time p o
g r
a te
x x
&
&
Intrinsic connections
Inhibitory cells in agranular layers
),( uxfx &
11812
10
2
1112511
1110
7
2
8938
87
2)(
2)()(
xxx
xxxSHx
xx
xxxSAAHx
xx
iiii
ee
LB
ee
hrv
• Parkinson’s disease (PD) is associated with abnormally synchronized oscillations in
the beta frequency band in the cortical-basal ganglia-thalamocortical network.
Amplitude changes in these oscillations correlate with variations in motor
impairment.
• To study effective connectivity in this network, we use a dynamic causal model
(DCM) of steady-state responses (SSR), which summarizes electrophysiological data
in terms of their cross-spectral density. These spectral features are generated by
biologically plausible, neural-mass models of coupled electromagnetic sources.
• Our ultimate goal is to use such models, once validated, to identify novel
therapeutic targets in patients with PD.
Beta synchrony in parkinsonian networks
Traditional theory of negative
unbalance in the striatal outputs of
direct ( ) /indirect ( ) pathways
synchrony: STN
20 Hz
Pathologic Beta Rythm in Parkinson`s
A B
Cortico-basal ganglia-thalamocortical
depletion of Parkinson's disease (PD),
leading to pathologically exaggerated beta
oscillations.
connectivity underlying these spectral
striatum, GPe and STN.
Time (sec)
F re
H z )
4. Subthalamic Nucleus (STN)
4. Subthalamic Nucleus (STN)
5. Entopedencular Nuclues (EPN)
Even with reduced circuit model & LFP recordings with EEG we have at least 2 hidden sources
Rat Limited network
sampling in rodents
Frequency (Hz)
0 20 40
0 20 40
exacerbate the problem oscillation?
d peak
What leads to an increase in beta overall when particular synapses are perturbed?
Contribution Analysis
exacerbate the problem oscillation?
exacerbate the problem oscillation?
4
6
8
10
12
14
16
2
4
6
8
10
12
4
6
8
10
12
14
exacerbate the problem oscillation?
4
6
8
10
12
14
16
2
4
6
8
10
12
4
6
8
10
12
14
Glutamatergic stellate cells
4. Subthalamic Nucleus (STN)
5. Internal globus pallidus (GPi)
Even with reduced circuit model & DBS recordings with EEG we have at least 3 hidden sources
Human Limited network
sampling in patients
Glutamatergic stellate cells
4. Subthalamic Nucleus (STN)
The problem: limited network sampling in patients
Even with reduced circuit model & DBS recordings with EEG we have at least 3 hidden sources
Human Human
Levedopa
OFF
ON
CTX-CTX
Levedopa
OFF
ON
0 20 40 0
5 Auto-Ctx
5 Auto-STN
5 Auto-GPi
5 Ctx-STN
5 Ctx-GPi
5 STN-GPi
5 Auto-Ctx
5 Auto-STN
5 Auto-GPi
5 Ctx-STN
5 Ctx-GPi
5 STN-GPi
OFF ON
4. Subthalamic Nucleus (STN)
-8%
4. Subthalamic Nucleus (STN)
-0.27
1 2 3 4 5 6 7 8 9 -1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 -100
-80
-60
-40
-20
0
20
40
60
80
100
10
20
30
40
50
60
70
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
(modulation connectivity measures) where,
connections 1 and 2
parameters
Bayesian Model Comparison
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
1. Cortex
2. Striatum
4. Subthalamic Nucleus (STN)
Model 1 Model 3 Model 2 Model 4
Bayesian Model Comparison
500
1000
1500
2000
2500
3000
3500
4000
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
4. Subthalamic Nucleus (STN)
STN source
0
2
4
6
8
10
12
14
Hz
-7
-6
-5
-4
-3
-2
-1
0
4. Subthalamic Nucleus (STN)
Lesioning connections to STN
10 20 30 40
10 20 30 40
10 20 30 40
10 20 30 40
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
Hz
-7
-6
-5
-4
-3
-2
-1
0
healthy to lesioned in rodents
Ctx-STN strengthened
STN-GPi strengthened
in rodents
Ctx-STN increased
GPe-STN increased
STN-GPe increased
STN-GPi increased
Striatum-GPe increased
GPe-STN increased
pathway in the Parkinsonian state and increased beta
promoting potency in the GPe to STN pathway.
Comparison between PD patients with 6OHDA midbrain lesion rodents
• Our results indicate that one can use DCM for SSR to estimate network connection strengths
within network models of Rat and Human PD, using LFPs.
• Using real data, we found good agreement on optimal model architecture and connectivity
parameter estimation when compared with previous studies in human and rat.
• This model was further validated through the prediction of the effects of standard
therapeutic procedures aimed at the STN.
• We are able to explore the effects of candidate therapeutic interventions through safe, cheap
and valid simulations.