Dynamic Causal Modelling (DCM)
Speaker: Ya-Yun Chen1, Chin-Hui Chen1,2
1RA at the Center for Research in Cognitive Science, CCU
2RA at the Machine Discovery Lab, NTU
20190706 @ NTHU
Before we start to learn DCM...
Standard (conventional) fMRI analysis
To be Biologically Plausible
Brain is dynamic
Brain is nonlinear
From “Where” to “How”
Anatomical connectivity
Functional connectivity
Effective connectivity
The Connected Brain
brain regions in macaque cortex
Spoms 2007, scholarpedia
Anatomical layout of axons and synaptic connections
Correlation among activity in different brain areas
Causal influence that one neuronal system exerts over another
Effective Connectivity
Functional Connectivity
Effective connectivity
Hypothesis-Free
Hypothesis-Driven
Resting-state fMRI
(Correlation)
Default-mode network
Psycho-physiological Interactions
(Linear regression analysis)
V1
a
V5
Dynamic causal modeling
(Nonlinear dynamic models)
One of the causal model is DCM�Dynamic Causal Modelling
Central Idea Behind DCM
DCM was originally developed for fMRI data.
Friston (2003):
“The central idea behind dynamic causal modelling (DCM) is to �treat the brain as a deterministic nonlinear dynamic system that is�
subject to inputs and produces outputs.”
Basis of DCM:
(Taken from: Statistical Parametric Mapping: The Analysis of Functional Brain Images. William D. Penny， Karl J. Friston， John T. Ashburner， Stefan J. Kiebel， Thomas E. Nichols)
Basis of DCM: State (brain system)
Neuronal priors
Hemodynamic priors
Basis of DCM: Outputs
Responses were measured in scanner...
Hemodynamic �Ballon Model
Inputs
Brain system
Outputs
Hemodynamic �Ballon Model
DCM modelling...
Aims to �model temporal evolution of set of neuronal states zt
General State modelling
z: current state of system
u: external input to system
θ: intrinsic connectivity
Neural State Equition in DCM
Example: �attention to motion or colour of visual stimulus (Chawla, 1999)
4 nodes (V1, V4, V5, and X)
Connections
Within nodes
Between nodes
External Inputs
Stimulus
Context
(Taken from: Stephan, 2004)
Neural State Equition in DCM
Example: �attention to motion or colour of visual stimulus (Chawla, 1999)
4 nodes (V1, V4, V5, and X)
Connections
Within nodes
Between nodes
External Inputs
Stimulus
Context
(Taken from: Stephan, 2004)
Neural State Equition in DCM
Example: �attention to motion or colour of visual stimulus (Chawla, 1999)
4 nodes (V1, V4, V5, and X)
Connections
Within nodes
Between nodes
External Inputs
Stimulus
Context
(Taken from: Stephan, 2004)
Neural State Equition in DCM
Example: �attention to motion or colour of visual stimulus (Chawla, 1999)
4 nodes (V1, V4, V5, and X)
Connections
Within nodes
Between nodes
External Inputs
Stimulus
Context
(Taken from: Stephan, 2004)
Neural State Equition in DCM
Example: �attention to motion or colour of visual stimulus (Chawla, 1999)
4 nodes (V1, V4, V5, and X)
Connections
Within nodes
Between nodes
External Inputs
Stimulus
Context
(Taken from: Stephan, 2004)
Neural State Equition in DCM
Neural State Equition in DCM
Z.: change in neural system
A: connectivity matrix if no input
Intrinsic coupling in absence of experimental perturbations
z: nodes (regions)
C: extrinsic influences of inputs on neuronal activity in regions
u: inputs
This equition cannot account for changes in connectivity due to input.
T___T
Neural State Equition in DCM
Z.: change in neural system
A: connectivity matrix if no input
Intrinsic coupling in absence of experimental perturbations
B: change in intrinsic coupling due to input
z: nodes (regions)
C: extrinsic influences of inputs on neuronal activity in regions
u: inputs
Neural State Equition in DCM
Having established this neural state equation, we can now specify DCMs to look at:
Contrast analysis as a specific case of DCM� #conventional analysis
Assuming that B=[ ] and only allowing for connectivity within regions…….
Hypothesis-Driven Model
Functional Connectivity
Effective connectivity
Hypothesis-Free
Hypothesis-Driven
Resting-state fMRI
(Correlation)
Default-mode network
Psycho-physiological Interactions
(Linear regression analysis)
V1
a
V5
Dynamic causal modeling
(Nonlinear dynamic models)
Tested Models
| Interhemisoheric connections | Projection into amygdala | Modulate by gun (alarm) |
1 | V1, FC, SM | bil.V1 | r.FC2SM |
2 | V1, FC, SM | V1, FC | r.FC2SM |
3 | V1, FC, SM | V1, FC | none |
4 | V1, SM | bil.V1 | r.FC2SM |
5 | V1, SM | V1, FC | r.FC2SM |
6 | V1, SM | V1, FC | none |
... | ……. | ……. | ……. |
Amygdala
Inference in DCM: Estimating model parameters
Original equation in �Bayes' theorem
Using Bayes’ theorem to estimate model parameters
BOLD signal
empirical (haemodynamic parameters) and non-empirical (eg. shrinkage priors, temporal scaling)
Baysian Model Selection
| Interhemisoheric connections | Projection into amygdala | Modulate by gun (alarm) |
1 | V1, FC, SM | bil.V1 | r.FC2SM |
2 | V1, FC, SM | V1, FC | r.FC2SM |
3 | V1, FC, SM | V1, FC | none |
4 | V1, SM | bil.V1 | r.FC2SM |
5 | V1, SM | V1, FC | r.FC2SM |
6 | V1, SM | V1, FC | none |
... | ……. | ……. | ……. |
…...
Baysian Model Selection
| Interhemisoheric connections | Projection into amygdala | Modulate by gun (alarm) |
1 | V1, FC, SM | bil.V1 | r.FC2SM |
2 | V1, FC, SM | V1, FC | r.FC2SM |
3 | V1, FC, SM | V1, FC | none |
4 | V1, SM | bil.V1 | r.FC2SM |
5 | V1, SM | V1, FC | r.FC2SM |
6 | V1, SM | V1, FC | none |
... | ……. | ……. | ……. |
Amygdala
Double-edged sword of the DCM
Amygdala
?
?
Double-edged sword of the DCM
Other references of DCM for optimizing
Next ->
DCM Implementation