DCM for ERP/ERF: Theory and
Practice
Methods for Dummies 2013
Helen Pikkat
Andrea Gajardo Vidal
Overview
DCM:Theory
• Introduction
• DCM
• Neural mass model
• Bayesian Model Comparison
DCM :Practice
• SPM analysis
• Pre processing
Introduction
Event related Fields (ERFs) and potentials (ERPs)
have been used for decades as putative magnetoand electrophysiological correlates of perceptual
and cognitive operations. However, the exact
neurobiological
mechanism
underlying
their
generation are largely unknown.
David et al., (2005), NeuroImage
Introduction
ERPs
• ERPs are measured with
electroencephalography
(EEG).
ERFs
• The magnetoencephalography
(MEG) equivalent of ERP is
the ERF, or event-related field.
Dynamic Causal Modelling (DCM)
Dynamic Causal Modelling (DCM) is based on an idea
initially developed for fMRI data: The measured data are
explained by a network model consisting of a few sources,
which are interacting dynamically. One can make inferences
about connections between sources, or the modulation of
connections by task.
Ashburner et al. (2013) SPM 8 Manual
Dynamic Causal Modelling (DCM)
Five essential aspects..
1. DCMs are dynamic, using (linear or nonlinear) differential equations
for describing neuronal dynamics.
2. Second, they are causal in the sense of control theory.
3. Third, DCMs strive for neurophysiological interpretability.
4. Fourth, they use a biophysically motivated and parameterized forward
model to link the modelled neuronal dynamics to specific features of
measured data.
5. Fifth, DCMs are Bayesian in all aspects. Each parameter is
constrained by a prior distribution.
Stephan et. al.,(2010), NeuroImage
DCM for ERPs and ERFs
• The dynamic causal models (DCMs) can explain
event-related potentials (ERPs) and fields (ERFs)
measured with electroencephalography (EEG)
and magnetoencephalography (MEG).
DCM for ERPs and ERFs:
Types of connectivity
Presence of
axonal
connections
Dependence
between regions
Causal influences
between neuronal
populations
DCM for ERPs and ERFs
• DCM for ERPs and ERFs uses the concept of effective
connectivity, as opposed to functional connectivity.
Effective connectivity refers explicitly to the influence one
neuronal system exerts over another.
• Effective connectivity is estimated by perturbing the
system and measuring the response using Bayesian
model inversion.
DCM for ERPs and ERFs: The Paradigm
Mismatch negativity (MMN):
Auditory mismatch negativity
Deviant conditions (D) can be embedded
in a stream of repeated or standards
condition (S) produce a distinct response
that can be recorded non-invasively with
EEG and MEG.
The MMN is the negative component of
the waveform obtained by subtracting
the event-related response to a
standard (common) from the deviant
condition (infrequent condition).
DCM for M/EEG: Strengths and Limitations
STRENGTHS
1.For M/EEG data, DCM is a powerful technique for inferring about parameters
that one doesn't observe with M/EEG directly.
2.In general DCM for M/EEG can test hypotheses about what is happening
between sources, in a network.
3.One of the most important thing is that DCM combines the spatial forward
model with a biologically informed temporal forward model, describing e.g.
the connectivity between sources. This critical ingredient not only makes the
source reconstruction more robust by implicitly constraining the spatial parameters,
but also allows one to infer about connectivity
DCM for M/EEG: strengths and limitations
LIMITATIONS
1.Model selection: the choosing between two or more alternative models
can generate problems. The most common problem is known as
“overfitting” (a model fit alone is not a sufficient criterion, as a good fit can
often be achieved by simply including a large number of unnecessary
parameters).
2. A model that explains only a very small portion of the variance of the
data does not inspire much confidence.
3.DCM is capable of identifying the “true” model provided it is among the
candidate set?
Hierarchical MEG/EEG Neural Mass
Model
• The majority of neural mass models of MEG/EEG
dynamics have been designed to generate spontaneous
rhythms (David and Friston, 2003) and epileptic activity
(Wendling et al.,2002). These models use a small number
of state variables to represent the expected state of large
neuronal populations, i.e.the neural mass.
• David et al. (2005) developed a hierarchical cortical
model to study the genesis of ERFs/ERPs.
Hierarchical MEG/EEG Neural Mass Model
DCMs for MEG/EEG use neural mass models to explain source activity in terms
of the ensemble dynamics of the interacting inhibitory and excitatory
subpopulations of neurons, based on the model of Jansen and Rit (1995).
This model emulates the activity of a source using three neural subpopulations,
each assigned to one of three cortical layers:
•
•
•
An excitatory subpopulation in the granular
layer.
An inhibitory subpopulation in the supragranular layer.
An population of deep pyramidal cells in the
infra-granular layer.
Hierarchical MEG/EEG Neural Mass Model
The excitatory pyramidal cells receive
excitatory and inhibitory input from local
interneurons (via intrinsic connections),
and send excitatory outputs to remote
cortical areas via extrinsic connections.
Using these connection rules, it is
straightforward
to
construct
any
hierarchical cortico-cortical network
model of cortical sources.
Hierarchical MEG/EEG Neural Mass Model
Bottom-up or forward
connections
• that originate in agranular layers and
terminate in layer 4.
Top-down or backward
connections
• that connect agranular layers.
Lateral connections
• that originate in agranular layers and target
all layers.
+
Canonical
MicroCircuit
(CMC)
Hierarchical MEG/EEG Neural Mass Model
• The cortex has a hierarchical organization (Crick and
Koch, 1998; Felleman and Van Essen, 1991).
• Forward, backward and lateral processes that can be
understood from an anatomical and cognitive perspective
(Engel et al., 2001).
• DCM for ERPs and ERFs takes the spatial forward
model into account. This makes DCM spatiotemporal
model of the full data set (over channels and peri-stimulus
time).
Hierarchical MEG/EEG Neural Mass Model
Bayesian Model Comparison
.
The inversion of a DCM provides information about the underlying
cortical pathways and their causal architecture.
SPM presentation (2012)
Bayesian Model Comparison
• What model fit better your data?
• Bayesian model comparison (Penny et al., 2004) selects
the model, among competing models, that best explains
the data.
• Given equal prior probabilities for the models considered,
they are compared using their marginal likelihood or
evidence for each model.
Bayesian Model Comparison
A
B
• How to compare models to data?
• What makes model A better than model B?
– If it describes the data better…
– What do we mean by “describing better”?
Bayesian Model comparison
Model comparison for group studies
Random
effect (RFX)
Fixed effect
(FFX)
For multi-subject analyses, two options exist depending on
whether one assumes that the parameters of interest are
fixed effects in the population (FFX) or are themselves
probabilistically distributed in the population (RFX).
Bayesian Model comparison
Fixed effect
(FFX)
In the FFX case, one assumes that the optimal
model is the same for each subject in the
population. This assumption is warranted when
studying a basic physiological mechanism that is
unlikely to vary across the subjects sampled.
Bayesian Model comparison
Random
effect (RFX)
On the other hand RFX accounts for heterogeneity of model
structure across subjects and yields posterior model
probabilities and exceedance probabilities. In either case,
model space partitioning and subsequent comparison of
model families (family-level inference) should be considered
when the hypothesis of interest concerns model structure and
not any particular model parameter.
DCM for ERP/ERF: practice

There are different DCMs for EEG/MEG data

This presentation focuses on ERPs
(based in large part on the sample SPM dataset for MMN)

DCM for ERP/ERFs recquires an experimental manipulation.
Steps to follow
Hypothesis
pre-DCM
Preprocessing
Model specification
Model inversion
Model comparison
DCM
pre-DCM
Hypothesis
Preprocessing
•
What kind of hypothesis can you test?
•
* about the model space (e.g. importance of specific areas)
•
* about the model parameters (e.g. connection strength, direction)
•
Preprocessing is done as for any other EEG data analysis...
DCM: SPM
DCM: SPM - data & design
DCM: SPM - data & design
Choose the period you want to model
Choose the neural model
(ERP, CMC, ...)
Choose the type of DCM
Insert the conditions
Choose the number of components
Specify contrasts for your conditions
Model specification
What cortical areas and connections might explain the
data?
Model specification
* Specify the areas for each model
Based on:
- the literature
- fMRI data
- the previous or current EEG data
Note that you can define models with different number of regions (which is
not possible in DCM for fMRI).
* Specify the connections for each model
Based on:
- anatomical/physiological knowledge
Model specification
+ a matrix for backwards
connections
+ a matrix for lateral connections
+ a matrix for connections that are
allowed to vary between conditions
(modulatory effects)
Model specification: SPM
Model specification: SPM
Name the sources
Insert the coordinates of the
sources (in MNI coordinates)
Specify the connections
Model inversion
Finds the parameters that minimize differences between observed
measurements and the predicted models.
As a result you will get:
- posterior distribution of parameters
You can plot the data for ERPs and model fit for each mode.
Model inversion
Predicted data (model)
Data
Expectation-Maximization algorithm
Compute model response using
current set of parameters
Compare model response with data
Improve model parameters if possible
(until the maximum likelyhood is found)
Result: posterior distributions of parameters
Make inferences on parameters
Model inversion: SPM
Then specify the connections for the other
model(s) and estimate the parameters for these
Check the results from here
Estimate the model
Model comparison
Remember - there is no right model!
We can get the information for:
1. The best model (BMS)
2. The coupling parameters of this model
Usually, BMS (Bayesian Model Selection) is first used to select an optimal model
from all alternatives, and then the posterior or conditional inferences about the
parameters of this optimal model are reported.
Model comparison: BMS
BMS (Bayesian Model Selection) computes the model evidence (the probability of
data) given some model and priors.
- The most likely model is the one with the largest log-evidence.
- Conventionally: log-evidence greater then 3 provides strong evidence.
*If you can't differentiate two models then they can be either too similar or the
data might be too noisy ot they might not have fitted well.
* If you were interested only in model structure you can just use BMS and don't
have to interpret the results from mode estimation
Model comparison: BMS in SPM
Compare models
Model comparison: BMS in SPM
Model comparison: BMS in SPM
Results:
- a bar plot of the log-model evidences for all models
Model comparison: BMS in SPM
Results:
- the probability, for each model, that it produced the data.
Back to model inference
When you are interested in specific parameters in the model(s)
use the results from the model estimation.
Use BMA (Bayesian model averaging) to compare parameters for
different models.
Final notes
• - DCM can tell you about the changes in connectivity between
sources.
• - ...but it can only compare the models that you provide
• - Therefore your models should be based on your hypothesis and be
plausible
• - Any result obtained is relative and dependent on the models that
you defined
• Thank very much to our expert Harriet
Brown!!
Reference List
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den Ouden, D-B., Saur, D., Mader, W., et al., (2012), Network modulation during complex
syntactic processing, Neuroimage, 59-1, p.815-823
David, O., Kiebel, S.J., Harrison, L.M., et al., (2006), Dynamic causal modeling of evoked
responses in EEG and MEG, Neuroimage, 30-4, p.1255-1272
Kiebel, S. J., Garrido, M. I.,; Moran, R. J., et al., (2008), Dynamic causal modelling for EEG
and MEG, Cognitive Neurodynamics, 2-2, p.121-136
David, O., Harrison, L., Friston, K.J., (2005), Modelling event-related responses in the brain,
Neuroimage, 25-3, p.756-770
Lohmann, G., Erfurth, K., Mueller, K. et al., (2012), Critical comments on dynamic causal
modelling, Neuroimage, 59-3, p.2322-2329
SPM8 Manual (2013)
Litvak, V. (2012, May). The principles of DCM. Talk given at SPM course London.
Daunizeau, J. (2012, May). DCM for evoked responses. Talk given at SPM course London.
Bastos, A. & Dietz, M., (2012, May). Demo - DCM. Talk given at SPM course London.
Stephan, K. E., Penny, W. D., Moran, R. J., Den Ouden, H. E. M., Daunizeau, J., & Friston, K.
J. (2010). Ten simple rules for dynamic causal modeling. NeuroImage, 49(4),
Previous MfD talks
Reference List
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David, O., Harrison, L., & Friston, K. ( 2005). Modelling event-related responses in the
brain. Neuroimage, 25, 3, 756-770.
David, O., Kiebel, S. J., Harrison, L. M., Mattout, J., Kilner, J. M., & Friston, K. J.
(2006). Dynamic causal modeling of evoked responses in EEG and MEG.
Neuroimage, 30, 4, 1255-1272
Friston, K. J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling.
Neuroimage, 19, 4, 1273-1302.
Garrido, M. I., Kilner, J. M., Kiebel, S. J., Stephan, K. E., & Friston, K. J. (2007).
Dynamic causal modelling of evoked potentials: a reproducibility study. Neuroimage,
36, 3, 571-80
Stephan, K. E., Penny, W. D., Moran, R. J., den, O. H. E. M., Daunizeau, J., &
Friston, K. J. (2010). Ten simple rules for dynamic causal modeling. Neuroimage, 49,
4, 3099-3109.
Ashburner et. al., (2012). SPM 8 MANUAL. Wellcome Trust Centre For
Neuroimaging.
http://www.fil.ion.ucl.ac.uk/spm/course/