DCM for ERP/ERF: Theory and Practice

Methods for Dummies 2013

Helen PikkatAndrea Gajardo Vidal

OverviewDCM: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 magneto- and electrophysiological correlates of perceptual and cognitive operations. However, the exact neurobiological mechanism underlying their generation are largely unknown.

David et al., (2005), NeuroImage

Introduction

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

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.

Dynamic Causal Modelling (DCM)

Five essential aspects..

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

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

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).

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Mismatch negativity (MMN):

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

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?

DCM for M/EEG: strengths and limitations

• 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

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 supra-granular layer.

• An population of deep pyramidal cells in the infra-granular layer.

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

Hierarchical MEG/EEG Neural Mass Model

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

SPM presentation (2012)

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The inversion of a DCM provides information about the underlying cortical pathways and their causal architecture.

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

• 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”?

A B

Bayesian Model comparison

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).

Model comparison for group studies

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

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.

Bayesian Model comparison

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

Preprocessing

Model specification

Model inversion

Model comparison

DCM

pre-DCM

Model comparisonModel comparison

pre-DCM

• 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...

Hypothesis

Preprocessing

DCM: SPM

DCM: SPM - data & design

DCM: SPM - data & design

Choose the type of DCM

Choose the neural model(ERP, CMC, ...)

Choose the period you want to model

Choose the number of components Specify contrasts for your conditions

Insert the conditions

What cortical areas and connections might explain the data?

Model specification

* Specify the areas for each modelBased 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 modelBased on:- anatomical/physiological knowledge

Model specification

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

Insert the coordinates of the sources (in MNI coordinates)

Name the sources

Specify the connections

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

Data Predicted data (model)

Model inversion

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

Estimate the model

Check the results from here

Then specify the connections for the othermodel(s) and estimate the parameters for these

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 (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

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.

Model comparison: BMS in SPM

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.

Back to model inference

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!!

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

Reference List•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/