This study evaluated the predictive validity of DCM by looking at its reproducibility over subjects in the context of the MMN. To this end we used DCM to explain differences in ERPs in terms of changes in effective connectivity. For each subject we used three models of connectivity, within the same underlying cortical architecture but differing in modulations of specific types of connections. There was a very reproducible pattern of results across subjects. Model comparison revealed that conjoint changes in forward and backward connections (FB-model), relative to changes in forward (F-model) or backward connections alone (B-model) are consistently better across subjects. In every subject, these models were better than a null model that precluded any coupling changes. The evidences for models F and FB were, overall, much bigger than the model evidence for B. A similar consistency was observed quantitatively, in terms of the conditional densities of each connection; as predicted, the coupling estimates change between the two event types, i.e., standards and deviants.
In all but one subject the F-model was better than the B-model. This is an important result because both of these models had the same number of parameters. This means that any difference in the model evidences can only be explained by their ability to predict the observed response. The probability that 10 out of 11 comparisons would select the same model, by chance is exceedingly small. This suggests the DCM is sensitive to a systematic difference in ERPs to oddballs and standards and that difference, formally, lies in the network architectures used to model the observed responses. Furthermore, the FB-model was significantly better than both, in 7 out of 11 subjects. This is another important result because it shows that a more complex model (that can fit the data more accurately) is not necessarily the most likely model.
Choice of paradigm
We have deliberately chosen a paradigm that evokes two responses exhibiting a large difference over peri-stimulus time. Note that this is not a classical oddball paradigm, as employed in the MMN literature. The large pitch difference between responses to standards and deviants elicits large differences for both N1 and MMN components, which cannot be disentangled. In this sense, this paradigm is not necessarily appropriate for modelling the MMN alone, but suitable for assessing the reproducibility of DCM: DCM is a model of dynamic responses or transients that are continuous in time. This means that the DCM is not an explanation for a particular response component (e.g., the MMN) but the compound response over all peristimulus times; it is likely that our paradigm induced N1 effects (due to the large different in standard and oddball tones) and, at least phenomenologically, a P300-like component (although the analysis presented here only went up to 250 ms). However, all these components could be explained by differences in a simple network model of interacting neuronal populations. It will be interesting to assess the ontological status of response components (e.g., N1, MMN, and P300) in the light of mechanistic models like DCM (see below).
Choice of model
DCM is not an exploratory technique; it does not explore all possible models: DCM tests specific models of connectivity and, through model selection, can provide evidence in favour of one model relative to others. The results of a DCM analysis depend explicitly upon the models evaluated, which are generally motivated by mechanistic hypotheses. This means there may exist other equally or more plausible models with different architectures (in respect of the areas and connections involved). The network we chose for our DCMs was motivated by the results of previous MMN (Opitz et al., 2002; Doeller et al., 2003
). It has been shown that the generators of the MMN lie bilaterally on the temporal cortex. In addition, some studies have shown bilateral generators on the frontal cortex, which are activated later than the auditory cortex generators (Rinne et al., 2000
). Recent studies showed a double peak over frontal scalp locations suggesting the existence of two sub-components for the MMN (Opitz et al., 2002
and Doeller et al., 2003
). The early component is reported to peak around 90–120 ms and can be modelled with sources located bilaterally in the superior temporal gyrus (STG). Components within peaking around 140–170 ms have been shown to be modelled effectively with dipoles in both left and right inferior frontal gyrus (IFG) that are usually stronger in the right hemisphere. Moreover, the right IFG is reported more consistently as in the literature than the homologous source on the left. This is why we used a unilateral right IFG. The inclusion of both left and right primary auditory cortices was necessary because DCM attempts to explain each ERP individually and any differences (in this case, responses to standards and deviants and the implicit mismatch). Therefore, left and right A1 were chosen as the cortical targets of thalamic input, for processing the auditory information.
Indeed there may be other plausible models. So, why not include more sources in the model, for example left IFG? This is an important question that has a principled answer. Each model is defined by its number of sources and their connectivity. Given a particular model, DCM will optimise the parameters of that model. To explore the space of models, one uses the marginal likelihood or log-evidence to compare one model with another. This enables one to adjudicate between different models with different number of sources. This is potentially an important application of DCM in the context of model selection. In this paper, we focussed on reproducibility of different connectivity architectures. In our next paper, we will present an exploration of model space.
Mechanisms of ERP generation
The mechanism of MMN generation is unknown. Two sorts of hypotheses have been suggested. Traditionally, this response is thought to be associated with an automatic cortical change-detection process, which detects a difference between the current and the preceding input. It has been proposed that the MMN would reflect modifications to existing parts of a model of the acoustic environment. This model adjustment hypothesis discusses the existence of a dynamic system of change detection which updates its model of sensory input as the changes occur (Winkler et al., 1996; Sussman and Winkler, 2001
). Doeller et al. (2003)
suggested that the prefrontal cortex is involved in a top-down modulation of the deviance detection system in the temporal cortices. The traditional interpretation has been criticised by Jääskeläinen et al. (2004)
who proposed that the MMN results from an adaptation
mechanism (see also May et al., 1999
) and is erroneously interpreted as a separate component generated by change-specific neurons. The N1 response to standard (or ‘non-novel’) sounds is thought to be delayed and suppressed (or attenuated
) as a function of its similarity to the preceding auditory events, reflecting short-lived adaptation of auditory cortex neurons. Under this hypothesis, the response termed as MMN, would therefore be a product of an N1 differential wave emerging in the subtraction of the standards from the deviant’s ERP. Recently, the MMN has been framed within a predictive coding scheme, interpreted as a failure to suppress prediction error, which can be explained quantitatively in terms of coupling changes among cortical regions (Friston, 2005
). This predicts the adjustment of a generative model of current stimulus trains (cf
., the model adjustment hypothesis) using plastic changes in synaptic connections (cf
. the adaptation hypothesis).
Frequently asked questions
In presenting this work to our colleagues and for peer review a number of key questions arose. In what follows, we summarise these questions and attempt to answer them briefly.
What is the relationship between “inverting” a DCM and inverting a classical electromagnetic forward model to locate intra-cranial source locations?
Model inversion is used in exactly the same way in both contexts. In fact, inverting a DCM subsumes the inversion of a conventional forward model. This is because DCM has two components; a neural-mass model of the interactions among a small number of dipole sources and a classical electromagnetic forward model that links these sources to extra-cranial measurements. Inverting the DCM implicitly optimises the location and orientation of the sources. Indeed, if we removed the neuronal part of the model, DCM would reduce to a conventional forward model. The current implementation of DCM for ERPs uses the electromagnetic forward model solutions encoded in the fieldtrip software (http://www2.ru.nl/fcdonders/fieldtrip
In this paper we used informative priors on source locations. How important are prior source locations in DCM? Not very important; in other words, changing the location priors would not change the results very much. This is because there is very little information in the EEG or MEG measurements about the spatial location of sources. In contrast, there is an enormous amount of information about their orientation. A usual heuristic is to imagine that one is trying to infer the location and orientation of a pen-torch that is illuminating the inside of a balloon. When looking at the balloon from outside, a small change in the position of the torch will have only a small effect on the pattern of illumination. Conversely, changing its orientation will have a large impact. In brief, location is not an important quantity, whereas orientation is. For this reason, we put relatively informative priors on location but leave the orientation parameters free. It is relatively straightforward to assess the impact of different location priors using model selection.
Here we used three eigenmodes to invert the DCM. Does DCM deal only with three channel data? No, DCM will fit any number of channels or modes. For computational reasons, the channel data are projected onto their principal eigenmodes to reduce the size of the matrices the inversion scheme has to handle. Generally, one would use the same number of modes as there are sources. This is because data generated by an n-source model can only span an n-dimensional subspace of sensor space. Provided the signal is large, relative to noise, the first n principal eigenvariates should capture the majority of signal.
What does DCM actually operate on, the channel data or some estimate of source dynamics? DCM operates on the channel data in the same way as sources are reconstructed in a conventional setting. In both cases, one needs to specify the number of sources and how their activity is expressed in sensor space. The only difference is that, with DCM, one also has to specify the connections among the sources and which sources receive sensorimotor input.
How is the significance of the difference between models evaluated at the between-subject level? For a single subject, a difference in log-evidence of about three is considered strong evidence in favour of the more likely model. This is because a difference of three means the evidence for the more likely model is about 20 times the evidence for the other. This can be compared to the use of p = 0.05 = 1/20 in classical inference. When pooling log-evidences from several subjects, one adds the evidences and, implicitly the differences. This is because adding logs is the same as multiplying probabilities and the probability of getting two independent sets of data is simply the product of the probabilities of getting each alone. It can be seen that one will quickly reach a threshold of three if, and only if, the difference in log-evidences is consistent over subjects.
How does one reconcile different results from different DCMs? In this paper, we have looked at the reproducibility of DCMs in terms of consistency over subjects in model space. Although not the focus of this paper, it is also interesting to address the consistency of the model parameters. Inference on the parameters of a particular DCM is conditional upon the specific model and data used. Clearly, one could get very different conclusions by changing the model, as we find here for F and FB models (see ). One may be very confident about contradictory results from two different models. This contradiction is resolved by considering the relative likelihoods of the two models. Generally, one only considers inference on the parameters of the best model. It is possible to use Bayesian model averaging; however, this is most useful when the models have roughly the same probability. If the results change under the same model with different datasets, then this speaks to inter-subject variability that may be real. Clearly, it would be re-assuring to see that the parameters estimates from each model were also consistent over subjects. This can be addressed with a second, between-subject analysis of the parameter estimates. To illustrate the consistency of DCM inversion in terms of model parameters, we used a classical multivariate statistical analysis (MANOVA) of subject-specific parameter estimates, from the best model (FB). In this analysis, we summarised the interesting DCM parameters using: the average coupling changes for the forward connections and the average changes for backward connections. Using just two dependent summary variables ensured we had sufficient (i.e., nine) degrees of freedom to infer the group averages where significantly different from zero. The resulting F-value (based on Wilk's lambda; df 2,9) was 4.725 corresponding to a p-value of 0.04. This implies a systematic and consistent pattern of changes over forward and backward connections, over subjects. The average change in forward connections was 80% and the average change in backward connections was 57%. This is in conformity with the average change in forward and backward connections for the DCM analysis of grand mean data, which was 42% and 52% respectively. A more informed way of addressing this issue would involve a hierarchical Bayesian model that includes random effects from each subject. Thus will be focus of future work.