DCM was invented because of theoretical concerns about the application of GCM to connectivity in the brain (see Box 2). However, following the publication of David et al. [1
], some of these conceptual issues are now empirical facts. This advance rests on an elegant study using multimodal techniques and a well-defined animal model of neuronal signal propagation and directed connections; namely a rat model of absence epilepsy with spontaneous spike and wave discharges. In brief, the authors were able to measure brain responses to sporadic epileptic events; both at their source (somatosensory cortex) and in connected brain regions. Critically, they measured both electrical and haemodynamic responses. This allowed them to infer the known connectivity using just the fMRI data (with DCM and GCM) and compare the estimates to the true connectivity based on electrophysiology. Furthermore, because they had a measure of the underlying neuronal (electrical) activity, they were able to assess regional variations in the haemodynamic response function that could confound GCM.
More specifically, David et al. recorded non-invasive EEG and fMRI signals during seizure activity and later recorded intracranial signals in the areas identified by the brain mapping. By recording both electrophysiological (neuronal) and fMRI (haemodynamic) responses, the authors were able to evaluate the haemodynamic response function empirically; in regions showing seizure-related responses. Critically, they found enormous differences between the haemodynamic response functions in different brain areas. The authors compared the results of DCM and GCM analyses of the fMRI data and showed that regional variation in the haemodynamic response function did indeed lead to different conclusions about the connectivity. They then went on to use the intracranial recordings to establish the face validity of the ensuing inferences. They did this by looking at the direction of neuronally mediated influences, in terms of delays and asymmetry in generalised synchronisation of these time-resolved measures. They were able to show that the driver of spike and wave discharges was correctly located in the somatosensory cortex when, and only when, haemodynamic effects were modelled appropriately by DCM.
This study highlights a key conceptual difference between DCM and GCM (see ): namely, that DCM has an explicit model of hidden states causing observed data; whereas GCM tries to establish dependencies among the observations themselves. This is fine when the brain states that cause each other are observed directly (EEG), but not when the data are some post hoc consequence of these states (fMRI). David et al. illustrate this point by applying GCM to the fMRI data and then to the implicit neuronal activity. They show that the inferences are very different and that only GCM of implicit neuronal states gives sensible results. David et al. were able to do this because they had direct (EEG) measures that enabled then to undo (deconvolve) the haemodynamic effects and convert the fMRI data into a surrogate for neuronal states (using region-specific dynamic causal models and spike-wave inputs). In real-world fMRI applications, however, this would not be possible because one does not know the underlying neuronal activity. This is no problem for DCM because it assumes hidden neuronal states and models the haemodynamic convolution in each region explicitly.