How Can One Model Brain Connectivity?
The fundamental difference between DCM and GCM is that DCM employs an explicit forward or generative model of how observed data were caused. These models invoke hidden neuronal and biophysical states that generate data. In contrast, GCM rests upon a phenomenological model of temporal dependencies among the data themselves [5], without reference to how those dependencies were caused (see Figure 1). In this sense DCM is a model of effective connectivity, whereas GCM is used to infer functional connectivity. This distinction becomes crucial for fMRI, because fMRI signals are haemodynamic convolutions of underlying neuronal signals. In other words, the fMRI signals are the products of a complicated chain of physiological events that are initiated by changes in neuronal activity. This means that the observed fMRI response to a neuronal activation can be delayed and dispersed by several seconds. The convolution or impulse response function, mapping from underlying neuronal activity to observ
