Measurements of blood oxygenation level dependent (BOLD) signals have produced some surprising observations. One is that their amplitude is proportional to the entire activity in a region of interest and not just the fluctuations in this activity. Another is that during sleep and anesthesia the average BOLD correlations between regions of interest decline as the activity declines. Mechanistic explanations of these phenomena are described here using a cortical network model consisting of modules with excitatory and inhibitory neurons, taken as regions of cortical interest, each receiving excitatory inputs from outside the network, taken as subcortical driving inputs in addition to extrinsic (intermodular) connections, such as provided by associational fibers. The model shows that the standard deviation of the firing rate is proportional to the mean frequency of the firing when the extrinsic connections are decreased, so that the mean BOLD signal is proportional to both as is observed experimentally. The model also shows that if these extrinsic connections are decreased or the frequency of firing reaching the network from the subcortical driving inputs is decreased, or both decline, there is a decrease in the mean firing rate in the modules accompanied by decreases in the mean BOLD correlations between the modules, consistent with the observed changes during NREM sleep and under anesthesia. Finally, the model explains why a transient increase in the BOLD signal in a cortical area, due to a transient subcortical input, gives rises to responses throughout the cortex as observed, with these responses mediated by the extrinsic (intermodular) connections.
Bennett, M. R., Farnell, L., Gibson, W. G., & Lagopoulos, J. (2015). Cortical network models of firing rates in the resting and active states predict bold responses. PLoS ONE, 10(12). https://doi.org/10.1371/journal.pone.0144796