Brain Mapping identifies regions where experimental effect sizes are significantly non-zero (orange). Brain connectivity then explains activity in a set of regions using (eg. differential equation) models with directed connections. For Brain Mapping the parameters of interest are regional activities and for Brain Connectivity they are directed pathways (blue). Both approaches can be applied to data from fMRI or M/EEG. For fMRI this requires Bayesian inversion of a forward model describing a temporal convolution, and for M/EEG a forward model describing a spatial mapping.
Dynamic Causal Modeling (DCM) is a Bayesian estimation framework for fitting differential equation models of neuronal activity to brain imaging data. Model comparison in this context allows researchers to formally compare different theories about the architectures of the large-scale neural networks that mediate human perception, cognition and action, using non-invasive brain imaging data. In the figure below the red traces indicate time series of neuronal activity that result when the modulatory connection from u2 is activated. This is a mathematical model of gain control effects mediated eg. by neuromodulators.
These methodological developments are in collaboration with Karl Friston, Klaas Stephan, Jean Daunizeau and Rosalyn Moran among others.
Collaborations with Alex Leff's group have involved the application of Dynamic Causal Models (for MEG/EEG) in studying recovery of language function after brain injury (eg. due to stroke). Work with Klaas Stephan's group aims to fractionate schizophrenic groups into sub-categories with distinct brain connectivity fingerprints.