PPI are one of the simplest models available to assess functional interactions in neuroimaging data (see Friston et al. 1997 for details). Given a chosen reference time series y0 (obtained from a reference voxel or region), PPI computes whole-brain connectivity maps of this reference voxel with all other voxels yi in the brain according to the regression-like equation yi = ayo + b(yo x u) + cu + Xß + e (9)
Here, a is the strength of the intrinsic (context-independent) connectivity between y0 and y;. The bilinear term y0 x u represents the interaction between physiological activity y0 and a psychological variable u which can be construed as a contextual input into the system, modulating the connectivity between y0 and y; (x represents the Hadamard product, i.e. element-by element multiplication). The third term describes the strength c by which the input u determines activity in y; directly, independent of y0. Finally, ß are parameters for effects of no interest X (e.g. confounds) and e is a Gaussian error term.
Notwithstanding the fact that this is a non-dynamic model, (9) contains the basic components of system descriptions as outlined in Sect. 2 and (3), and there is some similarity between its form and that of the state equation of DCM ((13), see below). However, since only pair-wise interactions are considered (i.e. separately between the reference voxel and all other brain voxels), this model is severely limited in its capacity to represent neural systems. This has also been highlighted in the initial description of PPIs (Friston et al. 1997). Although PPIs are not a proper system model, they have a useful role in exploring the functional interactions of a chosen region across the whole brain. This exploratory nature bears some similarity to analyses of functional connectivity. Unlike analyses of functional connectivity, however, PPIs model the contextual modulation of connectivity, and this modulation has a directional character, i.e. testing for a PPI from y0 to y; is not identical to testing for a PPI from y; to y0. This is because regressing y0 x u on y; is not equivalent to regressing yi x u on y0.
Was this article helpful?