Classical and Bayesian Inference in fMRI - Advance Image Processing in Magnetic Resonance Imaging - page 545

FIGURE 17.6 This schematic (upper panel) outlines the differential equations implied by
a bilinear model. The equations in each of the white areas describe the change in neuronal
activity z i in terms of linearly separable components that reflect the influence of other
regional state variables. Note particularly how the second contextual inputs enter these
equations. They effectively increase the intrinsic coupling parameters ( a ij ) in proportion to
the bilinear coupling parameters ( b ij ) . In this diagram, the hemodynamic component of the
DCM illustrates how the neuronal states enter a region-specific hemodynamic model to
produce the outputs y i that are a function of the region's biophysical states reflecting
deoxyhemoglobin content and venous volume ( q i and v i ). The lower panel reformulates the
differential equations in the upper panel into a matrix format. These equations can be
summarized more compactly in terms of coupling parameter matrices A , B j and C .