Classical and Bayesian Inference in fMRI - Advance Image Processing in Magnetic Resonance Imaging - page 544

Current DCMs for fMRI comprise a bilinear model for the neurodynamics
and an extended balloon model for the hemodynamics. These are shown in

Figure 17.6 and Figure 17.7 . The neurodynamics are described by the multivariate

differential equation shown in Figure 17.6. This is known as a bilinear model
because the dependent variable, , is linearly dependent on the product of z and
u . That u and z combine in a multiplicative fashion endows the model with
“nonlinear” dynamics, which can be understood as a nonstationary linear system
that changes according to experimental manipulation u . Importantly, because u
is known, parameter estimation is relatively simple.
Connectivity in DCM is characterized by a set of “intrinsic connections,” A ,
that specify which regions are connected and whether these connections are
unidirectional or bidirectional. We also define a set of input connections, C , that
specify which inputs are connected to which regions, and a set of modulatory or
bilinear connections, B j , that specify which intrinsic connections can be changed
by which inputs. The overall specification of input, intrinsic, and modulatory
connectivity comprise our assumptions about model structure. This in turn rep-
resents a scientific hypothesis about the structure of the large-scale neuronal
network mediating the underlying sensorimotor or cognitive function.
In DCM, neuronal activity gives rise to hemodynamic activity by a dynamic
process described by an extended balloon model. This involves a set of hemody-
namic state variables, state equations and hemodynamic parameters shown in
Figure 17.7. Together, these equations describe a nonlinear hemodynamic process
that may be regarded as a biophysically informed generalization of the linear
convolution models used in the GLM. It is possible to describe the second-order
behavior of this process (i.e., how the response to one stimulus is changed by a
preceding stimulus) using Volterra kernels.

z

17.6.1 E MPIRICAL E XAMPLE

We now return to the visual motion study described in Subsection 17.5.1 so as

to make inferences about functional integration. Figure 17.8b shows the location

of the regions that entered the DCM (Figure 17.8b). These regions were based

on maxima from conventional SPMs testing for the effects of photic stimulation,
motion, and attention. Regional time courses were taken as the first eigenvariate
of spherical volumes of interest centered on the maxima shown in Figure 17.8.
The inputs, in this example, comprise one sensory perturbation and two contextual
inputs. The sensory input was simply the presence of photic stimulation, and the
first contextual one was presence of motion in the visual field. The second
contextual input, encoding an attentional set, was unity during attention to speed
changes and zero otherwise. The outputs corresponded to the four regional eigen-
variates in (Figure 17.8b). The intrinsic connections were constrained to conform
to a hierarchical pattern in which each area was reciprocally connected to its
supraordinate area. Photic stimulation entered at, and only at, V1 . The effect of
motion in the visual field was modeled as a bilinear modulation of the V1 to V5