Activated region fitting: a robust high-power method for fMRI analysis using parameterized regions of activation

Abstract

An important issue in the analysis of fMRI is how to account for the spatial smoothness of activated regions. In this article a method is proposed to accomplish this by modeling activated regions with Gaussian shapes. Hypothesis tests on the location, spatial extent, and amplitude of these regions are performed instead of hypothesis tests of individual voxels. This increases power and eases interpretation. Simulation studies show robust hypothesis tests under misspecification of the shape model, and increased power over standard techniques especially at low signal-to-noise ratios. An application to real single-subject data also indicates that the method has increased power over standard methods.

Figure 1

Isocontours of an activated region. θ₁ and θ₂ define the center of the region; θ₃, θ₄, and θ₅ (not shown) define the spatial extent of the region; θ₆ (not shown) defines the amplitude of the region.

Figure 2

Standardized bias for location, spatial extent, and amplitude parameters as a function of signal‐to‐noise ratio.

Figure 3

Variance ratios for location and amplitude parameters of the different shape models (correct, pyramidal, and double) as a function of signal‐to‐noise ratio.

Figure 4

Proportion correct discoveries (power) for activated region fitting, Cluster size threshold, false discovery rate, and Bonferroni as a function of signal‐to‐noise ratio for three shape models [correct (a), pyramidal (b), and double (c)]. (a–c) The uncorrelated noise data. (d) The correlated noise data with the double model. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 5

Average activation (t‐values) of the left hemisphere from four runs of the experiment (unthresholded). Active voxels (based on FDR correction) are marked black. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 6

BIC values for 18 sequential models. The triangle indicates the best fitting model (13 regions). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 7

Activated region fitting solution with 13 active regions. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]