Kaundinya Gopinath^{1}, Simon Lacey^{2}, Randall Stilla^{2}, Venkatagiri Krishnamurthy^{1}, and Krish Sathian^{2}

Recent studies have shown that cluster-wise family-wise error rate (FWE) corrected inferences made in parametric statistical methods based fMRI studies over the past couple of decades were invalid due to incorrect these methods incorrectly specifying that spatial auto-correlation functions (sACF) of fMRI data had a gaussian shape. In this study we proposed a method to obtain fMRI inferential statistic residuals with gaussian sACF. Results show that this method substantially increases the detection power of group-level inference tests while not significantly changing the voxelwise statistic maps. Additionally it makes inferences based on assumption of gaussian sACF valid again.

**Purpose**

**Purpose**

Recent studies

Twenty-one right-handed normal subjects (11 male;
median age ~22 yrs) were scanned in a
Siemens 3T Tim Trio scanner using a 12-channel array Rx head coil. Informed
consent was obtained from all participants. The participants underwent a 7-minute fMRI
scan acquired with a sagittal whole-brain gradient echo EPI (TR/TE = 2000/24
ms, FA = 90°, 3x3x3.5mm voxels). The fMRI task paradigm consisted of fifteen 12
sec blocks of body, object, scene, face or scrambled pictures, interspersed
with 14 sec periods of fixation. Standard fMRI preprocessing steps were
employed including FWHM = 5 mm spatial smoothing. Brain activation was assessed
with multiple linear regression (MLR). The 4D residuals time-series dataset
(RSDL) was then subsequently decomposed with FSL’s MELODIC program ^{5}
into 100 ICs. We arbitrarily set the dimensionality of the ICA to 100 since
this was roughly 5 times the optimal model order estimated by MELODIC; the
rationale being such a high order ICA will account for all non-gaussian signal
content in the RSDL. Following this the GLM analysis was repeated with
simultaneous orthogonalization of the 100 component time-series with MLR.

The sACF of the original RSDL datasets and the IC-orthogonalized
residuals datasets (RSDL_ort100IC) was then estimated both at the whole-brain
level and within 25-mm radius spherical local neighborhoods across the brain.
The sACF was parameterized as *sACF(r) = a
* exp(-r*r/(2*b*b)) + (1-a)*exp(-r/c)*, where *r* is the radius, and *a* parameterizes
the ‘gaussianity’ of the sACF (*a*
varies from 0 to 1); and *b* and *c* are other fitted parameters ^{7}.
The apparent FWHM (FWHMap) of spatial correlation was also obtained from all sACF
calculations. The average sACF across the group was obtained for both the RSDL
and RSDL_ort100IC datasets. Cluster-wise FWE corrected p-values were then
obtained for a large number of different voxel p-values through Monte Carlo (MC)
simulation ^{6} incorporating these average sACFs through AFNI’s
3dClustSim program ^{7}.

1. Eklund A, et al., ’Cluster failure: Why fMRI inferences for spatial extent have inflated false-positive rates.’ Proc Natl Acad Sci U S A. 2016, 12;113(28):7900-5.

2. Fair DA, et al., ’A method for using blocked and event-related fMRI data to study “resting state” functional connectivity.’ Neuroimage 2007, 35(1):396–405.

3. Bianciardi M, et al., ’Sources of functional magnetic resonance imaging signal fluctuations in the human brain at rest: a 7 T study.’ Magn. Reson. Imag. 2009, 27: 1019–1029.

4. Salimi-Khorshidi G, et al., ’Automatic denoising of functional MRI data: Combining independent component analysis and hierarchical fusion of classifiers.’ NeuroImage 2014, 90:449–468.

5. Beckmann C, et al., ’Probabilistic independent component analysis for functional magnetic resonance imaging.’ IEEE Trans Med Imaging. 2004, 23(2):137-52.

6. Forman SD, et al., ’Improved assessment of significant activation in functional magnetic resonance imaging (fMRI): use of a cluster-size threshold.’ Magn Reson Med. 1995;33(5):636-47.

7. https://afni.nimh.nih.gov/pub/dist/doc/program_help/3dClustSim.html

Figure
1: Boxplot of spatial autocorrelation function gaussianity parameter *a* of the residuals of the original RSDL
datasets (FMRI_rsdl) and the RSDL_ort100IC datasets (FMRI_ort100ICs_rsdl).

Group
average local smoothness maps of the residuals expressed in average FWHMap mm
for (A) RSDL datasets; and (B) the RSDL_ort100IC datasets.

Table
showing cluster sizes needed to deem various voxel-pvalue thresholds
significant at cluster-wise FWE corrected p < 0.05.

Distribution
of the 1-sample t-test results expressed in z-scores for the RSDL dataset
(blue) and RSDL_ort100IC dataset (pink).