The impact of spherical projection on spin tests for brain maps
Poster No:
1618
Submission Type:
Abstract Submission
Authors:
Vincent Bazinet1, Zhen-Qi Liu1, Bratislav Misic1
Institutions:
1McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University, Montreal, Quebec
First Author:
Vincent Bazinet
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
Co-Author(s):
Zhen-Qi Liu
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
Bratislav Misic
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
McConnell Brain Imaging Centre, Montréal Neurological Institute, McGill University
Montreal, Quebec
Introduction:
Statistical comparison between brain maps is a standard procedure in neuroimaging. Numerous inferential methods have been developed to account for the effect of spatial autocorrelation when evaluating map-to-map similarity. Perhaps the most widely used method is a spatial permutation procedure colloquially referred to as the spin test that involves rotating spherical projection of brain maps [1]. Despite its popularity and conceptual appeal, multiple benchmarking studies have shown that in controlled simulated settings, the spin test does not perfectly control for false positive [2]. Here, we explore why this is the case and how this situation can be mitigated.
Methods:
The spin procedure consists in three main steps: projecting a brain map to a spherical mesh, rotating the sphere and projecting the brain map back to the brain surface. Importantly, the projection of a surface to a sphere distorts distance relationship between vertices [3] and thus disrupts the spatial autocorrelation structure of brain maps (Fig. 1). In this work, we ran ground-truth simulations using spatially autocorrelated random maps generated from a gaussian covariance model to explore the impact of spherical projection on the spin test.
·Figure 1
Results:
We first evaluated the statistical performance of the spin test when correlating pairs of maps generated either directly on a sphere or on the pial surface of the brain. Fig. 2a confirms that, for random maps generated on a sphere, the false positive rate (FPR) of our benchmarking experiment is, on average, 0.05 regardless of the map's spatial autocorrelation. Fig. 2b shows the same experiment, but with random maps generated directly on the brain's surface. We find that FPRs increase as the spatial autocorrelation of the map increases.
We then quantified the level of spatial autocorrelation of each map using Moran's I and calculated the deviation (standardized) in Moran's I between each map and their rotated versions. For random maps generated on the sphere, the spatial autocorrelation of the original maps is preserved. For maps generated on the brain's surface, the spatial autocorrelation is not preserved, and we find that FPRs are proportional to the deviation in spatial autocorrelation between the original and rotated maps. In other words, our results demonstrate that the spin procedure does not necessarily preserve distance relationships in the brain and that this results in greater false positive rates.
If a specific spherical rotation does not adequately preserve the spatial relationships in brain maps, then a straight-forward solution would be to remove it from the population of nulls. We quantified the quality of each rotation as the correlation between the vertex-to-vertex distance matrices of original and rotated surfaces and repeated the previous experiments while gradually removing individual rotated maps that are poorly aligned with the original map. As poorly aligned spins are gradually removed, we observe lower FPRs (Fig. 2c), which confirms that there is a direct link between the quality of rotations and the statistical accuracy of the spin test.
We then quantified the level of spatial autocorrelation of each map using Moran's I and calculated the deviation (standardized) in Moran's I between each map and their rotated versions. For random maps generated on the sphere, the spatial autocorrelation of the original maps is preserved. For maps generated on the brain's surface, the spatial autocorrelation is not preserved, and we find that FPRs are proportional to the deviation in spatial autocorrelation between the original and rotated maps. In other words, our results demonstrate that the spin procedure does not necessarily preserve distance relationships in the brain and that this results in greater false positive rates.
If a specific spherical rotation does not adequately preserve the spatial relationships in brain maps, then a straight-forward solution would be to remove it from the population of nulls. We quantified the quality of each rotation as the correlation between the vertex-to-vertex distance matrices of original and rotated surfaces and repeated the previous experiments while gradually removing individual rotated maps that are poorly aligned with the original map. As poorly aligned spins are gradually removed, we observe lower FPRs (Fig. 2c), which confirms that there is a direct link between the quality of rotations and the statistical accuracy of the spin test.
·Figure 2
Conclusions:
In summary, our results show that the inflated false positive rates in spatial permutation tests can be traced back to the initial step of projecting a brain surface to a sphere. We then show how a straight-forward modification of the method can reduce false positive rates to desirable levels. Collectively, this work is part of an emerging appreciation of the fact that the brain surface is irregular [4, 5] and point to a need to develop methods that accurately represent and manipulate cortical geometry.
Modeling and Analysis Methods:
Methods Development 2
Other Methods 1
Keywords:
Statistical Methods
Other - Null models
1|2Indicates the priority used for review
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[2] Markello, R. D. (2021). Comparing spatial null models for brain maps. NeuroImage, 236, 118052.
[3] Fischl, B. (1999). Cortical surface-based analysis: II: inflation, flattening, and a surface-based coordinate system. Neuroimage, 9(2), 195-207.
[4] Pang, J. C. et al. (2023). Geometric constraints on human brain function. Nature, 618(7965), 566-574.
[5] Feilong, M. et al. (2024). A cortical surface template for human neuroscience. Nature Methods, 21(9), 1736-1742.