Generating surrogate brain maps through random rotation of geometric eigenmodes

1856 

Abstract Submission 

Nikitas Koussis¹, James Pang², Jayson Jeganathan³, Bryan Paton¹, Alex Fornito², Peter Robinson⁴, Bratislav Misic⁵, Michael Breakspear¹

¹University of Newcastle, Newcastle, NSW, ²Monash University, Melbourne, Victoria, ³The University of Newcastle, Newcastle, NSW, ⁴University of Sydney, Sydney, NSW, ⁵McGill University, Montreal, Quebec

Nikitas Koussis  
University of Newcastle
Newcastle, NSW

James Pang, PhD  
Monash University
Melbourne, Victoria

Jayson Jeganathan, Dr  
The University of Newcastle
Newcastle, NSW

Bryan Paton  
University of Newcastle
Newcastle, NSW

Alex Fornito  
Monash University
Melbourne, Victoria

Peter Robinson  
University of Sydney
Sydney, NSW

Bratislav Misic  
McGill University
Montreal, Quebec

Michael Breakspear  
University of Newcastle
Newcastle, NSW

The brain expresses activity in complex spatiotemporal patterns, reflecting cytoarchitectural and genetic influences that possess specific spatial properties. These brain patterns, also known as brain maps, frequently have high smoothness and spatial organization, i.e., spatial autocorrelation (SA), reflecting its central position in modern neuroimaging analyses [1–6]. In regimes of high SA, correlation between two brain maps can be spuriously elevated leading to false positive associations. An appropriate null hypothesis test to exclude false positives requires surrogate brain maps that preserve SA. Here we introduce "eigenstrapping", a technique for generating null hypotheses for maps possessing SA. This method uses geometric eigenmodes derived from various surfaces to produce surrogate brain maps that preserve SA. We show that these surrogate maps appropriately represent the null distribution and control false positives for cortical maps with SA, providing a versatile approach for investigations of cortical and subcortical topography.

Geometric eigenmodes of the cortical surface, ψ, are first derived by solving the Helmholtz equation on high-resolution surface meshes [7,8]. A generalized linear model is then used to identify the contribution of each mode to an empirical map (coefficients β, Fig. 1A). The cortical eigenmodes are then projected onto the sphere with axes equivalent to eigenvalues μ. The modes are rotated independently per eigengroup Λ (Fig. 1B), preserving orthogonality within groups, while randomly disrupting the orientation of modes between groups. Rotated eigenmodes are projected back onto the cortex and multiplied by the original coefficients β, generating random maps that preserve the eigenspectrum of the original data while destroying the cross spectra (the alignment of modes across groups) (Fig. 1C). An optional amplitude adjustment step can then be performed to retain the empirical amplitude distribution. We then used standard benchmarks to assess whether the ensuing surrogate brain maps represent appropriate null hypotheses for spatially correlated brain maps.

Surrogate brain maps derived from eigenmode rotation retain the variogram of HCP task activation maps [9,10] (Fig. 1E), a measure of local SA. Surrogate maps are uncorrelated with the original brain map (Fig. 1F); and show pairwise correlations that are zero centered and drawn from a Gaussian-like distribution (Fig. 1G). These results show that eigenstrapped brain maps possess core properties necessary for a non-parametric null.

We next tested for false positive control by simulating [11,12] 1000 pairs of maps with an average cross-correlation of 0.15 using Gaussian random fields (GRFs) ranging from white spatial noise (SA~0,α = 0.0) to strongly autocorrelated (SA>>0; α = 4.0) in steps of 0.5 (Fig. 2A; 9000 pairs of maps in total). When SA is low (α < 1.5), these maps fall outside the eigenstrapped null distribution (p<<0.05) but appropriately within the null (p>0.05) when SA is high (α ≥ 1.5; Fig. 2C). Random surrogates which do not preserve the SA fail to control these false positives. To quantify a false positive rate (FPR), we randomized pairs of GRFs at each alpha, and performed the same null tests as above. We show in Fig. 2D that when SA is low (α ≤ 1.5), eigenstrapping performs as expected, with an FPR of around 5%. However, as SA increases (α ≥ 2), the probability of significant correlations increases dramatically and eigenstrapping FPR increases to a maximum of 14.9% at α=3. Note that the best-performing null to date has an FPR at 13.5% when SA is brain-like (α≅3), whereas eigenstrapping has a lower FPR at brain-like SA of 12.4%.

Resampling of geometric eigenmodes represents a novel method for non-parametric null hypothesis testing. Eigenstrapped nulls pass standard tests of null hypothesis testing including the control of false positives. Extensions include subcortical surrogate maps for cortico-subcortical connectivity gradients.

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Cortex

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Sub-Cortical

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