Estimating Registration Variance Using Deformation Field Perturbations

Jan Scholz^{1}, Kaitlyn Easson^{2}, and Jason P Lerch^{1,3}

The Jacobian determinant values seem to be equally distributed across repeated scans (Fig 1A), suggesting that registration performs robustly with respect to scan-to-scan variance. We then tested for volumetric differences (enriched vs control mice) using a linear model. We ran the voxel-wise test twice: once with the original determinant values (Fig 1B) and once with the mean of the determinant distributions (Fig 1C). In the latter case there were 8% more voxels across the brain where the two groups differed significantly (p < 0.001, uncorrected). The t-value was increased by 2 % in the hippocampal voxel, a region where we would expect volume increases. Here correlation between repeated scans was slightly increased when using the mean of the distribution (r^{2}, 0.56 vs 0.59). Across the brain the average t-value (3.3) remained the same within significant areas. Finally, we estimated bias by comparing the mean of the determinant distribution to the original determinants for each voxel. The mean absolute error is 0.01 (±0.01) implying that the original voxel-wise volume estimates are biased by 1 % on average. Specifically, we found that determinant values are underestimated in the dentate gyrus of the hippocampus when using the original determinants (Fig 1D). The enrichment effect on local volume is also underestimated in the same region (Fig 1E).

1. Klein A, et al. NeuroImage 46, 786–802 (2009). 2. Risholm P, et al. Medical Image Analysis 17, 538–55 (2013). 3. Simpson IJ, et al. NeuroImage 59, 2438–2451 (2012). 4. Simpson IJ, et al. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 8150 LNCS, 10–18 (2013). 5. Wassermann D, et al. Proc. Workshop on Biomedical Image Registration 72–82 (2014). 6. Scholz J, et al. NeuroImage 109, 190–198 (2015). 7. Friedel M, et al. Frontiers in Neuroinformatics 8, 67 (2014). 8. Avants BB, et al. Neuroinformatics 9, 381–400 (2011).

Hippocampal voxel from two example mice (dashed, original estimate; red, mean of distribution of determinants). Distributions are comparable across repeated scans.

Estimating the effect of enrichment (p<0.005, uncorrected) on local brain volume using the original determinants (A) and the mean of the distribution (B). Enriched mice have a larger hippocampus (blue, enriched > controls; red, enriched < controls). There are areas where determinants are underestimated (red, D) and where the enrichment effect is underestimated (red, E) when using the original determinants (red-yellow, 0.5%-1% bias).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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