Nonlinear registration of MR images has become a staple of MRI-based research. Most popular registration algorithms, however, do not output any information about the variability of the estimated transformations¹. Although an image registration algorithm that is designed to yield variance information is more desirable^2–5, there are reasons to derive this information from existing point-estimate algorithms. Most labs have invested significant effort into optimizing a particular method to their specific needs (sample type/species, imaging modality, computing requirements). Thus, here we investigate whether we can quantify variability in a standard registration algorithm without modifying the underlying algorithm.Mice & MRI: 21 male C57 mice were scanned twice in vivo. 11 mice were enriched for 24 h prior to the first scan⁶. Mice were scanned at 90 µm³ isotropic voxel resolution using a T1-weighted manganese-enhanced MRI protocol (3D-gradient echo, TR/TE = 26/5.4 ms, matrix = 224 × 224 × 854, repeats = 5, total imaging time = 1.5 h). Registration: Brain images were aligned using nonlinear image registration with iterative template refinement⁷ and the ANTS registration algorithm⁸. For the variance estimation we repeated the registration, but after affine alignment each image was perturbed with 21 deformation fields randomly chosen from the ones estimated during the previous registration. The resulting 882 images were then registered to a common target. Statistics: The corresponding 882 Jacobian determinants were then compared to the original determinants.

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 (r², 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).

Our results indicate that we can derive variance estimates of the estimated transformations without modifying the registration algorithm itself. The original determinants were close to the mean of the determinant distributions, suggesting that our choice of non-linear registration parameters yields highly robust results. However, bias varies across the brain, suggesting that the proposed approach could outperform singular estimates in specific regions. The perturbation approach might also improve co-registration of atlas labels while adding ‘probabilistic’ information about their extent and location. Finally, information about the variance of the determinant values could be incorporated into the analysis to decrease bias in high-variance regions.