Statistical group differences in anatomical shape analysis using Hotelling T2 metric

Abstract

Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical shape analysis. It has been applied in several studies on brain morphometry, but can potentially be employed in other 3D shape problems. Its main limitations is the necessity of spherical topology. The input of the proposed shape analysis is a set of binary segmentation of a single brain structure, such as the hippocampus or caudate. These segmentations are converted into a corresponding spherical harmonic description (SPHARM), which is then sampled into a triangulated surfaces (SPHARM-PDM). After alignment, differences between groups of surfaces are computed using the Hotelling T2 two sample metric. Statistical p-values, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information. The correction for multiple comparisons is performed via two separate methods that each have a distinct view of the problem. The first one aims to control the family-wise error rate (FWER) or false-positives via the extrema histogram of non-parametric permutations. The second method controls the false discovery rate and results in a less conservative estimate of the false-negatives. Prior versions of this shape analysis framework have been applied already to clinical studies on hippocampus and lateral ventricle shape in adult schizophrenics. The novelty of this submission is the use of the Hotelling T2 two-sample group difference metric for the computation of a template free statistical shape analysis. Template free group testing allowed this framework to become independent of any template choice, as well as it improved the sensitivity of our method considerably. In addition to our existing correction methodology for the multiple comparison problem using non-parametric permutation tests, we have extended the testing framework to include False Discovery Rate (FDR). FDR provides a significance correction with higher sensitivity while allowing a expected minimal amount of false-positives compared to our prior testing scheme.