Genome-wide association studies (GWAS) link full genome data to a handful of traits. However, in neuroimaging studies, there is an almost unlimited number of traits that can be extracted for full image-wide big data analyses. Large populations are needed to achieve the necessary power to detect statistically significant effects, emphasizing the need to pool data across multiple studies. Neuroimaging consortia, e.g., ENIGMA and CHARGE, are now analyzing MRI data from over 30,000 individuals. Distributed processing protocols extract harmonized features at each site, and pool together only the cohort statistics using meta analysis to avoid data sharing. To date, such MRI projects have focused on single measures such as hippocampal volume, yet voxelwise analyses (e.g., tensor-based morphometry; TBM) may help better localize statistical effects. This can lead to $10^{13}$1013 tests for GWAS and become underpowered. We developed an analytical framework for multi-site TBM by performing multi-channel registration to cohort-specific templates. Our results highlight the reliability of the method and the added power over alternative options while preserving single site specificity and opening the doors for well-powered image-wide genome-wide discoveries.

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve crossing fiber tracts. A number of high-angular resolution schemes with greater than 6 gradient directions have been employed to address this issue. In this paper, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF once this optimal TDF is determined, the diffusion orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function.

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or J-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the J-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.