Fractional anisotropy derived from the single-tensor model (FA<sup>DTI</sup>) in diffusion MRI (dMRI) is the most widely used metric to characterize white matter (WM) micro-architecture in disease, despite known limitations in regions with extensive fiber crossing. Models such as the tensor distribution function (TDF), which represents the diffusion profile as a probabilistic mixture of tensors, have been proposed to reconstruct multiple underlying fibers. Although complex HARDI acquisition protocols are rare in clinical studies, the TDF and TDF-derived scalar FA metric (FA<sup>TDF</sup>) have been shown to be advantageous even for data with modest angular resolution. However, further evaluation and validation of the metric are necessary. Here we compared the test-retest reliability of FA<sup>TDF</sup> and FA<sup>DTI</sup> in clinical quality data by computing the intra-class correlation (ICC) between dMRI scans collected 3 months apart. When FA<sup>TDF</sup> and FA<sup>DTI</sup> were calculated at various angular resolutions, FA<sup>TDF</sup> ICC in both the corpus callosum and in a full axial slice were consistently more stable across scans, as compared to FA<sup>DTI</sup>.
We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.<sup>7</sup> However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer’s patients and healthy elderly controls from the Alzheimer’s Disease Neuro Imaging Database.
Diffusion weighted 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-sensitizing gradients along a minimum of 6 directions, second-order tensors (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce Tensor Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.
In the past decade, information theory has been studied extensively in computational imaging. In particular,
image matching by maximizing mutual information has been shown to yield good results in multimodal image
registration. However, there have been few rigorous studies to date that investigate the statistical aspect of
the resulting deformation fields. Different regularization techniques have been proposed, sometimes generating
deformations very different from one another. In this paper, we present a novel model for multimodal image
registration. The proposed method minimizes a purely information-theoretic functional consisting of mutual
information matching and unbiased regularization. The unbiased regularization term measures the magnitude of
deformations using either asymmetric Kullback-Leibler divergence or its symmetric version. The new multimodal
unbiased matching method, which allows for large topology preserving deformations, was tested using pairs of
two and three dimensional serial MRI images. We compared the results obtained using the proposed model to
those computed with a well-known mutual information based viscous fluid registration. A thorough statistical
analysis demonstrated the advantages of the proposed model over the multimodal fluid registration method when
recovering deformation fields and corresponding Jacobian maps.