Abstract—We propose a unified computational framework to build a statistical atlas of the cardiac fiber architecture from diffusion tensor magnetic resonance images (DT-MRIs). We apply this framework to a small database of nine ex vivo canine hearts. An average cardiac fiber architecture and a measure of its variability are computed based on most recent advances in diffusion tensor statistics. This statistical analysis confirms the already established good stability of the fiber orientations and a higher variability of the laminar sheet orientations within a given species. The statistical comparison between the canine atlas and a standard human cardiac DT-MRI shows a better stability of the fiber orientations than their laminar sheet orientations between the two species. The proposed computational framework can be applied to larger databases of cardiac DT-MRIs from various species to better establish intra- and inter-species statistics on the anatomical structure of cardiac fibers. This information will be useful to guide the adjustment of average fiber models onto specific patients from in vivo anatomical imaging modalities. Index Terms—Atlas, cardiac, diffusion tensor magnetic resonance imaging, DTI, DT-MRI, fiber architecture, heart, laminar sheets, statistics. I.

Abstract—In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative

Abstract. In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation. 1

High angular resolution diffusion imaging has become an important magnetic resonance technique for in vivo imaging. Most current research in this field focuses on developing methods for computing the orientation distribution function (ODF), which is the probability distribution function of water molecule diffusion along any angle on the sphere. In this paper, we present a Riemannian framework to carry out computations on an ODF field. The proposed framework does not require that the ODFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a non-parametric representation of the ODF, and exploit the fact that under the square-root re-parameterization, the space of ODFs forms a Riemannian manifold, namely the unit Hilbert sphere. Specifically, we use Riemannian operations to perform various geometric data processing algorithms, such as interpolation, convolution and linear and nonlinear filtering. We illustrate these concepts with numerical experiments on synthetic and real datasets. 1.

Abstract. Diffusion tensor imaging has become an important research and clinical tool, owing to its unique ability to infer microstructural properties of living tissue. Increased use has led to a demand for statistical tools to analyze diffusion tensor data and perform, for example, confidence estimates, ROI analysis, and group comparisons. A first step towards developing a statistical framework is establishing the basic notion of distance between tensors. We investigate the properties of two previously proposed metrics that define a Riemannian manifold: the affine-invariant and Euclidean metrics. We find that the Euclidean metric is more appropriate for intra-voxel comparisons, and suggest that a context-dependent metric may be required for inter-voxel comparisons. 1

Diffusion tensor imaging (DTI) provides a unique source of information about the underlying tissue structure of brain white matter in vivo, including both the geom-etry of major fiber bundles as well as quantitative information about tissue prop-erties as represented by measures such as tensor orientation, anisotropy, and size. This paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images. Unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images. The smooth invertible nature of the transformations between each subject and the atlas provides spatial normalization for the comparison of tract statistics. Diffusion properties, such as fractional anisotropy (FA) and tensor size, of fiber tracts are modeled as multivariate functions of arc length. Hypothesis test-ing of tract models is performed non-parametrically with permutation testing based on the Hotelling T 2 statistic. The linear discriminant embedded in the T 2 metric provides an intuitive, localized interpretation of detected differences. The proposed methodology was tested on a clinical study of neurodevelopment. In a study of one Preprint submitted to Elsevier 9 June 2008 and two year old subjects, a significant increase in FA and a correlated decrease in Frobenius norm was found in several tracts. Significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly (MVM) demonstrating the potential of this method for clinical studies.

journal homepage: www.elsevier.com/locate/ynimg The effect of metric selection on the analysis of diffusion tensor MRI data☆

journal homepage: www.elsevier.com/locate/ynimg

journal homepage: www.elsevier.com/locate/ynimg The effect of metric selection on the analysis of diffusion tensor MRI data☆

difference in post-stroke patients using group-level covariance modeling