Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

We propose a new white matter atlas creation method that learns a model of the common white matter structures present in a group of subjects. We demonstrate that our atlas creation method, which is based on group spectral clustering of tractography, discovers structures corresponding to expected white matter anatomy such as the corpus callosum, uncinate fasciculus, cingulum bundles, arcuate fasciculus, and corona radiata. The white matter clusters are augmented with expert anatomical labels and stored in a new type of atlas that we call a high-dimensional white matter atlas. We then show how to perform automatic segmentation of tractography from novel subjects by extending the spectral clustering solution, stored in the atlas, using the Nystrom method. We present results regarding the stability of our method and parameter choices. Finally we give results from an atlas creation and automatic segmentation experiment. We demonstrate that our automatic tractography segmentation identifies corresponding white matter regions across hemispheres and across subjects, enabling group comparison of white matter anatomy.

Organ motion compensation in image-guided therapy is an active area of research. However, there has been little research on motion tracking and compensation in magnetic resonance imaging (MRI)-guided therapy. In this paper, we present a method to track a moving organ in MRI and control an active mechanical device for motion compensation. The method proposed is based on MRI navigator echo tracking enhanced by Kalman filtering for noise robustness. We also developed an extrapolation scheme to resolve any discrepancies between tracking and device control sampling rates. The algorithm was tested in a simulation study using a phantom and an active mechanical tool holder. We found that the method is feasible to use in a clinical MRI scanner with sufficient accuracy (0.36 mm to 1.51 mm depending on the range of phantom motion) and is robust to noise. The method proposed may be useful in MRI-guided targeted therapy, such as focused ultrasound therapy for a moving organ.

The logarithm of the odds ratio (LogOdds) is frequently used in areas such as artificial neural networks, economics, and biology, as an alternative representation of probabilities. Here, we use LogOdds to place probabilistic atlases in a linear vector space. This representation has several useful properties for medical imaging. For example, it not only encodes the shape of multiple anatomical structures but also captures some information concerning uncertainty. We demonstrate that the resulting vector space operations of addition and scalar multiplication have natural probabilistic interpretations. We discuss several examples for placing label maps into the space of LogOdds. First, we relate signed distance maps, a widely used implicit shape representation, to LogOdds and compare it to an alternative that is based on smoothing by spatial Gaussians. We find that the LogOdds approach better preserves shapes in a complex multiple object setting. In the second example, we capture the uncertainty of boundary locations by mapping multiple label maps of the same object into the LogOdds space. Third, we define a framework for non-convex interpolations among atlases that capture different time points in the aging process of a population. We evaluate the accuracy of our representation by generating a deformable shape atlas that captures the variations of anatomical shapes across a population. The deformable atlas is the result of a principal component analysis within the LogOdds space. This atlas is integrated into an existing segmentation approach for MR images. We compare the performance of the resulting implementation in segmenting 20 test cases to a similar approach that uses a more standard shape model that is based on signed distance maps. On this data set, the Bayesian classification model with our new representation outperformed the other approaches in segmenting subcortical structures.

A novel framework for joint clustering and point-by-point mapping of white matter fiber pathways is presented. Accurate clustering of the trajectories into fiber bundles requires point correspondence determined along the fiber pathways. This knowledge is also crucial for any tract-oriented quantitative analysis. We employ an expectation-maximization (EM) algorithm to cluster the trajectories in a Gamma mixture model context. The result of clustering is the probabilistic assignment of the fiber trajectories to each cluster, an estimate of the cluster parameters, and point correspondences along the trajectories. Point-by-point correspondence of the trajectories within a bundle is obtained by constructing a distance map and a label map from each cluster center at every iteration of the EM algorithm. This offers a time-efficient alternative to pairwise curve matching of all trajectories with respect to each cluster center. Probabilistic assignment of the trajectories to clusters is controlled by imposing a minimum threshold on the membership probabilities, to remove outliers in a principled way. The presented results confirm the efficiency and effectiveness of the proposed framework for quantitative analysis of diffusion tensor MRI.