Publications by Year: 2007

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.

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.

A mapping of unit vectors onto a 5D hypersphere is used to model and partition ODFs from HARDI data. This mapping has a number of useful and interesting properties and we make a link to interpretation of the second order spherical harmonic decompositions of HARDI data. The paper presents the working theory and experiments of using a von Mises-Fisher mixture model for directional samples. The MLE of the second moment of the HvMF pdf can also be related to fractional anisotropy. We perform error analysis of the estimation scheme in single and multi-fibre regions and then show how a penalised-likelihood model selection method can be employed to differentiate single and multiple fibre regions.

Geometric models of white matter architecture play an increasing role in neuroscientific applications of diffusion tensor imaging, and the most popular method for building them is fiber tractography. For some analysis tasks, however, a compelling alternative may be found in the first and second derivatives of diffusion anisotropy. We extend to tensor fields the notion from classical computer vision of ridges and valleys, and define anisotropy creases as features of locally extremal tensor anisotropy. Mathematically, these are the loci where the gradient of anisotropy is orthogonal to one or more eigenvectors of its Hessian. We propose that anisotropy creases provide a basis for extracting a skeleton of the major white matter pathways, in that ridges of anisotropy coincide with interiors of fiber tracts, and valleys of anisotropy coincide with the interfaces between adjacent but distinctly oriented tracts. The crease extraction algorithm we present generates high-quality polygonal models of crease surfaces, which are further simplified by connected-component analysis. We demonstrate anisotropy creases on measured diffusion MRI data, and visualize them in combination with tractography to confirm their anatomic relevance.

Multidimensional imaging resolving both the cardiac and respiratory cycles simultaneously has the potential to describe important physiological interdependences between the heart and pulmonary processes. A fully five-dimensional acquisition with three spatial and two temporal dimensions is hampered, however, by the long acquisition time and low spatial resolution. A technique is proposed to reduce the scan time substantially by extending the k-t BLAST framework to two temporal dimensions. By sampling the k-t space sparsely in a lattice grid, the signal in the transform domain, x-f space, can be densely packed, exploiting the fact that large regions in the field of view have low temporal bandwidth. A volumetric online prospective triggering approach with full cardiac and respiratory cycle coverage was implemented. Retrospective temporal interpolation was used to refine the timing estimates for the center of k-space, which is sampled for all cardiac and respiratory time frames. This resulted in reduced reconstruction error compared with conventional k-t BLAST reconstruction. The k-t(2) BLAST technique was evaluated by decimating a fully sampled five-dimensional data set, and feasibility was further demonstrated by performing sparsely sampled acquisitions. Compared to the fully sampled data, a fourfold improvement in spatial resolution was accomplished in approximately half the scan time.

This paper presents a novel method for phase unwrapping for phase sensitive reconstruction in MR imaging. The unwrapped phase is obtained by integrating the phase gradient by solving a Poisson equation. An efficient solver, which has been made publicly available, is used to solve the equation. The proposed method is demonstrated on a fat quantification MRI task that is a part of a prospective study of fat accumulation. The method is compared to a phase unwrapping method based on region growing. Results indicate that the proposed method provides more robust unwrapping. Unlike region growing methods, the proposed method is also straight-forward to implement in 3D.

Both post-mortem and neuroimaging studies have contributed significantly to what we know about the brain and schizophrenia. MRI studies of volumetric reduction in several brain regions in schizophrenia have confirmed early speculations that the brain is disordered in schizophrenia. There is also a growing body of evidence suggesting that a disturbance in connectivity between different brain regions, rather than abnormalities within the separate regions themselves, are responsible for the clinical symptoms and cognitive dysfunctions observed in this disorder. Thus an interest in white matter fiber tracts, subserving anatomical connections between distant, as well as proximal, brain regions, is emerging. This interest coincides with the recent advent of diffusion tensor imaging (DTI), which makes it possible to evaluate the organization and coherence of white matter fiber tracts. This is an important advance as conventional MRI techniques are insensitive to fiber tract direction and organization, and have not consistently demonstrated white matter abnormalities. DTI may, therefore, provide important new information about neural circuitry, and it is increasingly being used in neuroimaging studies of psychopathological disorders. Of note, in the past five years 18 DTI studies in schizophrenia have been published, most describing white matter abnormalities. Questions still remain, however, regarding what we are measuring that is abnormal in this disease, and how measures obtained using one method correspond to those obtained using other methods? Below we review the basic principles involved in MR-DTI, followed by a review of the different methods used to evaluate diffusion. Finally, we review MR-DTI findings in schizophrenia.

We present three different sequential Wiener filters, namely, isotropic, orientation and anisotropic. The first one is similar to the classical Wiener filter in the sense that it uses an isotropic neighborhood to estimate its parameters. Here we present a sequential version of it. The orientation Wiener filter uses oriented neighborhoods to estimate the structure orientation present at each voxel, giving rise to a modified estimator of the parameters. Finally, the anisotropic Wiener filter combines both approaches adaptively so that the appropriate approach is locally selected. Several synthetic experiments are presented showing the performance of the filters with respect to their parameters. A mean square error analysis is performed using a publicly available magnetic resonance imaging (MRI) brain phantom and a comparison with other filtering approaches is carried out. In addition, results from filtering real MRI data are presented.

In this paper, we present a novel approach for the segmentation of white matter tracts based on Finsler active contours. This technique provides an optimal measure of connectivity, explicitly segments the connecting fiber bundle, and is equipped with a metric which is able to utilize the directional information of high angular resolution data. We demonstrate the effectiveness of the algorithm for segmenting the cingulum bundle.