Publications

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

Noninvasive characterization of pore size and shape in opaque porous media is a formidable challenge. NMR diffusion-diffraction patterns were found to be exceptionally useful for obtaining such morphological features, but only when pores are monodisperse and coherently placed. When locally anisotropic pores are randomly oriented, conventional diffusion NMR methods fail. Here, we present a simple, direct, and general approach to obtain both compartment size and shape even in such settings and even when pores are characterized by internal field gradients. Using controlled porous media, we show that the bipolar-double-pulsed-field-gradient (bp-d-PFG) methodology yields diffusion-diffraction patterns from which pore size can be directly obtained. Moreover, we show that pore shape, which cannot be obtained by conventional methods, can be directly inferred from the modulation of the signal in angular bp-d-PFG experiments. This new methodology significantly broadens the types of porous media that can be studied using noninvasive diffusion-diffraction NMR.

We describe a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by those previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Using two- and three-fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.

We propose a novel probabilistic framework to merge information from DWI tractography and resting-state fMRI correlations. In particular, we model the interaction of latent anatomical and functional connectivity templates between brain regions and present an intuitive extension to population studies. We employ a mean-field approximation to fit the new model to the data. The resulting algorithm identifies differences in latent connectivity between the groups. We demonstrate our method on a study of normal controls and schizophrenia patients.

We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a ’streamline flow’ using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows for a robust inference of local tract geometry, which, in the context of the causal filter estimation, guides tractography through regions with partial volume effects. We validate the method on synthetic data and present results on two types in vivo data: diffusion tensors and a spherical harmonic reconstruction of the fibre orientation distribution function (fODF).

The measurement of the distance between diffusion tensors is the foundation on which any subsequent analysis or processing of these quantities, such as registration, regularization, interpolation, or statistical inference is based. In recent years a family of Riemannian tensor metrics based on geometric considerations has been introduced for this purpose. In this work we examine the properties one would use to select metrics for diffusion tensors, diffusion coefficients, and diffusion weighted MR image data. We show that empirical evidence supports the use of a Euclidean metric for diffusion tensors, based upon Monte Carlo simulations. Our findings suggest that affine invariance is not a desirable property for a diffusion tensor metric because it leads to substantial biases in tensor data. Rather, the relationship between distribution and distance is suggested as a novel criterion for metric selection.

We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions ("effective basis space") while the residual deformation in the rest of the state space ("residual space") is small. This property enables us to apply the particle filtering with mode tracking (PF-MT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PF-MT. It requires significant modifications compared to the original PF-MT because the space of contours is a non-Euclidean infinite dimensional space.

A spectrum of brain-related disorders are nowadays known to manifest themselves in degradation of the integrity and connectivity of neural tracts in the white matter of the brain. Such damage tends to affect the pattern of water diffusion in the white matter—the information which can be quantified by diffusion MRI (dMRI). Unfortunately, practical implementation of dMRI still poses a number of challenges which hamper its wide-spread integration into regular clinical practice. Chief among these is the problem of long scanning times. In particular, in the case of High Angular Resolution Diffusion Imaging (HARDI), the scanning times are known to increase linearly with the number of diffusion-encoding gradients. In this research, we use the theory of compressive sampling (aka compressed sensing) to substantially reduce the number of diffusion gradients without compromising the informational content of HARDI signals. The experimental part of our study compares the proposed method with a number of alternative approaches, and shows that the former results in more accurate estimation of HARDI data in terms of the mean squared error.

Visualization and analysis of the micro-architecture of brain parenchyma by means of magnetic resonance imaging is nowadays believed to be one of the most powerful tools used for the assessment of various cerebral conditions as well as for understanding the intracerebral connectivity. Unfortunately, the conventional diffusion tensor imaging (DTI) used for estimating the local orientations of neural fibers is incapable of performing reliably in the situations when a voxel of interest accommodates multiple fiber tracts. In this case, a much more accurate analysis is possible using the high angular resolution diffusion imaging (HARDI) that represents local diffusion by its apparent coefficients measured as a discrete function of spatial orientations. In this note, a novel approach to enhancing and modeling the HARDI signals using multiresolution bases of spherical ridgelets is presented. In addition to its desirable properties of being adaptive, sparsifying, and efficiently computable, the proposed modeling leads to analytical computation of the orientation distribution functions associated with the measured diffusion, thereby providing a fast and robust analytical solution for q-ball imaging.

Recent advances in diffusion weighted MR imaging (dMRI) has made it a tool of choice for investigating white matter abnormalities of the brain and central nervous system. In this work, we design a system that detects abnormal features (biomarkers) of first-episode schizophrenia patients and then classifies them using these features. We use two different models of the dMRI data, namely, spherical harmonics and the two-tensor model. The algorithm works by first computing several diffusion measures from each model. An affine-invariant representation of each subject is then computed, thus avoiding the need for registration. This representation is used within a kernel based feature selection algorithm to determine the biomarkers that are statistically different between the two populations. Confirmation of how well these biomarkers identify each population is obtained by using several classifiers such as, k-nearest neighbors, Parzen window classifier, and support vector machines to separate 21 first-episode patients from 20 age-matched normal controls. Classification results using leave-many-out cross-validation scheme are given for each representation. This algorithm is a first step towards early detection of schizophrenia.