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.
This paper addresses the problem of image segmentation by means of active contours, whose evolution is driven by the gradient flow derived from an energy functional that is based on the Bhattacharyya distance. In particular, given the values of a photometric variable (or of a set thereof), which is to be used for classifying the image pixels, the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours. The above discrepancy is measured by means of the Bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand. The proposed methodology can be viewed as a generalization of the segmentation methods, in which active contours maximize the difference between a finite number of empirical moments of the "inside" and "outside" distributions. Furthermore, it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed. As an additional contribution, a method for automatically adjusting the smoothness properties of the empirical distributions is proposed. Such a procedure is crucial in situations when the number of data samples (supporting a certain segmentation class) varies considerably in the course of the evolution of the active contour. In this case, the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over- or underestimation artifacts. Finally, a number of relevant segmentation results are demonstrated and some further research directions are discussed.
We present an algorithm to generate samples from probability distributions on the space of curves. We view a traditional curve evolution energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution by generating smooth perturbations to the normal of the curve and show how to compute the transition probabilities to ensure that the samples come from the posterior distribution. We demonstrate some advantages of sampling methods such as robustness to local minima, better characterization of multi-modal distributions, access to some measures of estimation error, and ability to easily incorporate constraints on the curve.
BACKGROUND AND PURPOSE: Formation of lesions in multiple sclerosis (MS) shows pronounced short-term fluctuation of MR imaging hyperintensity and size, a qualitatively known but poorly characterized phenomenon. With the use of time-series modeling of MR imaging intensity, our study relates the short-term dynamics of new T2 lesion formation to those of contrast enhancement and markers of long-term progression of disease.
MATERIALS AND METHODS: We analyzed 915 examinations from weekly to monthly MR imaging in 40 patients with MS using a time-series model, emulating 2 opposing processes of T2 prolongation and shortening, respectively. Patterns of activity, duration, and residual hyperintensity within new T2 lesions were measured and evaluated for relationships to disability, atrophy, and clinical phenotype in long-term follow-up.
RESULTS: Significant T2 activity was observed for 8 to 10 weeks beyond contrast enhancement, which suggests that T2 MR imaging is sensitive to noninflammatory processes such as degeneration and repair. Larger lesions showed longer subacute phases but disproportionally more recovery. Patients with smaller average peak lesion size showed trends toward greater disability and proportional residual damage. Higher rates of disability or atrophy were associated with subjects whose lesions showed greater residual hyperintensity.
CONCLUSION: Smaller lesions appeared disproportionally more damaging than larger lesions, with lesions in progressive MS smaller and of shorter activity than in relapsing-remitting MS. Associations of lesion dynamics with rates of atrophy and disability and clinical subtype suggest that changes in lesion dynamics may represent a shift from inflammatory toward degenerative disease activity and greater proximity to a progressive stage, possibly allowing staging of the progression of MS earlier, before atrophy or disability develops.
A method to estimate the magnitude MR data from several noisy samples is presented. It is based on the Linear Minimum Mean Squared Error (LMMSE) estimator for the Rician noise model when several scanning repetitions are available. This method gives a closed-form analytical solution that takes into account the probability distribution of the data as well as the existing level of noise, showing a better performance than methods such as the average or the median.
Multisubject statistical analyses of diffusion tensor images in regions of specific white matter tracts have commonly measured only the mean value of a scalar invariant such as the fractional anisotropy (FA), ignoring the spatial variation of FA along the length of fiber tracts. We propose to instead perform tract-based morphometry (TBM), or the statistical analysis of diffusion MRI data in an anatomical tract-based coordinate system. We present a method for automatic generation of white matter tract arc length parameterizations, based on learning a fiber bundle model from tractography from multiple subjects. Our tract-based coordinate system enables TBM for the detection of white matter differences in groups of subjects. We present example TBM results from a study of interhemispheric differences in FA.
We present software engineering methods to provide free open-source software for MR-guided therapy. We report that graphical representation of the surgical tools, interconnectively with the tracking device, patient-to-image registration, and MRI-based thermal mapping are crucial components of MR-guided therapy in sharing such software. Software process includes a network-based distribution mechanism by multi-platform compiling tool CMake, CVS, quality assurance software DART. We developed six procedures in four separate clinical sites using proposed software engineering and process, and found the proposed method is feasible to facilitate multicenter clinical trial of MR-guided therapies. Our future studies include use of the software in non-MR-guided therapies.
In functional connectivity analysis, networks of interest are defined based on correlation with the mean time course of a user-selected 'seed' region. In this work we propose to simultaneously estimate the optimal representative time courses that summarize the fMRI data well and the partition of the volume into a set of disjoint regions that are best explained by these representative time courses. Our approach offers two advantages. First, is removes the sensitivity of the analysis to the details of the seed selection. Second, it substantially simplifies group analysis by eliminating the need for a subject-specific threshold at which correlation values are deemed significant. This unsupervised technique generalizes connectivity analysis to situations where candidate seeds are difficult to identify reliably or are unknown. Our experimental results indicate that the functional segmentation provides a robust, anatomically meaningful and consistent model for functional connectivity in fMRI.
In this paper, we propose a unified framework for computing atlases from manually labeled data at various degrees of "sharpness" and the joint registration-segmentation of a new brain with these atlases. In non-rigid registration, the tradeoff between warp regularization and image fidelity is typically set empirically. In segmentation, this leads to a probabilistic atlas of arbitrary "sharpness": weak regularization results in well-aligned training images and a "sharp" atlas; strong regularization yields a "blurry" atlas. We study the effects of this tradeoff in the context of cortical surface parcellation by comparing three special cases of our framework, namely: progressive registration-segmentation of a new brain to increasingly "sharp" atlases with increasingly flexible warps; secondly, progressive registration to a single atlas with increasingly flexible warps; and thirdly, registration to a single atlas with fixed constrained warps. The optimal parcellation in all three cases corresponds to a unique balance of atlas "sharpness" and warp regularization that yield statistically significant improvements over the previously demonstrated parcellation results.
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.
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.
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.
In this paper, we explore the use of fiber bundles extracted from diffusion MR images for a nonlinear registration algorithm. We employ a white matter atlas to automatically label major fiber bundles and to establish correspondence between subjects. We propose a polyaffine framework to calculate a smooth and invertible nonlinear warp field based on these correspondences, and derive an analytical solution for the reorientation of the tensor fields under the polyaffine transformation. We demonstrate our algorithm on a group of subjects and show that it performs comparable to a higher dimensional nonrigid registration algorithm.
This paper introduces an outlier rejection and signal reconstruction method for high angular resolution diffusion weighted imaging. The approach is based on the thresholding of Laplacian measurements over the sphere of the apparent diffusion coefficient profiles defined for a given set of gradient directions. Exemplary results are presented.
This paper investigates and characterizes sources of variability in MEG signals in multi-site, multi-subject studies. Understanding these sources will help to develop efficient strategies for comparing and pooling data across repetitions of an experiment, across subjects, and across sites. In this work, we investigated somatosensory MEG data collected at three different sites and applied variance component analysis and nonparametric KL divergence analysis in order to characterize the sources of variability. Our analysis showed that inter-subject differences are the biggest factor in the signal variability. We demonstrated that the timing of the deflections is very consistent in the early somatosensory response, which justifies a direct comparison of deflection peak times acquired from different visits, subjects, and systems. Compared with deflection peak times, deflection magnitudes have larger variation across sites; modeling of this variability is necessary for data pooling.
OBJECTIVE: Scarless surgery is an innovative and promising technique that may herald a new era in surgical procedures. We have created a navigation system, named IRGUS, for endoscopic and transgastric access interventions and have validated it in in vivo pilot studies. Our hypothesis is that endoscopic ultrasound procedures will be performed more easily and efficiently if the operator is provided with approximately registered 3D and 2D processed CT images in real time that correspond to the probe position and ultrasound image.
MATERIALS AND METHODS: The system provides augmented visual feedback and additional contextual information to assist the operator. It establishes correspondence between the real-time endoscopic ultrasound image and a preoperative CT volume registered using electromagnetic tracking of the endoscopic ultrasound probe position. Based on this positional information, the CT volume is reformatted in approximately the same coordinate frame as the ultrasound image and displayed to the operator.
RESULTS: The system reduces the mental burden of probe navigation and enhances the operator's ability to interpret the ultrasound image. Using an initial rigid body registration, we measured the mis-registration error between the ultrasound image and the reformatted CT plane to be less than 5 mm, which is sufficient to enable the performance of novice users of endoscopic systems to approach that of expert users.
CONCLUSIONS: Our analysis shows that real-time display of data using rigid registration is sufficiently accurate to assist surgeons in performing endoscopic abdominal procedures. By using preoperative data to provide context and support for image interpretation and real-time imaging for targeting, it appears probable that both preoperative and intraoperative data may be used to improve operator performance.
The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.
The purpose of this paper is to describe certain alternative metrics for quantifying distances between distributions, and to explain their use and relevance in visual tracking. Besides the theoretical interest, such metrics may be used to design filters for image segmentation, that is for solving the key visual task of separating an object from the background in an image. The segmenting curve is represented as the zero level set of a signed distance function. Most existing methods in the geometric active contour framework perform segmentation by maximizing the separation of intensity moments between the interior and the exterior of an evolving contour. Here one can use the given distributional metric to determine a flow which minimizes changes in the distribution inside and outside the curve.
White matter hyperintense lesions on T2-weighted images are associated with late-life depression. Little work has been carried out examining differences in lesion location between elderly individuals with and without depression. In contrast to previous studies examining total brain white matter lesion volume, this study examined lobar differences in white matter lesion volumes derived from brain magnetic resonance imaging. This study examined 49 subjects with a DSM-IV diagnosis of major depression and 50 comparison subjects without depression. All participants were age 60 years or older. White matter lesion volumes were measured in each hemisphere using a semiautomated segmentation process and localized to lobar regions using a lobar atlas created for this sample using the imaging tools provided by the Biomedical Informatics Research Network (BIRN). The lobar lesion volumes were compared against depression status. After controlling for age and hypertension, subjects with depression exhibited significantly greater total white matter lesion volume in both hemispheres and in both frontal lobes than did control subjects. Although a similar trend was observed in the parietal lobes, the difference did not reach a level of statistical significance. Models of the temporal and occipital lobes were not statistically significant. Older individuals with depression have greater white matter disease than healthy controls, predominantly in the frontal lobes. These changes are thought to disrupt neural circuits involved in mood regulation, thus increasing the risk of developing depression.
A statistical model is presented that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image artifacts, anatomical labelmaps, and a structure-dependent hierarchical mapping from the atlas to the image space. The algorithm produces segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. On this set of images, the new approach performs significantly better than similar methods which sequentially apply registration and segmentation.