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 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.

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.