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.
We argue that registration should be thought of as a means to an end, and not as a goal by itself. In particular, we consider the problem of predicting the locations of hidden labels of a test image using observable features, given a training set with both the hidden labels and observable features. For example, the hidden labels could be segmentation labels or activation regions in fMRI, while the observable features could be sulcal geometry or MR intensity. We analyze a probabilistic framework for computing an optimal atlas, and the subsequent registration of a new subject using only the observable features to optimize the hidden label alignment to the training set. We compare two approaches for co-registering training images for the atlas construction: the traditional approach of only using observable features and a novel approach of only using hidden labels. We argue that the alternative approach is superior particularly when the relationship between the hidden labels and observable features is complex and unknown. As an application, we consider the task of registering cortical folds to optimize Brodmann area localization. We show that the alignment of the Brodmann areas improves by up to 25% when using the alternative atlas compared with the traditional atlas. To the best of our knowledge, these are the most accurate Brodmann area localization results (achieved via cortical fold registration) reported to date.
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.
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.