We present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and a spherical wavelet (SWC) shape representation. As an application, we analyze two brain structures, the caudate nucleus and the hippocampus, and compare the results obtained to shape analysis using a sampled point representation. Our results show that the SWC representation indicates new areas of significance preserved under the FDR correction for both the left caudate nucleus and left hippocampus. Additionally, the spherical wavelet representation provides a natural way to interpret the significance results in terms of scale in addition to knowing the spatial location of the regions.
RATIONALE AND OBJECTIVES: To perform a retrospective, quantitative assessment of the anatomic relationship between intra-axial, supratentorial, primary brain tumors, and adjacent white matter fiber tracts based on anatomic and diffusion tensor magnetic resonance imaging (MRI). We hypothesized that white matter infiltration may be common among different types of tumor.
MATERIAL AND METHODS: Preoperative, anatomic (T1- and T2-weighted), and LINESCAN diffusion tensor MRI were obtained in 12 patients harboring supratentorial gliomas (World Health Organization [WHO] Grades II and III). The two imaging modalities were rigidly registered. The tumors were manually segmented from the T1- and T2-weighted MRI, and their volume calculated. A three-dimensional tractography was performed in each case. A second segmentation and volume measurement was performed on the tumor regions intersecting adjacent white matter fiber tracts. Statistical methods included summary statistics to examine the fraction of tumor volume infiltrating adjacent white matter.
RESULTS: There were five patients with low-grade oligodendroglioma (WHO Grade II), one with low-grade mixed oligoastrocytoma (WHO Grade II), one with ganglioglioma, two with low-grade astrocytoma (WHO Grade II), and three with anaplastic astrocytoma (WHO Grade III). We identified white matter tracts infiltrated by tumor in all 12 cases. The median tumor volume (+/- standard deviation) in our patient population was 42.5 +/- 28.9 mL. The median tumor volume (+/- standard deviation) infiltrating white matter fiber tracts was 5.2 +/- 9.9 mL. The median percentage of tumor volume infiltrating white matter fiber tracts was 21.4% +/- 9.7%.
CONCLUSIONS: The information provided by diffusion tensor imaging combined with anatomic MRI might be useful for neurosurgical planning and intraoperative guidance. Our results confirm previous reports that extensive white matter infiltration by primary brain tumors is a common occurrence. However, prospective, large population studies are required to definitively clarify this issue, and how infiltration relates to histologic tumor type, tumor size, and location.
We describe a new approach for estimating the posterior probability of tissue labels. Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the Mean Field approach. Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logarithm-of-odds encoding of the posterior label probabilities in an unconstrained linear vector space. Applications with more than two labels are easily accommodated. The label assignment is accomplished by the Maximum A Posteriori rule, so there are no problems of "overlap" or "vacuum". We test the method on synthetic images with additive noise. In addition, we segment a magnetic resonance scan into the major brain compartments and subcortical structures.
Since the introduction of diffusion weighted imaging (DWI) as a method for examining neural connectivity, its accuracy has not been formally evaluated. In this study, we directly compared connections that were visualized using injected neural tract tracers (WGA-HRP) with those obtained using in-vivo diffusion tensor imaging (DTI) tractography. First, we injected the tracer at multiple sites in the brain of a macaque monkey; second, we reconstructed the histological sections of the labeled fiber tracts in 3D; third, we segmented and registered the fibers (somatosensory and motor tracts) with the anatomical in-vivo MRI from the same animal; and last, we conducted fiber tracing along the same pathways on the DTI data using a classical diffusion tracing technique with the injection sites as seeds. To evaluate the performance of DTI fiber tracing, we compared the fibers derived from the DTI tractography with those segmented from the histology. We also studied the influence of the parameters controlling the tractography by comparing Dice superimposition coefficients between histology and DTI segmentations. While there was generally good visual agreement between the two methods, our quantitative comparisons reveal certain limitations of DTI tractography, particularly for regions at remote locations from seeds. We have thus demonstrated the importance of appropriate settings for realistic tractography results.
Regional investigations of newborn MRI are important to understand the appearance and consequences of early brain injury. Previously, regionalization in neonates has been achieved with a Talairach parcellation, using internal landmarks of the brain. Non-synostotic dolichocephaly defines a bi-temporal narrowing of the preterm infant's head caused by pressure on the immature skull. The impact of dolichocephaly on brain shape and regional brain shift, which may compromise the validity of the parcellation scheme, has not yet been investigated. Twenty-four preterm and 20 fullterm infants were scanned at term equivalent. Skull shapes were investigated by cephalometric measurements and population registration. Brain tissue volumes were calculated to rule out brain injury underlying skull shape differences. The position of Talairach landmarks was evaluated. Cortical structures were segmented to determine a positional shift between both groups. The preterm group displayed dolichocephalic head shapes and had similar brain volumes compared to the mesocephalic fullterm group. In preterm infants, Talairach landmarks were consistently positioned relative to each other and to the skull base, but were displaced with regard to the calvarium. The frontal and superior region was enlarged; central and temporal gyri and sulci were shifted comparing preterm and fullterm infants. We found that, in healthy preterm infants, dolichocephaly led to a shift of cortical structures, but did not influence deep brain structures. We concluded that the validity of a Talairach parcellation scheme is compromised and may lead to a miscalculation of regional brain volumes and inconsistent parcel contents when comparing infant populations with divergent head shapes.
In this paper, we present a set of techniques for the evaluation of brain tissue classifiers on a large data set of MR images of the head. Due to the difficulty of establishing a gold standard for this type of data, we focus our attention on methods which do not require a ground truth, but instead rely on a common agreement principle. Three different techniques are presented: the Williams' index, a measure of common agreement; STAPLE, an Expectation Maximization algorithm which simultaneously estimates performance parameters and constructs an estimated reference standard; and Multidimensional Scaling, a visualization technique to explore similarity data. We apply these different evaluation methodologies to a set of eleven different segmentation algorithms on forty MR images. We then validate our evaluation pipeline by building a ground truth based on human expert tracings. The evaluations with and without a ground truth are compared. Our findings show that comparing classifiers without a gold standard can provide a lot of interesting information. In particular, outliers can be easily detected, strongly consistent or highly variable techniques can be readily discriminated, and the overall similarity between different techniques can be assessed. On the other hand, we also find that some information present in the expert segmentations is not captured by the automatic classifiers, suggesting that common agreement alone may not be sufficient for a precise performance evaluation of brain tissue classifiers.
Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter. The PF also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background.
Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.
Advanced magnetic resonance imaging (MRI) studies often require the transformation of large numbers of images into a common space. Calculating transformations that relate each image to every other and applying them to the images on demand are theoretically possible; however, these can be computationally prohibitive. Therefore, relating each image to only one other image, then linking those transforms together to relate any two images in the database, may be an efficient alternative. Evaluated were the feasibility and validity of image registration to bring intraindividual MR images into mutual correspondence for longitudinal analysis through the concatenation of precomputed transforms. A longitudinal data set of 10 multiple sclerosis patients with nine serial dual-echo spin-echo, 1.5-T MRI scans was used. Intrasubject registrations were performed stepwise between consecutive images and direct from each time point to the baseline. Consecutive transforms were concatenated and evaluated against direct registrations by comparing the resulting transformed images (using Pearson correlation coefficient). Confounding variables such as time between scans, brain atrophy, and change in lesion load were evaluated. We found the images resampled with the direct and the concatenated transforms to be highly correlated, and there was no significant difference between methods. Differences in brain parenchymal fraction (a measure of brain atrophy) showed significant inverse correlation with the correspondence of the resampled images. Results indicate that concatenating multiple transforms that link two images together produces near-identical results to that of direct registration; thus, this method is both useful and valid.
This article discusses and reviews advanced forms of serial morphometry in the context of a disease progression model in multiple sclerosis (MS). This model of disease activity distinguishes between overall disease activity and the proportion thereof that becomes permanent damage. This translates into a progression model that features a repair potential, which, when exhausted, marks the conversion or progression from relapsing to progressive disease. The level of repair capacity at a given time determines the rate of progression. Both clinical and MRI variables appear to be in support of such a model. We examine possible MRI markers for this repair capacity, particularly the short-term behavior of new MRI lesions, quantified by methods of time-series analysis--that is, capturing lesion dynamics in the form of MRI intensity change directly, rather than shape or volume change. Lower rates of individual lesion recovery may represent lower repair and greater proximity to a progressive stage. Individuals with low transient lesion turnover appear to undergo more rapid progression and atrophy. Because disease-modifying therapies aim to alter the pathophysiological chain of inflammation, demyelination, and axonal loss, a therapeutic effect may therefore be more readily apparent as a change in lesion dynamics and recovery rate and level, rather than a change in total lesion burden or enhancing lesion number.
Tracking deforming objects involves estimating the global motion of the object and its local deformations as a function of time. Tracking algorithms using Kalman filters or particle filters have been proposed for finite dimensional representations of shape, but these are dependent on the chosen parametrization and cannot handle changes in curve topology. Geometric active contours provide a framework which is parametrization independent and allow for changes in topology. In the present work, we formulate a particle filtering algorithm in the geometric active contour framework that can be used for tracking moving and deforming objects. To the best of our knowledge, this is the first attempt to implement an approximate particle filtering algorithm for tracking on a (theoretically) infinite dimensional state space.
System development for image-guided therapy (IGT), or image-guided interventions (IGI), continues to be an area of active interest across academic and industry groups. This is an emerging field that is growing rapidly: major academic institutions and medical device manufacturers have produced IGT technologies that are in routine clinical use, dozens of high-impact publications are published in well regarded journals each year, and several small companies have successfully commercialized sophisticated IGT systems. In meetings between IGT investigators over the last two years, a consensus has emerged that several key areas must be addressed collaboratively by the community to reach the next level of impact and efficiency in IGT research and development to improve patient care. These meetings culminated in a two-day workshop that brought together several academic and industrial leaders in the field today. The goals of the workshop were to identify gaps in the engineering infrastructure available to IGT researchers, develop the role of research funding agencies and the recently established US-based National Center for Image Guided Therapy (NCIGT), and ultimately to facilitate the transfer of technology among research centers that are sponsored by the National Institutes of Health (NIH). Workshop discussions spanned many of the current challenges in the development and deployment of new IGT systems. Key challenges were identified in a number of areas, including: validation standards; workflows, use-cases, and application requirements; component reusability; and device interface standards. This report elaborates on these key points and proposes research challenges that are to be addressed by a joint effort between academic, industry, and NIH participants.
We introduce the use of over-complete spherical wavelets for shape analysis of 2D closed surfaces. Bi-orthogonal spherical wavelets have been shown to be powerful tools in the segmentation and shape analysis of 2D closed surfaces, but unfortunately they suffer from aliasing problems and are therefore not invariant under rotations of the underlying surface parameterization. In this paper, we demonstrate the theoretical advantage of over-complete wavelets over bi-orthogonal wavelets and illustrate their utility on both synthetic and real data. In particular, we show that over-complete spherical wavelets allow us to build more stable cortical folding development models, and detect a wider array of regions of folding development in a newborn dataset.
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.
We introduce an algorithm for segmenting brain magnetic resonance (MR) images into anatomical compartments such as the major tissue classes and neuro-anatomical structures of the gray matter. The algorithm is guided by prior information represented within a tree structure. The tree mirrors the hierarchy of anatomical structures and the subtrees correspond to limited segmentation problems. The solution to each problem is estimated via a conventional classifier. Our algorithm can be adapted to a wide range of segmentation problems by modifying the tree structure or replacing the classifier. We evaluate the performance of our new segmentation approach by revisiting a previously published statistical group comparison between first-episode schizophrenia patients, first-episode affective psychosis patients, and comparison subjects. The original study is based on 50 MR volumes in which an expert identified the brain tissue classes as well as the superior temporal gyrus, amygdala, and hippocampus. We generate analogous segmentations using our new method and repeat the statistical group comparison. The results of our analysis are similar to the original findings, except for one structure (the left superior temporal gyrus) in which a trend-level statistical significance (p = 0.07) was observed instead of statistical significance.
We formalize the pair-wise registration problem in a maximum a posteriori (MAP) framework that employs a multinomial model of joint intensities with parameters for which we only have a prior distribution. To obtain an MAP estimate of the aligning transformation alone, we treat the multinomial parameters as nuisance parameters, and marginalize them out. If the prior on those is uninformative, the marginalization leads to registration by minimization of joint entropy. With an informative prior, the marginalization leads to minimization of the entropy of the data pooled with pseudo observations from the prior. In addition, we show that the marginalized objective function can be optimized by the Expectation-Maximization (EM) algorithm, which yields a simple and effective iteration for solving entropy-based registration problems. Experimentally, we demonstrate the effectiveness of the resulting EM iteration for rapidly solving a challenging intra-operative registration problem.
In this article, we have developed a simple model that describes the adsorption of polymer chains from a solution having a good solvent onto a reactive surface of varying curvatures. In order to evaluate the impact of particle size on the adsorption process, we have probed the adsorption of poly(methyl methacrylate) (PMMA) on aluminum oxide (Al2O3) surfaces belonging to particles of different sizes. The basic approach assumed that the details of the chemisorption mechanism of PMMA on aluminum oxide surfaces are independent of surface curvature. The combination of the experimental results with the theoretical approach that we have developed show the existence of three different regimes of adsorption of polymer chains onto the surfaces of metal nanoparticles.
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.
BACKGROUND: Mapping functional areas of the brain is important for planning tumour resections. With the increased use of functional magnetic resonance imaging (fMRI) for presurgical planning, there is a need to validate that fMRI activation mapping is consistent with the mapping obtained during surgery using direct electrocortical stimulation (DECS).
METHODS: A quantitative comparison of DECS and fMRI mapping techniques was performed, using a patient-specific conductivity model to find the current distribution resulting from each stimulation site. The resulting DECS stimulation map was compared to the fMRI activation map, using the maximal Dice similarity coefficient (MDSC).
RESULTS: Our results show some agreement between these two mapping techniques--the stimulation site with the largest MOSC was the only site that demonstrated intra-operative effect.
CONCLUSIONS: There is a substantial effort to improve the techniques used to map functional areas, particularly using fMRI. It seems likely that fMRI will eventually provide a valid non-invasive means for functional mapping.
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.