We present a particular formulation of optimal transport for matrix-valued density functions. Our aim is to devise a geometry which is suitable for comparing power spectral densities of multivariable time series. More specifically, the value of a power spectral density at a given frequency, which in the matricial case encodes power as well as directionality, is thought of as a proxy for a "matrix-valued mass density." Optimal transport aims at establishing a natural metric in the space of such matrix-valued densities which takes into account differences between power across frequencies as well as misalignment of the corresponding principle axes. Thus, our transportation cost includes a cost of transference of power between frequencies together with a cost of rotating the principle directions of matrix densities. The two endpoint matrix-valued densities can be thought of as marginals of a joint matrix-valued density on a tensor product space. This joint density, very much as in the classical Monge-Kantorovich setting, can be thought to specify the transportation plan. Contrary to the classical setting, the optimal transport plan for matrices is no longer supported on a thin zero-measure set.
Diffusion MRI is a useful probe of tissue microstructure. The conventional diffusion encoding sequence, the single pulsed field gradient, has recently been challenged as more general gradient waveforms have been introduced. Out of these, we focus on q-space trajectory imaging, which generalizes the scalar b-value to a tensor valued entity. To take full advantage of its capabilities, it is imperative to respect the constraints imposed by the hardware, while at the same time maximizing the diffusion encoding strength. We provide a tool that achieves this by solving a constrained optimization problem that accommodates constraints on maximum gradient amplitude, slew rate, coil heating and positioning of radio frequency pulses. The method's efficacy and flexibility is demonstrated both experimentally and by comparison with previous work on optimization of isotropic diffusion sequences.
We present an image segmentation method that transfers label maps of entire organs from the training images to the novel image to be segmented. The transfer is based on sparse correspondences between keypoints that represent automatically identified distinctive image locations. Our segmentation algorithm consists of three steps: (i) keypoint matching, (ii) voting-based keypoint labeling, and (iii) keypoint-based probabilistic transfer of organ label maps. We introduce generative models for the inference of keypoint labels and for image segmentation, where keypoint matches are treated as a latent random variable and are marginalized out as part of the algorithm. We report segmentation results for abdominal organs in whole-body CT and in contrast-enhanced CT images. The accuracy of our method compares favorably to common multi-atlas segmentation while offering a speed-up of about three orders of magnitude. Furthermore, keypoint transfer requires no training phase or registration to an atlas. The algorithm's robustness enables the segmentation of scans with highly variable field-of-view.
In this paper we report the set-up and results of the Multimodal Brain Tumor Image Segmentation Benchmark (BRATS) organized in conjunction with the MICCAI 2012 and 2013 conferences. Twenty state-of-the-art tumor segmentation algorithms were applied to a set of 65 multi-contrast MR scans of low- and high-grade glioma patients-manually annotated by up to four raters-and to 65 comparable scans generated using tumor image simulation software. Quantitative evaluations revealed considerable disagreement between the human raters in segmenting various tumor sub-regions (Dice scores in the range 74%-85%), illustrating the difficulty of this task. We found that different algorithms worked best for different sub-regions (reaching performance comparable to human inter-rater variability), but that no single algorithm ranked in the top for all sub-regions simultaneously. Fusing several good algorithms using a hierarchical majority vote yielded segmentations that consistently ranked above all individual algorithms, indicating remaining opportunities for further methodological improvements. The BRATS image data and manual annotations continue to be publicly available through an online evaluation system as an ongoing benchmarking resource.
We present a semi-parametric generative model for predicting anatomy of a patient in subsequent scans following a single baseline image. Such predictive modeling promises to facilitate novel analyses in both voxel-level studies and longitudinal biomarker evaluation. We capture anatomical change through a combination of population-wide regression and a non-parametric model of the subject's health based on individual genetic and clinical indicators. In contrast to classical correlation and longitudinal analysis, we focus on predicting new observations from a single subject observation. We demonstrate prediction of follow-up anatomical scans in the ADNI cohort, and illustrate a novel analysis approach that compares a patient's scans to the predicted subject-specific healthy anatomical trajectory.
BACKGROUND: Brain atrophy in subjects with mild cognitive impairment (MCI) introduces partial volume effects, limiting the sensitivity of diffusion tensor imaging to white matter microstructural degeneration. Appropriate correction isolates microstructural effects in MCI that might be precursors of Alzheimer's disease (AD). METHODS: Forty-eight participants (18 MCI, 15 AD, and 15 healthy controls) had magnetic resonance imaging scans and clinical evaluations at baseline and follow-up after 36 months. Ten MCI subjects were diagnosed with AD at follow-up and eight remained MCI. Free-water (FW) corrected measures on the white matter skeleton were compared between groups. RESULTS: FW corrected radial diffusivity, but not uncorrected radial diffusivity, was increased across the brain of the converted group compared with the nonconverted group (P < .05). The extent of increases was similar to that found comparing AD with controls. CONCLUSION: Partial volume elimination reveals microstructural alterations preceding dementia. These alterations may prove to be an effective and feasible early biomarker of AD.
Segmentation of anatomical structures in medical imagery is a key step in a variety of clinical applications. Designing a generic, automated method that works for various structures and imaging modalities is a daunting task. In this paper, we present an effective interactive segmentation method that reformulates the GrowCut algorithm as a clustering problem and computes a fast, approximate solution. The method is further improved by using an efficient updating scheme requiring only local computations when new user input becomes available, making it applicable to high resolution images. The algorithm may easily be included as a user-oriented software module in any number of available medical imaging/image processing platforms such as 3D Slicer. The efficiency and effectiveness of the algorithm are demonstrated through tests on several challenging data sets where it is also compared to standard GrowCut.
This tutorial demonstrates how to prepare data for 3D printing using the open source software 3D Slicer. The following topics are highlighted in the tutorial: introduction to the 3D Slicer interface, loading data into 3D Slicer, volume rendering, cropping image volumes, creating label maps, creating surface models, and saving data in file formats appropriate for 3D printing.
PURPOSE: To evaluate the ability of various software (SW) tools used for quantitative image analysis to properly account for source-specific image scaling employed by magnetic resonance imaging manufacturers.
METHODS: A series of gadoteridol-doped distilled water solutions (0%, 0.5%, 1%, and 2% volume concentrations) was prepared for manual substitution into one (of three) phantom compartments to create "variable signal," whereas the other two compartments (containing mineral oil and 0.25% gadoteriol) were held unchanged. Pseudodynamic images were acquired over multiple series using four scanners such that the histogram of pixel intensities varied enough to provoke variable image scaling from series to series. Additional diffusion-weighted images were acquired of an ice-water phantom to generate scanner-specific apparent diffusion coefficient (ADC) maps. The resulting pseudodynamic images and ADC maps were analyzed by eight centers of the Quantitative Imaging Network using 16 different SW tools to measure compartment-specific region-of-interest intensity.
RESULTS: Images generated by one of the scanners appeared to have additional intensity scaling that was not accounted for by the majority of tested quantitative image analysis SW tools. Incorrect image scaling leads to intensity measurement bias near 100%, compared to nonscaled images.
CONCLUSION: Corrective actions for image scaling are suggested for manufacturers and quantitative imaging community.
The normal human brain is characterized by a pattern of gross anatomical asymmetry. This pattern, known as the "torque", is associated with a sexual dimorphism: The male brain tends to be more asymmetric than that of the female. This fact, along with well-known sex differences in brain development (faster in females) and onset of psychosis (earlier with worse outcome in males), has led to the theory that schizophrenia is a disorder in which sex-dependent abnormalities in the development of brain torque, the correlate of the capacity for language, cause alterations in interhemispheric connectivity, which are causally related to psychosis (Crow TJ, Paez P, Chance SE. 2007. Callosal misconnectivity and the sex difference in psychosis. Int Rev Psychiatry. 19(4):449-457.). To provide evidence toward this theory, we analyze the geometry of interhemispheric white matter connections in adolescent-onset schizophrenia, with a particular focus on sex, using a recently introduced framework for white matter geometry computation in diffusion tensor imaging data (Savadjiev P, Kindlmann GL, Bouix S, Shenton ME, Westin CF. 2010. Local white geometry from diffusion tensor gradients. Neuroimage. 49(4):3175-3186.). Our results reveal a pattern of sex-dependent white matter geometry abnormalities that conform to the predictions of Crow's torque theory and correlate with the severity of patients' symptoms. To the best of our knowledge, this is the first study to associate geometrical differences in white matter connectivity with torque in schizophrenia.
OBJECTIVE: To evaluate the three-dimensional (3D) skeletal changes in the mandibles of Class III patients treated with bone-anchored maxillary protraction using shape correspondence analysis.
MATERIAL AND METHOD: Twenty-five consecutive patients with skeletal Class III who were between the ages of 9 and 13 years (mean age, 11.10 ± 1.1 years) were treated using Class III intermaxillary elastics and bilateral miniplates (two in the infrazygomatic crests of the maxilla and two in the anterior mandible). Cone-beam computed tomography (CBCT) was performed for each patient before initial loading (T1) and at 1 year out (T2). From the CBCT scans, 3D models were generated, registered on the anterior cranial base, and analyzed using 3D linear distances and vectors between corresponding point-based surfaces.
RESULTS: Bone-anchored traction produced anteroposterior and vertical skeletal changes in the mandible. The novel application of Shape correspondence analysis showed vectors of mean (± standard deviation) distal displacement of the posterior ramus of 3.6 ± 1.4 mm, while the chin displaced backward by 0.5 ± 3.92 mm. The lower border of the mandible at the menton region was displaced downward by 2.6 ± 1.2 mm, and the lower border at the gonial region moved downward by 3.6 ± 1.4 mm. There was a downward and backward displacement around the gonial region with a mean closure of the gonial angle by 2.1°. The condyles were displaced distally by a mean of 2.6 ± 1.5 mm, and there were three distinct patterns for displacement: 44% backward, 40% backward and downward, and 16% backward and upward.
CONCLUSION: This treatment approach induces favorable control of the mandibular growth pattern and can be used to treat patients with components of mandibular prognathism.
In this work, we present a faceted-search based approach for visualization of anatomy by combining a three dimensional digital atlas with an anatomy ontology. Specifically, our approach provides a drill-down search interface that exposes the relevant pieces of information (obtained by searching the ontology) for a user query. Hence, the user can produce visualizations starting with minimally specified queries. Furthermore, by automatically translating the user queries into the controlled terminology our approach eliminates the need for the user to use controlled terminology. We demonstrate the scalability of our approach using an abdominal atlas and the same ontology. We implemented our visualization tool on the opensource 3D Slicer software. We present results of our visualization approach by combining a modified Foundational Model of Anatomy (FMA) ontology with the Surgical Planning Laboratory (SPL) Brain 3D digital atlas, and geometric models specific to patients computed using the SPL brain tumor dataset.
Many studies have observed altered neurofunctional and structural organization in the aging brain. These observations from functional neuroimaging studies show a shift in brain activity from the posterior to the anterior regions with aging (PASA model), as well as a decrease in cortical thickness, which is more pronounced in the frontal lobe followed by the parietal, occipital, and temporal lobes (retrogenesis model). However, very little work has been done using diffusion MRI (dMRI) with respect to examining the structural tissue alterations underlying these neurofunctional changes in the gray matter. Thus, for the first time, we propose to examine gray matter changes using diffusion MRI in the context of aging. In this work, we propose a novel dMRI based measure of gray matter "heterogeneity" that elucidates these functional and structural models (PASA and retrogenesis) of aging from the viewpoint of diffusion MRI. In a cohort of 85 subjects (all males, ages 15-55 years), we show very high correlation between age and "heterogeneity" (a measure of structural layout of tissue in a region-of-interest) in specific brain regions. We examine gray matter alterations by grouping brain regions into anatomical lobes as well as functional zones. Our findings from dMRI data connects the functional and structural domains and confirms the "retrogenesis" hypothesis of gray matter alterations while lending support to the neurofunctional PASA model of aging in addition to showing the preservation of paralimbic areas during healthy aging.
OBJECT: Concussion, or mild traumatic brain injury (mTBI), is a commonly occurring sports-related injury, especially in contact sports such as hockey. Cerebral microbleeds (CMBs), which appear as small, hypointense lesions on T₂*-weighted images, can result from TBI. The authors use susceptibility-weighted imaging (SWI) to automatically detect small hypointensities that may be subtle signs of chronic and acute damage due to both subconcussive and concussive injury. The goal was to investigate how the burden of these hypointensities changes over time, over a playing season, and postconcussion, in comparison with subjects who did not suffer a medically observed and diagnosed concussion.
METHODS: Images were obtained in 45 university-level adult male and female ice hockey players before and after a single Canadian Interuniversity Sports season. In addition, 11 subjects (5 men and 6 women) underwent imaging at 72 hours, 2 weeks, and 2 months after concussion. To identify subtle changes in brain tissue and potential CMBs, nonvessel clusters of hypointensities on SWI were automatically identified, and a hypointensity burden index was calculated for all subjects at the beginning of the season (BOS), the end of the season (EOS), and at postconcussion time points (where applicable).
RESULTS: A statistically significant increase in the hypointensity burden, relative to the BOS, was observed for male subjects with concussions at the 2-week postconcussion time point. A smaller, nonsignificant rise in the burden for female subjects with concussions was also observed within the same time period. There were no significant changes in burden for nonconcussed subjects of either sex between the BOS and EOS time points. However, there was a statistically significant difference in the burden between male and female subjects in the nonconcussed group at both the BOS and EOS time points, with males having a higher burden.
CONCLUSIONS: This method extends the utility of SWI from the enhancement and detection of larger (> 5 mm) CMBs, which are often observed in more severe cases of TBI, to cases involving smaller lesions in which visual detection of injury is difficult. The hypointensity burden metric proposed here shows statistically significant changes over time in the male subjects. A smaller, nonsignificant increase in the burden metric was observed in the female subjects.
OBJECT: Concussion is a common injury in ice hockey and a health problem for the general population. Traumatic axonal injury has been associated with concussions (also referred to as mild traumatic brain injuries), yet the pathological course that leads from injury to recovery or to long-term sequelae is still not known. This study investigated the longitudinal course of concussion by comparing diffusion MRI (dMRI) scans of the brains of ice hockey players before and after a concussion.
METHODS: The 2011-2012 Hockey Concussion Education Project followed 45 university-level ice hockey players (both male and female) during a single Canadian Interuniversity Sports season. Of these, 38 players had usable dMRI scans obtained in the preseason. During the season, 11 players suffered a concussion, and 7 of these 11 players had usable dMRI scans that were taken within 72 hours of injury. To analyze the data, the authors performed free-water imaging, which reflects an increase in specificity over other dMRI analysis methods by identifying alterations that occur in the extracellular space compared with those that occur in proximity to cellular tissue in the white matter. They used an individualized approach to identify alterations that are spatially heterogeneous, as is expected in concussions.
RESULTS: Paired comparison of the concussed players before and after injury revealed a statistically significant (p < 0.05) common pattern of reduced free-water volume and reduced axial and radial diffusivities following elimination of free-water. These free-water-corrected measures are less affected by partial volumes containing extracellular water and are therefore more specific to processes that occur within the brain tissue. Fractional anisotropy was significantly increased, but this change was no longer significant following the free-water elimination.
CONCLUSIONS: Concussion during ice hockey games results in microstructural alterations that are detectable using dMRI. The alterations that the authors found suggest decreased extracellular space and decreased diffusivities in white matter tissue. This finding might be explained by swelling and/or by increased cellularity of glia cells. Even though these findings in and of themselves cannot determine whether the observed microstructural alterations are related to long-term pathology or persistent symptoms, they are important nonetheless because they establish a clearer picture of how the brain responds to concussion.