We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces.
This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second-and higher-order tensor-based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching.
In this paper, we present a novel method for texture mapping of closed surfaces. Our method is based on the technique of optimal mass transport (also known as the "earth-mover's metric"). This is a classical problem that concerns determining the optimal way, in the sense of minimal transportation cost, of moving a pile of soil from one site to another. In our context, the resulting mapping is area preserving and minimizes angle distortion in the optimal mass sense. Indeed, we first begin with an angle-preserving mapping (which may greatly distort area) and then correct it using the mass transport procedure derived via a certain gradient flow. In order to obtain fast convergence to the optimal mapping, we incorporate a multiresolution scheme into our flow. We also use ideas from discrete exterior calculus in our computations.
The flow behavior of nanostructure clusters, consisting of chemically bonded PbSe quantum dots and magnetic gamma-Fe(2)O(3) nanoparticles, has been investigated. The clusters are regarded as model nanoplatforms with multiple functionalities, where the gamma-Fe(2)O(3) magnets serve as transport vehicles, manipulated by an external magnetic field gradient, and the quantum dots act as fluorescence tags within an optical window in the near-infrared regime. The clusters' flow was characterized by visualizing their trajectories within a viscous fluid (mimicking a blood stream), using an optical imaging method, while the trajectory pictures were analyzed by a specially developed processing package. The trajectories were examined under various flow rates, viscosities and applied magnetic field strengths. The results revealed a control of the trajectories even at low magnetic fields (<1 T), validating the use of similar nanoplatforms as active targeting constituents in personalized medicine.
This work provides a model for tubular structures, and devises an algorithm to automatically extract tubular anatomical structures from medical imagery. Our model fits many anatomical structures in medical imagery, in particular, various fiber bundles in the brain (imaged through diffusion-weighted magnetic resonance (DW-MRI)) such as the cingulum bundle, and blood vessel trees in computed tomography angiograms (CTAs). Extraction of the cingulum bundle is of interest because of possible ties to schizophrenia, and extracting blood vessels is helpful in the diagnosis of cardiovascular diseases. The tubular model we propose has advantages over many existing approaches in literature: fewer degrees-of-freedom over a general deformable surface hence energies defined on such tubes are less sensitive to undesirable local minima, and the tube (in 3-D) can be naturally represented by a 4-D curve (a radius function and centerline), which leads to computationally less costly algorithms and has the advantage that the centerline of the tube is obtained without additional effort. Our model also generalizes to tubular trees, and the extraction algorithm that we design automatically detects and evolves branches of the tree. We demonstrate the performance of our algorithm on 20 datasets of DW-MRI data and 32 datasets of CTA, and quantify the results of our algorithm when expert segmentations are available.
Thomas Walter, David W Shattuck, Richard Baldock, Mark E Bastin, Anne E Carpenter, Suzanne Duce, Jan Ellenberg, Adam Fraser, Nicholas Hamilton, Steve Pieper, Mark A Ragan, Jurgen E Schneider, Pavel Tomancak, and Jean-Karim Hériché. 2010. “Visualization of image data from cells to organisms.” Nat Methods, 7, 3 Suppl, Pp. S26-41.Abstract
Advances in imaging techniques and high-throughput technologies are providing scientists with unprecedented possibilities to visualize internal structures of cells, organs and organisms and to collect systematic image data characterizing genes and proteins on a large scale. To make the best use of these increasingly complex and large image data resources, the scientific community must be provided with methods to query, analyze and crosslink these resources to give an intuitive visual representation of the data. This review gives an overview of existing methods and tools for this purpose and highlights some of their limitations and challenges.
We describe a neuroimaging protocol that utilizes an anatomical atlas of the human head to guide diffuse optical tomography of human brain activation. The protocol is demonstrated by imaging the hemodynamic response to median-nerve stimulation in three healthy subjects, and comparing the images obtained using a head atlas with the images obtained using the subject-specific head anatomy. The results indicate that using the head atlas anatomy it is possible to reconstruct the location of the brain activation to the expected gyrus of the brain, in agreement with the results obtained with the subject-specific head anatomy. The benefits of this novel method derive from eliminating the need for subject-specific head anatomy and thus obviating the need for a subject-specific MRI to improve the anatomical interpretation of diffuse optical tomography images of brain activation.
Recent advances in diffusion weighted MR imaging (dMRI) has made it a tool of choice for investigating white matter abnormalities of the brain and central nervous system. In this work, we design a system that detects abnormal features (biomarkers) of first-episode schizophrenia patients and then classifies them using these features. We use two different models of the dMRI data, namely, spherical harmonics and the two-tensor model. The algorithm works by first computing several diffusion measures from each model. An affine-invariant representation of each subject is then computed, thus avoiding the need for registration. This representation is used within a kernel based feature selection algorithm to determine the biomarkers that are statistically different between the two populations. Confirmation of how well these biomarkers identify each population is obtained by using several classifiers such as, k-nearest neighbors, Parzen window classifier, and support vector machines to separate 21 first-episode patients from 20 age-matched normal controls. Classification results using leave-many-out cross-validation scheme are given for each representation. This algorithm is a first step towards early detection of schizophrenia.
BACKGROUND: While the neuroanatomical underpinnings of the functional brain disconnectivity observed in patients with schizophrenia (SZ) remain elusive, white matter fiber bundles of the brain are a likely candidate, given that they represent the infrastructure for long-distance neural communication. METHODS: This study investigated for diffusion abnormalities in 19 patients with chronic SZ, relative to 19 matched control subjects, across tractography-defined segments of the corpus callosum. Diffusion-weighted images were acquired with 51 noncollinear gradients on a 3T scanner (1.7 mm isotropic voxels). The corpus callosum was extracted by means of whole-brain tractography and automated fiber clustering and was parcelled into six segments on the basis of fiber trajectories. The diffusion indexes of fractional anisotropy (FA) and mode were calculated for each segment. RESULTS: Relative to the healthy control subjects, the SZ patients exhibited mode increases in the parietal fibers, suggesting a relative absence of crossing fibers. Schizophrenia patients also exhibited FA reductions in the frontal fibers, which were underpinned by increases in radial diffusivity, consistent with myelin abnormalities. Significant correlations were observed between patients' degree of reality distortion and their FA and radial diffusivity, such that the most severely psychotic patients were the least abnormal in terms of their frontal fiber diffusivity. CONCLUSIONS: The SZ patients exhibited a variety of diffusion abnormalities in the corpus callosum, which were related to the severity of their psychotic symptoms. To the extent that diffusion abnormalities influence axonal transmission velocities, these results provide support for those theories that emphasize neural timing abnormalities in the etiology of schizophrenia.
In healthy adult individuals, late life is a dynamic time of change with respect to the microstructural integrity of white matter tracts. Yet, elderly individuals are generally excluded from diffusion tensor imaging studies in schizophrenia. Therefore, we examined microstructural integrity of frontotemporal and interhemispheric white matter tracts in schizophrenia across the adult lifespan. Diffusion tensor imaging data from 25 younger schizophrenic patients (< or = 55 years), 25 younger controls, 25 older schizophrenic patients (> or = 56 years) and 25 older controls were analysed. Patients with schizophrenia in each group were individually matched to controls. Whole-brain tractography and clustering segmentation were employed to isolate white matter tracts. Groups were compared using repeated measures analysis of variance with 12 within-group measures of fractional anisotropy: (left and right) uncinate fasciculus, arcuate fasciculus, inferior longitudinal fasciculus, inferior occipito-frontal fasciculus, cingulum bundle, and genu and splenium of the corpus callosum. For each white matter tract, fractional anisotropy was then regressed against age in patients and controls, and correlation coefficients compared. The main effect of group (F(3,92) = 12.2, P < 0.001), and group by tract interactions (F(26,832) = 1.68, P = 0.018) were evident for fractional anisotropy values. Younger patients had significantly lower fractional anisotropy than younger controls (Bonferroni-corrected alpha = 0.0042) in the left uncinate fasciculus (t(48) = 3.7, P = 0.001) and right cingulum bundle (t(48) = 3.6, P = 0.001), with considerable effect size, but the older groups did not differ. Schizophrenic patients did not demonstrate accelerated age-related decline compared with healthy controls in any white matter tract. To our knowledge, this is the first study to examine the microstructural integrity of frontotemporal white matter tracts across the adult lifespan in schizophrenia. The left uncinate fasciculus and right cingulum bundle are disrupted in younger chronic patients with schizophrenia compared with matched controls, suggesting that these white matter tracts are related to frontotemporal disconnectivity. The absence of accelerated age-related decline, or differences between older community-dwelling patients and controls, suggests that these patients may possess resilience to white matter disruption.
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L(2) mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61-97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data.
The quantification of brain asymmetries may provide biomarkers for presurgical localization of language function and can improve our understanding of neural structure-function relationships in health and disease. We propose a new method for studying the asymmetry of the white matter tracts in the entire brain, and we apply it to a preliminary study of normal subjects across the handedness spectrum. Methods for quantifying white matter asymmetry using diffusion MRI tractography have thus far been based on comparing numbers of fibers or volumes of a single fiber tract across hemispheres. We propose a generalization of such methods, where the "number of fibers" laterality measurement is extended to the entire brain using a soft fiber comparison metric. We summarize the distribution of fiber laterality indices over the whole brain in a histogram, and we measure properties of the distribution such as its skewness, median, and inter-quartile range. The whole-brain fiber laterality histogram can be measured in an exploratory fashion without hypothesizing asymmetries only in particular structures. We demonstrate an overall difference in white matter asymmetry in consistent- and inconsistent-handers: the skewness of the fiber laterality histogram is significantly different across handedness groups.
We introduce a fibre tractography framework based on a particle filter which estimates a local geometrical model of the underlying white matter tract, formulated as a 'streamline flow' using generalized helicoids. The method is not dependent on the diffusion model, and is applicable to diffusion tensor (DT) data as well as to high angular resolution reconstructions. The geometrical model allows for a robust inference of local tract geometry, which, in the context of the causal filter estimation, guides tractography through regions with partial volume effects. We validate the method on synthetic data and present results on two types in vivo data: diffusion tensors and a spherical harmonic reconstruction of the fibre orientation distribution function (fODF).
The Funk-Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model. The FRT consists in the integration of the attenuation signal, sampled by the MRI scanner on the unit sphere, along equators orthogonal to the directions of interest. It is easily proved that this calculation is equivalent to the integration of the diffusion propagator along such directions, although a characteristic blurring with a Bessel kernel is introduced. Under a different point of view, the FRT can be seen as an efficient way to compute the angular part of the integral of the attenuation signal in the plane orthogonal to each direction of the diffusion propagator. In this paper, Stoke's theorem is used to prove that the FRT can in fact be used to compute accurate estimates of the true integrals defining the functions of interest in HARDI, keeping the diffusion model as little restrictive as possible. Varying the assumptions on the attenuation signal, we derive new estimators of fiber orientations, generalizing both Q-Balls and the OPDT. Extensive experiments with both synthetic and real data have been intended to show that the new techniques improve existing ones in many situations.
The corticospinal tract (CST) is one of the most well studied tracts in human neuroanatomy. Its clinical significance can be demonstrated in many notable traumatic conditions and diseases such as stroke, spinal cord injury (SCI) or amyotrophic lateral sclerosis (ALS). With the advent of diffusion MRI and tractography the computational representation of the human CST in a 3D model became available. However, the representation of the entire CST and, specifically, the hand motor area has remained elusive. In this paper we propose a novel method, using manually drawn ROIs based on robustly identifiable neuroanatomic structures to delineate the entire CST and isolate its hand motor representation as well as to estimate their variability and generate a database of their volume, length and biophysical parameters. Using 37 healthy human subjects we performed a qualitative and quantitative analysis of the CST and the hand-related motor fiber tracts (HMFTs). Finally, we have created variability heat maps from 37 subjects for both the aforementioned tracts, which could be utilized as a reference for future studies with clinical focus to explore neuropathology in both trauma and disease states.
BACKGROUND: Extracellular free water within cerebral white matter tissue has been shown to increase with age and pathology, yet the cognitive consequences of free water in typical aging prior to the development of neurodegenerative disease remains unclear. Understanding the contribution of free water to cognitive function in older adults may provide important insight into the neural mechanisms of the cognitive aging process. METHODS: A diffusion-weighted MRI measure of extracellular free water as well as a commonly used diffusion MRI metric (fractional anisotropy) along nine bilateral white matter pathways were examined for their relationship with cognitive function assessed by the NIH Toolbox Cognitive Battery in 47 older adults (mean age = 74.4 years, SD = 5.4 years, range = 65-85 years). Probabilistic tractography at the 99th percentile level of probability (Tracts Constrained by Underlying Anatomy; TRACULA) was utilized to produce the pathways on which microstructural characteristics were overlaid and examined for their contribution to cognitive function independent of age, education, and gender. RESULTS: When examining the 99th percentile probability core white matter pathway derived from TRACULA, poorer fluid cognitive ability was related to higher mean free water values across the angular and cingulum bundles of the cingulate gyrus, as well as the corticospinal tract and the superior longitudinal fasciculus. There was no relationship between cognition and mean FA or free water-adjusted FA across the 99th percentile core white matter pathway. Crystallized cognitive ability was not associated with any of the diffusion measures. When examining cognitive domains comprising the NIH Toolbox Fluid Cognition index relationships with these white matter pathways, mean free water demonstrated strong hemispheric and functional specificity for cognitive performance, whereas mean FA was not related to age or cognition across the 99th percentile pathway. CONCLUSIONS: Extracellular free water within white matter appears to increase with normal aging, and higher values are associated with significantly lower fluid but not crystallized cognitive functions. When using TRACULA to estimate the core of a white matter pathway, a higher degree of free water appears to be highly specific to the pathways associated with memory, working memory, and speeded decision-making performance, whereas no such relationship existed with FA. These data suggest that free water may play an important role in the cognitive aging process, and may serve as a stronger and more specific indicator of early cognitive decline than traditional diffusion MRI measures, such as FA.
RATIONALE AND OBJECTIVES: To explore a role for multiparametric MRI (mpMRI) as a biomarker of response to neoadjuvant androgen deprivation therapy (ADT) for prostate cancer (PCa).
MATERIALS AND METHODS: This prospective study was approved by the institutional review board and was HIPAA compliant. Eight patients with localized PCa had a baseline mpMRI, repeated after 6-months of ADT, followed by prostatectomy. mpMRI indices were extracted from tumor and normal regions of interest (TROI/NROI). Residual cancer burden (RCB) was measured on mpMRI and on the prostatectomy specimen. Paired t-tests compared TROI/NROI mpMRI indices and pre/post-treatment TROI mpMRI indices. Spearman's rank tested for correlations between MRI/pathology-based RCB, and between pathological RCB and mpMRI indices.
RESULTS: At baseline, TROI apparent diffusion coefficient (ADC) was lower and dynamic contrast enhanced (DCE) metrics were higher, compared to NROI (ADC: 806 ± 137 × 10 vs. 1277 ± 213 × 10 mm/sec, p = 0.0005; K: 0.346 ± 0.16 vs. 0.144 ± 0.06 min, p = 0.002; AUC: 0.213 ± 0.08 vs. 0.11 ± 0.03, p = 0.002). Post-treatment, there was no change in TROI ADC, but a decrease in TROI K (0.346 ± 0.16 to 0.188 ± 0.08 min; p = 0.02) and AUC (0.213 ± 0.08 to 0.13 ± 0.06; p = 0.02). Tumor volume decreased with ADT. There was no difference between mpMRI-based and pathology-based RCB, which positively correlated (⍴ = 0.74-0.81, p < 0.05). Pathology-based RCB positively correlated with post-treatment DCE metrics (⍴ = 0.76-0.70, p < 0.05) and negatively with ADC (⍴ = -0.79, p = 0.03).
CONCLUSION: Given the heterogeneity of PCa, an individualized approach to ADT may maximize potential benefit. This pilot study suggests that mpMRI may serve as a biomarker of ADT response and as a surrogate for RCB at prostatectomy.
INTRODUCTION: Before using blood-oxygen-level-dependent magnetic resonance imaging (BOLD MRI) during maternal hyperoxia as a method to detect individual placental dysfunction, it is necessary to understand spatiotemporal variations that represent normal placental function. We investigated the effect of maternal position and Braxton-Hicks contractions on estimates obtained from BOLD MRI of the placenta during maternal hyperoxia. METHODS: For 24 uncomplicated singleton pregnancies (gestational age 27-36 weeks), two separate BOLD MRI datasets were acquired, one in the supine and one in the left lateral maternal position. The maternal oxygenation was adjusted as 5 min of room air (21% O), followed by 5 min of 100% FiO. After datasets were corrected for signal non-uniformities and motion, global and regional BOLD signal changes in R* and voxel-wise Time-To-Plateau (TTP) in the placenta were measured. The overall placental and uterine volume changes were determined across time to detect contractions. RESULTS: In mothers without contractions, increases in global placental R* in the supine position were larger compared to the left lateral position with maternal hyperoxia. Maternal position did not alter global TTP but did result in regional changes in TTP. 57% of the subjects had Braxton-Hicks contractions and 58% of these had global placental R* decreases during the contraction. CONCLUSION: Both maternal position and Braxton-Hicks contractions significantly affect global and regional changes in placental R* and regional TTP. This suggests that both factors must be taken into account in analyses when comparing placental BOLD signals over time within and between individuals.
We investigated brain wiring in chronic schizophrenia and healthy controls in frontostriatal circuits using diffusion magnetic resonance imaging tractography in a novel way. We extracted diffusion streamlines in 27 chronic schizophrenia and 26 healthy controls connecting 4 frontal subregions to the striatum. We labeled the projection zone striatal surface voxels into 2 subtypes: dominant-input from a single cortical subregion, and, functionally integrative, with mixed-input from diverse cortical subregions. We showed: 1) a group difference for total striatal surface voxel number (P = .045) driven by fewer mixed-input voxels in the left (P = .007), but not right, hemisphere; 2) a group by hemisphere interaction for the ratio quotient between voxel subtypes (P = .04) with a left (P = .006), but not right, hemisphere increase in schizophrenia, also reflecting fewer mixed-input voxels; and 3) fewer mixed-input voxel counts in schizophrenia (P = .045) driven by differences in left hemisphere limbic (P = .007) and associative (P = .01), but not sensorimotor, striatum. These results demonstrate a less integrative pattern of frontostriatal structural connectivity in chronic schizophrenia. A diminished integrative pattern yields a less complex input pattern to the striatum from the cortex with less circuit integration at the level of the striatum. Further, as brain wiring occurs during early development, aberrant brain wiring could serve as a developmental biomarker for schizophrenia.