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.
PURPOSE: Diffusion encoding with asymmetric gradient waveforms is appealing because the asymmetry provides superior efficiency. However, concomitant gradients may cause a residual gradient moment at the end of the waveform, which can cause significant signal error and image artifacts. The purpose of this study was to develop an asymmetric waveform designs for tensor-valued diffusion encoding that is not sensitive to concomitant gradients. METHODS: The "Maxwell index" was proposed as a scalar invariant to capture the effect of concomitant gradients. Optimization of "Maxwell-compensated" waveforms was performed in which this index was constrained. Resulting waveforms were compared to waveforms from literature, in terms of the measured and predicted impact of concomitant gradients, by numerical analysis as well as experiments in a phantom and in a healthy human brain. RESULTS: Maxwell-compensated waveforms with Maxwell indices below 100 (mT/m) ms showed negligible signal bias in both numerical analysis and experiments. By contrast, several waveforms from literature showed gross signal bias under the same conditions, leading to a signal bias that was large enough to markedly affect parameter maps. Experimental results were accurately predicted by theory. CONCLUSION: Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient diffusion encoding that negates the effects of concomitant fields while enabling arbitrary shapes of the b-tensor. This waveform design is especially useful in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition, and large FOVs.
Motion is a major confound in diffusion-weighted imaging (DWI) in the body, and it is a common cause of image artefacts. The effects are particularly severe in cardiac applications, due to the nonrigid cyclical deformation of the myocardium. Spin echo-based DWI commonly employs gradient moment-nulling techniques to desensitise the acquisition to velocity and acceleration, ie, nulling gradient moments up to the 2nd order (M2-nulled). However, current M2-nulled DWI scans are limited to encode diffusion along a single direction at a time. We propose a method for designing b-tensors of arbitrary shapes, including planar, spherical, prolate and oblate tensors, while nulling gradient moments up to the 2nd order and beyond. The design strategy comprises initialising the diffusion encoding gradients in two encoding blocks about the refocusing pulse, followed by appropriate scaling and rotation, which further enables nulling undesired effects of concomitant gradients. Proof-of-concept assessment of in vivo mean diffusivity (MD) was performed using linear and spherical tensor encoding (LTE and STE, respectively) in the hearts of five healthy volunteers. The results of the M2-nulled STE showed that (a) the sequence was robust to cardiac motion, and (b) MD was higher than that acquired using standard M2-nulled LTE, where diffusion-weighting was applied in three orthogonal directions, which may be attributed to the presence of restricted diffusion and microscopic diffusion anisotropy. Provided adequate signal-to-noise ratio, STE could significantly shorten estimation of MD compared with the conventional LTE approach. Importantly, our theoretical analysis and the proposed gradient waveform design may be useful in microstructure imaging beyond diffusion tensor imaging where the effects of motion must be suppressed.
Posterior circulation ischemic stroke (PCiS) constitutes 20-30% of ischemic stroke cases. Detailed information about differences between PCiS and anterior circulation ischemic stroke (ACiS) remains scarce. Such information might guide clinical decision making and prevention strategies. We studied risk factors and ischemic stroke subtypes in PCiS vs. ACiS and lesion location on magnetic resonance imaging (MRI) in PCiS.
Out of 3,301 MRIs from 12 sites in the National Institute of Neurological Disorders and Stroke (NINDS) Stroke Genetics Network (SiGN), we included 2,381 cases with acute DWI lesions. The definition of ACiS or PCiS was based on lesion location. We compared the groups using Chi-squared and logistic regression.
PCiS occurred in 718 (30%) patients and ACiS in 1663 (70%). Diabetes and male sex were more common in PCiS vs. ACiS (diabetes 27% vs. 23%, p < 0.05; male sex 68% vs. 58%, p < 0.001). Both were independently associated with PCiS (diabetes, OR = 1.29; 95% CI 1.04-1.61; male sex, OR = 1.46; 95% CI 1.21-1.78). ACiS more commonly had large artery atherosclerosis (25% vs. 20%, p < 0.01) and cardioembolic mechanisms (17% vs. 11%, p < 0.001) compared to PCiS. Small artery occlusion was more common in PCiS vs. ACiS (20% vs. 14%, p < 0.001). Small artery occlusion accounted for 47% of solitary brainstem infarctions.
Ischemic stroke subtypes differ between the two phenotypes. Diabetes and male sex have a stronger association with PCiS than ACiS. Definitive MRI-based PCiS diagnosis aids etiological investigation and contributes additional insights into specific risk factors and mechanisms of injury in PCiS.
Although brain functionality is often remarkably robust to lesions and other insults, it may be fragile when these take place in specific locations. Previous attempts to quantify robustness and fragility sought to understand how the functional connectivity of brain networks is affected by structural changes, using either model-based predictions or empirical studies of the effects of lesions. We advance a geometric viewpoint relying on a notion of network curvature, the so-called Ollivier-Ricci curvature. This approach has been proposed to assess financial market robustness and to differentiate biological networks of cancer cells from healthy ones. Here, we apply curvature-based measures to brain structural networks to identify robust and fragile brain regions in healthy subjects. We show that curvature can also be used to track changes in brain connectivity related to age and autism spectrum disorder (ASD), and we obtain results that are in agreement with previous MRI studies.
The Human Placenta Project has focused attention on the need for noninvasive magnetic resonance imaging (MRI)-based techniques to diagnose and monitor placental function throughout pregnancy. The hope is that the management of placenta-related pathologies would be improved if physicians had more direct, real-time measures of placental health to guide clinical decision making. As oxygen alters signal intensity on MRI and oxygen transport is a key function of the placenta, many of the MRI methods under development are focused on quantifying oxygen transport or oxygen content of the placenta. For example, measurements from blood oxygen level-dependent imaging of the placenta during maternal hyperoxia correspond to outcomes in twin pregnancies, suggesting that some aspects of placental oxygen transport can be monitored by MRI. Additional methods are being developed to accurately quantify baseline placental oxygenation by MRI relaxometry. However, direct validation of placental MRI methods is challenging and therefore animal studies and ex vivo studies of human placentas are needed. Here we provide an overview of the current state of the art of oxygen transport and quantification with MRI. We suggest that as these techniques are being developed, increased focus be placed on ensuring they are robust and reliable across individuals and standardized to enable predictive diagnostic models to be generated from the data. The field is still several years away from establishing the clinical benefit of monitoring placental function in real time with MRI, but the promise of individual personalized diagnosis and monitoring of placental disease in real time continues to motivate this effort.