We have compared the three-dimensional (3D) morphology of stubby and spiny neurons derived from the human small intestine. After immunohistochemical triple staining for leu-enkephalin (ENK), vasoactive intestinal peptide (VIP) and neurofilament (NF), neurons were selected and scanned based on their immunoreactivity, whether ENK (stubby) or VIP (spiny). For the 3D reconstruction, we focused on confocal data pre-processing with intensity drop correction, non-blind deconvolution, an additional compression procedure in z-direction, and optimizing segmentation reliability. 3D Slicer software enabled a semi-automated segmentation based on an objective threshold (interrater and intrarater reliability, both 0.99). We found that most dendrites of stubby neurons emerged only from the somal circumference, whereas in spiny neurons, they also emerged from the luminal somal surface. In most neurons, the nucleus was positioned abluminally in its soma. The volumes of spiny neurons were significantly larger than those of stubby neurons (total mean of stubbies 806 +/- 128 mum(3), of spinies 2,316 +/- 545 mum(3)), and spiny neurons had more dendrites (26.3 vs. 11.3). The ratios of somal versus dendritic volumes were 1:1.2 in spiny and 1:0.3 in stubby neurons. In conclusion, 3D reconstruction revealed new differences between stubby and spiny neurons and allowed estimations of volumetric data of these neuron populations.
Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.
BACKGROUND: White matter fiber tracts, especially those interconnecting the frontal and temporal lobes, are likely implicated in pathophysiology of schizophrenia. Very few studies, however, have focused on the fornix, a compact bundle of white matter fibers, projecting from the hippocampus to the septum, anterior nucleus of the thalamus and the mamillary bodies. Diffusion Tensor Imaging (DTI), and a new post-processing method, fiber tractography, provides a unique opportunity to visualize and to quantify entire trajectories of fiber bundles, such as the fornix, in vivo. We applied these techniques to quantify fornix diffusion anisotropy in schizophrenia. METHODS: DTI images were used to evaluate the left and the right fornix in 36 male patients diagnosed with chronic schizophrenia and 35 male healthy individuals, group matched on age, parental socioeconomic status, and handedness. Regions of interest were drawn manually, blind to group membership, to guide tractography, and fractional anisotropy (FA), a measure of fiber integrity, was calculated and averaged over the entire tract for each subject. The Doors and People test (DPT) was used to evaluate visual and verbal memory, combined recall and combined recognition. RESULTS: Analysis of variance was performed and findings demonstrated a difference between patients with schizophrenia and controls for fornix FA (p=0.006). Protected post-hoc independent sample t-tests demonstrated a bilateral FA decrease in schizophrenia, compared with control subjects (left side: p=0.048; right side p=0.006). Higher fornix FA was statistically significantly correlated with DPT and measures of combined visual memory (r=0.554, p=0.026), combined verbal memory (r=0.647, p=0.007), combined recall (r=0.516, p=0.041), and combined recognition (r=0.710, p=0.002) for the control group. No such statistically significant correlations were found in the patient group. CONCLUSIONS: Our findings show the utility of applying DTI and tractography to study white matter fiber tracts in vivo in schizophrenia. Specifically, we observed a bilateral disruption in fornix integrity in schizophrenia, thus broadening our understanding of the pathophysiology of this disease.
This paper addresses the problem of creating probabilistic brain atlases from manually labeled training data. Probabilistic atlases are typically constructed by counting the relative frequency of occurrence of labels in corresponding locations across the training images. However, such an "averaging" approach generalizes poorly to unseen cases when the number of training images is limited, and provides no principled way of aligning the training datasets using deformable registration. In this paper, we generalize the generative image model implicitly underlying standard "average" atlases, using mesh-based representations endowed with an explicit deformation model. Bayesian inference is used to infer the optimal model parameters from the training data, leading to a simultaneous group-wise registration and atlas estimation scheme that encompasses standard averaging as a special case. We also use Bayesian inference to compare alternative atlas models in light of the training data, and show how this leads to a data compression problem that is intuitive to interpret and computationally feasible. Using this technique, we automatically determine the optimal amount of spatial blurring, the best deformation field flexibility, and the most compact mesh representation. We demonstrate, using 2-D training datasets, that the resulting models are better at capturing the structure in the training data than conventional probabilistic atlases. We also present experiments of the proposed atlas construction technique in 3-D, and show the resulting atlases' potential in fully-automated, pulse sequence-adaptive segmentation of 36 neuroanatomical structures in brain MRI scans.
Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. However, the availability of comprehensive, reliable and suitable manual segmentations for atlas construction is limited. We therefore propose a joint segmentation of corresponding, aligned structures in the entire population that does not require a probability atlas. Instead, a latent atlas, initialized by a single manual segmentation, is inferred from the evolving segmentations of the ensemble. The proposed method is based on probabilistic principles but is solved using partial differential equations (PDEs) and energy minimization criteria, We evaluate the method by segmenting 50 brain MR volumes. Segmentation accuracy for cortical and subcortical structures approaches the quality of state-of-the-art atlas-based segmentation results, suggesting that the latent atlas method is a reasonable alternative when existing atlases are not compatible with the data to be processed.
We introduce a framework for computing geometrical properties of white matter fibres directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation makes it possible to define scalar geometrical measures that describe the underlying white matter fibres, directly from the diffusion tensor field and its gradient, without requiring prior tractography. We define two new scalar measures of (1) fibre dispersion and (2) fibre curving, and we demonstrate them on synthetic and in-vivo datasets. Finally, we illustrate their applicability in a group study on schizophrenia.
This paper investigates an approach to model the space of brain images through a low-dimensional manifold. A data driven method to learn a manifold from a collections of brain images is proposed. We hypothesize that the space spanned by a set of brain images can be captured, to some approximation, by a low-dimensional manifold, i.e. a parametrization of the set of images. The approach builds on recent advances in manifold learning that allow to uncover nonlinear trends in data. We combine this manifold learning with distance measures between images that capture shape, in order to learn the underlying structure of a database of brain images. The proposed method is generative. New images can be created from the manifold parametrization and existing images can be projected onto the manifold. By measuring projection distance of a held out set of brain images we evaluate the fit of the proposed manifold model to the data and we can compute statistical properties of the data using this manifold structure. We demonstrate this technology on a database of 436 MR brain images.
This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation approach by Bresson et al. allows for a convex optimization formulation of the segmentation problem, combining orientation statistics and spatial regularization. The approach compares favorably with segmentation by full-brain streamline tractography.
A natural requirement in pairwise image registration is that the resulting deformation is independent of the order of the images. This constraint is typically achieved via a symmetric cost function and has been shown to reduce the effects of local optima. Consequently, symmetric registration has been successfully applied to pairwise image registration as well as the spatial alignment of individual images with a template. However, recent work has shown that the relationship between an image and a template is fundamentally asymmetric. In this paper, we develop a method that reconciles the practical advantages of symmetric registration with the asymmetric nature of image-template registration by adding a simple correction factor to the symmetric cost function. We instantiate our model within a log-domain diffeomorphic registration framework. Our experiments show exploiting the asymmetry in image-template registration improves alignment in the image coordinates.
We describe a method for atlas-based segmentation of structural MRI for calculation of magnetic fieldmaps. CT data sets are used to construct a probabilistic atlas of the head and corresponding MR is used to train a classifier that segments soft tissue, air, and bone. Subject-specific fieldmaps are computed from the segmentations using a perturbation field model. Previous work has shown that distortion in echo-planar images can be corrected using predicted fieldmaps. We obtain results that agree well with acquired fieldmaps: 90% of voxel shifts from predicted fieldmaps show subvoxel disagreement with those computed from acquired fieldmaps. In addition, our fieldmap predictions show statistically significant improvement following inclusion of the atlas.
Least Squares (LS) and its weighted version are standard techniques to estimate the Diffusion Tensor (DT) from Diffusion Weighted Images (DWI). They require to linearize the problem by computing the logarithm of the DWI. For the single-coil Rician noise model it has been shown that this model does not introduce a significant bias, but for multiple array coils and parallel imaging, the noise cannot longer be modeled as Rician. As a result the validity of LS approaches is not assured. An analytical study of noise statistics for a multiple coil system is carried out, together with the Weighted LS formulation and noise analysis for this model. Results show that the bias in the computation of the components of the DT may be comparable to their variance in many cases, stressing the importance of unbiased filtering previous to DT estimation.
We propose an integrated registration and clustering algorithm, called "consistency clustering", that automatically constructs a probabilistic white-matter atlas from a set of multi-subject diffusion weighted MR images. We formulate the atlas creation as a maximum likelihood problem which the proposed method solves using a generalized Expectation Maximization (EM) framework. Additionally, the algorithm employs an outlier rejection and denoising strategy to produce sharp probabilistic maps of certain bundles of interest. We test this algorithm on synthetic and real data, and evaluate its stability against initialization. We demonstrate labeling a novel subject using the resulting spatial atlas and evaluate the accuracy of this labeling. Consistency clustering is a viable tool for completely automatic white-matter atlas construction for sub-populations and the resulting atlas is potentially useful for making diffusion measurements in a common coordinate system to identify pathology related changes or developmental trends.
This paper presents feature-based morphometry (FBM), a new, fully data-driven technique for identifying group-related differences in volumetric imagery. In contrast to most morphometry methods which assume one-to-one correspondence between all subjects, FBM models images as a collage of distinct, localized image features which may not be present in all subjects. FBM thus explicitly accounts for the case where the same anatomical tissue cannot be reliably identified in all subjects due to disease or anatomical variability. A probabilistic model describes features in terms of their appearance, geometry, and relationship to subgroups of a population, and is automatically learned from a set of subject images and group labels. Features identified indicate group-related anatomical structure that can potentially be used as disease biomarkers or as a basis for computer-aided diagnosis. Scale-invariant image features are used, which reflect generic, salient patterns in the image. Experiments validate FBM clinically in the analysis of normal (NC) and Alzheimer's (AD) brain images using the freely available OASIS database. FBM automatically identifies known structural differences between NC and AD subjects in a fully data-driven fashion, and obtains an equal error classification rate of 0.78 on new subjects.
The standard general linear model (GLM) for rapid event-related fMRI design protocols typically ignores reduction in hemodynamic responses in successive stimuli in a train due to incomplete recovery from the preceding stimuli. To capture this adaptation effect, we incorporate a region-specific adaptation model into GLM. The model quantifies the rate of adaptation across brain regions, which is of interest in neuroscience. Empirical evaluation of the proposed model demonstrates its potential to improve detection sensitivity. In the fMRI experiments using visual and auditory stimuli, we observed that the adaptation effect is significantly stronger in the visual area than in the auditory area, suggesting that we must account for this effect to avoid bias in fMRI detection.
Segmentation of medical images is commonly formulated as a supervised learning problem, where manually labeled training data are summarized using a parametric atlas. Summarizing the data alleviates the computational burden at the expense of possibly losing valuable information on inter-subject variability. This paper presents a novel framework for Supervised Nonparametric Image Parcellation (SNIP). SNIP models the intensity and label images as samples of a joint distribution estimated from the training data in a non-parametric fashion. By capitalizing on recently developed fast and robust pairwise image alignment tools, SNIP employs the entire training data to segment a new image via Expectation Maximization. The use of multiple registrations increases robustness to occasional registration failures. We report experiments on 39 volumetric brain MRI scans with manual labels for the white matter, cortex and subcortical structures. SNIP yields better segmentation than state-of-the-art algorithms in multiple regions of interest.
In this paper, we propose a framework for learning the parameters of registration cost functions--such as the tradeoff between the regularization and image similiarity term--with respect to a specific task. Assuming the existence of labeled training data, we specialize the framework for the task of localizing hidden labels via image registration. We learn the parameters of the weighted sum of squared differences (wSSD) image similarity term that are optimal for the localization of Brodmann areas (BAs) in a new subject based on cortical geometry. We demonstrate state-of-the-art localization of V1, V2, BA44 and BA45.
We describe a technique to simultaneously estimate a weighted, positive-definite multi-tensor fiber model and perform tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a weighted mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Further, we modify the Kalman filter to enforce model constraints, i.e. positive eigenvalues and convex weights. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach significantly improves the angular resolution at crossings and branchings while consistently estimating the mixture weights. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.
In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.
BACKGROUND: A critical challenge in neuroscience is organizing, managing, and accessing the explosion in neuroscientific knowledge, particularly anatomic knowledge. We believe that explicit knowledge-based approaches to make neuroscientific knowledge computationally accessible will be helpful in tackling this challenge and will enable a variety of applications exploiting this knowledge, such as surgical planning.
RESULTS: We developed ontology-based models of neuroanatomy to enable symbolic lookup, logical inference and mathematical modeling of neural systems. We built a prototype model of the motor system that integrates descriptive anatomic and qualitative functional neuroanatomical knowledge. In addition to modeling normal neuroanatomy, our approach provides an explicit representation of abnormal neural connectivity in disease states, such as common movement disorders. The ontology-based representation encodes both structural and functional aspects of neuroanatomy. The ontology-based models can be evaluated computationally, enabling development of automated computer reasoning applications.
CONCLUSION: Neuroanatomical knowledge can be represented in machine-accessible format using ontologies. Computational neuroanatomical approaches such as described in this work could become a key tool in translational informatics, leading to decision support applications that inform and guide surgical planning and personalized care for neurological disease in the future.
Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.