A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI

Imaging and finite element analysis: a methodology for non-invasive characterization of aortic tissue

Characterization of the mechanical properties of arterial tissues usually involves an invasive procedure requiring tissue removal. In this work we propose a non-invasive method to perform a biomechanical analysis of cardiovascular aortic tissue. This method is based on combining medical imaging and finite element analysis (FEA). Magnetic resonance imaging (MRI) was chosen since it presents relatively low risks for human health. A finite element model was created from the MRI images and loaded with systolic physiological pressures. By means of an optimization routine, the structural material properties were changed until average strains matched those measured by MRI. The method outlined in this work produced an estimate of the in situ properties of cardiovascular tissue based on non-invasive image datasets and finite element analysis.

Joint fractional segmentation and multi-tensor estimation in diffusion MRI

In this paper we present a novel Bayesian approach for fractional segmentation of white matter tracts and simultaneous estimation of a multi-tensor diffusion model. Our model consists of several white matter tracts, each with a corresponding weight and tensor compartment in each voxel. By incorporating a prior that assumes the tensor fields inside each tract are spatially correlated, we are able to reliably estimate multiple tensor compartments in fiber crossing regions, even with low angular diffusion-weighted imaging (DWI). Our model distinguishes the diffusion compartment associated with each tract, which reduces the effects of partial voluming and achieves more reliable statistics of diffusion measurements. We test our method on synthetic data with known ground truth and show that we can recover the correct volume fractions and tensor compartments. We also demonstrate that the proposed method results in improved segmentation and diffusion measurement statistics on real data in the presence of crossing tracts and partial voluming.

Improved segmentation of white matter tracts with adaptive Riemannian metrics

We present a novel geodesic approach to segmentation of white matter tracts from diffusion tensor imaging (DTI). Compared to deterministic and stochastic tractography, geodesic approaches treat the geometry of the brain white matter as a manifold, often using the inverse tensor field as a Riemannian metric. The white matter pathways are then inferred from the resulting geodesics, which have the desirable property that they tend to follow the main eigenvectors of the tensors, yet still have the flexibility to deviate from these directions when it results in lower costs. While this makes such methods more robust to noise, the choice of Riemannian metric in these methods is ad hoc. A serious drawback of current geodesic methods is that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. In this paper we propose a method for learning an adaptive Riemannian metric from the DTI data, where the resulting geodesics more closely follow the principal eigenvector of the diffusion tensors even in high-curvature regions. We also develop a way to automatically segment the white matter tracts based on the computed geodesics. We show the robustness of our method on simulated data with different noise levels. We also compare our method with tractography methods and geodesic approaches using other Riemannian metrics and demonstrate that the proposed method results in improved geodesics and segmentations using both synthetic and real DTI data.

The structural-functional connectome and the default mode network of the human brain

An emerging field of human brain imaging deals with the characterization of the connectome, a comprehensive global description of structural and functional connectivity within the human brain. However, the question of how functional and structural connectivity are related has not been fully answered yet. Here, we used different methods to estimate the connectivity between each voxel of the cerebral cortex based on functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) data in order to obtain observer-independent functional-structural connectomes of the human brain. Probabilistic fiber-tracking and a novel global fiber-tracking technique were used to measure structural connectivity whereas for functional connectivity, full and partial correlations between each voxel pair's fMRI-timecourses were calculated. For every voxel, two vectors consisting of functional and structural connectivity estimates to all other voxels in the cortex were correlated with each other. In this way, voxels structurally and functionally connected to similar regions within the rest of the brain could be identified. Areas forming parts of the 'default mode network' (DMN) showed the highest agreement of structure-function connectivity. Bilateral precuneal and inferior parietal regions were found using all applied techniques, whereas the global tracking algorithm additionally revealed bilateral medial prefrontal cortices and early visual areas. There were no significant differences between the results obtained from full and partial correlations. Our data suggests that the DMN is the functional brain network, which uses the most direct structural connections. Thus, the anatomical profile of the brain seems to shape its functional repertoire and the computation of the whole-brain functional-structural connectome appears to be a valuable method to characterize global brain connectivity within and between populations.

3D stochastic completion fields for mapping connectivity in diffusion MRI

The 2D stochastic completion field algorithm, introduced by Williams and Jacobs [1], [2], uses a directional random walk to model the prior probability of completion curves in the plane. This construct has had a powerful impact in computer vision, where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery. Motivated by these developments, we extend the algorithm to 3D, using a spherical harmonics basis to achieve a rotation invariant computational solution to the Fokker-Planck equation describing the evolution of the probability density function underlying the model. This provides a principled way to compute 3D completion patterns and to derive connectivity measures for orientation data in 3D, as arises in 3D tracking, motion capture, and medical imaging. We demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging, where we derive connectivity maps for synthetic data, on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain.

The translational role of diffusion tensor image analysis in animal models of developmental pathologies

Diffusion tensor magnetic resonance imaging (DTI) has proven itself a powerful technique for clinical investigation of the neurobiological targets and mechanisms underlying developmental pathologies. The success of DTI in clinical studies has demonstrated its great potential for understanding translational animal models of clinical disorders, and preclinical animal researchers are beginning to embrace this new technology to study developmental pathologies. In animal models, genetics can be effectively controlled, drugs consistently administered, subject compliance ensured, and image acquisition times dramatically increased to reduce between-subject variability and improve image quality. When pairing these strengths with the many positive attributes of DTI, such as the ability to investigate microstructural brain organization and connectivity, it becomes possible to delve deeper into the study of both normal and abnormal development. The purpose of this review is to provide new preclinical investigators with an introductory source of information about the analysis of data resulting from small animal DTI studies to facilitate the translation of these studies to clinical data. In addition to an in-depth review of translational analysis techniques, we present a number of relevant clinical and animal studies using DTI to investigate developmental insults in order to further illustrate techniques and to highlight where small animal DTI could potentially provide a wealth of translational data to inform clinical researchers.

Measures for Validation of DTI Tractography

The evaluation of analysis methods for diffusion tensor imaging (DTI) remains challenging due to the lack of gold standards and validation frameworks. Significant work remains in developing metrics for comparing fiber bundles generated from streamline tractography. We propose a set of volumetric and tract oriented measures for evaluating tract differences. The different methods developed for this assessment work are: an overlap measurement, a point cloud distance and a quantification of the diffusion properties at similar locations between fiber bundles. The application of the measures in this paper is a comparison of atlas generated tractography to tractography generated in individual images. For the validation we used a database of 37 subject DTIs, and applied the measurements on five specific fiber bundles: uncinate, cingulum (left and right for both bundles) and genu. Each measurments is interesting for specific use: the overlap measure presents a simple and comprehensive metric but is sensitive to partial voluming and does not give consistent values depending on the bundle geometry. The point cloud distance associated with a quantile interpretation of the distribution gives a good intuition of how close and similar the bundles are. Finally, the functional difference is useful for a comparison of the diffusion properties since it is the focus of many DTI analysis to compare scalar invariants. The comparison demonstrated reasonable similarity of results. The tract difference measures are also applicable to comparison of tractography algorithms, quality control, reproducibility studies, and other validation problems.

Diffusion tensor imaging-based characterization of brain neurodevelopment in primates

Primate neuroimaging provides a critical opportunity for understanding neurodevelopment. Yet the lack of a normative description has limited the direct comparison with changes in humans. This paper presents for the first time a cross-sectional diffusion tensor imaging (DTI) study characterizing primate brain neurodevelopment between 1 and 6 years of age on 25 healthy undisturbed rhesus monkeys (14 male, 11 female). A comprehensive analysis including region-of-interest, voxel-wise, and fiber tract-based approach demonstrated significant changes of DTI properties over time. Changes in fractional anisotropy (FA), mean diffusivity, axial diffusivity (AD), and radial diffusivity (RD) exhibited a heterogeneous pattern across different regions as well as along fiber tracts. Most of these patterns are similar to those from human studies yet a few followed unique patterns. Overall, we observed substantial increase in FA and AD and a decrease in RD for white matter (WM) along with similar yet smaller changes in gray matter (GM). We further observed an overall posterior-to-anterior trend in DTI property changes over time and strong correlations between WM and GM development. These DTI trends provide crucial insights into underlying age-related biological maturation, including myelination, axonal density changes, fiber tract reorganization, and synaptic pruning processes.

Automated probabilistic reconstruction of white-matter pathways in health and disease using an atlas of the underlying anatomy

We have developed a method for automated probabilistic reconstruction of a set of major white-matter pathways from diffusion-weighted MR images. Our method is called TRACULA (TRActs Constrained by UnderLying Anatomy) and utilizes prior information on the anatomy of the pathways from a set of training subjects. By incorporating this prior knowledge in the reconstruction procedure, our method obviates the need for manual interaction with the tract solutions at a later stage and thus facilitates the application of tractography to large studies. In this paper we illustrate the application of the method on data from a schizophrenia study and investigate whether the inclusion of both patients and healthy subjects in the training set affects our ability to reconstruct the pathways reliably. We show that, since our method does not constrain the exact spatial location or shape of the pathways but only their trajectory relative to the surrounding anatomical structures, a set a of healthy training subjects can be used to reconstruct the pathways accurately in patients as well as in controls.

Direct segmentation of the major white matter tracts in diffusion tensor images

Diffusion-weighted images of the human brain are acquired more and more routinely in clinical research settings, yet segmenting and labeling white matter tracts in these images is still challenging. We present in this paper a fully automated method to extract many anatomical tracts at once on diffusion tensor images, based on a Markov random field model and anatomical priors. The approach provides a direct voxel labeling, models explicitly fiber crossings and can handle white matter lesions. Experiments on simulations and repeatability studies show robustness to noise and reproducibility of the algorithm, which has been made publicly available.

Efficient, Graph-based White Matter Connectivity from Orientation Distribution Functions via Multi-directional Graph Propagation

The use of regional connectivity measurements derived from diffusion imaging datasets has become of considerable interest in the neuroimaging community in order to better understand cortical and subcortical white matter connectivity. Current connectivity assessment methods are based on streamline fiber tractography, usually applied in a Monte-Carlo fashion. In this work we present a novel, graph-based method that performs a fully deterministic, efficient and stable connectivity computation. The method handles crossing fibers and deals well with multiple seed regions. The computation is based on a multi-directional graph propagation method applied to sampled orientation distribution function (ODF), which can be computed directly from the original diffusion imaging data. We show early results of our method on synthetic and real datasets. The results illustrate the potential of our method towards subject-specific connectivity measurements that are performed in an efficient, stable and reproducible manner. Such individual connectivity measurements would be well suited for application in population studies of neuropathology, such as Autism, Huntington's Disease, Multiple Sclerosis or leukodystrophies. The proposed method is generic and could easily be applied to non-diffusion data as long as local directional data can be derived.

Adaptive Riemannian metrics for improved geodesic tracking of white matter

We present a new geodesic approach for studying white matter connectivity from diffusion tensor imaging (DTI). Previous approaches have used the inverse diffusion tensor field as a Riemannian metric and constructed white matter tracts as geodesics on the resulting manifold. These geodesics have the desirable property that they tend to follow the main eigenvectors of the tensors, yet still have the flexibility to deviate from these directions when it results in lower costs. While this makes such methods more robust to noise, it also has the serious drawback that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. In this paper we formulate a modification of the Riemannian metric that results in geodesics adapted to follow the principal eigendirection of the tensor even in high-curvature regions. We show that this correction can be formulated as a simple scalar field modulation of the metric and that the appropriate variational problem results in a Poisson's equation on the Riemannian manifold. We demonstrate that the proposed method results in improved geodesics using both synthetic and real DTI data.

Rotation invariant completion fields for mapping diffusion MRI connectivity

Partial differential equations have been successfully used for fibre tractography and for mapping connectivity indices in the brain. However, the current implementation of methods which require 3D orientation to be tracked can suffer from serious shortcomings when invariance to 3D rotation is desired. In this paper we focus on the 3D stochastic completion field and introduce a new methodology to solve the underlying PDE in a manner that achieves rotation invariance. The key idea is to use spherical harmonics to solve the Fokker-Planck equation representing the evolution of the probability density function of a 3D directional random walk. We validate the new approach by presenting improved connectivity indices on synthetic data, on the MICCAI 2009 Fibre Cup phantom and on a biological phantom comprised of two rat spinal chords in a crossing configuration.

Statistical analysis of minimum cost path based structural brain connectivity

Diffusion MRI can be used to study the structural connectivity within the brain. Brain connectivity is often represented by a binary network whose topology can be studied using graph theory. We present a framework for the construction of weighted structural brain networks, containing information about connectivity, which can be effectively analyzed using statistical methods. Network nodes are defined by segmentation of subcortical structures and by cortical parcellation. Connectivity is established using a minimum cost path (mcp) method with an anisotropic local cost function based directly on diffusion weighted images. We refer to this framework as Statistical Analysis of Minimum cost path based Structural Connectivity (SAMSCo) and the weighted structural connectivity networks as mcp-networks. In a proof of principle study we investigated the information contained in mcp-networks by predicting subject age based on the mcp-networks of a group of 974 middle-aged and elderly subjects. Using SAMSCo, age was predicted with an average error of 3.7 years. This was significantly better than predictions based on fractional anisotropy or mean diffusivity averaged over the whole white matter or over the corpus callosum, which showed average prediction errors of at least 4.8 years. Additionally, we classified subjects, based on the mcp-networks, into groups with low and high white matter lesion load, while correcting for age, sex and white matter atrophy. The SAMSCo classification outperformed the classification based on the diffusion measures with a classification accuracy of 76.0% versus 63.2%. We also performed a classification in groups with mild and severe atrophy, correcting for age, sex and white matter lesion load. In this case, mcp-networks and diffusion measures yielded similar classification accuracies of 68.3% and 67.8% respectively. The SAMSCo prediction and classification experiments indicate that the mcp-networks contain information regarding age, white matter lesion load and white matter atrophy, and that in case of age and white matter lesion load the mcp-network based models outperformed the predictions based on diffusion measures.

MR diffusion tensor imaging: a window into white matter integrity of the working brain

As Norman Geschwind asserted in 1965, syndromes resulting from white matter lesions could produce deficits in higher-order functions and "disconnexion" or the interruption of connection between gray matter regions could be as disruptive as trauma to those regions per se. The advent of in vivo diffusion tensor imaging, which allows quantitative characterization of white matter fiber integrity in health and disease, has served to strengthen Geschwind's proposal. Here we present an overview of the principles of diffusion tensor imaging (DTI) and its contribution to progress in our current understanding of normal and pathological brain function.

Microstructural connectivity of the arcuate fasciculus in adolescents with high-functioning autism

The arcuate fasciculus is a white matter fiber bundle of great importance in language. In this study, diffusion tensor imaging (DTI) was used to infer white matter integrity in the arcuate fasciculi of a group of subjects with high-functioning autism and a control group matched for age, handedness, IQ, and head size. The arcuate fasciculus for each subject was automatically extracted from the imaging data using a new volumetric DTI segmentation algorithm. The results showed a significant increase in mean diffusivity (MD) in the autism group, due mostly to an increase in the radial diffusivity (RD). A test of the lateralization of DTI measurements showed that both MD and fractional anisotropy (FA) were less lateralized in the autism group. These results suggest that white matter microstructure in the arcuate fasciculus is affected in autism and that the language specialization apparent in the left arcuate of healthy subjects is not as evident in autism, which may be related to poorer language functioning.

Statistical analysis of structural brain connectivity

We present a framework for statistical analysis in large cohorts of structural brain connectivity, derived from diffusion weighted MRI. A brain network is defined between subcortical gray matter structures and a cortical parcellation obtained with FreeSurfer. Connectivity is established through minimum cost paths with an anisotropic local cost function and is quantified per connection. The connectivity network potentially encodes important information about brain structure, and can be analyzed using multivariate regression methods. The proposed framework can be used to study the relation between connectivity and e.g. brain function or neurodegenerative disease. As a proof of principle, we perform principal component regression in order to predict age and gender, based on the connectivity networks of 979 middle-aged and elderly subjects, in a 10-fold cross-validation. The results are compared to predictions based on fractional anisotropy and mean diffusivity averaged over the white matter and over the corpus callosum. Additionally, the predictions are performed based on the best predicting connection in the network. Principal component regression outperformed all other prediction models, demonstrating the age and gender information encoded in the connectivity network.

Brain tractography using Q-ball imaging and graph theory: Improved connectivities through fibre crossings via a model-based approach

Brain tractography techniques utilize a set of diffusion-weighted magnetic resonance images to reconstruct white matter tracts, non-invasively and in-vivo. Streamline tracking techniques propagate curves from a seed to imply connectivity to distal voxels. Alternative approaches have been developed that attempt to quantify connection strength between all voxels and the seed. Tractography based on graph theory is amongst them. Despite its potential, graph-based tracking through complex fibre configurations has not been extensively studied and existing methods have inherent limitations. Anatomically unlikely connections may be identified in fibre crossing regions, by assigning relatively high connection strengths to all crossing populations. In this study, we discuss these limitations and present a new approach for robustly propagating through fibre crossings, as described by the orientation distribution functions (ODFs) derived from Q-ball imaging. Each image voxel is treated as a graph node and graph arcs connect neighbouring voxels. Weights representative of both structural and diffusivity features are assigned to each arc. To account for the existence of crossing fibre populations within a voxel, complex ODFs are decomposed into components representative of single-fibre populations and an image multigraph is created. The multigraph is searched exhaustively, but efficiently, to find the strongest paths and assign connectivity strengths between a seed and all the other image voxels. A comparison with the existing graph-based tractography as well as Q-ball driven front evolution tractography is performed on simulated data, and on human Q-ball imaging data acquired from five healthy volunteers. The new approach improves the connection strengths through fibre crossing regions, reducing the strengths of paths that are less anatomically plausible.

Near-tubular fiber bundle segmentation for diffusion weighted imaging: segmentation through frame reorientation

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.

Group analysis of DTI fiber tract statistics with application to neurodevelopment

Diffusion tensor imaging (DTI) provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures. This paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images. Unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images. The diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics. Diffusion properties, such as fractional anisotropy (FA) and tensor norm, along fiber tracts are modeled as multivariate functions of arc length. Hypothesis testing is performed non-parametrically using permutation testing based on the Hotelling T(2) statistic. The linear discriminant embedded in the T(2) metric provides an intuitive, localized interpretation of detected differences. The proposed methodology was tested on two clinical studies of neurodevelopment. In a study of 1 and 2 year old subjects, a significant increase in FA and a correlated decrease in Frobenius norm was found in several tracts. Significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly (MVM) demonstrating the potential of this method for clinical studies.

Active fibers: matching deformable tract templates to diffusion tensor images

Reliable quantitative analysis of white matter connectivity in the brain is an open problem in neuroimaging, with common solutions requiring tools for fiber tracking, tractography segmentation and estimation of intersubject correspondence. This paper proposes a novel, template matching approach to the problem. In the proposed method, a deformable fiber-bundle model is aligned directly with the subject tensor field, skipping the fiber tracking step. Furthermore, the use of a common template eliminates the need for tractography segmentation and defines intersubject shape correspondence. The method is validated using phantom DTI data and applications are presented, including automatic fiber-bundle reconstruction and tract-based morphometry.

Probabilistic white matter fiber tracking using particle filtering and von Mises-Fisher sampling

Standard particle filtering technique have previously been applied to the problem of fiber tracking by Brun et al. [Brun, A., Bjornemo, M., Kikinis, R., Westin, C.F., 2002. White matter tractography using sequential importance sampling. In: Proceedings of the ISMRM Annual Meeting, p. 1131] and Bjornemo et al. [Bjornemo, M., Brun, A., Kikinis, R., Westin, C.F., 2002. Regularized stochastic white matter tractography using diffusion tensor MRI, In: Proc. MICCAI, pp. 435-442]. However, these previous attempts have not utilised the full power of the technique, and as a result the fiber paths were tracked in a goal directed way. In this paper, we provide an advanced technique by presenting a fast and novel probabilistic method for white matter fiber tracking in diffusion weighted MRI (DWI), which takes advantage of the weighting and resampling mechanism of particle filtering. We formulate fiber tracking using a non-linear state space model which captures both smoothness regularity of the fibers and the uncertainties in the local fiber orientations due to noise and partial volume effects. Global fiber tracking is then posed as a problem of particle filtering. To model the posterior distribution, we classify voxels of the white matter as either prolate or oblate tensors. We then construct the orientation distributions for prolate and oblate tensors separately. Finally, the importance density function for particle filtering is modeled using the von Mises-Fisher distribution on a unit sphere. Fast and efficient sampling is achieved using Ulrich-Wood's simulation algorithm. Given a seed point, the method is able to rapidly locate the globally optimal fiber and also provides a probability map for potential connections. The proposed method is validated and compared to alternative methods both on synthetic data and real-world brain MRI datasets.

Belief propagation based segmentation of white matter tracts in DTI

This paper presents a belief propagation approach to the segmentation of the major white matter tracts in diffusion tensor images of the human brain. Unlike tractography methods that sample multiple fibers to be bundled together, we define a Markov field directly on the diffusion tensors to separate the main fiber tracts at the voxel level. A prior model of shape and direction guides a full segmentation of the brain into known fiber tracts; additional, unspecified fibers; and isotropic regions. The method is evaluated on various data sets from an atlasing project, healthy subjects, and multiple sclerosis patients.

Group statistics of DTI fiber bundles using spatial functions of tensor measures

We present a framework for hypothesis testing of differences between groups of DTI fiber tracts. An anatomical, tract-oriented coordinate system provides a basis for estimating the distribution of diffusion properties. The parametrization of sampled, smooth functions is normalized across a population using DTI atlas building. Functional data analysis, an extension of multivariate statistics to continuous functions is applied to the problem of hypothesis testing and discrimination. B-spline models of fractional anisotropy (FA) and Frobenius norm measures are analyzed jointly. Plots of the discrimination direction provide a clinical interpretation of the group differences. The methodology is tested on a pediatric study of subjects aged one and two years.

The geometric median on Riemannian manifolds with application to robust atlas estimation

One of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images. The study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space, which map one anatomy to another. It is now well established that representing the geometry of shapes or images in Euclidian spaces undermines our ability to represent natural variability in populations. In our previous work we have extended classical statistical analysis techniques, such as averaging, principal components analysis, and regression, to Riemannian manifolds, which are more appropriate representations for describing anatomical variability. In this paper we extend the notion of robust estimation, a well established and powerful tool in traditional statistical analysis of Euclidian data, to manifold-valued representations of anatomical variability. In particular, we extend the geometric median, a classic robust estimator of centrality for data in Euclidean spaces. We formulate the geometric median of data on a Riemannian manifold as the minimizer of the sum of geodesic distances to the data points. We prove existence and uniqueness of the geometric median on manifolds with non-positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds. Generalizing the Weiszfeld procedure for finding the geometric median of Euclidean data, we present an algorithm for computing the geometric median on an arbitrary manifold. We show that this algorithm converges to the unique solution when it exists. In this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images. Using this approach, we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images.

Connecting and merging fibres: pathway extraction by combining probability maps

Probability mapping of connectivity is a powerful tool to determine the fibre structure of white matter in the brain. Probability maps are related to the degree of connectivity to a chosen seed area. In many applications, however, it is necessary to isolate a fibre bundle that connects two areas. A frequently suggested solution is to select curves, which pass only through two or more areas. This is very inefficient, especially for long-distance pathways and small areas. In this paper, a novel probability-based method is presented that is capable of extracting neuronal pathways defined by two seed points. A Monte Carlo simulation based tracking method, similar to the Probabilistic Index of Connectivity (PICo) approach, was extended to preserve the directional information of the main fibre bundles passing a voxel. By combining two of these extended visiting maps arising from different seed points, two independent parameters are determined for each voxel: the first quantifies the uncertainty that a voxel is connected to both seed points; the second represents the directional information and estimates the proportion of fibres running in the direction of the other seed point (connecting fibre) or face a third area (merging fibre). Both parameters are used to calculate the probability that a voxel is part of the bundle connecting both seed points. The performance and limitations of this DTI-based method are demonstrated using simulations as well as in vivo measurements.

Localized Statistics for DW-MRI Fiber Bundle Segmentation

We describe a method for segmenting neural fiber bundles in diffusion-weighted magnetic resonance images (DWMRI). As these bundles traverse the brain to connect regions, their local orientation of diffusion changes drastically, hence a constant global model is inaccurate. We propose a method to compute localized statistics on orientation information and use it to drive a variational active contour segmentation that accurately models the non-homogeneous orientation information present along the bundle. Initialized from a single fiber path, the proposed method proceeds to capture the entire bundle. We demonstrate results using the technique to segment the cingulum bundle and describe several extensions making the technique applicable to a wide range of tissues.

Locally-Constrained Region-Based Methods for DW-MRI Segmentation

In this paper, we describe a method for segmenting fiber bundles from diffusion-weighted magnetic resonance images using a locally-constrained region based approach. From a pre-computed optimal path, the algorithm propagates outward capturing only those voxels which are locally connected to the fiber bundle. Rather than attempting to find large numbers of open curves or single fibers, which individually have questionable meaning, this method segments the full fiber bundle region. The strengths of this approach include its ease-of-use, computational speed, and applicability to a wide range of fiber bundles. In this work, we show results for segmenting the cingulum bundle. Finally, we explain how this approach and extensions thereto overcome a major problem that typical region-based flows experience when attempting to segment neural fiber bundles.