Resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging

CHIASM, the human brain albinism and achiasma MRI dataset

We describe a collection of T1-, diffusion- and functional T2*-weighted magnetic resonance imaging data from human individuals with albinism and achiasma. This repository can be used as a test-bed to develop and validate tractography methods like diffusion-signal modeling and fiber tracking as well as to investigate the properties of the human visual system in individuals with congenital abnormalities. The MRI data is provided together with tools and files allowing for its preprocessing and analysis, along with the data derivatives such as manually curated masks and regions of interest for performing tractography.

Physical and digital phantoms for validating tractography and assessing artifacts

Fiber tractography is widely used to non-invasively map white-matter bundles in vivo using diffusion-weighted magnetic resonance imaging (dMRI). As it is the case for all scientific methods, proper validation is a key prerequisite for the successful application of fiber tractography, be it in the area of basic neuroscience or in a clinical setting. It is well-known that the indirect estimation of the fiber tracts from the local diffusion signal is highly ambiguous and extremely challenging. Furthermore, the validation of fiber tractography methods is hampered by the lack of a real ground truth, which is caused by the extremely complex brain microstructure that is not directly observable non-invasively and that is the basis of the huge network of long-range fiber connections in the brain that are the actual target of fiber tractography methods. As a substitute for in vivo data with a real ground truth that could be used for validation, a widely and successfully employed approach is the use of synthetic phantoms. In this work, we are providing an overview of the state-of-the-art in the area of physical and digital phantoms, answering the following guiding questions: "What are dMRI phantoms and what are they good for?", "What would the ideal phantom for validation fiber tractography look like?" and "What phantoms, phantom datasets and tools used for their creation are available to the research community?". We will further discuss the limitations and opportunities that come with the use of dMRI phantoms, and what future direction this field of research might take.

The Connectomes: Methods of White Matter Tractography and Contributions of Resting State fMRI

A comprehensive mapping of the structural and functional circuitry of the brain is a major unresolved problem in contemporary neuroimaging research. Diffusion-weighted and functional MRI have provided investigators with the capability to assess structural and functional connectivity in-vivo, driven primarily by methods of white matter tractography and resting-state fMRI, respectively. These techniques have paved the way for the construction of the functional and structural connectomes, which are quantitative representations of brain architecture as neural networks, comprised of nodes and edges. The connectomes, typically depicted as matrices or graphs, possess topological properties that inherently characterize the strength, efficiency, and organization of the connections between distinct brain regions. Graph theory, a general mathematical framework for analyzing networks, can be implemented to derive metrics from the connectomes that are sensitive to changes in brain connectivity associated with age, sex, cognitive function, and disease. These quantities can be assessed at either the global (whole brain) or local levels, allowing for the identification of distinct regional connectivity hubs and associated localized brain networks, which together serve crucial roles in establishing the structural and functional architecture of the brain. As a result, structural and functional connectomes have each been employed to study the brain circuitry underlying early brain development, neuroplasticity, developmental disorders, psychopathology, epilepsy, aging, neurodegenerative disorders, and traumatic brain injury. While these studies have yielded important insights into brain structure, function, and pathology, a precise description of the innate relationship between functional and structural networks across the brain remains unachieved. To date, connectome research has merely scratched the surface of potential clinical applications and related characterizations of brain-wide connectivity. Continued advances in diffusion and functional MRI acquisition, the delineation of functional and structural networks, and the quantification of neural network properties in specific brain regions, will be invaluable to future progress in neuroimaging science.

Cellular Automata Tractography: Fast Geodesic Diffusion MR Tractography and Connectivity Based Segmentation on the GPU

Geodesic based tractography on diffusion magnetic resonance data is a method to devise long distance connectivities among the brain regions. In this study, cellular automata technique is applied to the geodesic tractography problem and the algorithm is implemented on a graphics processing unit. Cellular automaton based method is preferable to current techniques due to its parallel nature and ability to solve the connectivity based segmentation problem with the same computational complexity, which has important applications in neuroimaging. An application to prior-less tracking and connectivity based segmentation of corpus callosum fibers is presented as an example. A geodesic tractography based corpus callosum atlas is provided, which reveals high projections to the cortical language areas. The developed method not only allows fast computation especially for segmentation but also provides a powerful and intuitive framework, suitable to derive new algorithms to perform connectivity calculations and allowing novel applications.

Mapping connectomes with diffusion MRI: deterministic or probabilistic tractography?

PURPOSE

Human connectomics necessitates high-throughput, whole-brain reconstruction of multiple white matter fiber bundles. Scaling up tractography to meet these high-throughput demands yields new fiber tracking challenges, such as minimizing spurious connections and controlling for gyral biases. The aim of this study is to determine which of the two broadest classes of tractography algorithms-deterministic or probabilistic-is most suited to mapping connectomes.

METHODS

This study develops numerical connectome phantoms that feature realistic network topologies and that are matched to the fiber complexity of in vivo diffusion MRI (dMRI) data. The phantoms are utilized to evaluate the performance of tensor-based and multi-fiber implementations of deterministic and probabilistic tractography.

RESULTS

For connectome phantoms that are representative of the fiber complexity of in vivo dMRI, multi-fiber deterministic tractography yields the most accurate connectome reconstructions (F-measure = 0.35). Probabilistic algorithms are hampered by an abundance of false-positive connections, leading to lower specificity (F = 0.19). While omitting connections with the fewest number of streamlines (thresholding) improves the performance of probabilistic algorithms (F = 0.38), multi-fiber deterministic tractography remains optimal when it benefits from thresholding (F = 0.42).

CONCLUSIONS

Multi-fiber deterministic tractography is well suited to connectome mapping, while connectome thresholding is essential when using probabilistic algorithms.

Strengths and weaknesses of state of the art fiber tractography pipelines--A comprehensive in-vivo and phantom evaluation study using Tractometer

Many different tractography approaches and corresponding isolated evaluation attempts have been presented over the last years, but a comparative and quantitative evaluation of tractography algorithms still remains a challenge, particularly in-vivo. The recently presented evaluation framework Tractometer is the first attempt to approach this challenge in a quantitative, comparative, persistent and open-access way. Tractometer is currently based on the evaluation of several global connectivity and tract-overlap metrics on hardware phantom data. The work presented in this paper focuses on extending Tractometer with a metric that enables the assessment of the local consistency of tractograms with the underlying image data that is not only applicable to phantom dataset but allows the quantitative and purely data-driven evaluation of in-vivo tractography. We furthermore present an extensive reference-based evaluation study of 25,000 tractograms obtained on phantom and in-vivo datasets using the presented local metric as well as all the methods already established in Tractometer. The experiments showed that the presented local metric successfully reflects the behavior of in-vivo tractography under different conditions and that it is consistent with the results of previous studies. Additionally our experiments enabled a multitude of conclusions with implications for fiber tractography in general, including recommendations regarding optimal choice of a local modeling technique, tractography algorithm, and parameterization, confirming and complementing the results of earlier studies.

Visualization of Brain Microstructure Through Spherical Harmonics Illumination of High Fidelity Spatio-Angular Fields

Diffusion kurtosis imaging (DKI) is gaining rapid adoption in the medical imaging community due to its ability to measure the non-Gaussian property of water diffusion in biological tissues. Compared to traditional diffusion tensor imaging (DTI), DKI can provide additional details about the underlying microstructural characteristics of the neural tissues. It has shown promising results in studies on changes in gray matter and mild traumatic brain injury where DTI is often found to be inadequate. The DKI dataset, which has high-fidelity spatio-angular fields, is difficult to visualize. Glyph-based visualization techniques are commonly used for visualization of DTI datasets; however, due to the rapid changes in orientation, lighting, and occlusion, visually analyzing the much more higher fidelity DKI data is a challenge. In this paper, we provide a systematic way to manage, analyze, and visualize high-fidelity spatio-angular fields from DKI datasets, by using spherical harmonics lighting functions to facilitate insights into the brain microstructure.

Network-based analysis reveals stronger local diffusion-based connectivity and different correlations with oral language skills in brains of children with high functioning autism spectrum disorders

Neuroimaging has uncovered both long-range and short-range connectivity abnormalities in the brains of individuals with autism spectrum disorders (ASD). However, the precise connectivity abnormalities and the relationship between these abnormalities and cognition and ASD symptoms have been inconsistent across studies. Indeed, studies find both increases and decreases in connectivity, suggesting that connectivity changes in the ASD brain are not merely due to abnormalities in specific connections, but rather, due to changes in the structure of the network in which the brain areas interact (i.e., network topology). In this study, we examined the differences in the network topology between high-functioning ASD patients and age and gender matched typically developing (TD) controls. After quantitatively characterizing the whole-brain connectivity network using diffusion tensor imaging (DTI) data, we searched for brain regions with different connectivity between ASD and TD. A measure of oral language ability was then correlated with the connectivity changes to determine the functional significance of such changes. Whole-brain connectivity measures demonstrated greater local connectivity and shorter path length in ASD as compared to TD. Stronger local connectivity was found in ASD, especially in regions such as the left superior parietal lobule, the precuneus and angular gyrus, and the right supramarginal gyrus. The relationship between oral language ability and local connectivity within these regions was significantly different between ASD and TD. Stronger local connectivity was associated with better performance in ASD and poorer performance in TD. This study supports the notion that increased local connectivity is compensatory for supporting cognitive function in ASD.

Diffusion tensor magnetic resonance imaging in the analysis of neurodegenerative diseases

Diffusion tensor imaging (DTI) techniques provide information on the microstructural processes of the cerebral white matter (WM) in vivo. The present applications are designed to investigate differences of WM involvement patterns in different brain diseases, especially neurodegenerative disorders, by use of different DTI analyses in comparison with matched controls. DTI data analysis is performed in a variate fashion, i.e. voxelwise comparison of regional diffusion direction-based metrics such as fractional anisotropy (FA), together with fiber tracking (FT) accompanied by tractwise fractional anisotropy statistics (TFAS) at the group level in order to identify differences in FA along WM structures, aiming at the definition of regional patterns of WM alterations at the group level. Transformation into a stereotaxic standard space is a prerequisite for group studies and requires thorough data processing to preserve directional inter-dependencies. The present applications show optimized technical approaches for this preservation of quantitative and directional information during spatial normalization in data analyses at the group level. On this basis, FT techniques can be applied to group averaged data in order to quantify metrics information as defined by FT. Additionally, application of DTI methods, i.e. differences in FA-maps after stereotaxic alignment, in a longitudinal analysis at an individual subject basis reveal information about the progression of neurological disorders. Further quality improvement of DTI based results can be obtained during preprocessing by application of a controlled elimination of gradient directions with high noise levels. In summary, DTI is used to define a distinct WM pathoanatomy of different brain diseases by the combination of whole brain-based and tract-based DTI analysis.

Adaptive multi-modal particle filtering for probabilistic white matter tractography

Particle filtering has recently been introduced to perform probabilistic tractography in conjunction with DTI and Q-Ball models to estimate the diffusion information. Particle filters are particularly well adapted to the tractography problem as they offer a way to approximate a probability distribution over all paths originated from a specified voxel, given the diffusion information. In practice however, they often fail at consistently capturing the multi-modality of the target distribution. For brain white matter tractography, this means that multiple fiber pathways are unlikely to be tracked over extended volumes. We propose to remedy this issue by formulating the filtering distribution as an adaptive M-component non-parametric mixture model. Such a formulation preserves all the properties of a classical particle filter while improving multi-modality capture. We apply this multi-modal particle filter to both DTI and Q-Ball models and propose to estimate dynamically the number of modes of the filtering distribution. We show on synthetic and real data how this algorithm outperforms the previous versions proposed in the literature.

Probabilistic tractography using Q-ball imaging and particle filtering: application to adult and in-utero fetal brain studies

By assuming that orientation information of brain white matter fibers can be inferred from Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) measurements, tractography algorithms provide an estimation of the brain connectivity in vivo. The two key ingredients of tractography are the diffusion model (tensor, high-order tensor, Q-ball, etc.) and the means to deal with uncertainty during the tracking process (deterministic vs probabilistic mathematical framework). In this paper, we investigate the use of an analytical Q-ball model for the diffusion data within a well-formalized particle filtering framework. The proposed method is validated and compared to other tracking algorithms on the MICCAI'09 contest Fiber Cup phantom. Tractographies of in vivo adult and fetal brain Diffusion-Weighted Images (DWIs) are also shown to illustrate the robustness of the algorithm.

Diffusion magnetic resonance imaging for Brainnetome: a critical review

Increasing evidence shows that the human brain is a highly self-organized system that shows attributes of small-worldness, hierarchy and modularity. The "connectome" was conceived several years ago to identify the underpinning physical connectivities of brain networks. The need for an integration of multi-spatial and -temporal approaches is becoming apparent. Therefore, the "Brainnetome" (brain-net-ome) project was proposed. Diffusion magnetic resonance imaging (dMRI) is a non-invasive way to study the anatomy of brain networks. Here, we review the principles of dMRI, its methodologies, and some of its clinical applications for the Brainnetome. Future research in this field is discussed.

A new approach for corticospinal tract reconstruction based on navigated transcranial stimulation and standardized fractional anisotropy values

PURPOSE

To establish a novel approach for fiber tracking based on navigated transcranial magnetic stimulation (nTMS) mapping of the primary motor cortex and to propose a new algorithm for determination of an individualized fractional anisotropy value for reliable and objective fiber tracking.

METHODS

50 patients (22 females, 28 males, median age 58 years (20-80)) with brain tumors compromising the primary motor cortex and the corticospinal tract underwent preoperative MR imaging and nTMS mapping. Stimulation spots evoking muscle potentials (MEP) closest to the tumor were imported into the fiber tracking software and set as seed points for tractography. Next the individual FA threshold, i.e. the highest FA value leading to visualization of tracts at a predefined minimum fiber length of 110 mm, was determined. Fiber tracking was then performed at a fractional anisotropy value of 75% and 50% of the individual FA threshold. In addition, fiber tracking according to the conventional knowledge-based approach was performed. Results of tractography of either method were presented to the surgeon for preoperative planning and integrated into the navigation system and its impact was rated using a questionnaire.

RESULTS

Mapping of the motor cortex was successful in all patients. A fractional anisotropy threshold for corticospinal tract reconstruction could be obtained in every case. TMS-based results changed or modified surgical strategy in 23 of 50 patients (46%), whereas knowledge-based results would have changed surgical strategy in 11 of 50 patients (22%). Tractography results facilitated intraoperative orientation and electrical stimulation in 28 of 50 (56%) patients. Tracking at 75% of the individual FA thresholds was considered most beneficial by the respective surgeons.

CONCLUSIONS

Fiber tracking based on nTMS by the proposed standardized algorithm represents an objective visualization method based on functional data and provides a valuable instrument for preoperative planning and intraoperative orientation and monitoring.

Fast approximate stochastic tractography

Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore enabling interactive probabilistic tractography: the user can quickly modify the seed region if he is not satisfied with the output without having to wait on average 7 min.

Fasciculography: robust prior-free real-time normalized volumetric neural tract parcellation

Fiber tracking in diffusion tensor magnetic resonance images (DTIs) reveals 3-D structural connectivity of the brain conveniently and thus is a viable tool for investigating neural differences. Unfortunately, local noise, image artifacts and numerical tracking errors during integration-based techniques are cumulative. Prematurely terminated fibers and under-sampled fiber bundles result in incomplete reconstruction of white matter fiber tracts and hence incorrect anatomical measurements. Quantitative cross-subject tract analysis, which is critical for abnormality detection, is complicated by inefficient and inaccurate tract reconstruction and normalization from fiber bundles. Because of the above problems, we propose a parcellation method that aims for lower sensitivity to initialization and local orientation error by directly segmenting full white matter tracts (Fasciculography), rather than reconstructing individual curves, from diffusion tensor fields. A fast, robust volumetric, and intrinsically normalized solution is achieved by noise-filtering using a generic parametrized tract model to prevent premature tract termination. At the same time, orientation information reduces the search space, significantly speeding up the tract parcellation process with less human intervention. Detailed comparisons against streamline tracking, shortest-path tracking, and nonrigid registration using synthetic and real DTIs confirmed the superior properties of Fasciculography. Since a normalized tract can be delineated interactively in a just few seconds using the proposed method, accurate high volume tract comparisons become feasible.

Probabilistic tractography using Q-ball modeling and particle filtering

By assuming that orientation information of brain white matter fibers can be inferred from Diffusion Weighted Magnetic Resonance Imaging (DWMRI) measurements, tractography algorithms provide an estimation of the brain connectivity in-vivo. The two key ingredients of tractography are the diffusion model (tensor, high-order tensor, Q-ball, etc.) and the way to deal with uncertainty during the tracking process (deterministic vs probabilistic). In this paper, we investigate the use of an analytical Q-ball model for the diffusion data within a well-formalized particle filtering framework. The proposed method is validated and compared to other tracking algorithms on the MICCAI'09 contest Fiber Cup phantom and on in-vivo brain DWMRI data.

Evaluation of diffusion models of fiber tracts using diffusion tensor magnetic resonance imaging

Modeling of water diffusion in white matter is useful for revealing microstructure of the brain tissue and hence diagnosis and evaluation of white matter diseases. Researchers have modeled diffusion in white matter using mathematical and mechanical analysis at the cellular level. However, less work has been devoted to evaluate these models using macroscopic real data such as diffusion tensor magnetic resonance imaging (DTMRI) data. DTMRI is a noninvasive tool for evaluating white matter microstructure by measuring random motion of water molecules referred to as diffusion. It reflects directional information of microscopic structures such as fibers. Thus, it is applicable for evaluation and modification of mathematical models of white matter. Nevertheless, a realistic relation between a fiber model and imaging data does not exist. This work opens a promising avenue for relating DTMRI data to microstructural parameters of white matter. First, we propose a strategy for relating DTMRI and fiber model parameters to evaluate mathematical models in light of real data. The proposed strategy is then applied to evaluate and extend an existing model of white matter based on clinically available DTMRI data. Next, the proposed strategy is used to estimate microstructural characteristics of fiber tracts. We illustrate this approach through its application to approximation of myelin sheath thickness and fraction of volume occupied by fibers. Using sufficiently small imaging voxels, the proposed approach is capable of estimating model parameters with desirable precision.

Advanced MRI in multiple sclerosis: current status and future challenges

MRI has rapidly become a leading research tool in the study of multiple sclerosis (MS). Conventional imaging is useful in diagnosis and management of the inflammatory stages of MS but has limitations in describing the degree of tissue injury and cause of progressive disability seen in later stages. Advanced MRI techniques hold promise for filling this void. These imaging tools hold great promise to increase understanding of MS pathogenesis and provide greater insight into the efficacy of new MS therapies.

Diffusion tensor-based fast marching for modeling human brain connectivity network

Diffusion tensor imaging (DTI) is an effective modality in studying the connectivity of the brain. To eliminate possible biases caused by fiber extraction approaches due to low spatial resolution of DTI and the number of fibers obtained, the fast marching (FM) algorithm based on the whole diffusion tensor information is proposed to model and study the brain connectivity network. Our observation is that the connectivity extracted from the whole tensor field would be more robust and reliable for constructing brain connectivity network using DTI data. To construct the connectivity network, in this paper, the arrival time map and the velocity map generated by the FM algorithm are combined to define the connectivity strength among different brain regions. The conventional fiber tracking-based and the proposed tensor-based FM connectivity methods are compared, and the results indicate that the connectivity features obtained using the FM-based method agree better with the neuromorphical studies of the human brain.

Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents

This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and "texture" (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles.

A review of diffusion tensor magnetic resonance imaging computational methods and software tools

In this work we provide an up-to-date short review of computational magnetic resonance imaging (MRI) and software tools that are widely used to process and analyze diffusion-weighted MRI data. A review of different methods used to acquire, model and analyze diffusion-weighted imaging data (DWI) is first provided with focus on diffusion tensor imaging (DTI). The major preprocessing, processing and post-processing procedures applied to DTI data are discussed. A list of freely available software packages to analyze diffusion MRI data is also provided.

Accurate anisotropic fast marching for diffusion-based geodesic tractography

Using geodesics for inferring white matter fibre tracts from diffusion-weighted MR data is an attractive method for at least two reasons: (i) the method optimises a global criterion, and hence is less sensitive to local perturbations such as noise or partial volume effects, and (ii) the method is fast, allowing to infer on a large number of connexions in a reasonable computational time. Here, we propose an improved fast marching algorithm to infer on geodesic paths. Specifically, this procedure is designed to achieve accurate front propagation in an anisotropic elliptic medium, such as DTI data. We evaluate the numerical performance of this approach on simulated datasets, as well as its robustness to local perturbation induced by fiber crossing. On real data, we demonstrate the feasibility of extracting geodesics to connect an extended set of brain regions.

A local fast marching-based diffusion tensor image registration algorithm by simultaneously considering spatial deformation and tensor orientation

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration.

Optimum b value for resolving crossing fibers: a study with standard clinical b value using 1.5-T MR

INTRODUCTION

We sought to investigate the optimum b value for resolving crossing fiber using high-angular resolution diffusion imaging (HARDI)-based multi-tensor tractography. The study tested the standard b values that are commonly used in the routine clinical setting.

METHODS

Ten normal volunteers (five men and five women) with a mean age of 26.3 years (range, 22-32 years) were scanned using a 1.5-T clinical magnetic resonance unit. Single-shot echo-planar imaging was used for diffusion-weighted imaging with a diffusion-sensitizing gradient in 32 orientations. The b values of 700, 1,400, 2,100, and 2,800 s/m(2) were used. Data postprocessing was performed using multi-tensor methods. The depiction of the optic nerves, optic tracts, and decussation of superior cerebellar peduncles were assessed.

RESULTS

The depictions of the nerve fibers were independent of the b values tested.

CONCLUSION

The depiction of crossing fibers by HARDI-based multi-tensor tractography is not substantially influenced by b values ranging from 700 to 2,800 s/m(2). Thus, the optimum b value within this range may be the lowest one considering the higher signal to noise ratio.

Principles and limitations of computational algorithms in clinical diffusion tensor MR tractography

There have been numerous reports documenting the graphic reconstruction of 3D white matter architecture in the human brain by means of diffusion tensor MR tractography. Different from other reviews addressing the physics and clinical applications of DTI, this article reviews the computational principles of tractography algorithms appearing in the literature. The simplest voxel-based method and 2 widely used subvoxel approaches are illustrated first, together with brief notes on parameter selection and the restrictions arising from the distinct attributes of tract estimations. Subsequently, some advanced techniques attempting to offer improvement in various aspects are briefly introduced, including the increasingly popular research tracking tool using HARDI. The article explains the inherent technical limitations in most of the algorithms reported to date and concludes by providing a reference guideline for formulating routine applications of this important tool to clinical neuroradiology in an objective and reproducible manner.

Performing real-time interactive fiber tracking

Fiber tracking is a technique that, based on a diffusion tensor magnetic resonance imaging dataset, locates the fiber bundles in the human brain. Because it is a computationally expensive process, the interactivity of current fiber tracking tools is limited. We propose a new approach, which we termed real-time interactive fiber tracking, which aims at providing a rich and intuitive environment for the neuroradiologist. In this approach, fiber tracking is executed automatically every time the user acts upon the application. Particularly, when the volume of interest from which fiber trajectories are calculated is moved on the screen, fiber tracking is executed, even while it is being moved. We present our fiber tracking tool, which implements the real-time fiber tracking concept by using the video card's graphics processing units to execute the fiber tracking algorithm. Results show that real-time interactive fiber tracking is feasible on computers equipped with common, low-cost video cards.

MR connectomics: Principles and challenges

MR connectomics is an emerging framework in neuro-science that combines diffusion MRI and whole brain tractography methodologies with the analytical tools of network science. In the present work we review the current methods enabling structural connectivity mapping with MRI and show how such data can be used to infer new information of both brain structure and function. We also list the technical challenges that should be addressed in the future to achieve high-resolution maps of structural connectivity. From the resulting tremendous amount of data that is going to be accumulated soon, we discuss what new challenges must be tackled in terms of methods for advanced network analysis and visualization, as well data organization and distribution. This new framework is well suited to investigate key questions on brain complexity and we try to foresee what fields will most benefit from these approaches.

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.

Simultaneous consideration of spatial deformation and tensor orientation in diffusion tensor image registration using local fast marching patterns

Diffusion tensor imaging (DTI) plays increasingly important roles in surgical planning, neurological disease diagnosis, and follow-up studies in recent years. In order to compare the tractography obtained from different subjects or the same subject at different timepoints, a key step is to spatially align DTI images. Different from scalar or multi-channel image registration, tensor orientation should be considered in DTI registration. Several DTI registration methods have been proposed before, and some of them are based on first extracting the orientation-invariant features and then registering images using traditional scalar or multi-channel registration techniques followed by tensor reorientation. They essentially do not fully use the tensor information. Other methods such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms use analytical gradients of the registration objective functions by considering the reorientation of tensor during the registration. However, only local tensor information such as voxel tensor similarity is utilized in these algorithms, which can be regarded as a counterpart of the traditional intensity similarity-based image registration in the DTI case. This paper proposes a novel DTI image registration algorithm, called fast marching-based simultaneous registration. It not only considers the orientation of tensors but also utilizes the neighborhood tensor information of each voxel, which is extracted from a local fast marching algorithm around voxels of interest. Compared to the voxel-wise tensor similarity-based registration, richer and more distinctive tensor features are used in this algorithm to better define correspondences between DTI images. Thus, more robust and accurate registration results can be obtained. In the experiments, comparative results using the real DTI data show the advantages of the proposed algorithm.

Fuzzy anatomical connectedness of the brain using single and multiple fibre orientations estimated from diffusion MRI

A new fuzzy algorithm for assessing white matter connectivity in the brain using diffusion-weighted magnetic resonance images is presented. The proposed method considers anatomical paths as chains of linked neighbouring voxels. Links between neighbours are assigned weights using the respective fibre orientation estimates. By checking all possible paths between any two voxels, a connectedness value is assigned, representative of the weakest link of the strongest path connecting the voxel pair. Multiple orientations within a voxel can be incorporated, thus allowing the utilization of fibre crossing information, while fibre branching is inherently considered. Under the assumption that paths connected strongly to a seed will exhibit adequate orientational coherence, fuzzy connectedness values offer a relative measure of path feasibility. The algorithm is validated using simulations and results are shown on diffusion tensor and Q-ball images.

Reliability of fiber tracking measurements in diffusion tensor imaging for longitudinal study

The statistical reliability of diffusion property measurements was evaluated in ten healthy subjects using deterministic fiber tracking to localize tracts affected in motor neuron disease: corticospinal tract (CST), uncinate fasciculus (UNC), and the corpus callosum in its entirety (CC), and its genu (GE), motor (CCM), and splenium (SP) fibers separately. Measurements of fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (lambda(1)), transverse diffusivity (lambda( perpendicular)), and volume of voxels containing fibers (VV) were obtained within each tract. To assess intra-rater and inter-rater reliability, two raters carried out fiber tracking five times on each scan. Scan-rescan and longitudinal reliability were assessed in a subset of four subjects who had six scans, with two sets of three scans separated by 1 year. The statistical reliability of repeated measurements was evaluated using intraclass correlation coefficients (ICC) and coefficients of variation (CV). Spatial agreement of tract shape was assessed using the kappa (kappa) statistic.

RESULTS

Repeated same-scan fiber tracking evaluations showed good geometric alignment (intra-rater kappa >0.90, inter-rater kappa >0.76) and reliable diffusion property measurements (intra-rater ICC >0.92, inter-rater ICC >0.77). FA, MD, and lambda( perpendicular) were highly reliable with repeated scans on different days, up to a year apart (ICC >0.8). VV also exhibited good reliability, but with higher CVs. We were unable to demonstrate reproducibility of lambda(1). Longitudinal reliability after one year was improved by averaging measurements from multiple scans at each time point. Fiber tracking provides a reliable tool for the longitudinal evaluation of white matter diffusion properties.

A DTI-derived measure of cortico-cortical connectivity

We arm researchers with a simple method to chart a macroscopic cortico-cortical connectivity network in living human subjects. The researcher provides a diffusion-magnetic resonance imaging (MRI) data set and N cortical regions of interest. In return, we provide an N xN structural adjacency matrix (SAM) quantifying the relative connectivity between all cortical region pairs. We also return a connectivity map for each pair to enable visualization of interconnecting fiber bundles. The measure of connectivity we devise is: 1) free of length bias, 2) proportional to fiber bundle cross-sectional area, and 3) invariant to an exchange of seed and target. We construct a 3-D lattice scaffolding (graph) for white-matter by drawing a link between each pair of voxels in a 26-voxel neighborhood for which their two respective principal eigenvectors form a sufficiently small angle. The connectivity between a cortical region pair is then measured as the maximum number of link-disjoint paths that can be established between them in the white-matter graph. We devise an efficient Edmonds-Karp-like algorithm to compute a conservative bound on the maximum number of link-disjoint paths. Using both simulated and authentic diffusion-tensor imaging data, we demonstrate that the number of link-disjoint paths as a measure of connectivity satisfies properties 1)-3), unlike the fraction of intersecting streamlines-the measure intrinsic to most existing probabilistic tracking algorithms. Finally, we present connectivity maps of some notoriously difficult to track longitudinal and contralateral fasciculi.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

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.

Diffusion tensor imaging of the kidney with parallel imaging: initial clinical experience

OBJECTIVE

To evaluate the clinical feasibility of diffusion tensor imaging (DTI) of the kidney in volunteers and patients with renal diseases.

MATERIAL AND METHODS

Ten volunteers and 22 patients (mean age, 56 +/- 14.3) with renal masses and renal artery stenosis underwent breath-hold coronal fat-saturated echo-planar DTI (as provided by the manufacturer, 6 diffusion directions, diffusion weightings b = 0 and 300 s/mm2, repetition time 730 ms/echo time 72 ms; 5 slices; slice thickness, 6 mm; inplane resolution, 2.1 x 2.1 mm2; acquisition time, 26 seconds) of the kidneys at 1.5 T (MAGNETOM Avanto, Siemens Medical Solutions, Erlangen, Germany). The parallel imaging technique, generalized autocalibrating partially parallel acquisitions with an acceleration factor 2, was applied. Using the commercially available Syngo DTI task card software, regions of interests were placed in the cortex, medulla, and in renal masses if present. Fractional anisotropy (FA) and apparent diffusion coefficients (ADC) were determined, and tractography was used to visualize the renal diffusion properties. Statistical analysis was performed using the Wilcoxon signed-rank sum test and paired t tests.

RESULTS

In all volunteers, FA was significantly (P < 0.01) higher in the medulla (0.36 +/- 0.03) than in the cortex (0.21 +/- 0.02), whereas the ADC was significantly (P < 0.01) higher in the cortex (2.43 +/- 0.19) than in the medulla (2.16 +/- 0.22). Tractography typically revealed a radial preferred direction of medullary diffusion basically reflecting medullary flow.FA/ADC of simple renal cysts (n = 8) was 0.14 +/- 0.05/2.86 +/- 0.15. Renal cell carcinoma (n = 10) showed a wide FA range from 0.11 to 0.56. Using tractography, the structural organization of renal cell carcinoma such as pseudocapsules could be visualized.In 1 patient with unilateral high-grade renal artery stenosis, the cortical ADC of the affected kidney was lower than on the contralateral side (1.77/2.27) and the FA was increased (0.33/0.18). The FA of the medulla was increased (0.70/0.41) and the ADC decreased (1.43/1.90).

CONCLUSIONS

Using parallel imaging, DTI measurements of the kidneys are feasible within a single breath-hold with good discrimination between cortex and medulla. Parallel imaging allows more slices and a superior resolution. DTI measurements of the kidney allows visualization of medullary flow, in pathology ADC and FA were altered. Further investigations will be required to evaluate the role of DTI for studying and monitoring renal ultrastructure.

DT-MRI fiber tracking: a shortest paths approach

We derive a new fiber tracking algorithm for DT-MRI that parts with the locally "greedy" paradigm intrinsic to conventional tracking algorithms. We demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer-generated DT-MRI data, for which well-known conventional tracking algorithms are shown to fail. Our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph. Voxels serve as vertices, and edges are included between neighboring voxels. We assign probabilities (weights) to edges using a Bayesian framework. Higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity. We compute optimal paths of maximum probability using computationally scalable shortest path algorithms. The salient features of our approach are: global optimality--unlike conventional tracking algorithms, local errors do not accumulate and one "wrong-turn" does not spell disaster; a target point is specified a priori; precise reconstruction is demonstrated for extremely low signal-to-noise ratio; impartiality to which of two endpoints is used as a seed; and, faster computation times than conventional all-paths tracking. We can use our new tracking algorithm in either a single-path tracking mode (deterministic tracking) or an all-paths tracking mode (probabilistic tracking).

Imaging structural and functional connectivity: towards a unified definition of human brain organization?

PURPOSE OF REVIEW

Diffusion tractography and functional/effective connectivity MRI provide a better understanding of the structural and functional human brain connectivity. This review will underline the major recent methodological developments and their exceptional respective contributions to physiological and pathophysiological studies in vivo. We will also emphasize the benefits provided by computational models of complex networks such as graph theory.

RECENT FINDINGS

Imaging structural and functional brain connectivity has revealed the complex brain organization into large-scale networks. Such an organization not only permits the complex information segregation and integration during high cognitive processes but also determines the clinical consequences of alterations encountered in development, ageing, or neurological diseases. Recently, it has also been demonstrated that human brain networks shared topological properties with the so-called 'small-world' mathematical model, allowing a maximal efficiency with a minimal energy and wiring cost.

SUMMARY

Separately, magnetic resonance tractography and functional MRI connectivity have both brought new insights into brain organization and the impact of injuries. The small-world topology of structural and functional human brain networks offers a common framework to merge structural and functional imaging as well as dynamical data from electrophysiology that might allow a comprehensive definition of the brain organization and plasticity.

Resolving crossings in the corticospinal tract by two-tensor streamline tractography: Method and clinical assessment using fMRI

An inherent drawback of the traditional diffusion tensor model is its limited ability to provide detailed information about multidirectional fiber architecture within a voxel. This leads to erroneous fiber tractography results in locations where fiber bundles cross each other. This may lead to the inability to visualize clinically important tracts such as the lateral projections of the corticospinal tract. In this report, we present a deterministic two-tensor eXtended Streamline Tractography (XST) technique, which successfully traces through regions of crossing fibers. We evaluated the method on simulated and in vivo human brain data, comparing the results with the traditional single-tensor and with a probabilistic tractography technique. By tracing the corticospinal tract and correlating with fMRI-determined motor cortex in both healthy subjects and patients with brain tumors, we demonstrate that two-tensor deterministic streamline tractography can accurately identify fiber bundles consistent with anatomy and previously not detected by conventional single-tensor tractography. When compared to the dense connectivity maps generated by probabilistic tractography, the method is computationally efficient and generates discrete geometric pathways that are simple to visualize and clinically useful. Detection of crossing white matter pathways can improve neurosurgical visualization of functionally relevant white matter areas.

Modified fast marching tractography algorithm and its ability to detect fibre crossing

White matter fibre tractography is a non-invasive method for reconstructing three dimensional trajectories of fibre pathways. Fast Marching is one of fibre tracking methods in which co-linearity of principal eigenvectors determines the speed of front's evolution. In this algorithm effect of tensor's eigenvalues are not considered. In the current work, the speed function of standard fast marching was modified by considering the strength of tensor's eigenvectors. The proposed speed function has an adaptive Fractional Anisotropy (FA) weighted factor which can be set by type of brain's environments (i.e. isotropic and anisotropic regions). This modification was found to have high accuracy for detecting fibres by reducing false pathways. The proposed method has performed high accuracy in detection of fibre crossing.

Diffusion-tensor MR imaging and tractography: exploring brain microstructure and connectivity

Diffusion magnetic resonance (MR) imaging is evolving into a potent tool in the examination of the central nervous system. Although it is often used for the detection of acute ischemia, evaluation of directionality in a diffusion measurement can be useful in white matter, which demonstrates strong diffusion anisotropy. Techniques such as diffusion-tensor imaging offer a glimpse into brain microstructure at a scale that is not easily accessible with other modalities, in some cases improving the detection and characterization of white matter abnormalities. Diffusion MR tractography offers an overall view of brain anatomy, including the degree of connectivity between different regions of the brain. However, optimal utilization of the wide range of data provided with directional diffusion MR measurements requires careful attention to acquisition and postprocessing. This article will review the principles of diffusion contrast and anisotropy, as well as clinical applications in psychiatric, developmental, neurodegenerative, neoplastic, demyelinating, and other types of disease.

Multitensor tractography enables better depiction of motor pathways: initial clinical experience using diffusion-weighted MR imaging with standard b-value

BACKGROUND AND PURPOSE

The purpose of this work was to test the feasibility of using high angular resolution diffusion imaging (HARDI)-based multitensor tractography to depict motor pathways in patients with brain tumors.

MATERIALS AND METHODS

Ten patients (6 males and 4 females) with a mean age of 52 years (range, 9-77 years) were scanned using a 1.5T clinical MR unit. Single-shot echo-planar imaging was used for diffusion-weighted imaging (repetition time, 6000 ms; excitation time, 88 ms) with a diffusion-sensitizing gradient in 32 orientations and a b-value of 1000 s/mm(2). Data postprocessing was performed using both the conventional single- and multitensor methods. The depiction rate of the 5 major components of the motor pathways, that is, the lower extremity, trunk, hand, face, and tongue, was assessed.

RESULTS

Motor fibers on both lesional and contralesional sides were successfully depicted by both the single-tensor and multitensor techniques. However, with the single-tensor model, the depiction of motor pathways was typically limited to the fibers of trunk areas. With the multitensor technique, at least 4 of 5 major fiber bundles arising from the primary motor cortex could be identified.

CONCLUSION

HARDI-based multitensor tractography using a standard b-value (1000 s/mm(2)) can depict the fiber tracts from the face and tongue regions of the primary motor cortex.

Characterizing brain anatomical connections using diffusion weighted MRI and graph theory

A new methodology based on Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) and Graph Theory is presented for characterizing the anatomical connections between brain gray matter areas. In a first step, brain voxels are modeled as nodes of a non-directed graph in which the weight of an arc linking two neighbor nodes is assumed to be proportional to the probability of being connected by nervous fibers. This probability is estimated by means of probabilistic tissue segmentation and intravoxel white matter orientational distribution function, obtained from anatomical MRI and DW-MRI, respectively. A new tractography algorithm for finding white matter routes is also introduced. This algorithm solves the most probable path problem between any two nodes, leading to the assessment of probabilistic brain anatomical connection maps. In a second step, for assessing anatomical connectivity between K gray matter structures, the previous graph is redefined as a K+1 partite graph by partitioning the initial nodes set in K non-overlapped gray matter subsets and one subset clustering the remaining nodes. Three different measures are proposed for quantifying anatomical connections between any pair of gray matter subsets: Anatomical Connection Strength (ACS), Anatomical Connection Density (ACD) and Anatomical Connection Probability (ACP). This methodology was applied to both artificial and actual human data. Results show that nervous fiber pathways between some regions of interest were reconstructed correctly. Additionally, mean connectivity maps of ACS, ACD and ACP between 71 gray matter structures for five healthy subjects are presented.