Fiber Tracking Algorithms Research Articles

Parameter Sensitivity Visualization for DTI Fiber Tracking

Fiber tracking of Diffusion Tensor Imaging (DTI) data offers a unique insight into the three-dimensional organisation of white matter structures in the living brain. However, fiber tracking algorithms require a number of user-defined input parameters that strongly affect the output results. Usually the fiber tracking parameters are set once and are then re-used for several patient datasets. However, the stability of the chosen parameters is not evaluated and a small change in the parameter values can give very different results. The user remains completely unaware of such effects. Furthermore, it is difficult to reproduce output results between different users. We propose a visualization tool that allows the user to visually explore how small variations in parameter values affect the output of fiber tracking. With this knowledge the user cannot only assess the stability of commonly used parameter values but also evaluate in a more reliable way the output results between different patients. Existing tools do not provide such information. A small user evaluation of our tool has been done to show the potential of the technique.

Probabilistic Tracking can improve the delineation of cortico-spinal tract for neurosurgical planning

Problem: White matter fiber tracking based on diffusion MRI is the only technique able to localize the white matter pathways in the brain in vivo. There has been tremendous recent interest in utilization of diffusion MRI fiber tracking for mapping eloquent regions during brain surgery. While some manufacturers have begun to address this demand, the algorithms used tend to be the most basic determinsitic tracking. Furthermore, there is very little data supporting the accuracy of any fiber tracking method in this context where the pathways could be damaged or displaced. Intraoperative electrical stimulation (IES) provides a clinical gold standard for the existence of a functional motor pathway that can be used to determine the accuracy of fiber tracking algorithms. Probabilistic fiber tracking algorithms explore other “high probability” pathways. Residual bootstrap is a non-parametric statistical technique based on data resampling that has been showed to be useful in probabilistic tractography and in assessing DTI methods. In this work we used IES data to evaluate the importance of probabilistic versus deterministic tractography, seeding density, and choice of seed regions.

Combinatorial fiber-tracking of the human brain

This paper presents a novel fiber-tracking algorithm, termed combinatorial tracking, which uses stochastic process modeling and global optimization algorithm for tractography. Combinatorial tracking is a probabilistic tracking algorithm that transforms the brain's white matter into a grid in which each voxel has 26 weighted connections with adjacent voxels. We model the random walk on this graph using a Markov Chain model and suggest two approaches for fiber reconstruction. In the first approach, we find the most probable paths between two voxels with prior connectivity knowledge using a shortest path algorithm. In the second approach, the all-pairs mean first passage time (MFPT) matrix M (or hitting time as referred to in the Spectral Graph theory literature) is calculated analytically. We suggest that M can be interpreted as a global connectivity matrix and use it for fiber reconstruction. We also introduce a simulation framework that can be used to calculate specific elements of the matrix M, and show how it can be employed to select the target of a fiber in a high resolution diffusion tensor imaging (DTI) dataset. Because any source and any target voxel can be connected, combinatorial tracking permits true connectivity analysis, overcoming the limitations of conventional tracking, especially stopping criteria (e.g. low FA). We applied combinatorial tracking to a standard DTI dataset and demonstrated the reconstruction of the cortico-thalamic pathway, the pyramidal decussation, and the medial cerebellar peduncle fibers. While the DTI ellipsoid served as input for the algorithms, any diffusion imaging based orientation density function (ODF) can be used. This framework can potentially turn diffusion imaging tractography into a true connectivity measure.

A software tool to generate simulated white matter structures for the assessment of fibre-tracking algorithms

The assessment of Diffusion-Weighted MRI (DW-MRI) fibre-tracking algorithms has been limited by the lack of an appropriate ‘gold standard’. Practical limitations of alternative methods and physical models have meant that numerical simulations have become the method of choice in practice. However, previous numerical phantoms have consisted of separate fibres embedded in homogeneous backgrounds, which do not capture the true nature of white matter. In this paper we describe a method that is able to randomly generate numerical structures consisting of densely packed bundles of fibres, which are much more representative of human white matter, and simulate the DW-MR images that would arise from them under many imaging conditions. User-defined parameters may be adjusted to produce structures with a range of complexities that spans the levels we would expect to find in vivo. These structures are shown to contain many different features that occur in human white matter and which could confound fibre-tracking algorithms, such as tract kissing and crossing. Furthermore, combinations of such features can be sampled by the random generation of many different structures with consistent levels of complexity. The proposed software provides means for quantitative assessment via direct comparison between tracking results and the exact location of the generated fibres. This should greatly improve our understanding of algorithm performance and therefore prove an important tool for fibre tracking development.

Theory of diffusion tensor imaging and fiber tractography analysis

Magnetic Resonance Imaging (MRI) techniques have been increasingly applied to the study of molecular displacement (diffusion) in biologic tissue. The magnetic resonance measurement of an effective diffusion tensor of water in tissues can provide unique biologically and clinically relevant information that is not available from other imaging modalities. For this purpose Diffusion Tensor Imaging (DTI) is applied. DTI is an MRI variation that may significantly improve our understanding of brain structure and neural connectivity. DTI measures are thought to be representative of brain tissue microstructure and are particularly useful for examining organized brain regions, such as white matter tract areas. DTI measures the water diffusion tensor using diffusion weighted pulse sequences sensitive to microscopic random water motion. The resultant images display and allow for quantification of how water diffuses along axes or diffusion encoding directions. This can help measure and quantify a tissue's orientation and structure, making it an ideal tool for examining cerebral white matter and neural fiber tracts. In this article we discuss the theory on which DTI depends on, how can be used in mapping fiber tracts. Also the fiber tracking algorithms are presented.

Characterizing fiber directional uncertainty in diffusion tensor MRI

Image noise in diffusion tensor MRI (DT-MRI) causes errors in the measured tensor and hence variance in the estimated fiber orientation. Uncertainty in fiber orientation has been described using a circular "cone of uncertainty" (CU) around the principal eigenvector of the DT. The CU has proved to be a useful construct for quantifying and visualizing the variability of DT-MRI parameters and fiber tractography. The assumption of circularity of the CU has not been tested directly, however. In this work, bootstrap analysis and simple theoretical arguments were used to show that the CU is elliptical and multivariate normal in the vast majority of white matter (WM) voxels for typical measurement conditions. The dependence of the cone angle on the signal-to-noise ratio (SNR) and eigenvalue contrast was established. The major and minor cone axes are shown to be coincident with the second and third eigenvectors of the tensor, respectively, in the limit of many uniformly spaced diffusion-encoding directions. The deviation between the major cone axis and the second eigenvector was quantified for typical sets of diffusion-weighting (DW) directions. The elliptical CU provides more realistic error information for fiber-tracking algorithms and a quantitative basis for selecting DT imaging acquisition protocols.

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).

Gibbs tracking: A novel approach for the reconstruction of neuronal pathways

Reconstruction of neuronal fibers using diffusion-weighted (DW) MRI is an emerging method in biomedical research. Existing fiber-tracking algorithms are commonly based on the "walker principle." Fibers are reconstructed as trajectories of "walkers," which are guided according to local diffusion properties. In this study, a new method of fiber tracking is proposed that does not engage any "walking" algorithm. It resolves a number of inherent problems of the "walking" approach, in particular the reconstruction of crossing and spreading fibers. In the proposed method, the fibers are built with small line elements. Each line element contributes an anisotropic term to the simulated DW signal, which is adjusted to the measured signal. This method demonstrates good results for simulated fibers. A single in vivo result demonstrates the successful reconstruction of the dominant neuronal pathways. A comparison with the diffusion tensor imaging (DTI)-based fiber assignment with continuous tracking (FACT) method and the probabilistic index of connectivity (PICo) method based on a multitensor model is performed for the callosal fibers. The result shows a strong increase in the number of reconstructed fibers. These almost fill the total white matter (WM) volume and connect a large area of the cortex. The method is very computationally expensive. Possible ways to address this problem are discussed.

Tractography Gone Wild: Probabilistic Fibre Tracking Using the Wild Bootstrap With Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) permits the noninvasive assessment of tissue microstructure and, with fibre-tracking algorithms, allows for the 3-D trajectories of white matter fasciculi to be reconstructed noninvasively. Probabilistic algorithms allow one to assign a "confidence" to a given reconstructed pathway--but often rely on a priori assumptions about sources of uncertainty in the data. Bootstrap methods have been proposed as a way of circumventing this problem, deriving the uncertainty from the data themselves--but acquisition times for data amenable to precise and robust bootstrapping are clinically prohibitive. By combining the wild bootstrap, recently introduced to the DT-MRI literature, with tractography, we show how confidence can be assigned to reconstructed trajectories using data collected in a fraction of the time required for regular bootstrapping. We compare in vivo wild bootstrap tracking results with regular tracking results and show that results are comparable. This approach therefore allows users who have collected data sets for use with deterministic tracking algorithms, rather than those specifically designed for bootstrapping, to be able to apply bootstrap analyses and retrospectively assign confidence to their reconstructed trajectories with minimum additional effort.

Labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion MRI

Whereas high angular resolution reconstruction methods for diffusion MRI can estimate multiple dominant fibre orientations within a single imaging voxel, they are fundamentally limited in certain cases of complex subvoxel fibre structures, resulting in ambiguous local orientation distribution functions. In this article we address the important problem of disambiguating such complex subvoxel fibre tract configurations, with the purpose of improving the performance of fibre tractography. We do so by extending a curve inference method to distinguish between the cases of curving and fanning fibre bundles using differential geometric estimates in a local neighbourhood. The key benefit of this method is the inference of curves, instead of only fibre orientations, to model the underlying fibre bundles. This in turn allows distinct fibre geometries that contain nearly identical sets of fibre orientations at a voxel, to be distinguished from one another. Experimental results demonstrate the ability of the method to successfully label voxels into one of the above categories and improve the performance of a fibre-tracking algorithm.

Whole brain-based computerized neuroimaging in ALS and other motor neuron disorders

Advanced neuroimaging applications to patients suffering from ALS and other motor neuron disorders (MND) have a high potential in terms of understanding the pathophysiology and visualizing the in vivo pathoanatomy of the diseases. In this context, particularly observer-independent computerized analyses of magnetic resonance imaging (MRI) data are of special interest since they overcome shortcomings of region-of-interest-based techniques. For three-dimensional structural T1-weighted MRI of the whole brain, voxel-based morphometry (VBM) has proven the most valuable approach to analyse regional volume alterations of the grey or white matter at group level. For the analysis of the white matter integrity with respect to tissue diffusivity and white matter connectivity including fibre tracking algorithms, diffusion tensor imaging (DTI) which can also be performed on a whole brain-basis is of the highest potential to date. Both VBM and DTI have been applied to various MND, in particular ALS, in multiple studies over recent years and have substantially broadened our knowledge about their in vivo pathoanatomy and mechanisms of neurodegeneration. Especially both the degree of damage to motor areas and the involvement of non-motor areas are of interest to be subjected to quantitative assessment, in order to establish quantitative surrogate markers for disease progression usable in clinical trials. Here, the technical state-of-the-art and the results of VBM and DTI studies in MND as the current state are reviewed, and future perspectives for further neuroimaging applications are highlighted.

Frontostriatal Connectivity and Its Role in Cognitive Control in Parent-Child Dyads With ADHD

Many studies have linked the structure and function of frontostriatal circuitry to cognitive control deficits in attention deficit hyperactivity disorder (ADHD). Few studies have examined the role of white matter tracts between these structures or the extent to which white matter tract myelination and regularity correlate in family members with the disorder. Functional imaging maps from a go/nogo task were used to identify portions of the ventral prefrontal cortex and striatum involved in suppressing an inappropriate action (i.e., cognitive control) in 30 parent-child dyads (N=60), including 20 dyads (N=40) with ADHD and 10 dyads (N=20) without ADHD. An automated fiber-tracking algorithm was used to delineate white matter fibers adjacent to these functionally defined regions based on diffusion tensor images. Fractional anisotropy, an index of white matter tract myelination and regularity derived from diffusion tensor images, was calculated to characterize the associations between white matter tracts and function. Fractional anisotropy in right prefrontal fiber tracts correlated with both functional activity in the inferior frontal gyrus and caudate nucleus and performance of a go/nogo task in parent-child dyads with ADHD, even after controlling for age. Prefrontal fiber tract measures were tightly associated between ADHD parents and their children. Collectively, these findings support previous studies suggesting heritability of frontostriatal structures among individuals with ADHD and suggest disruption in frontostriatal white matter tracts as one possible pathway to the disorder.

Motor and language DTI Fiber Tracking combined with intraoperative subcortical mapping for surgical removal of gliomas

Preoperative DTI Fiber Tracking (DTI-FT) reconstruction of functional tracts combined with intraoperative subcortical mapping (ISM) is potentially useful to improve surgical procedures in gliomas located in eloquent areas. Aims of the study are: (1) to evaluate the modifications of fiber trajectory induced by the tumor; (2) to validate preoperative DTI-FT results with intraoperative identification of functional subcortical sites through direct subcortical stimulation; (3) to evaluate the impact of preoperative DTI-FT reconstructions in a neuronavigational setup combined with ISM technique on duration and modalities of surgical procedures, and on functional outcome of the patients. Data are available on 64 patients (52 low-grade and 12 high-grade gliomas). DTI-FT was acquired by a 3-T MR scanner with a single-shot EPI sequence (TR/TE 8986/80 ms, b = 1000 s/mm) with gradients applied along 32 non-collinear directions. 3D Fast Field Echo (FFE) T1-weighted imaging (TR/TE 8/4 ms) was performed for anatomic guidance. The corticospinal tract (CST), superior longitudinal, inferior fronto-occipital and uncinatus fasciculi were reconstructed. Data were transferred to the neuronavigational system. Functional subcortical sites identified during ISM were correlated with fiber tracts depicted by DTI-FT. In high-grade gliomas, DTI-FT depicted tracts mostly at the tumor periphery; in low-grade gliomas, fibers were frequently located inside the tumor mass. There was a high correlation between DTI-FT and ISM (sensitivity for CST = 95%, language tracts = 97%). For a proper reconstruction of the tracts, it was necessary to use a low FA threshold of fiber tracking algorithm and to position additional regions of interest (ROIs). The combination of DTI-FT and ISM decreased the duration of surgery, patient fatigue, and intraoperative seizures. Combination of DTI-FT and ISM allows accurate identification of eloquent fiber tracts and enhances surgical performance and safety maintaining a high rate of functional preservation.

Probabilistic streamline q-ball tractography using the residual bootstrap

Q-ball imaging has the ability to discriminate multiple intravoxel fiber populations within regions of complex white matter architecture. This information can be used for fiber tracking; however, diffusion MR is susceptible to noise and multiple other sources of uncertainty affecting the measured orientation of fiber bundles. The proposed residual bootstrap method utilizes a spherical harmonic representation for high angular resolution diffusion imaging (HARDI) data in order to estimate the uncertainty in multimodal q-ball reconstructions. The accuracy of the q-ball residual bootstrap technique was examined through simulation. The residual bootstrap method was then used in combination with q-ball imaging to construct a probabilistic streamline fiber tracking algorithm. The residual bootstrap q-ball fiber tracking algorithm is capable of following the corticospinal tract and corpus callosum through regions of crossing white matter tracts in the centrum semiovale. This fiber tracking algorithm is an improvement upon prior diffusion tensor methods and the q-ball data can be acquired in a clinically feasible time frame.

Diffusion Tensor MRI Assessment of Skeletal Muscle Architecture.

Diffusion-tensor magnetic resonance imaging (DTI) offers great potential for understanding structure-function relationships in skeletal muscle. The basis for these studies is that water diffuses more readily along the long axes of muscle fibers than along their transverse axes. This diffusion anisotropy can be characterized using a tensor, with the orientation of the principal eigenvalue corresponding to the long axis of the muscle fiber. These local, voxel-based directions can be combined by a fiber tracking algorithm to reconstruct the whole-muscle architecture. The fiber tracking data can be used to characterize important muscle architectural parameters, such as pennation angle, fiber length, and physiological cross-sectional area. The second and third eigenvalues convey information about muscle structural properties along the fibers' transverse axes. A comprehensive description of the sources of transverse diffusion restriction in muscle and how their relative importance may vary with the image acquisition conditions does not yet exist, but may ultimately make DTI a useful tool in studies of skeletal muscle microstructure as well. Ultimately, DTI-based longitudinal studies of changes in muscle architecture may provide insight into the relationships between structure and function in muscle, the time frames of muscle wasting, and in studying adaptations that maintain muscle functionality.

3D curve inference for diffusion MRI regularization and fibre tractography☆

We develop a differential geometric framework for regularizing diffusion MRI data. The key idea is to model white matter fibres as 3D space curves and to then extend Parent and Zucker's 2D curve inference approach [Parent, P., Zucker, S., 1989. Trace inference, curvature consistency, and curve detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 823-839] by using a notion of co-helicity to indicate compatibility between fibre orientations at each voxel with those in a local neighborhood. We argue that this provides several advantages over earlier regularization methods. We validate the approach quantitatively on a biological phantom and on synthetic data, and qualitatively on data acquired in vivo from a human brain. We also demonstrate the use of the technique to improve the performance of a fibre tracking algorithm.

Evaluation of the GTRACT diffusion tensor tractography algorithm: A validation and reliability study

Fiber tracking, based on diffusion tensor imaging (DTI), is the only approach available to non-invasively study the three-dimensional structure of white matter tracts. Two major obstacles to this technique are partial volume artifacts and tracking errors caused by image noise. In this paper, a novel fiber tracking algorithm called Guided Tensor Restore Anatomical Connectivity Tractography (GTRACT) is presented. This algorithm utilizes a multi-pass approach to fiber tracking. In the first pass, a 3D graph search algorithm is utilized. The second pass incorporates anatomical connectivity information generated in the first pass to guide the tracking in this stage. This approach improves the ability to reconstruct complex fiber paths as well as the tracking accuracy. Validation and reliability studies using this algorithm were performed on both synthetic phantom data and clinical human brain data. A method is also proposed for the evaluating reliability of fiber tract generation based both on the position of the fiber tracts, as well the anisotropy values along the path. The results demonstrate that the GTRACT algorithm is less sensitive to image noise and more capable of handling areas of complex fiber crossing, compared to conventional streamline methods.

Visualization of tissue velocity data from cardiac wall motion measurements with myocardial fiber tracking: principles and implications for cardiac fiber structures

The spatial arrangement of myocardial fiber structure affects the mechanical and electrical properties of the heart. Therefore, information on the structure and dynamics of the orientation of the muscle fibers in the human heart might provide significant insight into principles of the mechanics of normal ventricular contraction and electrical propagation and may subsequently aid pre- and postsurgical evaluation of patients. Fiber orientation is inherently linked to cardiac wall motion, which can be measured with phase contrast magnetic resonance imaging (MRI), also termed tissue phase mapping (TPM). This study provides initial results of the visualization of velocity data with fiber tracking algorithms and discusses implications for the fiber orientations. In order to generate datasets with sufficient volume coverage and resolution TPM measurements with three-dimensional (3D) velocity encoding were executed during breath-hold periods and free breathing. Subsequent postprocessing evaluation with a tracking algorithm for acceleration fields derived from the velocity data was performed. Myocardial acceleration tracking illustrated the dynamics of fiber structure during four different phases of left ventricular performance, that include isovolumetric contraction (IVC), mid-systole, isovolumetric relaxation (IVR), and mid-diastole. Exact reconstruction of the myocardial fiber structure from velocity data requires mathematical modeling of spatiotemporal evolution of the velocity fields. 'Acceleration fibers' were reconstructed at these four phases during the cardiac cycle, and these findings may become (a) surrogate parameters in the normal ventricle, (b) baseline markers for subsequent clinical studies of abnormal hearts with altered architecture, and (c) may help to explain and illustrate functional features of cardiac performance in structural models like the helical ventricular myocardial band.

Structure-function relationships in the human visual system using DTI, fMRI and visual field testing: pre- and post-operative assessments in patients with anterior visual pathway compression.

The focus of this project is to improve our understanding of the relationships between brain structure and function in patients presenting with anterior visual pathway compression using functional MRI (fMRI), visual field(VF) maps and diffusion tensor imaging (DTI). Significant visual loss can occur when large pituitary lesions compress the optic chiasm. Surgical resection of these lesions decompresses the chiasm and can lead to visual recovery. In this preliminary study, we selected patients presenting with slowly progressive visual loss secondary to a compressive pituitary region mass. Using preoperative DTI data, we reconstructed white matter projections of the optic radiations and demonstrated a structural correlation with functional vision as quantified by formal visual field mapping and fMRI. The structural data generated through a fiber tracking algorithm may represent a potentially powerful tool to better understand functional visual deficits in patients with anterior visual pathway compression. Furthermore, we believe that specific patterns in preoperative DTI data may predict the likelihood of postoperative visual recovery in a select group of patients.

Three‐dimensional fiber architecture of the nonpregnant human uterus determined ex vivo using magnetic resonance diffusion tensor imaging

The global muscle and collagen fiber orientation in the human uterus has been analyzed hitherto by various standard microscopic techniques. However, no widely accepted model of the fiber architecture of the myometrium could be acquired. The purpose of the present study was to investigate the uterus by magnetic resonance (MR) diffusion tensor imaging (DTI) in a 3D macroscopic approach. Ex vivo MR DTI measurements were performed on five uteri from nonpregnant patients. The main diffusion directions reflecting the orientation of directional structures in the examined tissues were determined from diffusion-weighted spin-echo measurements. A fiber tracking algorithm was used to extrapolate the fiber architecture. The method was validated against histological slides and indirectly through the analysis of leiomyomas, which exhibit less anisotropy than normal myometrium. Significant anisotropy was found in most regions of all examined nonpregnant human uteri. But only two systems of fibers were found running circularly along the intramural part of the uterine tubes. They merged caudally and built a close fitting envelope of circular layers around the uterine cavity. On the cervix, circular fibers were observed in the outer part as well as mostly longitudinal fibers in the inner part. These results confirm the existence of directional structures in the complex fiber architecture of the human uterus. They also indicate that MR DTI is a beneficial and complementary tool to standard microscopic techniques to determine the intrinsic fiber architecture in human organs.