Fiber Orientation Estimation Research Articles

PopTract: population-based tractography.

White matter fiber tractography plays a key role in the in vivo understanding of brain circuitry. For tract-based comparison of a population of images, a common approach is to first generate an atlas by averaging, after spatial normalization, all images in the population, and then perform tractography using the constructed atlas. The reconstructed fiber trajectories form a common geometry onto which diffusion properties of each individual subject can be projected based on the corresponding locations in the subject native space. However, in the case of high angular resolution diffusion imaging (HARDI), where modeling fiber crossings is an important goal, the above-mentioned averaging method for generating an atlas results in significant error in the estimation of local fiber orientations and causes a major loss of fiber crossings. These limitatitons have significant impact on the accuracy of the reconstructed fiber trajectories and jeopardize subsequent tract-based analysis. As a remedy, we present in this paper a more effective means of performing tractography at a population level. Our method entails determining a bipolar Watson distribution at each voxel location based on information given by all images in the population, giving us not only the local principal orientations of the fiber pathways, but also confidence levels of how reliable these orientations are across subjects. The distribution field is then fed as an input to a probabilistic tractography framework for reconstructing a set of fiber trajectories that are consistent across all images in the population. We observe that the proposed method, called PopTract, results in significantly better preservation of fiber crossings, and hence yields better trajectory reconstruction in the atlas space.

ESTIMATION OF FIBRE ORIENTATION FROM DIGITAL IMAGES

In this paper, estimation of fibre orientation is studied for fibre systems observable as a blurred greyscale image. The estimation method is based on scaled variograms observed along a set of sampling lines in different directions. The parameters of the orientation distribution are obtained numerically. Simulated data are used to study the statistical properties of the method.

Longitudinal Enhancement of the Hyperechoic Regions in Ultrasonography of Muscles Using a Gabor Filter Bank Approach: A Preparation for Semi-Automatic Muscle Fiber Orientation Estimation

In this study, to complement our previously proposed method for estimating muscle fiber orientation, the Gabor filter bank (GF) technique was applied to sonograms of the biceps and forearm muscles to longitudinally enhance the coherently oriented and hyperechoic perimysiums regions. The method involved three steps: orientation field estimation, frequency map computation and Gabor filtering. The method was evaluated using a simulated image distorted with multiplicative speckle noises where the “muscles” were arranged in a bipennate fashion with an “aponeurosis” located in the middle. After enhancement using the GF approach, most of the original hyperechoic bands in the simulated image could be recovered. The proposed method was also tested using a group of biceps and forearm muscle sonograms collected from healthy adult subjects. Compared with the sonograms without enhancement, the enhanced images led to the detection of more linear patterns including muscle fascicles and smaller angle differences compared with the mean of manual results from two operators, therefore, were better prepared for the automatic estimation of muscle fiber orientation. The proposed method has the potential of assisting in the visualization of strongly oriented patterns in skeletal muscle sonograms as well as in the semi-automatic estimation of muscle fiber orientations. (E-mail: yongjin.zhou@inet.polyu.edu.hk)

Tensor kernels for simultaneous fiber model estimation and tractography.

This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second-and higher-order tensor-based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching.

Diffusion Tensor Imaging: A Review for Pediatric Researchers and Clinicians

Diffusion tensor imaging (DTI) is a magnetic resonance imaging technique that allows for the visualization and characterization of the white matter tracts of the brain in vivo. DTI does not assess white matter directly. Rather, it capitalizes on the fact that diffusion is isotropic (equal in all directions) in cerebral spinal fluid and cell bodies but anisotropic (greater in one direction than the other directions) in axons that comprise white matter. It provides quantitative information about the degree and direction of water diffusion within individual units of volume within the magnetic resonance image, and by inference, about the integrity of white matter. Measures from DTI can be applied throughout the brain or to regions of interest. Fiber tract reconstruction, or tractography, creates continuous 3-dimensional tracts by sequentially piecing together estimates of fiber orientation from the direction of diffusion within individual volume units. DTI has increased our understanding of white matter structure and function. DTI shows nonlinear growth of white matter tracts from childhood to adulthood. Delayed maturation of the white matter in the frontal lobes may explain the continued growth of cognitive control into adulthood. Relative to good readers, adults and children who are poor readers have evidence of white matter differences in a specific region of the temporo-parietal lobe, implicating differences in connections among brain regions as a factor in reading disorder. Measures from DTI changed in poor readers who improved their reading skills after intense remediation. DTI documents injury to white matter tracts after prematurity. Measures indicative of white matter injury are associated with motor and cognitive impairment in children born prematurely. Further research on DTI is necessary before it can become a routine clinical procedure.

The effect of finite diffusion gradient pulse duration on fibre orientation estimation in diffusion MRI

An essential step for fibre-tracking is the accurate estimation of neuronal fibre orientations within each imaging voxel, and a number of methods have been proposed to reconstruct the orientation distribution function based on sampling three-dimensional q-space. In the q-space formalism, very short (infinitesimal) gradient pulses are the basic requirement to obtain the true spin displacement probability density function. On current clinical MR systems however, the diffusion gradient pulse duration (δ) is inevitably finite due to the limit on the achievable gradient intensity. The failure to satisfy the short gradient pulse (SGP) requirement has been a recurrent criticism for fibre orientation estimation based on the q-space approach. In this study, the influence of a finite δ on the DW signal measured as a function of gradient direction is described theoretically and demonstrated through simulations and experimental models. Our results suggest that the current practice of using long δ for DW imaging on human clinical MR scanners, which is enforced by hardware limitations, might in fact be beneficial for estimating fibre orientations. For a given b-value, the prolongation of δ is advantageous for estimating fibre orientations for two reasons: first, it leads to a boost in DW signal in the transverse plane of the fibre. Second, it stretches out the shape of the measured diffusion profile, which improves the contrast between DW orientations. This is especially beneficial for resolving crossing fibres, as this contrast is essential to discriminate between different fibre directions.

A filtered approach to neural tractography using the Watson directional function.

We propose a technique to simultaneously estimate the local fiber orientations and perform multi-fiber tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. Further, to overcome noise, many algorithms use a filter as a post-processing step to obtain a smooth trajectory. We formulate fiber tracking as causal estimation: at each step of tracing the fiber, the current estimate of the signal is guided by the previous. To do this, we model the signal as a discrete mixture of Watson directional functions and perform tractography within a filtering framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides an accurate estimate of the local structure at each point along the fiber. We choose the Watson function since it provides a compact representation of the signal parameterized by the principal diffusion direction and a scaling parameter describing anisotropy, and also allows analytic reconstruction of the oriented diffusion function from those parameters. Using a mixture of two and three components (corresponding to two-fiber and three-fiber models) we demonstrate in synthetic experiments that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments examine the corpus callosum and internal capsule and confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.

A modified damped Richardson–Lucy algorithm to reduce isotropic background effects in spherical deconvolution

Spherical deconvolution methods have been applied to diffusion MRI to improve diffusion tensor tractography results in brain regions with multiple fibre crossing. Recent developments, such as the introduction of non-negative constraints on the solution, allow a more accurate estimation of fibre orientations by reducing instability effects due to noise robustness. Standard convolution methods do not, however, adequately model the effects of partial volume from isotropic tissue, such as gray matter, or cerebrospinal fluid, which may degrade spherical deconvolution results. Here we use a newly developed spherical deconvolution algorithm based on an adaptive regularization (damped version of the Richardson–Lucy algorithm) to reduce isotropic partial volume effects. Results from both simulated and in vivo datasets show that, compared to a standard non-negative constrained algorithm, the damped Richardson–Lucy algorithm reduces spurious fibre orientations and preserves angular resolution of the main fibre orientations. These findings suggest that, in some brain regions, non-negative constraints alone may not be sufficient to reduce spurious fibre orientations. Considering both the speed of processing and the scan time required, this new method has the potential for better characterizing white matter anatomy and the integrity of pathological tissue.

Potential in reducing scan times of HARDI by accurate correction of the cross‐term in a hemispherical encoding scheme

To reduce the scan time of high angular resolution diffusion imaging (HARDI) by using the hemispherical encoding scheme with the cross-term correction. Unidirectional and 45 degrees crossing phantoms were built to evaluate the accuracy of the fiber orientation estimation when using a hemispherical encoding scheme with and without the cross-term correction. The q-ball imaging using the spherical harmonic basis was adopted for estimation of fiber orientation. By recalculating the diffusion gradient strengths, we make the actual b value in all directions equal to the expected b value for the correction of the cross-term. The separation angles measured on the crossing phantom are 42.67 degrees +/- 1.50 degrees , 42.75 degrees +/- 2.10 degrees , and 42.93 degrees +/- 2.78 degrees for cross-term-free results, for the results from the hemispherical encoding scheme with and without the cross-term correction. The angular errors in mapping the unidirectional phantom are 1.87 degrees -2.29 degrees and 4.01 degrees -4.92 degrees for the results using the hemispherical encoding scheme with and without correcting for the cross-term at different b values. Using the hemispherical encoding scheme with the cross-term correction can potentially halve the scan time of HARDI and obtain accurate fiber orientation estimation simultaneously. This will be helpful in the clinical application of HARDI.

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.

Variational inference of the fiber orientation density using diffusion MR imaging

Diffusion MR imaging has enabled the in vivo exploration of the connectional architecture in human brain. This method particularly reveals the complex system of long-range nerve fibers that integrate the functionally distinct areas of the cerebral cortex. Since the fibers are not directly observed but the diffusion process of water molecules in the underlying material, a forward model is established that maps the microgeometry of nervous tissue onto the diffusion-weighted signals. This article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel Hilbert space, thereby generalizing previous approaches that perform a truncated Fourier analysis on the sphere. The specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function, namely its normalization and non-negativity. A Gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters, here the high-frequency content in the density function and the noise variance of the MR observations. In addition, we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology. The novel approach, which uncovers the fiber orientation field of white matter, is demonstrated with diffusion-weighted data sets featuring high angular resolution.

Resolving crossing fibres using constrained spherical deconvolution: Validation using diffusion-weighted imaging phantom data

Diffusion-weighted imaging can potentially be used to infer the connectivity of the human brain in vivo using fibre-tracking techniques, and is therefore of great interest to neuroscientists and clinicians. A key requirement for fibre tracking is the accurate estimation of white matter fibre orientations within each imaging voxel. The diffusion tensor model, which is widely used for this purpose, has been shown to be inadequate in crossing fibre regions. A number of approaches have recently been proposed to address this issue, based on high angular resolution diffusion-weighted imaging (HARDI) data. In this study, an experimental model of crossing fibres, consisting of water-filled plastic capillaries, is used to thoroughly assess three such techniques: constrained spherical deconvolution (CSD), super-resolved CSD (super-CSD) and Q-ball imaging (QBI). HARDI data were acquired over a range of crossing angles and b-values, from which fibre orientations were computed using each technique. All techniques were capable of resolving the two fibre populations down to a crossing angle of 45°, and down to 30° for super-CSD. A bias was observed in the fibre orientations estimated by QBI for crossing angles other than 90°, consistent with previous simulation results. Finally, for a 45° crossing, the minimum b-value required to resolve the fibre orientations was 4000s/mm2 for QBI, 2000s/mm2 for CSD, and 1000s/mm2 for super-CSD. The quality of estimation of fibre orientations may profoundly affect fibre tracking attempts, and the results presented provide important additional information regarding performance characteristics of well-known methods.

Quantitative Diffusion Tensor Analysis Using Multiple Tensor Ellipsoids Model and Tensor Field Interpolation at Fiber Crossing

In regions of intravoxel fiber crossing, the single-tensor model does not provide accurate results. The previously published models could resolve this issue but needed a long scan time and long computational time. This article aims to present the new model, which uses interpolated diffusion tensor orientations and requires the estimation of fewer parameters than the previously published model, where all parameters for the two diffusion ellipsoids have to be estimated. Fiber orientation information was reconstructed by using the radial basis function-based interpolation technique from tensor information in given seed regions of interest. Synthetic phantom data were generated, and the proposed method was compared with the conventional two-ellipsoid method. Data from one normal volunteer were analyzed to determine the effectiveness of the proposed method. The number of parameters to be estimated could be reduced by using the estimated fiber orientation information so that diffusion parameter calculation at fiber crossing becomes robust. The human study showed that fractional anisotropy (FA) values estimated by the proposed method (FA = 0.67 for the corpus callosum, 0.65 for the corticospinal tract) were significantly higher than that estimated by the standard single-tensor-based method (FA = 0.35), and the estimated FA value showed good agreement with the FA value in the adjacent fiber bundle. The proposed radial basis function-based technique could reconstruct diffusion properties at the fiber-crossing volume from sparse sampling of high angular diffusion weighted images.

Theoretical Examination of the Methods for Estimating Fiber Orientation Distribution and Length Estimation from the Surface of a Short Fiber Reinforced Composite

In this study, the method of estimating fiber orientation distribution in a short fiber reinforced composite is numerically examined. Accuracy of fiber length obtained by the simple theory is also examined. For this purpose, packing of the fibers in space is simulated by a computer. The fibers are packed on a cubic. Position and orientation are given to a candidate fiber by random numbers. The candidate fiber is arranged in the cubic. If the fiber does not overlap other fibers already existing, the candidate fiber is adopted as a regular fiber in the composite. This procedure is repeated until becoming prescribed fiber volume fraction. The short fiber reinforced composite made on the computer is sliced to prescribed thickness. The sliced composite is observed, and orientation of fibers is measured from the composite surface. Fiber orientation distribution is calculated from the data obtained by the measurement. The estimated distribution is well near actual distribution in the composite. Furthermore, the average fiber length is estimated by substituting the number of the fiber tips counted from the composite surface to the simple theory. The estimated fiber length is about 8% to 20% larger than the actual fiber length.

Just how much data need to be collected for reliable bootstrap DT‐MRI?

Diffusion tensor MRI (DT-MRI) can provide estimates of fiber orientation derived from the orientational dependence of the diffusivity of water molecules, enabling the reconstruction of white matter fiber pathways using tractography methods. However, noise arising from various sources can introduce uncertainty into the estimates of the elements of the diffusion tensor, resulting in errors in fiber orientation estimates such that tractography reconstructions of fiber pathways potentially can be imprecise and inaccurate. Recently, attempts have been made to characterize the uncertainty in DT-MRI-derived parameters using the bootstrap method; however, several questions remain open regarding the number of repeat measurements and bootstraps required to accurately and precisely reconstruct the probability distributions of the DT-MRI parameters. This study investigates the accuracy and precision of the bootstrap method for characterizing distributions of DT-MRI parameters. A number of experimental bootstrap designs and sampling schemes containing different numbers of isotropically distributed gradient vectors are considered, using an idealized system where the true variability in each parameter is known. This study demonstrates that for most DT-MRI experiments, robust results will be obtained if the minimum number of bootstraps is approximately 500, and that at least five repeat samples of each diffusion-weighted intensity should be used for bootstrapping.

Measurement of fiber orientation distributions using high angular resolution diffusion imaging

High angular resolution measurements of diffusion are used to estimate the angular distribution and diffusion anisotropy of fibers in a voxel. A simple, axially symmetric model of diffusion in white matter fibers is used to relate diffusion measurements to fiber properties. The new technique is called fiber orientation estimated using continuous axially symmetric tensors (FORECAST). It is tested using both numerical simulation and in vivo measurements. The new method agrees with other methods in voxels containing single fibers, but resolves crossing fibers better, at least at the level of diffusion weighting used in this study (tr(b) = 1480 s/mm2). The simplifying assumptions of the model are tested by comparison with the "model-free" q-ball analysis of in vivo data and the results are shown to be in good agreement. The new method addresses the problem of partial volume averaging in diffusion tensor imaging and provides a basis for more reliable estimates of fiber orientation and fractional anisotropy.

Simultaneous estimation of muscle fibre conduction velocity and muscle fibre orientation using 2D multichannel surface electromyogram

The paper presents a new approach for simultaneous estimation of muscle fibre conduction velocity (MFCV) and muscle fibre orientation (MFO) for motor units (MUs) in two-dimensional (2D) multichannel surface electromyography recordings. This is an important tool for detecting changes and abnormalities in muscle function and structure. In addition, simultaneous estimation of MFO and MFCV avoids the necessity of manual electrode alignment. The proposed method detected propagating MU action potentials (MUAPs) in a running time window as moving components in amplitude maps. Thereafter, estimations were obtained by fitting a three-dimensional function to these maps. The performance was evaluated using synthetic MU signals at 10 dB SNR and authentic biceps brachii measurements. Results demonstrated MFCV and MFO estimates with standard deviations of less than 0.05 m s(-1) and 1 degrees for simulated signals, and less than 0.2 m s(-1) and 4 degrees for experimental data. However, standard deviations as low as 0.12 m s(-1) and 1.6 degrees from real signals were demonstrated. It was concluded that the method performs as well as, or better than, linear array multichannel methods when individual propagating MUAPs can be identified, even if electrodes are not aligned with fibre direction.

Estimation of orientation characteristic of fibrous material

A new statistical method for estimating the orientation distribution of fibres in a fibre process is suggested where the process is observed in the form of a degraded digital greyscale image. The method is based on line transect sampling of the image in a few fixed directions. A well-known method based on stereology is available if the intersections between the transects and fibres can be counted. We extend this to the case where, instead of the intersection points, only scaled variograms of grey levels along the transects are observed. The nonlinear estimation equations for a parametric orientation distribution as well as a numerical algorithm are given. The method is illustrated by a real-world example and simulated examples where the elliptic orientation distribution is applied. In its simplicity, the new approach is intended for industrial on-line estimation of fibre orientation in disordered fibrous materials.

Estimation of orientation characteristic of fibrous material

A new statistical method for estimating the orientation distribution of fibres in a fibre process is suggested where the process is observed in the form of a degraded digital greyscale image. The method is based on line transect sampling of the image in a few fixed directions. A well-known method based on stereology is available if the intersections between the transects and fibres can be counted. We extend this to the case where, instead of the intersection points, only scaled variograms of grey levels along the transects are observed. The nonlinear estimation equations for a parametric orientation distribution as well as a numerical algorithm are given. The method is illustrated by a real-world example and simulated examples where the elliptic orientation distribution is applied. In its simplicity, the new approach is intended for industrial on-line estimation of fibre orientation in disordered fibrous materials.

Paced activation mapping reveals organization of myocardial fibers: a simulation study.

A three-dimensional bidomain model of a block section of both the right and left ventricular walls that included rotational anisotropy and fiber curvature was used to investigate potential distributions generated during paced activation mapping. Unlike previous large-scale tissue models, the extracellular stimulus was included. The model was used to test the hypothesis that information about the underlying tissue structure (surface fiber angle gradients, amount of fiber rotation per unit depth, and anisotropy) can be extracted from surface potential distributions during stimulation. Results from distributions during stimulation were compared to those obtained using the distributions during activation. To better correlate results to possible experimental measurements, the analysis was performed using a 21 X 21 grid of "electrode" sites, each separated by 1 mm. Fiber orientation was estimated from the surface data by: (1) curve-fitting the elliptical shape of the epicardial potential distribution during stimulation; (2) identifying the location of the potential maxima leading the wavefront during early activation; and (3) for epicardial stimuli, curve-fitting the elliptical shape of the activation isochrones. Results show that surface potential distributions from the stimulus can be used to estimate fiber orientation; however, the accuracy of the reconstruction is highly dependent on the amount of fiber rotation per unit depth. Extracellular potential data during and after stimulation is shown to reflect the organization of myocardial fibers and, as such, could be used to characterize the three-dimensional anisotropic electrical properties in situ.