Atlas-based fiber bundle segmentation using principal diffusion directions and spherical harmonic coefficients

PurposeTo develop an automatic atlas-based method for segmentation of fiber bundles using High Angular Resolution Diffusion Imaging (HARDI) data.HypothesisQuantitative evaluation of diffusion characteristics inside specific fiber bundles provides new insights into disease developments, evolutions, therapy effects, and surgical interventions.BackgroundMost of previous segmentation methods use similarity measures and strategies that do not lead to accurate segmentation results. They also suffer from subjectivity of initial seeds and regions of interest (ROI) defined by operator.Materials and methodsWe propose a novel method that uses Spherical Harmonic Coefficients (SHC) of HARDI diffusion signals to compute Orientation Distribution Function (ODF) and to extract Principal Diffusion Directions (PDDs). The proposed method selects most collinear PDD of neighbors of each voxel. Then, based on SHC and selected PDD, a similarity measure is proposed and used as a speed function in the level set framework that segments fiber bundles. To automate the process, an atlas-based method is used to select initial seeds for fiber bundles. To generate data for evaluation of the proposed method, an artificial pattern consisting of three crossing bundles intersected by a circular bundle is created. Also, two normal controls are imaged by two different HARDI protocols.ResultsSegmentation results for different fiber bundles in simulated data and normal control data are presented. Influence of threshold selection on the proposed segmentation method is evaluated using Dice coefficient. Also, effect of increasing the number of gradient directions on accuracy of extracted PDDs is evaluated.ConclusionThe proposed segmentation method has advantages over previous methods especially those that use similarity measures based on diffusion tensor imaging (DTI) data. These advantages are achieved by proper propagation of a hyper-surface in fiber crossing areas without making assumptions about diffusivity profile and selection of initial seeds or ROI.     

Directional functions for orientation distribution estimation

Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation.Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a “hybrid” framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF’s.     

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.     

Spherical wavelet transform for ODF sharpening

The choice of local HARDI reconstruction technique is crucial for discerning multiple fiber orientations, which is itself of substantial importance for tractography, and reliable and accurate assessment of white matter fiber geometry. Due to the complexity of the diffusion process and its milieu, distinct diffusion compartments can have different frequency signatures, making the HARDI signal spread over multiple frequency bands. Therefore, we put forth the idea of multiscale analysis with localized basis functions, ensuring that different frequency ranges are probed. With the aim of truthful recovery of fiber orientations, we reconstruct the orientation distribution function (ODF), by incorporating a spherical wavelet transform (SWT) into the Funk–Radon transform. First, we apply and validate our proposed SWT method on real physical phantoms emulating fiber bundle crossings. Then, we apply the SWT method to a real brain data set. The analysis of the real data set suggests that different angular frequencies may capture different information, thus stressing the importance of multiscale analysis. For both phantom and real data, we compare the SWT reconstruction with state-of-the-art q-ball imaging and spherical deconvolution reconstruction methods. We demonstrate the algorithm efficiency in diffusion ODF denoising and sharpening that is of particular importance for applications to fiber tracking (especially for probabilistic approaches), and brain connectome mapping. Also, the algorithm results in considerable data compression that could prove beneficial in applications to fiber bundle segmentation, and for HARDI based white matter morphometry methods.     

Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

Diffusion-weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers. The diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel. However, this model has been shown to fail in regions containing several fiber populations with distinct orientations. A number of alternative models have been suggested, such as multiple tensor fitting, q-space, and Q-ball imaging. However, each of these has inherent limitations. In this study, we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion-weighted MR data without the need for prior assumptions regarding the number of fiber populations present. We assume that all white matter fiber bundles in the brain share identical diffusion characteristics, thus implicitly assigning any differences in diffusion anisotropy to partial volume effects. The diffusion-weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function (the diffusion-weighted attenuation profile for a typical fiber bundle) with the fiber orientation density function (ODF). The fiber ODF (the distribution of fiber orientations within the voxel) can therefore be obtained using spherical deconvolution. The properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1.5-T clinical scanner. The technique can recover the fiber ODF in regions of multiple fiber crossing and holds promise for applications such as tractography.     

A new methodology for the estimation of fiber populations in the white matter of the brain with the Funk–Radon transform

The Funk–Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model. The FRT consists in the integration of the attenuation signal, sampled by the MRI scanner on the unit sphere, along equators orthogonal to the directions of interest. It is easily proved that this calculation is equivalent to the integration of the diffusion propagator along such directions, although a characteristic blurring with a Bessel kernel is introduced. Under a different point of view, the FRT can be seen as an efficient way to compute the angular part of the integral of the attenuation signal in the plane orthogonal to each direction of the diffusion propagator. In this paper, Stoke's theorem is used to prove that the FRT can in fact be used to compute accurate estimates of the true integrals defining the functions of interest in HARDI, keeping the diffusion model as little restrictive as possible. Varying the assumptions on the attenuation signal, we derive new estimators of fiber orientations, generalizing both Q-Balls and the OPDT. Extensive experiments with both synthetic and real data have been intended to show that the new techniques improve existing ones in many situations.     

Optimal real-time Q-ball imaging using regularized Kalman filtering with incremental orientation sets

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation. Since its inception, Diffusion MRI has expanded considerably to include a number of variations such as diffusion tensor imaging (DTI), diffusion spectrum imaging (DSI) and Q-ball imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real-time during the repetition time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace–Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace–Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard offline processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. This work enables a clinician to start an acquisition with just the minimum number of gradient directions and an initial estimate of the orientation distribution functions (ODF) and then the next gradient directions and ODF estimates can be recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal ODF estimates. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and real-time fiber tracking and connectivity mapping.     

White matter atlas generation using HARDI based automated parcellation

Most diffusion imaging studies have used subject registration to an atlas space for enhanced quantification of anatomy. However, standard diffusion tensor atlases lack information in regions of fiber crossing and are based on adult anatomy. The degree of error associated with applying these atlases to studies of children for example has not yet been estimated but may lead to suboptimal results. This paper describes a novel technique for generating population-specific high angular resolution diffusion imaging (HARDI)-based atlases consisting of labeled regions of homogenous white matter. Our approach uses a fiber orientation distribution (FOD) diffusion model and a data driven clustering algorithm. White matter regional labeling is achieved by our automated data driven clustering algorithm that has the potential to delineate white matter regions based on fiber complexity and orientation. The advantage of such an atlas is that it is study specific and more comprehensive in describing regions of white matter homogeneity as compared to standard anatomical atlases. We have applied this state of the art technique to a dataset consisting of adolescent and preadolescent children, creating one of the first examples of a HARDI-based atlas, thereby establishing the feasibility of the atlas creation framework. The white matter regions generated by our automated clustering algorithm have lower FOD variance than when compared to the regions created from a standard anatomical atlas.     

SPHERE: SPherical Harmonic Elastic REgistration of HARDI data

In contrast to the more common Diffusion Tensor Imaging (DTI), High Angular Resolution Diffusion Imaging (HARDI) allows superior delineation of angular microstructures of brain white matter, and makes possible multiple-fiber modeling of each voxel for better characterization of brain connectivity. However, the complex orientation information afforded by HARDI makes registration of HARDI images more complicated than scalar images. In particular, the question of how much orientation information is needed for satisfactory alignment has not been sufficiently addressed. Low order orientation representation is generally more robust than high order representation, although the latter provides more information for correct alignment of fiber pathways. However, high order representation, when na?vely utilized, might not necessarily be conducive to improving registration accuracy since similar structures with significant orientation differences prior to proper alignment might be mistakenly taken as non-matching structures. We present in this paper a HARDI registration algorithm, called SPherical Harmonic Elastic REgistration (SPHERE), which in a principled means hierarchically extracts orientation information from HARDI data for structural alignment. The image volumes are first registered using robust, relatively direction invariant features derived from the Orientation Distribution Function (ODF), and the alignment is then further refined using spherical harmonic (SH) representation with gradually increasing orders. This progression from non-directional, single-directional to multi-directional representation provides a systematic means of extracting directional information given by diffusion-weighted imaging. Coupled with a template-subject-consistent soft-correspondence-matching scheme, this approach allows robust and accurate alignment of HARDI data. Experimental results show marked increase in accuracy over a state-of-the-art DTI registration algorithm.     

Flow-based fiber tracking with diffusion tensor and q-ball data: validation and comparison to principal diffusion direction techniques

In this study, we evaluate the performance of a flow-based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity. We introduce a novel speed function for surface evolution that is derived from either diffusion tensor (DT) data, high angular resolution diffusion (HARD) data, or a combined DT-HARD hybrid approach. We use the model-free q-ball imaging (QBI) approach for HARD reconstruction. The anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts, noise, and subvoxel partial volume averaging of fiber directions. The surface evolution approach, using the full diffusion tensor as opposed to the principal diffusion direction (PDD) only, is compared to PDD-based line propagation fiber tracking. Additionally, DT reconstruction is compared to HARD reconstruction for fiber tracking, both using surface evolution. We show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions, which can be difficult to map with PDD-based methods. We then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly.     

Hybrid diffusion imaging

Diffusion measurements in the human central nervous system are complex to characterize and a broad spectrum of methods have been proposed. In this study, a comprehensive diffusion encoding and analysis approach, hybrid diffusion imaging (HYDI), is described. The HYDI encoding scheme is composed of multiple concentric "shells" of constant diffusion weighting, which may be used to characterize the signal behavior with low, moderate and high diffusion weighting. HYDI facilitates the application of multiple data analyses strategies including diffusion tensor imaging (DTI), multi-exponential diffusion measurements, diffusion spectrum imaging (DSI) and q-ball imaging (QBI). These different analysis strategies may provide complementary information. DTI measures (mean diffusivity and fractional anisotropy) may be estimated from either data in the inner shells or the entire HYDI data. Fast and slow diffusivities were estimated using a nonlinear least squares bi-exponential fit on geometric means of the HYDI shells. DSI measurements from the entire HYDI data yield empirical model-independent diffusion information and are well-suited for characterizing tissue regions with complex diffusion behavior. DSI measurements were characterized using the zero displacement probability and the mean-squared displacement. The outermost HYDI shell was analyzed using QBI analysis to estimate the orientation distribution function (ODF), which is useful for characterizing the directions of multiple fiber groups within a voxel. In this study, an HYDI encoding scheme with 102 diffusion-weighted measurements was obtained over most of the human cerebrum in under 30 min.     

Diffusion-regularized susceptibility tensor imaging (DRSTI) of tissue microstructures in the human brain

Susceptibility tensor imaging (STI) has been proposed as an alternative to diffusion tensor imaging (DTI) for non-invasive in vivo characterization of brain tissue microstructure and white matter fiber architecture, potentially benefitting from its high spatial resolution. In spite of different biophysical mechanisms, animal studies have demonstrated white matter fiber directions measured using STI to be reasonably consistent with those from diffusion tensor imaging (DTI). However, human brain STI is hampered by its requirement of acquiring data at more than 10 head rotations and a complicated processing pipeline. In this paper, we propose a diffusion-regularized STI method (DRSTI) that employs a tensor spectral decomposition constraint to regularize the STI solution using the fiber directions estimated by DTI as a priori. We then explore the high-resolution DRSTI with MR phase images acquired at only 6 head orientations. Compared to other STI approaches, the DRSTI generated susceptibility tensor components, mean magnetic susceptibility (MMS), magnetic susceptibility anisotropy (MSA) and fiber direction maps with fewer artifacts, especially in regions with large susceptibility variations, and with less erroneous quantifications. In addition, the DRSTI method allows us to distinguish more structural features that could not be identified in DTI, especially in deep gray matters. DRSTI enables a more accurate susceptibility tensor estimation with a reduced number of sampling orientations, and achieves better tracking of fiber pathways than previous STI attempts on in vivo human brain.     

Estimation of individual axon bundle properties by a Multi-Resolution Discrete-Search method

A stable, accurate and robust-to-noise method for the estimation of the intra-voxel bundle-wise diffusion properties for diffusion-weighted magnetic resonance imaging is presented. The proposed method overcomes some of the limitations of most of the multi-fiber algorithms in the literature and extends them to estimate the diffusion profiles, improving the estimation of the intra-voxel geometry at challenging microstructure configurations, that is to say: relatively small crossing angles, different voxel-wise anisotropic diffusion profiles and low SNR. The proposed methodology is based on four key novel ideas: (i) A Multi-Resolution Discrete-Search determines the orientation of the fiber bundles accurately and naturally constrains the sparsity on the recovered solutions; (ii) the determination of the number of fiber bundles using the F-test combined with a Rician bias correction; (iii) a Simultaneous Denoising and Fitting procedure that exploits the spatial redundancy of the axon bundles to achieve robustness with respect to noise; and (iv) a general framework for the estimation of the axial and radial diffusivity parameters independently for each voxel. A new useful evaluation metric is also proposed, which combines the information of the success rate in the estimated number of bundles and the angular error, avoiding in this way, some of the limitations these metrics have individually. A novel methodology for the evaluation of the methods on in-vivo data is also proposed. This work presents an extensive evaluation: the proposed methodology has been tested on state-of-the-art biophysical synthetic data for a variety of conditions, on the challenging spatially coherent phantom used on the HARDI reconstruction Challenge 2012, and on the recently released in-vivo MASSIVE data-set. Our results present significant improvements on the estimation of the number and orientation of the fiber bundles over the Spherical Deconvolution algorithm for multi-shell data, which is one of the most widely used multi-fiber algorithm. The results also show that, by the voxel-wise estimation of the diffusion profiles, the axial and radial diffusivity parameters are robustly estimated, being this essential for a better understanding of the individual bundle diffusion properties at challenging structural configurations.     

A polynomial approach for extracting the extrema of a spherical function and its application in diffusion MRI

Antipodally symmetric spherical functions play a pivotal role in diffusion MRI in representing sub-voxel-resolution microstructural information of the underlying tissue. This information is described by the geometry of the spherical function. In this paper we propose a method to automatically compute all the extrema of a spherical function. We then classify the extrema as maxima, minima and saddle-points to identify the maxima. We take advantage of the fact that a spherical function can be described equivalently in the spherical harmonic (SH) basis, in the symmetric tensor (ST) basis constrained to the sphere, and in the homogeneous polynomial (HP) basis constrained to the sphere. We extract the extrema of the spherical function by computing the stationary points of its constrained HP representation. Instead of using traditional optimization approaches, which are inherently local and require exhaustive search or re-initializations to locate multiple extrema, we use a novel polynomial system solver which analytically brackets all the extrema and refines them numerically, thus missing none and achieving high precision.To illustrate our approach we consider the Orientation Distribution Function (ODF). In diffusion MRI the ODF is a spherical function which represents a state-of-the-art reconstruction algorithm whose maxima are aligned with the dominant fiber bundles. It is, therefore, vital to correctly compute these maxima to detect the fiber bundle directions. To demonstrate the potential of the proposed polynomial approach we compute the extrema of the ODF to extract all its maxima. This polynomial approach is, however, not dependent on the ODF and the framework presented in this paper can be applied to any spherical function described in either the SH basis, ST basis or the HP basis.     

NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain

This paper introduces neurite orientation dispersion and density imaging (NODDI), a practical diffusion MRI technique for estimating the microstructural complexity of dendrites and axons in vivo on clinical MRI scanners. Such indices of neurites relate more directly to and provide more specific markers of brain tissue microstructure than standard indices from diffusion tensor imaging, such as fractional anisotropy (FA). Mapping these indices over the whole brain on clinical scanners presents new opportunities for understanding brain development and disorders. The proposed technique enables such mapping by combining a three-compartment tissue model with a two-shell high-angular-resolution diffusion imaging (HARDI) protocol optimized for clinical feasibility. An index of orientation dispersion is defined to characterize angular variation of neurites. We evaluate the method both in simulation and on a live human brain using a clinical 3T scanner. Results demonstrate that NODDI provides sensible neurite density and orientation dispersion estimates, thereby disentangling two key contributing factors to FA and enabling the analysis of each factor individually. We additionally show that while orientation dispersion can be estimated with just a single HARDI shell, neurite density requires at least two shells and can be estimated more accurately with the optimized two-shell protocol than with alternative two-shell protocols. The optimized protocol takes about 30 min to acquire, making it feasible for inclusion in a typical clinical setting. We further show that sampling fewer orientations in each shell can reduce the acquisition time to just 10 min with minimal impact on the accuracy of the estimates. This demonstrates the feasibility of NODDI even for the most time-sensitive clinical applications, such as neonatal and dementia imaging.     

Bootstrap white matter tractography (BOOT-TRAC)

White matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging (DTI) data. Sources of experimental noise may induce errors in the measured fiber directions, which will reduce the accuracy of the estimated white matter trajectories. In this study, a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results. Prior studies have derived models of tractography error using the signal-to-noise ratio (SNR) and diffusion anisotropy of the DTI data. Tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident. White matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions. The approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions.     

Effects of image distortions originating from susceptibility variations and concomitant fields on diffusion MRI tractography results

In this work we investigate the effects of echo planar imaging (EPI) distortions on diffusion tensor imaging (DTI) based fiber tractography results. We propose a simple experimental framework that would enable assessing the effects of EPI distortions on the accuracy and reproducibility of fiber tractography from a pilot study on a few subjects. We compare trajectories computed from two diffusion datasets collected on each subject that are identical except for the orientation of phase encode direction, either right-left (RL) or anterior-posterior (AP). We define metrics to assess potential discrepancies between RL and AP trajectories in association, commissural, and projection pathways. Results from measurements on a 3 Tesla clinical scanner indicated that the effects of EPI distortions on computed fiber trajectories are statistically significant and large in magnitude, potentially leading to erroneous inferences about brain connectivity. The correction of EPI distortion using an image-based registration approach showed a significant improvement in tract consistency and accuracy. Although obtained in the context of a DTI experiment, our findings are generally applicable to all EPI-based diffusion MRI tractography investigations, including high angular resolution (HARDI) methods. On the basis of our findings, we recommend adding an EPI distortion correction step to the diffusion MRI processing pipeline if the output is to be used for fiber tractography.     

DWI filtering using joint information for DTI and HARDI

The filtering of the Diffusion Weighted Images (DWI) prior to the estimation of the diffusion tensor or other fiber Orientation Distribution Functions (ODF) has been proved to be of paramount importance in the recent literature. More precisely, it has been evidenced that the estimation of the diffusion tensor without a previous filtering stage induces errors which cannot be recovered by further regularization of the tensor field. A number of approaches have been intended to overcome this problem, most of them based on the restoration of each DWI gradient image separately. In this paper we propose a methodology to take advantage of the joint information in the DWI volumes, i.e., the sum of the information given by all DWI channels plus the correlations between them. This way, all the gradient images are filtered together exploiting the first and second order information they share. We adapt this methodology to two filters, namely the Linear Minimum Mean Squared Error (LMMSE) and the Unbiased Non-Local Means (UNLM). These new filters are tested over a wide variety of synthetic and real data showing the convenience of the new approach, especially for High Angular Resolution Diffusion Imaging (HARDI). Among the techniques presented, the joint LMMSE is proved a very attractive approach, since it shows an accuracy similar to UNLM (or even better in some situations) with a much lighter computational load.     

DTI segmentation via the combined analysis of connectivity maps and tensor distances

We describe a novel approach to extract the neural tracts of interest from a diffusion tensor image (DTI). Compared to standard streamline tractography, existing probabilistic methods are able to capture fiber paths that deviate from the main tensor diffusion directions. At the same time, tensor clustering methods are able to more precisely delimit the border of the bundle. To the best of our knowledge, we propose the first algorithm which combines the advantages supplied by probabilistic and tensor clustering approaches. The algorithm includes a post-processing step to limit partial-volume related segmentation errors. We extensively test the accuracy of our algorithm on different configurations of a DTI software phantom for which we systematically vary the image noise, the number of gradients, the geometry of the fiber paths and the angle between adjacent and crossing fiber bundles. The reproducibility of the algorithm is supported by the segmentation of the corticospinal tract of nine patients. Additional segmentations of the corticospinal tract, the arcuate fasciculus, and the optic radiations are in accordance with anatomical knowledge. The required user interaction is comparable to that of streamline tractography, which allows for an uncomplicated integration of the algorithm into the clinical routine.     

Axon diameter mapping in the presence of orientation dispersion with diffusion MRI

Direct measurement of tissue microstructure with diffusion MRI offers a new class of markers, such as axon diameters, that give more specific information about tissue than measures derived from diffusion tensor imaging. The existing techniques of this kind assume a single axon orientation in the tissue model, which may be a reasonable approximation only for the most coherently oriented brain white matter, such as the corpus callosum. For most other areas, orientation dispersion is not negligible and, if unaccounted for, leads to overestimation of the axon diameters, prohibiting their accurate mapping over the whole brain. Here we propose a new model that captures the effect of orientation dispersion explicitly. A numerical scheme is developed to compute the diffusion signal prescribed by the proposed model efficiently, which supports the simultaneous estimation of the axon diameter and orientation dispersion. Synthetic data experiments demonstrate that the new model provides an axon diameter index that is robust to the presence of orientation dispersion. Results on in vivo human data show reduced axon diameter index and better agreement with histology compared to previous methods suggesting improvements in the axon diameter estimate.