An Optimal Transport-Based Restoration Method for Q-Ball Imaging

Q-Ball imaging (QBI) is a successful and widely used high angular resolution diffusion imaging (HARDI) technique which can compute orientation distribution function (ODF). This technique only needs single shell HARDI data and does not require any assumption about the diffusion signal outside the sampling sphere. However the originally proposed ODF (the radial project of the probability density function (PDF)) is not a true ODF. In contrast the marginal ODF with solid angle consideration, represents a true ODF with a correct probabilistic interpretation. In this paper a novel model-free and single-shell HARDI method for analytical reconstruction of the marginal ODF based on Funk-Radon transform (FRT) is proposed. In other words, a transformation of QBI for marginal ODF is proposed in this paper. While there's also a proportional factor introduced by FRT. Its complexity is comparable to that of the original QBI. Finally the present paper verify the algorithm and show the improved result of my method compared to the original QBI on synthetic data, biological phantom data and real human brain data.

High angular resolution diffusion imaging (HARDI) improves upon more traditional diffusion tensor imaging (DTI) in its ability to resolve the orientations of crossing and branching neural fibre tracts. The HARDI signals are measured over a spherical shell in q-space, and are usually used as an input to q-ball imaging (QBI) which allows estimation of the diffusion orientation distribution functions (ODFs) associated with a given region-of interest. Unfortunately, the partial nature of single-shell sampling imposes limits on the estimation accuracy. As a result, the recovered ODFs may not possess sufficient resolution to reveal the orientations of fibre tracts which cross each other at acute angles. A possible solution to the problem of limited resolution of QBI is provided by means of spherical deconvolution, a particular instance of which is sparse deconvolution. However, while capable of yielding high-resolution reconstructions over spacial locations corresponding to white matter, such methods tend to become unstable when applied to anatomical regions with a substantial content of isotropic diffusion. To resolve this problem, a new deconvolution approach is proposed in this paper. Apart from being uniformly stable across the whole brain, the proposed method allows one to quantify the isotropic component of cerebral diffusion, which is known to be a useful diagnostic measure by itself.

We consider the problem of tracking white matter fibers in high angular resolution diffusion imaging (HARDI) data while simultaneously estimating the local fiber orientation profile. Prior work showed that an unscented Kalman filter (UKF) can be used for this problem, yet existing algorithms employ parametric mixture models to represent water diffusion and to define the state space. To address this restrictive model dependency, we propose to extend the UKF to HARDI data modeled by orientation distribution functions (ODFs), a more generic diffusion model. We consider the spherical harmonic representation of the HARDI signal as the state, enforce nonnegativity of the ODFs, and perform tractography using the directions at which the ODFs attain their peaks. In simulations, our method outperforms filtered two-tensor tractography at different levels of noise by achieving a reduction in mean Chamfer error of 0.05 to 0.27 voxels; it also produced in vivo fiber tracking that is consistent with the neuroanatomy.

Geodesic regression on orientation distribution functions with its application to an aging study

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.

High angular resolution diffusion imaging (HARDI) permits the computation of water molecule displacement probabilities over the sphere. This probability is often referred to as the orientation distribution function (ODF). In this paper we present a novel model for representing this diffusion ODF namely, a mixture of von Mises-Fisher (vMF) distributions. Our model is compact in that it requires very few parameters to represent complicated ODF geometries which occur specifically in the presence of heterogeneous nerve fiber orientations. We present a Riemannian geometric framework for computing intrinsic distances (in closed-form) and for performing interpolation between ODFs represented by vMF mixtures. We also present closed-form equations for entropy and variance based anisotropy measures that are then computed and illustrated for real HARDI data from a rat brain.

We introduce a new framework based on Riemann-Finsler geometry for the analysis of 3D images with spherical codomain, more precisely, for which each voxel contains a set of directional measurements represented as samples on the unit sphere (antipodal points identified). The application we consider here is in medical imaging, notably in High Angular Resolution Diffusion Imaging (HARDI), but the methods are general and can be applied also in other contexts, such as material science, et cetera, whenever direction dependent quantities are relevant. Finding neural axons in human brain white matter is of significant importance in understanding human neurophysiology, and the possibility to extract them from a HARDI image has a potentially major impact on clinical practice, such as in neuronavigation, deep brain stimulation, et cetera. In this paper we introduce a novel fiber tracking method which is a generalization of the streamline tracking used extensively in Diffusion Tensor Imaging (DTI). This method is capable of finding intersecting fibers in voxels with complex diffusion profiles, and does not involve solving extrema of these profiles. We also introduce a single tensor representation for the orientation distribution function (ODF) to model the probability that a vector corresponds to a tangent of a fiber. The single tensor representation is chosen because it allows a natural choice of Finsler norm as well as regularization via the Laplace-Beltrami operator. In addition we define a new connectivity measure for HARDI-curves to filter the most prominent fiber candidates. We show some very promising results on both synthetic and real data.

The acquisition of high angular resolution diffusion MRI is particularly long and subject motion can become an issue. The orientation distribution function (ODF) can be reconstructed online incrementally from diffusion-weighted MRI with a Kalman filtering framework. This online reconstruction provides real-time feedback throughout the acquisition process. In this article, the Kalman filter is first adapted to the reconstruction of the ODF in constant solid angle. Then, a method called STAR (STatistical Analysis of Residuals) is presented and applied to the online detection of motion in high angular resolution diffusion images. Compared to existing techniques, this method is image based and is built on top of a Kalman filter. Therefore, it introduces no additional scan time and does not require additional hardware. The performance of STAR is tested on simulated and real data and compared to the classical generalized likelihood ratio test. Successful detection of small motion is reported (rotation under 2°) with no delay and robustness to noise.

High angular resolution diffusion imaging (HARDI) allows in vivo analysis of the white matter structure and connectivity. Based on orientation distribution functions (ODFs) that represent the directionality of water diffusion at each point in the brain, tractography methods can recover major axonal pathways. This enables tract-based analysis of fiber integrity and connectivity. For multi-subject comparisons, fibers may be clustered into bundles that are consistently found across subjects. To do this, we scanned 20 young adults with HARDI at 4 T. From the reconstructed ODFs, we performed whole-brain tractography with a novel Hough transform method. We then used measures of agreement between the extracted 3D curves and a co-registered probabilistic DTI atlas to select key pathways. Using median filtering and a shortest path graph search, we derived the maximum density path to compactly represent each tract in the population. With this tract-based method, we performed tract-based analysis of fractional anisotropy, and assessed how the chosen tractography algorithm influenced the results. The resulting method may expedite population-based statistical analysis of HARDI and DTI.

Diffusion tensor imaging (DTI) accurately delineates white matter pathways when the Gaussian model of diffusion is valid. However, DTI yields erroneous results when diffusion takes on a more complex distribution, as is the case in the brain when fiber tracts cross. High angular resolution diffusion imaging (HARDI) overcomes this limitation of DTI by more fully characterizing the angular dependence of intravoxel diffusion. Among the various HARDI methods that have been proposed, QBI offers advantages such as linearity, model independence, and relatively easy implementation. In this work, reconstruction of the q-ball orientation distribution function (ODF) is reformulated in terms of spherical harmonic basis functions, yielding an analytic solution with useful properties of a frequency domain representation. The harmonic basis is parsimonious for typical b-values, which enables the ODF to be synthesized from a relatively small number of noisy measurements and thus brings the technique closer to clinical feasibility from the standpoint of total imaging time. The proposed method is assessed using Monte Carlo computer simulations and compared with conventional q-ball reconstruction using spherical RBFs. In vivo results from 3T whole-brain HARDI of adult volunteers are also provided to verify the underlying mathematical theory.

Diffusion MRI provides important information about the brain white matter structures and has opened new avenues for neuroscience and translational research. However, acquisition time needed for advanced applications can still be a challenge in clinical settings. There is consequently a need to accelerate diffusion MRI acquisitions. A multi-task Bayesian compressive sensing (MT-BCS) framework is proposed to directly estimate the constant solid angle orientation distribution function (CSA-ODF) from under-sampled (i.e., accelerated image acquisition) multi-shell high angular resolution diffusion imaging (HARDI) datasets, and accurately recover HARDI data at higher resolution in q-space. The proposed MT-BCS approach exploits the spatial redundancy of the data by modeling the statistical relationships within groups (clusters) of diffusion signal. This framework also provides uncertainty estimates of the computed CSA-ODF and diffusion signal, directly computed from the compressive measurements. Experiments validating the proposed framework are performed using realistic multi-shell synthetic images and in vivo multi-shell high angular resolution HARDI datasets. Results indicate a practical reduction in the number of required diffusion volumes (q-space samples) by at least a factor of four to estimate the CSA-ODF from multi-shell data. This work presents, for the first time, a multi-task Bayesian compressive sensing approach to simultaneously estimate the full posterior of the CSA-ODF and diffusion-weighted volumes from multi-shell HARDI acquisitions. It demonstrates improvement of the quality of acquired datasets by means of CS de-noising, and accurate estimation of the CSA-ODF, as well as enables a reduction in the acquisition time by a factor of two to four, especially when "staggered" q-space sampling schemes are used. The proposed MT-BCS framework can naturally be combined with parallel MR imaging to further accelerate HARDI acquisitions.

High angular resolution diffusion imaging (HARDI) methods have enabled the reconstruction of complex spin diffusion profiles in central nervous system white matter through diffusion-weighted MRI. For recovery of the underlying fiber orientations, conventional spherical deconvolution techniques based on spherical harmonics typically have difficulty producing fiber orientation distributions (FODs) that simultaneously satisfy the physical constraints of being real, symmetric, and non-negative. In this work, we propose a novel approach for HARDI reconstruction that is guaranteed to generate FODs satisfying these constraints. By using a meshed representation of the unit sphere, we formulate the spherical deconvolution as a convex optimization problem and compute the solution using a projected gradient descent algorithm. Flexible regularization is also included in our method to allow for tuning the sharpness of the reconstructed FOD. In our experiments, we present simulated results to examine the effects of varying the regularization parameters, and we illustrate the robustness of our method by applying it to several biological data sets to reconstruct known white matter fiber geometry.

The study of neural connectivity has grown rapidly in the past decade. Revealing brain anatomical connection improves not only clinical measures but also cognition understanding. In order to achieve this goal, we have to track neural fiber pathways first. Aiming to estimate 3D fiber pathways more accurately from orientation distribution function (ODF) fields, we presented a novel tracking method based on nonuniform rational B-splines (NURBS) curve fitting. First, we constructed ODF fields from high angular resolution diffusion imaging (HARDI) datasets using diffusion orientation transform (DOT) method. Second, under the angular and length constraints, the consecutive diffusion directions were extracted along each fiber pathway starting from a seed voxel. Finally, after the coordinates of the control points and their corresponding weights were determined, NURBS curve fitting was employed to track fiber pathways. The performance of the proposal has been evaluated on the tractometer phantom and real brain datasets. Based on several measure metrics, the resulting fiber pathways show promising anatomic consistency.

Diffusion MRI (dMRI) is a unique imaging modality for in vivo delineation of the anatomical structure of white matter in the brain. In particular, high angular resolution diffusion imaging (HARDI) is a specific instance of dMRI which is known to excel in detection of multiple neural fibers within a single voxel. Unfortunately, the angular resolution of HARDI is known to be inversely proportional to SNR, which makes the problem of denoising of HARDI data be of particular practical importance. Since HARDI signals are effectively band-limited, denoising can be accomplished by means of linear filtering. However, the spatial dependency of diffusivity in brain tissue makes it impossible to find a single set of linear filter parameters which is optimal for all types of diffusion signals. Hence, adaptive filtering is required. In this paper, we propose a new type of non-local means (NLM) filtering which possesses the required adaptivity property. As opposed to similar methods in the field, however, the proposed NLM filtering is applied in the spherical domain of spatial orientations. Moreover, the filter uses an original definition of adaptive weights, which are designed to be invariant to both spatial rotations as well as to a particular sampling scheme in use. As well, we provide a detailed description of the proposed filtering procedure, its efficient implementation, as well as experimental results with synthetic data. We demonstrate that our filter has substantially better adaptivity as compared to a number of alternative methods.

Event Abstract Back to Event Technical and functional validations of High Angular Resolution Diffusion Imaging (HARDI)-MR tractography in paediatric epilepsy patients Sarah M. Barton1*, Joseph Y. Yang2, Wirginia Maixner2, A. Simon Harvey3, 4, Jeremy Freeman3, Richard Beare1, Marc Seal1, 4 and Vicki Anderson4, 5, 6 1 Murdoch Childrens Research Institute, Developmental Imaging, Australia 2 The Royal Children’s Hospital, Department of Neurosurgery, Australia 3 The Royal Children’s Hospital, Department of Neurology, Australia 4 The University of Melbourne, Department of Paediatrics, Australia 5 Murdoch Childrens Research Institute, Child Neuropsychology, Australia 6 The University of Melbourne, School of Psychological Sciences, Australia Background: HARDI-MR tractography is a neuroimaging technique that allows modelling of white matter tracts in the brain. The ability to visualise white matter tracts pre-operatively has the potential to improve neurosurgery accuracy and outcome. However despite its growing popularity, questions remain regarding its technical reproducibility and validity in routine clinical use. Here we examine the reliability of a locally practised HARDI-MR tractography method in paediatric epilepsy patients and in a novel demonstration present the functional validation of the technique against multimodal clinical investigations. Methods: Eight patients were identified retrospectively from our Children’s Epilepsy Program database. All cases had pre-operative diffusion MRI sequences and motor and/or language functional MRI (fMRI). In select cases, intra- or extra-operative motor and/or language cortical mapping results were available. Corticospinal (CST) and superior longitudinal fasciculus (SLF) tracts were generated by two different operators. Coefficients of variation (CV), intra-class correlation coefficients (ICC) and dice similarity coefficients (DSC) were calculated to assess reproducibility of tract metrics and degree of tract overlap between the operators. Tractography results were compared to fMRI activation, cortical mapping results and the patient’s clinical assessment findings. Results: All white matter tracts generated were visually comparable between operators. The tract measures showed low CV values, high ICC values and high DSC scores, indicating there was a high degree of reproducibility and overlap within and between the two operators. Cortical origin and terminations of all CST and SLF tracts matched with the patient’s areas of motor or language fMRI activation. In all but one case, tractography results matched cortical stimulation findings. Tracts were also compatible with the clinical assessment findings. Discussion: In a group of paediatric epilepsy patients, tractography results could be reliably generated and reproduced. In a novel demonstration, there was correspondence between the anatomical course of the tracts with areas of fMRI activation and, in all but one case, cortical stimulation findings. This suggests that in experienced hands, HARDI-MR tractography can be a reliable and valid technique in clinical settings. HARDI-MR tractography has the potential to make valuable contributions to neurosurgery planning to improve outcome for patients. Keywords: tractography, corticospinal tract, Superior longitudinal fasciculus, Paediatric, Epilepsy, Neurosurgery, diffusion imaging Conference: ACNS-2013 Australasian Cognitive Neuroscience Society Conference, Clayton, Melbourne, Australia, 28 Nov - 1 Dec, 2013. Presentation Type: Poster Topic: Other Citation: Barton SM, Yang JY, Maixner W, Harvey A, Freeman J, Beare R, Seal M and Anderson V (2013). Technical and functional validations of High Angular Resolution Diffusion Imaging (HARDI)-MR tractography in paediatric epilepsy patients. Conference Abstract: ACNS-2013 Australasian Cognitive Neuroscience Society Conference. doi: 10.3389/conf.fnhum.2013.212.00059 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 15 Oct 2013; Published Online: 25 Nov 2013. * Correspondence: Dr. Sarah M Barton, Murdoch Childrens Research Institute, Developmental Imaging, Parkville, Victoria, Australia, sarah.barton@mcri.edu.au Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Sarah M Barton Joseph Y Yang Wirginia Maixner A. Simon Harvey Jeremy Freeman Richard Beare Marc Seal Vicki Anderson Google Sarah M Barton Joseph Y Yang Wirginia Maixner A. Simon Harvey Jeremy Freeman Richard Beare Marc Seal Vicki Anderson Google Scholar Sarah M Barton Joseph Y Yang Wirginia Maixner A. Simon Harvey Jeremy Freeman Richard Beare Marc Seal Vicki Anderson PubMed Sarah M Barton Joseph Y Yang Wirginia Maixner A. 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