Mesh-based spherical deconvolution for physically valid fiber orientation reconstruction from diffusion-weighted MRI

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a non-invasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. Significant partial volume effects (PVEs) are present in the DW signal due to relatively large voxel sizes. These PVEs can be caused by both non-WM tissue, such as gray matter (GM) and cerebrospinal fluid (CSF), and by multiple non-parallel WM fiber populations. High angular resolution diffusion imaging (HARDI) methods have been developed to correctly characterize complex WM fiber configurations, but to date, many of the HARDI methods do not account for non-WM PVEs. In this work, we investigated the isotropic PVEs caused by non-WM tissue in WM voxels on fiber orientations extracted with constrained spherical deconvolution (CSD). Experiments were performed on simulated and real DW-MRI data. In particular, simulations were performed to demonstrate the effects of varying the diffusion weightings, signal-to-noise ratios (SNRs), fiber configurations, and tissue fractions. Our results show that the presence of non-WM tissue signal causes a decrease in the precision of the detected fiber orientations and an increase in the detection of false peaks in CSD. We estimated 35–50% of WM voxels to be affected by non-WM PVEs. For HARDI sequences, which typically have a relatively high degree of diffusion weighting, these adverse effects are most pronounced in voxels with GM PVEs. The non-WM PVEs become severe with 50% GM volume for maximum spherical harmonics orders of 8 and below, and already with 25% GM volume for higher orders. In addition, a low diffusion weighting or SNR increases the effects. The non-WM PVEs may cause problems in connectomics, where reliable fiber tracking at the WM–GM interface is especially important. We suggest acquiring data with high diffusion-weighting 2500–3000 s/mm2, reasonable SNR (~30) and using lower SH orders in GM contaminated regions to minimize the non-WM PVEs in CSD.

Diffusion weighted (DW) MRI facilitates non-invasive quantification of tissue microstructure and, in combination with appropriate signal processing, three-dimensional estimates of fibrous orientation. In recent years, attention has shifted from the diffusion tensor model, which assumes a unimodal Gaussian diffusion displacement profile to recover fibre orientation (with various well-documented limitations), towards more complex high angular resolution diffusion imaging (HARDI) analysis techniques.Spherical deconvolution (SD) approaches assume that the fibre orientation density function (fODF) within a voxel can be obtained by deconvolving a ‘common’ single fibre response function from the observed set of DW signals. In practice, this common response function is not known a priori and thus an estimated fibre response must be used. Here the establishment of this single-fibre response function is referred to as ‘calibration’. This work examines the vulnerability of two different SD approaches to inappropriate response function calibration: (1) constrained spherical harmonic deconvolution (CSHD)—a technique that exploits spherical harmonic basis sets and (2) damped Richardson–Lucy (dRL) deconvolution—a technique based on the standard Richardson–Lucy deconvolution.Through simulations, the impact of a discrepancy between the calibrated diffusion profiles and the observed (‘Target’) DW-signals in both single and crossing-fibre configurations was investigated. The results show that CSHD produces spurious fODF peaks (consistent with well known ringing artefacts) as the discrepancy between calibration and target response increases, while dRL demonstrates a lower over-all sensitivity to miscalibration (with a calibration response function for a highly anisotropic fibre being optimal). However, dRL demonstrates a reduced ability to resolve low anisotropy crossing-fibres compared to CSHD. It is concluded that the range and spatial-distribution of expected single-fibre anisotropies within an image must be carefully considered to ensure selection of the appropriate algorithm, parameters and calibration. Failure to choose the calibration response function carefully may severely impact the quality of any resultant tractography.

We introduce a geodesic based tractography method for High Angular Resolution Diffusion Imaging (HARDI). The concepts used are similar to the ones in geodesic based tractography for Diffusion Tensor Imaging (DTI). In DTI, the inverse of the second-order diffusion tensor is used to define the manifold where the geodesics are traced. HARDI models have been developed to resolve complex fiber populations within a voxel, and higher order tensors (HOT) are possible representations for HARDI data. In our framework, we apply Finsler geometry, which extends Riemannian geometry to a directionally dependent metric. A Finsler metric is defined in terms of HARDI higher order tensors. Furthermore, the Euler-Lagrange geodesic equations are derived based on the Finsler geometry. In contrast to other geodesic based tractography algorithms, the multi-valued numerical solution of the geodesic equations can be obtained. This gives the possibility to capture all geodesics arriving at a single voxel instead of only computing the shortest one. Results are analyzed to show the potential and characteristics of our algorithm.

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. Simon Harvey Jeremy Freeman Richard Beare Marc Seal Vicki Anderson Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

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.

The reproducibility of three evaluation techniques for high angular resolution diffusion imaging (HARDI) data, the diffusion tensor model, q-ball reconstruction and spherical deconvolution, are compared. Two healthy volunteers were measured in a 3 T MR system six times with the same measurement parameters; one subject was measured with different b-values. The data was evaluated to compare the consistency and reproducibility of reconstructed diffusion directions and anisotropy values for the three investigated diffusion evaluation techniques. The angle difference between the reconstructed main directions of diffusion for the investigated techniques was evaluated. For q-ball and spherical deconvolution the consistency of the second dominant diffusion direction was additionally examined. The differences between the tensor model and q-ball or spherical deconvolution in the estimated diffusion direction decrease with an increase in fractional anisotropy. Increasing the smoothing kernel in q-ball reconstruction renders the results similar to the ones from the diffusion tensor evaluation. Consistency in the reconstructed directions did increase for larger b-values. The evaluation of HARDI data in clinical conditions with q-ball or spherical deconvolution shows consistency and reproducibility similar to the diffusion tensor model, but provides valuable additional information about a second dominant direction of diffusion.

A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank tensors without using the computationally-difficult spherical harmonic transform. General theoretical relations between the diffusion tensor (DT) components measured by traditional (rank-2) DT imaging (DTI) and 3D distribution of diffusivities, as measured by high angular resolution diffusion imaging (HARDI) methods, are derived. Also, the spherical tensor components from HARDI are related to the rank-2 DT. The relationships between higher- and lower-rank Cartesian DTs are also presented. The inadequacy of the traditional rank-2 tensor model is demonstrated with simulations, and the method is applied to excised rat brain data collected in a spin-echo HARDI experiment.

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.

Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data

Diffusion weighted magnetic resonance imaging (DW-MRI) is interpreted as a quantitative method that is sensitive to tissue microarchitecture at a millimeter scale. However, the sensitization is dependent on acquisition sequences (e.g., diffusion time, gradient strength, etc.) and susceptible to imaging artifacts. Hence, comparison of quantitative DW-MRI biomarkers across field strengths (including different scanners, hardware performance, and sequence design considerations) is a challenging area of research. We propose a novel method to estimate microstructure using DW-MRI that is robust to scanner difference between 1.5T and 3T imaging. We propose to use a null space deep network (NSDN) architecture to model DW-MRI signal as fiber orientation distributions (FOD) to represent tissue microstructure. The NSDN approach is consistent with histologically observed microstructure (on previously acquired ex vivo squirrel monkey dataset) and scan-rescan data. The contribution of this work is that we incorporate identical dual networks (IDN) to minimize the influence of scanner effects via scan-rescan data. Briefly, our estimator is trained on two datasets. First, a histology dataset was acquired on three squirrel monkeys with corresponding DW-MRI and confocal histology (512 independent voxels). Second, 37 control subjects from the Baltimore Longitudinal Study of Aging (67-95 y/o) were identified who had been scanned at 1.5T and 3T scanners (b-value of 700 s/mm2, voxel resolution at 2.2mm, 30-32 gradient volumes) with an average interval of 4 years (standard deviation 1.3 years). After image registration, we used paired white matter (WM) voxels for 17 subjects and 440 histology voxels for training and 20 subjects and 72 histology voxels for testing. We compare the proposed estimator with super-resolved constrained spherical deconvolution (CSD) and a previously presented regression deep neural network (DNN). NSDN outperformed CSD and DNN in angular correlation coefficient (ACC) 0.81 versus 0.28 and 0.46, mean squared error (MSE) 0.001 versus 0.003 and 0.03, and general fractional anisotropy (GFA) 0.05 versus 0.05 and 0.09. Further validation and evaluation with contemporaneous imaging are necessary, but the NSDN is promising avenue for building understanding of microarchitecture in a consistent and device-independent manner.

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.

The detection of white matter microstructural changes using diffusion magnetic resonance imaging (dMRI) often involves extracting a small set of scalar features, such as fractional anisotropy (FA) and mean diffusivity (MD) in diffusion tensor imaging (DTI). With the advent of more advanced dMRI techniques, such as high angular resolution diffusion imaging (HARDI), a number of mathematically inspired new scalar features have been proposed. However, it is unclear how to select the most biologically informative combinations of features for biomarker discovery. This paper proposes an automatic HARDI feature selection algorithm which is based on registering HARDI features to feature atlases for optimal clinical usability in population studies. We apply our framework to the characterization of beta-amyloid (Aβ) pathology for the early detection of Alzheimer’s disease (AD) to better understand the relationship between Aβ pathology and degenerative changes in neuroanatomy.

Spatial HARDI: Improved visualization of complex white matter architecture with Bayesian spatial regularization

Adenosine 5′ triphosphate evoked mobilization of intracellular calcium in central nervous system white matter of adult mouse optic nerve

This paper presents a report about work in progress of research on the influence of the flow of SCFRC on the fiber orientations. Mechanical properties of the short steel fiber reinforced cementitious materials mostly depend on the fiber orientation and spatial dispersion. Many studies have shown that it is possible to achieve the desired fiber orientation by optimizing the parameters of rheological properties or the casting process. In order to improve the key mechanical properties, multiple statistical experiments with various factors are needed. This paper analyzes the influence of casting velocity and formwork surface quality on the fiber distribution and orientation. A suitable technique for our method was to replace Steel Fiber Reinforced Self-Compacting Concrete (SFRSCC) by a transparent polymer with similar rheological properties as SFRSCC. Preliminary analysis of the experimental results shows that the fibers tend to orient mostly perpendicular to the flow direction and turn their orientation longitudinally near the walls. Experiments showed that the fiber spatial distribution was affected by the casting velocity. Faster casting velocities provided more preferable homogeneous distribution. Moreover, the roughness of the bottom of the formwork demonstrated some influence on the fiber orientations but no significant impact on the spatial dispersion. In addition, we used the image analysis method to estimate fiber orientation and distribution.