Fiber Orientation Estimation Research Articles

NVAM-Net: deep learning networks for reconstructing high-quality fiber orientation distributions.

Diffusion magnetic resonance imaging (dMRI) is a widely used non-invasive method for investigating brain anatomical structures. Conventional techniques for estimating fiber orientation distribution (FOD) from dMRI data often neglect voxel-level spatial relationships, leading to ambiguous associations between target voxels and their neighbors, which, in turn, adversely impacts FOD accuracy. This study aims to address this issue by introducing a novel neural network, the neighboring voxel attention mechanism network (NVAM-Net), designed to reconstruct high-quality FOD images. The NVAM-Net leverages a Transformer architecture and incorporates two innovative attention mechanisms: voxel attention and surface attention. These mechanisms are specifically designed to capture overlooked features among neighboring voxels. The processed features are subsequently passed through two fully connected layers, further enhancing FOD estimation accuracy by separately estimating spherical harmonics (SH) coefficients of varying orders. The experimental findings, based on the Human Connectome Project (HCP) dataset, reveal that the reconstructed super-resolution FOD images achieve results comparable to those obtained through more advanced dMRI acquisition protocols. These results underscore the NVAM-Net's robust performance in reconstructing multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD). In summary, this research underscores the NVAM-Net's advantages and practical feasibility in reconstructing high-quality FOD images. It provides a reliable reference point for clinical applications in the field of diffusion magnetic resonance imaging.

Estimating fiber orientation distribution with application to study brain lateralization using HCP D-MRI data

Estimating fiber orientation distribution with application to study brain lateralization using HCP D-MRI data

VSTNet: Robust watermarking scheme based on voxel space transformation for diffusion tensor imaging images

Deep watermarking has been successfully applied to real-value domain (e.g., CT, MRI, DWI) medical images for copyright protection; however, manifold-value domain images, such as diffusion tensor imaging (DTI), have received less academic attention. The non-Euclidean nature of DTI images hinders deep models from generating plausible DTI images because it is difficult to guarantee that each generated DTI image voxel lies on a 3 × 3 symmetric positive definite manifold. In this paper, we propose a robust watermarking scheme based on voxel space transformation for DTI images. First, a voxel space transformation is proposed, which effectively solves the problem of fiber orientation estimation in Riemann networks for DTI images and obtains the eigenvalues and eigenvectors of each voxel using singular value decomposition (SVD) to transform the DTI voxels from the 3 × 3 symmetric positive definite manifold space to Euclidean space. Second, SVD is combined with a deep neural network to extract the high-level features of each voxel eigenvalue in the DTI images and embedding watermarking messages, avoiding the false positive errors problem in traditional watermarking algorithms based on an SVD transform. Finally, using a deep neural network combining multiscale dilated convolution, dense residual connection and channel attention, the algorithm demonstrates high robustness against various intentional or unintentional attacks on DTI images while ensuring the good visual quality and diffusion characteristics of the DTI images embedded with watermarking messages. Experiments show that the watermarking message extraction accuracy reaches 97.8% for Crop (p = 0.7) attacks and 95.4% for Gaussian Blur (k = 7) attacks.

Fiber Orientation Estimation from X-ray Dark Field Images of Fiber Reinforced Polymers Using Constrained Spherical Deconvolution

The properties of fiber reinforced polymers are strongly related to the length and orientation of the fibers within the polymer matrix, the latter of which can be studied using X-ray computed tomography (XCT). Unfortunately, resolving individual fibers is challenging because they are small compared to the XCT voxel resolution and because of the low attenuation contrast between the fibers and the surrounding resin. To alleviate both problems, anisotropic dark field tomography via grating based interferometry (GBI) has been proposed. Here, the fiber orientations are extracted by applying a Funk-Radon transform (FRT) to the local scatter function. However, the FRT suffers from a low angular resolution, which complicates estimating fiber orientations for small fiber crossing angles. We propose constrained spherical deconvolution (CSD) as an alternative to the FRT to resolve fiber orientations. Instead of GBI, edge illumination phase contrast imaging is used because estimating fiber orientations with this technique has not yet been explored. Dark field images are generated by a Monte Carlo simulation framework. It is shown that the FRT cannot estimate the fiber orientation accurately for crossing angles smaller than 70∘, while CSD performs well down to a crossing angle of 50∘. In general, CSD outperforms the FRT in estimating fiber orientations.

Compressive strength prediction of carbon fiber-reinforced pultruded profiles including realistic volumetric fiber orientations

A compressive strength prediction method considering 3D fiber orientation distributions is developed. The method quantifies volumetric fiber orientations using the structure tensor image analysis method on X-ray computed micro-tomography data. The estimated fiber orientations are subsequently mapped to a finite element mesh. The finite element model is solved using a three-dimensional non-linear constitutive model implemented as a user-subroutine in AbaqusTM. A model capable of describing the elastic–plastic behavior of fibrous composites and simulating strain localization in the form of kink bands. The compressive strength of a carbon-epoxy pultruded profile is predicted based on three volumetric subsets of the profile and compared with experimental obtained compression test measurements. The strength predictions of the three volumetric subsets are in the range of 16%–42% higher than the experimental results. It is argued that the experimental results do not represent the full potential of the material compressive strength due to stress concentrations at the load introduction and that the model predictions can describe a potential for the actual compressive strength of the carbon-epoxy pultruded profile.

T 2 orientation anisotropy mapping of articular cartilage using qMRI

Objective. To provide orientation-independent MR parameters potentially sensitive to articular cartilage degeneration by measuring isotropic and anisotropic components of T 2 relaxation, as well as 3D fiber orientation angle and anisotropy via multi-orientation MR scans. Approach. Seven bovine osteochondral plugs were scanned with a high angular resolution of thirty-seven orientations spanning 180° at 9.4 T. The obtained data was fitted to the magic angle model of anisotropic T 2 relaxation to produce pixel-wise maps of the parameters of interest. Quantitative Polarized Light Microscopy (qPLM) was used as a reference method for the anisotropy and fiber orientation. Main results. The number of scanned orientations was found to be sufficient for estimating both fiber orientation and anisotropy maps. The relaxation anisotropy maps demonstrated a high correspondence with qPLM reference measurements of the collagen anisotropy of the samples. The scans also enabled calculating orientation-independent T 2 maps. Little spatial variation was observed in the isotropic component of T 2 while the anisotropic component was much faster in the deep radial zone of cartilage. The estimated fiber orientation spanned the expected 0°–90° in samples that had a sufficiently thick superficial layer. The orientation-independent magnetic resonance imaging (MRI) measures can potentially reflect the true properties of articular cartilage more precisely and robustly. Significance. The methods presented in this study will likely improve the specificity of cartilage qMRI by allowing the assessment of the physical properties such as orientation and anisotropy of collagen fibers in articular cartilage.

Reconstruction for 7T high-resolution whole-brain diffusion MRI using two-stage N/2 ghost correction and L1-SPIRiT without single-band reference.

To combine a new two-stage N/2 ghost correction and an adapted L1-SPIRiT method for reconstruction of 7T highly accelerated whole-brain diffusion MRI (dMRI) using only autocalibration scans (ACS) without the need of additional single-band reference (SBref) scans. The proposed ghost correction consisted of a 3-line reference approach in stage 1 and the reference-free entropy method in stage 2. The adapted L1-SPIRiT method was formulated within the 3D k-space framework. Its efficacy was examined by acquiring two dMRI data sets at 1.05-mm isotropic resolutions with a total acceleration of 6 or 9 (i.e., 2-fold or 3-fold slice and 3-fold in-plane acceleration). Diffusion analysis was performed to derive DTI metrics and estimate fiber orientation distribution functions (fODFs). The results were compared with those of 3D k-space GRAPPA using only ACS, all in reference to 3D k-space GRAPPA using both ACS and SBref (serving as a reference). The proposed ghost correction eliminated artifacts more robustly than conventional approaches. Our adapted L1-SPIRiT method outperformed 3D k-space GRAPPA when using only ACS, improving image quality to what was achievable with 3D k-space GRAPPA using both ACS and SBref scans. The improvement in image quality further resulted in an improvement in estimation performances for DTI and fODFs. The combination of our new ghost correction and adapted L1-SPIRiT method can reliably reconstruct 7T highly accelerated whole-brain dMRI without the need of SBref scans, increasing acquisition efficiency and reducing motion sensitivity.

An iterative algorithm for computing gradient directions for white matter fascicles detection in brain MRI.

This paper proposes a new iterative algorithm for computing gradient directions (GD) to reconstruct the brain's white matter fascicles. In particular, the proposed algorithm extensively overcomes the limitations of existing approaches like Uniform Gradient Directions and Adaptive Gradient Directions (AGD) for this task. The proposed algorithm uses the AGD approach to have a coarse estimation of the fibers in the initial step, and then a refinement is done using an iterative strategy. We begin with GD distributed uniformly inside a grid of bigger size and larger spacing between the points. Both (grid size and spacing between the points) reduce iteratively. The proposed algorithm has higher chance of capturing the fibers' actual position within the grid at each iteration. Hence, the solution tends to the actual position of fiber in each iteration, leading to a better estimation of fiber orientations. Multiple artificial simulations and real dataset experiments on the human brain and optic chiasm of a rat's brain are performed. The excellent performance of the proposed algorithm at different noises ensures stability and robustness. Hence, after processing the MRI data, the proposed algorithm can accurately reflect the ground truth of white matter fascicles connections in reconstructed images. The proposed algorithm helps resolve the structural complexities of the brain caused due to presence of crossing fascicles to a great extent.

Regularized Asymmetric Susceptibility Tensor Imaging in the Human Brain in Vivo.

Susceptibility tensor imaging (STI) is a promising tool for studying orientation-dependent tissue magnetic susceptibility and for mapping white matter fiber orientations complementary to diffusion tensor imaging (DTI). However, the limited head rotation range within modern head coils for data acquisition makes in vivo STI reconstruction ill-conditioned. Conventional STI reconstruction method is usually vulnerable to noise and requires sufficiently large head rotations to solve this ill-conditioned inverse problem. In this study, based on the recently proposed asymmetric STI (aSTI) model, a new method termed aSTI+ was proposed to improve in vivo STI reconstruction by enforcing isotropic susceptibility tensor inside cerebrospinal fluid (CSF) and applying morphology constraint in white matter. Experimental results showed superior performance of the proposed method with reduced noise, improved tissue contrast and better fiber orientation estimation over previous methods. Thus aSTI+ may promote in vivo human brain STI studies on white matter and myelin-related brain diseases.

CTtrack: A CNN+Transformer-based framework for fiber orientation estimation & tractography

In recent years, multiple data-driven fiber orientation distribution function (fODF) estimation algorithms and automatic tractography pipelines have been proposed to address the limitations of traditional methods. However, these approaches lack precision and generalizability. To tackle these shortcomings, we introduce CTtrack, a CNN+Transformer-based pipeline to estimate fODFs and perform tractography. In this approach, a convolutional neural network (CNN) module is employed to project the resampled diffusion-weighted magnetic resonance imaging (DW-MRI) data to a lower dimension. Then, a transformer model estimates the fiber orientation distribution functions using the projected data within a local block around each voxel. The proposed model represents the extracted fODFs by spherical harmonics coefficients. The predicted fiber ODFs can be used for both deterministic and probabilistic tractography. Our pipeline was tested in terms of the precision and robustness in estimating fODFs and performing tractography using both simulated and real diffusion data. The Tractometer tool was employed to compare our method with the classical and data-driven tractography approaches. The qualitative and quantitative assessments illustrate the competitive performance of our framework compared to other available algorithms.

Comparison of CPU and GPU bayesian estimates of fibre orientations from diffusion MRI.

BackgroundThe correct estimation of fibre orientations is a crucial step for reconstructing human brain tracts. Bayesian Estimation of Diffusion Parameters Obtained using Sampling Techniques (bedpostx) is able to estimate several fibre orientations and their diffusion parameters per voxel using Markov Chain Monte Carlo (MCMC) in a whole brain diffusion MRI data, and it is capable of running on GPUs, achieving speed-up of over 100 times compared to CPUs. However, few studies have looked at whether the results from the CPU and GPU algorithms differ. In this study, we compared CPU and GPU bedpostx outputs by running multiple trials of both algorithms on the same whole brain diffusion data and compared each distribution of output using Kolmogorov-Smirnov tests.ResultsWe show that distributions of fibre fraction parameters and principal diffusion direction angles from bedpostx and bedpostx_gpu display few statistically significant differences in shape and are localized sparsely throughout the whole brain. Average output differences are small in magnitude compared to underlying uncertainty.ConclusionsDespite small amount of differences in output between CPU and GPU bedpostx algorithms, results are comparable given the difference in operation order and library usage between CPU and GPU bedpostx.

General orientation transform for the estimation offiberorientations in white matter tissues.

The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by ( is the radial length), has been used to estimate fiber orientations of white matter tissues. Currently, there is no general expression of the ODF that is suitable for any n value in the HARDI methods. A novel methodology is proposed to calculate the ODF for any through the Taylor series expansion and a generalized expression for is provided. Then a series of single-shell HARDI methods, termed the general orientation transform (GOT), is developed based on the obtained expression. By combining complementary GOTs, a composite estimator is obtained and further optimized via constrained optimization to take full advantage of individual merits. The final optimized HARDI method is termed the combined GOT with constrained optimization (coGOT). The proposed method is compared with other commonly used HARDI methods on the simulated data, the physical phantom data, the ISMRM 2015 Tractography challenge data, and in vivo HCP datasets. coGOT can resolve crossing fibers with higher resolution, performs better robustness, generates fewer spurious lobes in glyphs, and thus provides distinct improvement in the tractography. The evaluations show coGOT's superior capability in reconstructing the fiber orientations from dMRI signals. Generalization of the ODF allows us to obtain a wide range of HARDI estimators to select suitable candidates for composite formulation. The optimized estimator coGOT has great potential for studying neural architecture and serving as fiber tracking tools.

VRfRNet: Volumetric ROI fODF reconstruction network for estimation of multi-tissue constrained spherical deconvolution with only single shell dMRI

Diffusion MRI (dMRI) is one of the most popular techniques for studying the brain structure, mainly the white matter region. Among several sampling methods in dMRI, the high angular resolution diffusion imaging (HARDI) technique has attracted researchers due to its more accurate fiber orientation estimation. However, the current single-shell HARDI makes the intravoxel structure challenging to estimate accurately. While multi-shell acquisition can address this problem, it takes a longer scanning time, restricting its use in clinical applications. In addition, most existing dMRI scanners with low gradient-strengths often acquire single-shell up to b=1000s/mm2 because of signal-to-noise ratio issues and severe image artefacts. Hence, we propose a novel generative adversarial network, VRfRNet, for the reconstruction of multi-shell multi-tissue fiber orientation distribution function from single-shell HARDI volumes. Such a transformation learning is performed in the spherical harmonics (SH) space, as raw input HARDI volume is transformed to SH coefficients to soften gradient directions. The proposed VRfRNet consists of several modules, such as multi-context feature enrichment module, feature level attention, and softmax level attention. In addition, three loss functions have been used to optimize network learning, including L1, adversarial, and total variation. The network is trained and tested using standard qualitative and quantitative performance metrics on the publicly available HCP data-set.

Comprehensive diffusion MRI dataset for in vivo human brain microstructure mapping using 300 mT/m gradients

Strong gradient systems can improve the signal-to-noise ratio of diffusion MRI measurements and enable a wider range of acquisition parameters that are beneficial for microstructural imaging. We present a comprehensive diffusion MRI dataset of 26 healthy participants acquired on the MGH-USC 3 T Connectome scanner equipped with 300 mT/m maximum gradient strength and a custom-built 64-channel head coil. For each participant, the one-hour long acquisition systematically sampled the accessible diffusion measurement space, including two diffusion times (19 and 49 ms), eight gradient strengths linearly spaced between 30 mT/m and 290 mT/m for each diffusion time, and 32 or 64 uniformly distributed directions. The diffusion MRI data were preprocessed to correct for gradient nonlinearity, eddy currents, and susceptibility induced distortions. In addition, scan/rescan data from a subset of seven individuals were also acquired and provided. The MGH Connectome Diffusion Microstructure Dataset (CDMD) may serve as a test bed for the development of new data analysis methods, such as fiber orientation estimation, tractography and microstructural modelling.

White Matter Integrity in a Rat Model of Epileptogenesis: Structural Connectomics and Fixel-Based Analysis.

Introduction: Electrophysiological and neuroimaging studies have demonstrated that large-scale brain networks are affected during the development of epilepsy. These networks can be investigated by using diffusion magnetic resonance imaging (dMRI). The most commonly used model to analyze dMRI is diffusion tensor imaging (DTI). However, DTI metrics are not specific to microstructure or pathology and the DTI model does not take into account crossing fibers, which may lead to erroneous results. To overcome these limitations, a more advanced model based on multi-shell multi-tissue constrained spherical deconvolution was used in this study to perform tractography with more precise fiber orientation estimates and to assess changes in intra-axonal volume by using fixel-based analysis. Methods: dMRI images were acquired before and at several time points after induction of status epilepticus in the intraperitoneal kainic acid (IPKA) rat model of temporal lobe epilepsy. Tractography was performed, and fixel metrics were calculated in several white matter tracts. The tractogram was analyzed by using the graph theory. Results: Global degree, global and local efficiency were decreased in IPKA animals compared with controls during epileptogenesis. Nodal degree was decreased in the limbic system and default-mode network, mainly during early epileptogenesis. Further, fiber density (FD) and fiber-density-and-cross-section (FDC) were decreased in several white matter tracts. Discussion: These results indicate a decrease in overall structural connectivity, integration, and segregation and decreased structural connectivity in the limbic system and default-mode network. Decreased FD and FDC point to a decrease in intra-axonal volume fraction during epileptogenesis, which may be related to neuronal degeneration and gliosis. Impact statement To the best of our knowledge, this is the first longitudinal multi-shell diffusion magnetic resonance imaging study that combines whole-brain tractography and fixel-based analysis to investigate changes in structural brain connectivity and white matter integrity during epileptogenesis in a rat model of temporal lobe epilepsy. Our findings present better insights into how the topology of the structural brain network changes during epileptogenesis and how these changes are related to white matter integrity. This could improve the understanding of the basic mechanisms of epilepsy and aid the rational development of imaging biomarkers and epilepsy therapies.

Update 3.0 to “PuMA: The Porous Microstructure Analysis software”, (PII:S2352711018300281)

A major update of the Porous Microstructure Analysis (PuMA) software is presented. PuMA is a framework for computing effective material properties and response based on material microstructures. Version 3.0 of the software extends the PuMA capabilities to include computation of anisotropic conductivity, elasticity, permeability, per-voxel material or fiber orientation estimation, as well as expanded computational material generation capabilities. Version 3.0 also introduces pumapy, a Python version of the PuMA software.

Simultaneous multi-slice image reconstruction using regularized image domain split slice-GRAPPA for diffusion MRI.

The main goal of this work is to improve the quality of simultaneous multi-slice (SMS) reconstruction for diffusion MRI. We accomplish this by developing an image domain method that reaps the benefits of both SENSE and GRAPPA-type approaches and enables image regularization in an optimization framework. We propose a new approach termed regularized image domain split slice-GRAPPA (RI-SSG), which establishes an optimization framework for SMS reconstruction. Within this framework, we use a robust forward model to take advantage of both the SENSE model with explicit sensitivity estimations and the SSG model with implicit kernel relationship among coil images. The proposed approach also allows combining of coil images to increase the SNR and enables image domain regularization on estimated coil-combined single slices. We compare the performance of RI-SSG with that of SENSE and SSG using in-vivo diffusion EPI datasets with simulated and actual SMS acquisitions collected on a 3T MR scanner. Reconstructed diffusion-weighted images (DWIs) and the resulting diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) maps are analyzed to evaluate the quantitative and qualitative performance of the three methods. The DWIs reconstructed by RI-SSG are closer to the single-band ground truth images than SENSE and SSG. Specifically, the proposed RI-SSG reduces the normalized root-mean-square-error (nRMSE) against ground truth images by ∼5% and increases the structural similarity index (SSIM) by ∼4% compared to SSG. All three methods produce similar fractional anisotropy (FA) maps using DTI representation, but mean diffusivity (MD) and fiber orientation estimates using RI-SSG are closer to the reference than SENSE and SSG. RI-SSG results in NODDI maps with noticeably smaller errors than those of SENSE and SSG and improves the accuracy of the mean value of orientation dispersion index (ODI) by ∼5% and the mean value of intracellular volume fraction by ∼7% in regions of interest in brain white matter compared to SSG.

Estimation of muscle fiber orientation in multi-pennate muscle using DTI

Estimation of muscle fiber orientation in multi-pennate muscle using DTI

Comparison of diffusion MRI and CLARITY fiber orientation estimates in both gray and white matter regions of human and primate brain

Diffusion MRI (dMRI) represents one of the few methods for mapping brain fiber orientations non-invasively. Unfortunately, dMRI fiber mapping is an indirect method that relies on inference from measured diffusion patterns. Comparing dMRI results with other modalities is a way to improve the interpretation of dMRI data and help advance dMRI technologies. Here, we present methods for comparing dMRI fiber orientation estimates with optical imaging of fluorescently labeled neurofilaments and vasculature in 3D human and primate brain tissue cuboids cleared using CLARITY. The recent advancements in tissue clearing provide a new opportunity to histologically map fibers projecting in 3D, which represents a captivating complement to dMRI measurements. In this work, we demonstrate the capability to directly compare dMRI and CLARITY in the same human brain tissue and assess multiple approaches for extracting fiber orientation estimates from CLARITY data. We estimate the three-dimensional neuronal fiber and vasculature orientations from neurofilament and vasculature stained CLARITY images by calculating the tertiary eigenvector of structure tensors. We then extend CLARITY orientation estimates to an orientation distribution function (ODF) formalism by summing multiple sub-voxel structure tensor orientation estimates. In a sample containing part of the human thalamus, there is a mean angular difference of 19o±15o between the primary eigenvectors of the dMRI tensors and the tertiary eigenvectors from the CLARITY neurofilament stain. We also demonstrate evidence that vascular compartments do not affect the dMRI orientation estimates by showing an apparent lack of correspondence (mean angular difference = 49o±23o) between the orientation of the dMRI tensors and the structure tensors in the vasculature stained CLARITY images. In a macaque brain dataset, we examine how the CLARITY feature extraction depends on the chosen feature extraction parameters. By varying the volume of tissue over which the structure tensor estimates are derived, we show that orientation estimates are noisier with more spurious ODF peaks for sub-voxels below 30 µm3 and that, for our data, the optimal gray matter sub-voxel size is between 62.5 µm3 and 125 µm3. The example experiments presented here represent an important advancement towards robust multi-modal MRI-CLARITY comparisons.

The effect of gradient nonlinearities on fiber orientation estimates from spherical deconvolution of diffusion magnetic resonance imaging data.

Gradient nonlinearities in magnetic resonance imaging (MRI) cause spatially varying mismatches between the imposed and the effective gradients and can cause significant biases in rotationally invariant diffusion MRI measures derived from, for example, diffusion tensor imaging. The estimation of the orientational organization of fibrous tissue, which is nowadays frequently performed with spherical deconvolution techniques ideally using higher diffusion weightings, can likewise be biased by gradient nonlinearities. We explore the sensitivity of two established spherical deconvolution approaches to gradient nonlinearities, namely constrained spherical deconvolution (CSD) and damped Richardson‐Lucy (dRL). Additionally, we propose an extension of dRL to take into account gradient imperfections, without the need of data interpolation. Simulations show that using the effective b‐matrix can improve dRL fiber orientation estimation and reduces angular deviations, while CSD can be more robust to gradient nonlinearity depending on the implementation. Angular errors depend on a complex interplay of many factors, including the direction and magnitude of gradient deviations, underlying microstructure, SNR, anisotropy of the effective response function, and diffusion weighting. Notably, angular deviations can also be observed at lower b‐values in contrast to the perhaps common assumption that only high b‐value data are affected. In in vivo Human Connectome Project data and acquisitions from an ultrastrong gradient (300 mT/m) scanner, angular differences are observed between applying and not applying the effective gradients in dRL estimation. As even small angular differences can lead to error propagation during tractography and as such impact connectivity analyses, incorporating gradient deviations into the estimation of fiber orientations should make such analyses more reliable.