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Diffusion magnetic resonance imaging (dMRI) is widely used to probe tissue microstructure, and is currently the only non-invasive way to measure the brain's fiber architecture. While a large number of approaches to recover the intra-voxel fiber structure have been utilized in the scientific community, a direct, 3D, quantitative validation of these methods against relevant histological fiber geometries is lacking. In this study, we investigate how well different high angular resolution diffusion imaging (HARDI) models and reconstruction methods predict the ground-truth histologically defined fiber orientation distribution (FOD), as well as investigate their behavior over a range of physical and experimental conditions. The dMRI methods tested include constrained spherical deconvolution (CSD), Q-ball imaging (QBI), diffusion orientation transform (DOT), persistent angular structure (PAS), and neurite orientation dispersion and density imaging (NODDI) methods. Evaluation criteria focus on overall agreement in FOD shape, correct assessment of the number of fiber populations, and angular accuracy in orientation. In addition, we make comparisons of the histological orientation dispersion with the fiber spread determined from the dMRI methods. As a general result, no HARDI method outperformed others in all quality criteria, with many showing tradeoffs in reconstruction accuracy. All reconstruction techniques describe the overall continuous angular structure of the histological FOD quite well, with good to moderate correlation (median angular correlation coefficient > 0.70) in both single- and multiple-fiber voxels. However, no method is consistently successful at extracting discrete measures of the number and orientations of FOD peaks. The major inaccuracies of all techniques tend to be in extracting local maxima of the FOD, resulting in either false positive or false negative peaks. Median angular errors are ∼10° for the primary fiber direction and ∼20° for the secondary fiber, if present. For most methods, these results did not vary strongly over a wide range of acquisition parameters (number of diffusion weighting directions and b value). Regardless of acquisition parameters, all methods show improved successes at resolving multiple fiber compartments in a voxel when fiber populations cross at near-orthogonal angles, with no method adequately capturing low to moderate angle (<60°) crossing fibers. Finally, most methods are limited in their ability to capture orientation dispersion, resulting in low to moderate, yet statistically significant, correlation with histologically-derived dispersion with both HARDI and NODDI methodologies. Together, these results provide quantitative measures of the reliability and limitations of dMRI reconstruction methods and can be used to identify relative advantages of competing approaches as well as potential strategies for improving accuracy. •3D histological validation of diffusion MRI measures of fiber orientation.•All methods capture the overall structure of the FOD quite well.•Most inaccuracies occur when extracting discrete peaks from the FOD.•No method consistently resolves fibers crossing at low to moderate angles.•Measures of dispersion show modest correlation with histological measures.

•We propose to use machine learning to estimate fiber orientation distribution (fODF).•Our model maps the resampled diffusion signal to fODF using a multilayer perceptron.•We develop methods for synthesizing reliable training data in-silico.•We show that the proposed method has important merits compared with existing methods. Estimation of white matter fiber orientation distribution function (fODF) is the essential first step for reliable brain tractography and connectivity analysis. Most of the existing fODF estimation methods rely on sub-optimal physical models of the diffusion signal or mathematical simplifications, which can impact the estimation accuracy. In this paper, we propose a data-driven method that avoids some of these pitfalls. Our proposed method is based on a multilayer perceptron that learns to map the diffusion-weighted measurements, interpolated onto a fixed spherical grid in the q space, to the target fODF. Importantly, we also propose methods for synthesizing reliable simulated training data. We show that the model can be effectively trained with simulated or real training data. Our phantom experiments show that the proposed method results in more accurate fODF estimation and tractography than several competing methods including the multi-tensor model, Bayesian estimation, spherical deconvolution, and two other machine learning techniques. On real data, we compare our method with other techniques in terms of accuracy of estimating the ground-truth fODF. The results show that our method is more accurate than other methods, and that it performs better than the competing methods when applied to under-sampled diffusion measurements. We also compare our method with the Sparse Fascicle Model in terms of expert ratings of the accuracy of reconstruction of several commissural, projection, association, and cerebellar tracts. The results show that the tracts reconstructed with the proposed method are rated significantly higher by three independent experts. Our study demonstrates the potential of data-driven methods for improving the accuracy and robustness of fODF estimation.

The ability of diffusion MRI (dMRI) fiber tractography to non-invasively map three-dimensional (3D) anatomical networks in the human brain has made it a valuable tool in both clinical and research settings. However, there are many assumptions inherent to any tractography algorithm that can limit the accuracy of the reconstructed fiber tracts. Among them is the assumption that the diffusion-weighted images accurately reflect the underlying fiber orientation distribution (FOD) in the MRI voxel. Consequently, validating dMRI's ability to assess the underlying fiber orientation in each voxel is critical for its use as a biomedical tool. Here, using post-mortem histology and confocal microscopy, we present a method to perform histological validation of orientation functions in 3D, which has previously been limited to two-dimensional analysis of tissue sections. We demonstrate the ability to extract the 3D FOD from confocal z-stacks, and quantify the agreement between the MRI estimates of orientation information obtained using constrained spherical deconvolution (CSD) and the true geometry of the fibers. We find an orientation error of approximately 6° in voxels containing nearly parallel fibers, and 10–11° in crossing fiber regions, and note that CSD was unable to resolve fibers crossing at angles below 60° in our dataset. This is the first time that the 3D white matter orientation distribution is calculated from histology and compared to dMRI. Thus, this technique serves as a gold standard for dMRI validation studies — providing the ability to determine the extent to which the dMRI signal is consistent with the histological FOD, and to establish how well different dMRI models can predict the ground truth FOD. •We present a method to perform histological validation of diffusion MRI orientation distribution functions in 3D•Previous validation studies have been limited to 2D analysis of tissue sections•Structure Tensor analysis is performed on confocal z-stacks to extract the ground truth fiber orientation distribution•Comparisons are made between the histological fiber orientation distribution and the corresponding diffusion MRI estimates

The tensile strength and modulus of elasticity of a jute/polylactic acid (PLA) composite were found to vary nonlinearly with the loading angle of the specimen through the tensile test. The variation in these properties was related to the fiber orientation distribution (FOD) and fiber length distribution (FLD). In order to study the effects of the FOD and FLD of short fibers on the mechanical properties and to better predict the mechanical properties of short-fiber composites, the true distribution of short fibers in the composite was accurately obtained using X-ray computed tomography (XCT), in which about 70% of the jute fibers were less than 300 μm in length and the fibers were mainly distributed along the direction of mold flow. The probability density functions of the FOD and FLD were obtained by further analyzing the XCT data. Strength and elastic modulus prediction models applicable to short-fiber-reinforced polymer (SFRP) composites were created by modifying the laminate theory and the rule of mixtures using the probability density functions of the FOD and FLD. The experimental measurements were in good agreement with the model predictions.

Tissue microstructure modeling of diffusion MRI signal is an active research area striving to bridge the gap between macroscopic MRI resolution and cellular-level tissue architecture. Such modeling in neuronal tissue relies on a number of assumptions about the microstructural features of axonal fiber bundles, such as the axonal shape (e.g., perfect cylinders) and the fiber orientation dispersion. However, these assumptions have not yet been validated by sufficiently high-resolution 3-dimensional histology. Here, we reconstructed sequential scanning electron microscopy images in mouse brain corpus callosum, and introduced a random-walker (RaW)-based algorithm to rapidly segment individual intra-axonal spaces and myelin sheaths of myelinated axons. Confirmed by a segmentation based on human annotations initiated with conventional machine-learning-based carving, our semi-automatic algorithm is reliable and less time-consuming. Based on the segmentation, we calculated MRI-relevant estimates of size-related parameters (inner axonal diameter, its distribution, along-axon variation, and myelin g-ratio), and orientation-related parameters (fiber orientation distribution and its rotational invariants; dispersion angle). The reported dispersion angle is consistent with previous 2-dimensional histology studies and diffusion MRI measurements, while the reported diameter exceeds those in other mouse brain studies. Furthermore, we calculated how these quantities would evolve in actual diffusion MRI experiments as a function of diffusion time, thereby providing a coarse-graining window on the microstructure, and showed that the orientation-related metrics have negligible diffusion time-dependence over clinical and pre-clinical diffusion time ranges. However, the MRI-measured inner axonal diameters, dominated by the widest cross sections, effectively decrease with diffusion time by ~ 17% due to the coarse-graining over axonal caliber variations. Furthermore, our 3d measurement showed that there is significant variation of the diameter along the axon. Hence, fiber orientation dispersion estimated from MRI should be relatively stable, while the “apparent” inner axonal diameters are sensitive to experimental settings, and cannot be modeled by perfectly cylindrical axons.

Carbon staple fiber composites are materials reinforced with discrete-length carbon fibers processed using traditional textile technologies, offering moderate mechanical properties and flexibility in manufacturing. These composites can be produced from recycled carbon staple fibers, aligned into yarn and tape-like structures, providing a more sustainable alternative while balancing performance, cost-effectiveness, and environmental impact. Aligning staple fibers into tape-like structures enables similar applications to those of continuous-fiber-based products, while allowing control over fiber orientation distribution, fiber volume fraction, and length distribution, which are all critical factors influencing both mechanical and thermo-mechanical properties. This study focuses on the experimental characterization and numerical investigation of Coefficients of Thermal Expansion (CTEs) in aligned carbon staple fiber composites. The effects of fiber orientation and volume fraction on coefficients of thermal expansion under different fiber alignment parameters are analyzed, revealing distinct thermal expansion behavior compared to typical aligned unidirectional continuous carbon fiber composite laminates. Unlike continuous unidirectional laminates, which typically exhibit transversely isotropic behavior without tensile–shear coupling, staple fiber composites demonstrate different in-plane axial, transverse, and out-of-plane CTE characteristics. To explain these deviations, a modeling approach is introduced, incorporating detailed experimental information on fiber distributions and microstructural features rather than averaged fiber orientation values. This involves a multi-scale analysis based on a laminate analogy through which all composite thermo-elastic properties can be predicted, accounting for variations in fiber orientations, volume fractions, and tape thicknesses. It is shown that while the local variation of fiber volume fraction has a small effect on the homogenized value of the coefficients of thermal expansion, fiber misalignment, tape thickness, and asymmetry in fiber orientation distribution will significantly affect the measurements of CTEs. For the case of carbon staple fiber composites, the asymmetry in fiber orientation distribution significantly influences the measurements of axial CTE. Fiber orientation asymmetry causes tensile–shear coupling under mechanical and thermal loading, leading to an unbalanced laminate with in-plane shear–tensile deformation. This coupling disrupts uniform displacement, complicating strain measurements and the determination of composite properties.

There is accumulating evidence that at current acquisition resolutions for diffusion-weighted (DW) MRI, the vast majority of white matter voxels contains “crossing fibers”, referring to complex fiber configurations in which multiple and distinctly differently oriented fiber populations exist. Spherical deconvolution based techniques are appealing to characterize this DW intra-voxel signal heterogeneity, as they provide a balanced trade-off between constraints on the required hardware performance and acquisition time on the one hand, and the reliability of the reconstructed fiber orientation distribution function (fODF) on the other hand. Recent findings, however, suggest that an inaccurate calibration of the response function (RF), which represents the DW signal profile of a single fiber orientation, can lead to the detection of spurious fODF peaks which, in turn, can have a severe impact on tractography results. Currently, the computation of this RF is either model-based or estimated from selected voxels that have a fractional anisotropy (FA) value above a predefined threshold. For both approaches, however, there are user-defined settings that affect the RF and, consequently, fODF estimation and tractography. Moreover, these settings still rely on the second-rank diffusion tensor, which may not be the appropriate model, especially at high b-values. In this work, we circumvent these issues for RF calibration by excluding “crossing fibers” voxels in a recursive framework. Our approach is evaluated with simulations and applied to in vivo and ex vivo data sets with different acquisition settings. The results demonstrate that with the proposed method the RF can be calibrated in a robust and automated way without needing to define ad-hoc FA threshold settings. Our framework facilitates the use of spherical deconvolution approaches in data sets in which it is not straightforward to define RF settings a priori. [Display omitted] •We propose robust response function estimation for spherical deconvolution.•This recursive framework is completely independent of the diffusion tensor model.•Method excludes crossing fiber voxels recursively using an fODF peak ratio threshold.•It is robust towards the threshold and less dependent on underlying data properties.•It can be applied to data sets with different acquisition settings and properties.

Modern μ-CT scans offer non-destructive three-dimensional microstructure analysis of various materials. Despite small density contrasts, this technology also accurately captures the complex network structure of paper and paperboard. It provides detailed insight into the fiber orientation distribution in paper, which was previously unattainable with existing measurement methods. The image analysis results are applicable for numerical fiber network models, and simulations based on these models can significantly improve our understanding of the microstructural influence on macrostructural paper properties, such as strength, stiffness, and curl tendency. This work presents a new method for investigating the microstructural fiber orientation in paperboard. Orientation tensors obtained from μ-CT scan image processing are extracted and evaluated. Based on the direction of the orientation tensor’s first eigenvector, the fiber orientation distribution is determined and then approximated by periodic and non-periodic probability density functions (PDFs). In this study, 40 commercial paperboard samples, each consisting of three plies, were analyzed. From a given set of commonly used PDFs, the best fitting ones have been identified based on their original location in the paper roll and on their ply. It was found that the von Mises PDF provided the most accurate representation of fiber orientation distribution in the middle ply, while the Elliptical PDF was the most suitable for the outer plies. Moreover, a more pronounced fiber orientation anisotropy was observed at the edges of the paper roll than in its center. The best PDFs and their function parameters are provided to allow for direct usage in numerical microstructure models of paperboard, thus enhancing their representativeness.

Quantification of magnetization-transfer (MT) experiments is typically based on a model comprising a liquid pool “a” of free water and a semisolid pool “b” of motionally restricted macromolecules or membrane compounds. By a comprehensive fitting approach, high quality MT parameter maps of the human brain are obtained. In particular, a distinct correlation between the diffusion-tensor orientation with respect to the B0-magnetic field and the apparent transverse relaxation time, T2b, of the semisolid pool (i.e., the width of its absorption line) is observed. This orientation dependence is quantitatively explained by a refined dipolar lineshape for pool b that explicitly considers the specific geometrical arrangement of lipid bilayers wrapped around a cylindrical axon. The model inherently reduces the myelin membrane to its lipid constituents, which is motivated by previous studies on efficient interaction sites (e.g., cholesterol or galactocerebrosides) in the myelin membrane and on the origin of ultrashort T2 signals in cerebral white matter. The agreement between MT orientation effects and corresponding forward simulations using empirical diffusion imaging results as input as well as results from fits employing the novel lineshape support previous suggestions that the fiber orientation distribution in a voxel can be modeled as a scaled Bingham distribution. [Display omitted] •Observation of a correlation of qMT parameters and the orientation of WM fibers.•A novel RF absorption lineshape is derived considering the fiber orientation distribution.•The novel lineshape is used in simulations with typical in-vivo parameters.•Simulated data predict orientation dependence that follows the observations.•Novel lineshape is used for MT parameter fitting.

In recent years, due to the rapid development of industrial lightweight technology, composite materials based on fiber reinforced plastics (FRP) have been widely used in the industry. However, the environmental impact of the FRPs is higher each year. To overcome this impact, co-injection molding could be one of the good solutions. But how to make the suitable control on the skin/core ratio and how to manage the glass fiber orientation features are still significant challenges. In this study, we have applied both computer-aided engineering (CAE) simulation and experimental methods to investigate the fiber feature in a co-injection system. Specifically, the fiber orientation distributions and their influence on the tensile properties for the single-shot and co-injection molding have been discovered. Results show that based on the 60:40 of skin/core ratio and same materials, the tensile properties of the co-injection system, including tensile stress and modulus, are a little weaker than that of the single-shot system. This is due to the overall fiber orientation tensor at flow direction (A11) of the co-injection system being lower than that of the single-shot system. Moreover, to discover and verify the influence of the fiber orientation features, the fiber orientation distributions (FOD) of both the co-injection and single-shot systems have been observed using micro-computerized tomography (μ-CT) technology to scan the internal structures. The scanned images were further utilizing Avizo software to perform image analyses to rebuild the fiber structure. Specifically, the fiber orientation tensor at flow direction (A11) of the co-injection system is about 89% of that of the single-shot system in the testing conditions. This is because the co-injection part has lower tensile properties. Furthermore, the difference of the fiber orientation tensor at flow direction (A11) between the co-injection and the single-shot systems is further verified based on the fiber morphology of the μ-CT scanned image. The observed result is consistent with that of the FOD estimation using μ-CT scan plus image analysis.