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Quantifying the myelin sheath radius of myelinated axons in vivo is important for understanding, diagnosing, and monitoring various neurological disorders. Despite advancements in diffusion MRI (dMRI) microstructure techniques, models specifically designed to estimate myelin sheath radii remain unavailable. In this proof-of-concept theoretical study, we present two novel dMRI models that characterize the signal from water diffusion confined to cylindrical surfaces, approximating myelin water diffusion. We derive their spherical mean signals, which conveniently eliminate fiber orientation and dispersion effects. These models are further extended to account for multiple concentric cylinders, mimicking the layered structure of myelin. Additionally, we introduce a method to convert histological distributions of axonal inner radii from the literature into myelin sheath radius distributions and derive analytical expressions to estimate the effective myelin sheath radius expected from these distributions. Monte Carlo (MC) simulations conducted in cylindrical and spiral geometries validate the models, demonstrating agreement with analytical predictions across various diffusion regimes and significant correlations between the effective radii estimated from the histological distributions and the effective radius obtained by fitting the resulting dMRI signal to a single-cylinder model. These models may be integrated into existing multi-compartment dMRI techniques, opening the door to non-invasive, in vivo assessments of myelin sheath radii in MRI scanners equipped with strong diffusion gradients that enable measurements with short echo times. Further work is required to validate the technique with real dMRI data., Comment: 55 pages, 7 figures, 1 table, manuscript under review

Prior work on the Image Quality Transfer on Diffusion MRI (dMRI) has shown significant improvement over traditional interpolation methods. However, the difficulty in obtaining ultra-high resolution Diffusion MRI scans poses a problem in training neural networks to obtain high-resolution dMRI scans. Here we hypothesise that the inclusion of structural MRI images, which can be acquired at much higher resolutions, can be used as a guide to obtaining a more accurate high-resolution dMRI output. To test our hypothesis, we have constructed a novel framework that incorporates structural MRI scans together with dMRI to obtain high-resolution dMRI scans. We set up tests which evaluate the validity of our claim through various configurations and compare the performance of our approach against a unimodal approach. Our results show that the inclusion of structural MRI scans do lead to an improvement in high-resolution image prediction when T1w data is incorporated into the model input.

Purpose: This study aims to evaluate two distinct approaches for fibre radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfibre phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approach and a T2-based pore size estimation technique. Theory and Methods: A general diffusion-relaxation theoretical model for the spherical mean signal from water molecules within a distribution of cylinders with varying radii was introduced, encompassing the evaluated models as particular cases. Additionally, a new numerical approach was presented for estimating effective radii (i.e., MRI-visible mean radii) from the ground truth radii distributions, not reliant on previous theoretical approximations and adaptable to various acquisition sequences. The ground truth radii were obtained from Scanning Electron Microscope images. Results: Both methods show a linear relationship between effective radii estimated from MRI data and ground-truth radii distributions, though some discrepancies were observed. The spherical mean power-law method overestimated fibre radii. Conversely, the T2-based method exhibited higher sensitivity to smaller fibre radii but faced limitations in accurately estimating the radius in one particular phantom, possibly due to material-specific relaxation changes. Conclusion: The study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibres. The T2-based technique, unlike the spherical mean power-law method, does not demand ultra-high diffusion gradients but requires calibration with known radius distributions. This research contributes to the ongoing development and evaluation of neuroimaging techniques for fibre radius estimation, highlights the advantages and limitations of both methods and provides datasets for reproducible research., Comment: 37 pages, 8 figures. Accepted in Magnetic Resonance in Medicine, Dec, 2023

Biophysical models of diffusion tailored to quantify gray matter microstructure are gathering increasing interest. The two-compartment Neurite EXchange Imaging ($NEXI$) model has been proposed recently to account for neurites, extra-cellular space and exchange across the cell membrane. $NEXI$ parameter estimation requires multi-shell multi-diffusion time data and has so far only been implemented experimentally on animal data collected on a preclinical MRI set-up. In this work, the first ever translation of $NEXI$ to the human cortex in vivo was achieved using a 3T Connectom MRI system with 300 mT/m gradients, that enables the acquisition of a broad range of b-values (0 - 7.5 ms/$\mu m^{2}$) with a window of diffusion times (20 - 49 ms) suitable for the expected characteristic exchange times (10 - 50 ms). Microstructure estimates of four model variants: $NEXI$, $NEXI_{dot}$ (its extension with the addition of a dot compartment) and their respective versions that correct for the Rician noise floor ($NEXI_{RM}$ and $NEXI_{dot,RM}$) that particularly impacts high b-value signal, were compared. The reliability of estimates in each model variant was evaluated in synthetic and human in vivo data. In the latter, the intra-subject (scan-rescan) vs between-subjects variability of microstructure estimates were compared in the cortex. The better performance of $NEXI_{RM}$ highlights the importance of correcting for Rician bias in the $NEXI$ model to obtain accurate estimates of microstructure parameters in the human cortex, and the sensitivity of the $NEXI$ framework to individual differences in cortical microstructure. This groundbreaking application of $NEXI$ in humans marks a pivotal moment, unlocking new avenues for studying neurodevelopment, ageing, and various neurodegenerative disorders., Comment: Article: 24 pages, 9 figures, 3 tables. Supplementary material: 11 pages, 5 figures

Axon radius is a potential biomarker for brain diseases and a crucial tissue microstructure parameter that determines the speed of action potentials. Diffusion MRI (dMRI) allows non-invasive estimation of axon radius, but accurately estimating the radius of axons in the human brain is challenging. Most axons in the brain have a radius below one micrometer, which falls below the sensitivity limit of dMRI signals even when using the most advanced human MRI scanners. Therefore, new MRI methods that are sensitive to small axon radii are needed. In this proof-of-concept investigation, we examine whether a surface-based axonal relaxation process could mediate a relationship between intra-axonal T2 and T1 times and inner axon radius, as measured using postmortem histology. A unique in vivo human diffusion-T1-T2 relaxation dataset was acquired on a 3T MRI scanner with ultra-strong diffusion gradients, using a strong diffusion-weighting (i.e., b = 6,000 s/mm$^2$) and multiple inversion and echo times. A second reduced diffusion-T2 dataset was collected at various echo times to evaluate the model further. The intra-axonal relaxation times were estimated by fitting a diffusion-relaxation model to the orientation-averaged spherical mean signals. Our analysis revealed that the proposed surface-based relaxation model effectively explains the relationship between the estimated relaxation times and the histological axon radius measured in various corpus callosum regions. Using these histological values, we developed a novel calibration approach to predict axon radius in other areas of the corpus callosum. Notably, the predicted radii and those determined from histological measurements were in close agreement., Comment: 47 pages, 10 figures

In this work, we evaluate how neural networks with periodic activation functions can be leveraged to reliably compress large multidimensional medical image datasets, with proof-of-concept application to 4D diffusion-weighted MRI (dMRI). In the medical imaging landscape, multidimensional MRI is a key area of research for developing biomarkers that are both sensitive and specific to the underlying tissue microstructure. However, the high-dimensional nature of these data poses a challenge in terms of both storage and sharing capabilities and associated costs, requiring appropriate algorithms able to represent the information in a low-dimensional space. Recent theoretical developments in deep learning have shown how periodic activation functions are a powerful tool for implicit neural representation of images and can be used for compression of 2D images. Here we extend this approach to 4D images and show how any given 4D dMRI dataset can be accurately represented through the parameters of a sinusoidal activation network, achieving a data compression rate about 10 times higher than the standard DEFLATE algorithm. Our results show that the proposed approach outperforms benchmark ReLU and Tanh activation perceptron architectures in terms of mean squared error, peak signal-to-noise ratio and structural similarity index. Subsequent analyses using the tensor and spherical harmonics representations demonstrate that the proposed lossy compression reproduces accurately the characteristics of the original data, leading to relative errors about 5 to 10 times lower than the benchmark JPEG2000 lossy compression and similar to standard pre-processing steps such as MP-PCA denosing, suggesting a loss of information within the currently accepted levels for clinical application.

Diffusion weighted imaging techniques permit us to infer microstructural detail in biological tissue in vivo and noninvasively. Modern sequences are based on advanced diffusion encoding schemes, allowing probing of more revealing measures of tissue microstructure than the standard apparent diffusion coefficient or fractional anisotropy. Though these methods may result in faster or more revealing acquisitions, they generally demand prior knowledge of sequence-specific parameters for which there is no accepted sharing standard. Here, we present a metadata labelling scheme suitable for the needs of developers and users within the diffusion neuroimaging community alike: a lightweight, unambiguous parametric map relaying acqusition parameters. This extensible scheme supports a wide spectrum of diffusion encoding methods, from single diffusion encoding to highly complex sequences involving arbitrary gradient waveforms. Built under the brain imaging data structure (BIDS), it allows storage of advanced diffusion MRI data comprehensively alongside any other neuroimaging information, facilitating processing pipelines and multimodal analyses. We illustrate the usefulness of this BIDS-extension with a range of example data, and discuss the extension's impact on pre- and post-processing software.

Diffusion magnetic resonance imaging (dMRI) is a relatively modern technique used to study tissue microstructure in a non-invasive way. Non-Gaussian diffusion representation is related to the restricted diffusion and can provide information about the underlying tissue properties. In this paper, we analytically derive $n$-th order statistics of the signal considering a stretched-exponential representation of the diffusion. Then, we retrieve the Q-space quantitative measures such as the Return-To-the-Origin Probability (RTOP), Q-space mean square displacement (QMSD), Q-space mean fourth-order displacement (QMFD). The stretched-exponential representation enables the handling of the diffusion contributions from a higher $b$-value regime under a non-Gaussian assumption, which can be useful in diagnosing or prognosis of neurodegenerative diseases in the early stages. Numerical implementation of the method is freely available at https://github.com/TPieciak/Stretched.

There is an urgent need for a paradigm shift from group-wise comparisons to individual diagnosis in diffusion MRI (dMRI) to enable the analysis of rare cases and clinically-heterogeneous groups. Deep autoencoders have shown great potential to detect anomalies in neuroimaging data. We present a framework that operates on the manifold of white matter (WM) pathways to learn normative microstructural features, and discriminate those at genetic risk from controls in a paediatric population., Comment: Medical Imaging with Deep Learning (MIDL2020) Conference Short Paper

Magnetic Resonance Fingerprinting (MRF) enables the simultaneous quantification of multiple properties of biological tissues. It relies on a pseudo-random acquisition and the matching of acquired signal evolutions to a precomputed dictionary. However, the dictionary is not scalable to higher-parametric spaces, limiting MRF to the simultaneous mapping of only a small number of parameters (proton density, T1 and T2 in general). Inspired by diffusion-weighted SSFP imaging, we present a proof-of-concept of a novel MRF sequence with embedded diffusion-encoding gradients along all three axes to efficiently encode orientational diffusion and T1 and T2 relaxation. We take advantage of a convolutional neural network (CNN) to reconstruct multiple quantitative maps from this single, highly undersampled acquisition. We bypass expensive dictionary matching by learning the implicit physical relationships between the spatiotemporal MRF data and the T1, T2 and diffusion tensor parameters. The predicted parameter maps and the derived scalar diffusion metrics agree well with state-of-the-art reference protocols. Orientational diffusion information is captured as seen from the estimated primary diffusion directions. In addition to this, the joint acquisition and reconstruction framework proves capable of preserving tissue abnormalities in multiple sclerosis lesions.

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation., Comment: 22 pages, 7 figures

In machine learning, novelty detection is the task of identifying novel unseen data. During training, only samples from the normal class are available. Test samples are classified as normal or abnormal by assignment of a novelty score. Here we propose novelty detection methods based on training variational autoencoders (VAEs) on normal data. Since abnormal samples are not used during training, we define novelty metrics based on the (partially complementary) assumptions that the VAE is less capable of reconstructing abnormal samples well; that abnormal samples more strongly violate the VAE regularizer; and that abnormal samples differ from normal samples not only in input-feature space, but also in the VAE latent space and VAE output. These approaches, combined with various possibilities of using (e.g. sampling) the probabilistic VAE to obtain scalar novelty scores, yield a large family of methods. We apply these methods to magnetic resonance imaging, namely to the detection of diffusion-space (q-space) abnormalities in diffusion MRI scans of multiple sclerosis patients, i.e. to detect multiple sclerosis lesions without using any lesion labels for training. Many of our methods outperform previously proposed q-space novelty detection methods. We also evaluate the proposed methods on the MNIST handwritten digits dataset and show that many of them are able to outperform the state of the art., Comment: 11 pages, 2 figures