arXiv subjects

Derek K. Jones

Publications and source records attributed to Derek K. Jones.

17 recordsLinked to original sources

arXiv2026

Contextual Cellular Growth (ConCeG) of neural cells for realistic grey matter tissue generation for diffusion MRI simulations

Accurate interpretation of diffusion magnetic resonance imaging (dMRI) signals in grey matter (GM) remains challenging due to the complex, heterogeneous, and densely packed cellular environment. Numerical phantoms provide a controlled framework for investigating the relationship between microstructure and diffusion signals, yet existing approaches often lack the morphological realism and multi-cellular organisation required to faithfully represent GM tissue. In this work, we introduce Contextual Cellular Growth (ConCeG), a generative framework for creating individual cells or constructing dense, three-dimensional, multi-cellular GM substrates informed by real neuronal and glial morphologies. The method combines topological neuron synthesis with a spatially constrained growth network, allowing for the controlled generation of heterogeneous cellular environments with realistic intra- and extracellular compartments. Synthetic cells are generated using morphological and topological characteristics derived from biological reconstructions. We validate the framework through comparisons of structural features with real cellular data, demonstrating strong agreement in branch order, length, angle, and tortuosity distributions. Power spectrum analysis further shows that both intracellular compartments reproduce the spatial correlations observed in biological tissue. Together, these results show ConCeG provides a biologically grounded framework for generating grey matter substrates suitable for large scale diffusion MRI simulation.

physics.med-ph↗

arXiv2026

Exact analytical PGSE signal for diffusion confined to a cylindrical surface using a spectral Laplacian formalism

Pulsed-gradient spin-echo (PGSE) MRI experiments probe molecular self-diffusion through spin phase accumulation under time-dependent magnetic field gradients. For diffusion confined to cylindrical surfaces, existing analytical signal models typically rely on the narrow-pulse limit, approximate treatments of finite gradient durations, or the Gaussian phase approximation, which become increasingly inaccurate at high diffusion weightings. Here, we derive an exact analytical solution of the Bloch-Torrey equation for diffusion confined to a cylindrical surface under finite PGSE gradients and obtain the corresponding diffusion MRI signal expression valid for arbitrary gradient durations and separations. The derivation is based on a spectral matrix formalism of the Laplace operator in the eigenbasis of the confining geometry. The signal is expressed as a product of non-commuting matrix exponentials, without approximations to the diffusion propagator or the spin phase distribution. We further introduce a reduced real spectral basis exploiting the symmetry of the cylindrical surface, substantially improving computational efficiency. Building on this exact formulation, we develop efficient numerical strategies for repeated signal evaluations, including a Strang splitting approximation of the matrix exponentials and an efficient computation of the spherical mean signal using Gauss-Legendre quadrature. The analytical signal is validated against Monte Carlo simulations over a wide range of cylinder radii and experimental parameters. The accelerated implementations are benchmarked against the exact formulation to quantify accuracy-runtime trade-offs. These results establish a computationally efficient framework for evaluating directional and orientationally averaged diffusion MRI signals in applications requiring large numbers of model evaluations.

physics.med-ph↗

arXiv2025

Ultra-Strong Gradient Diffusion MRI with Self-Supervised Learning for Prostate Cancer Characterization

Diffusion MRI (dMRI) enables non-invasive assessment of prostate microstructure but conventional dMRI metrics such as the Apparent Diffusion Coefficient in multiparametric MRI and reflect a mixture of underlying tissues features rather than distinct histologic characteristics. Integrating dMRI with the compartment-based biophysical VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumours) framework offers richer microstructural insights, though clinical gradient systems (40-80 mT/m) often suffer from poor signal-to-noise ratio at stronger diffusion weightings due to prolonged echo times. Ultra-strong gradients (e.g., 300 mT/m) can mitigate these limitations by improving SNR and contrast-to-noise ratios. This study investigates whether physics-informed self-supervised VERDICT (ssVERDICT) fitting when combined with ultra-strong gradient data, enhances prostate microstructural characterization relative to current fitting approaches and clinical gradient systems. We developed enhanced ssVERDICT fitting approaches using dense multilayer perceptron and convolutional U-Net architectures, comparing them against non-linear least-squares (NLLS) VERDICT fitting, original ssVERDICT implementation, and Diffusion Kurtosis Imaging across clinical- to ultra-strong gradient systems. For the same ultra-strong gradient data, Dense ssVERDICT outperformed NLLS VERDICT, boosting median CNR by 47%, cutting inter-patient Coefficient of Variation by 52%, and reducing pooled $f_{ic}$ variation by 50%. Overall, Dense ssVERDICT delivered the highest CNR, the most stable parameter estimates, and the clearest tumour-normal contrast compared with conventional fitting methods and clinical gradient systems. These findings underscore that meaningful gains in non-invasive prostate cancer characterization arise from the combination of advanced gradient systems and deep learning-based modelling.

eess.IV↗

arXiv2025

Bayesian Insights into Exchange and Restriction in Gray Matter Diffusion MRI

Biophysical models in diffusion MRI (dMRI) hold promise for characterizing gray matter tissue microstructure. Yet, the reliability of their parameter estimates remains largely under-studied, especially in models that incorporate water exchange. In this study, we investigate the accuracy, precision, and presence of degeneracy of two recently proposed gray matter models, NEXI and SANDIX, using established acquisition protocols, on both simulated and \textit{in vivo} data. We employ $\mu$GUIDE, a Bayesian inference framework based on deep learning, to quantify parameter uncertainty and detect degeneracies, enabling a more interpretable assessment of model fits. Our results show that while some microstructural parameters, such as extra-cellular diffusivity and neurite signal fraction, are robustly estimated, others, including exchange time and soma radius, are often associated with high uncertainty and estimation bias, particularly under realistic noise conditions and reduced acquisition protocols. Comparison with non-linear least squares fitting highlights the critical advantage of uncertainty-aware methods: the ability to flag and filter out unreliable estimates. Together, these findings emphasize the need to report uncertainty and account for model degeneracies when interpreting model-based estimates. Our study advocates for the integration of probabilistic fitting approaches into imaging pipelines to improve reproducibility and biological interpretability.

physics.med-ph↗

arXiv2025

Decoding Gray Matter: large-scale analysis of brain cell morphometry to inform microstructural modeling of diffusion MR signals

The structure of grey matter has long been a key focus in neuroscience, as cell morphology varies by type and can be affected by neurological conditions. Understanding these variations is essential for studying brain function and disease. Diffusion-weighted MRI (dMRI) is a powerful non-invasive tool for examining cellular microstructure in vivo. However, for dMRI to accurately reflect cellular features, it is crucial to determine which aspects of morphology influence its measurements. Proper interpretation of dMRI data depends on understanding its sensitivity to different cellular characteristics. Despite growing interest in cellular morphology, there has been no systematic report on the key features defining different neural cell types. To address this, we analyzed over 11,500 three-dimensional cellular reconstructions across three species and nine cell types, establishing reference values for critical morphological traits. These traits fall into three categories: structural features that define the cell's skeletal framework, shape features that describe spatial organization, and topological features that break down cellular structure to distinguish cell types. Beyond reporting these reference values, we examine their relevance for dMRI, identifying which neural features dMRI can detect and which cell types may be distinguishable. To complement the statistical analysis, we also provide high resolution 3D surface meshes representative of each cell type and species. This work provides essential benchmarks for grey matter research, offering new guidelines on linking neuroimaging measurements to neurobiology. These reference values will be a valuable resource for neuroscientists and neuroimaging researchers, aiding in the interpretation of imaging data and the refinement of brain tissue models.

physics.bio-ph↗

arXiv2025

A diffusion MRI model for random walks confined on cylindrical surfaces: Towards non-invasive quantification of myelin sheath radius

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, there are currently no models specifically designed to estimate myelin sheath radii. This proof-of-concept theoretical study presents 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, eliminating fiber orientation and dispersion effects for convenience. 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. We also 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. These simulations demonstrate agreement with analytical predictions. Furthermore, we observe significant correlations between the effective radii derived from histological distributions and those obtained by fitting the dMRI signal to a single-cylinder model. These models may be integrated with existing multi-compartment dMRI techniques, opening the door to non-invasive in vivo assessments of myelin sheath radii. Such assessments would require MRI scanners equipped with strong diffusion gradients, allowing measurements with short echo times. Further work is required to validate the technique with real dMRI data and histological measurements.

physics.med-ph↗

arXiv2024

Image Quality Transfer of Diffusion MRI Guided By High-Resolution Structural MRI

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.

eess.IV↗

arXiv2023

Pore size estimation in axon-mimicking microfibres with diffusion-relaxation MRI

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.

physics.med-ph↗

arXiv2023

Estimating axon radius using diffusion-relaxation MRI: calibrating a surface-based relaxation model with histology

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.

physics.med-ph↗

arXiv2023

Quantifying human gray matter microstructure using NEXI and 300 mT/m gradients

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/$μm^{2}$) 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.

physics.med-ph↗

arXiv2022

Lossy compression of multidimensional medical images using sinusoidal activation networks: an evaluation study

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.

eess.IV↗

arXiv2021

aDWI-BIDS: an extension to the brain imaging data structure for advanced diffusion weighted imaging

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.

physics.med-ph↗

arXiv2020

Q-space quantitative diffusion MRI measures using a stretched-exponential representation

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.

eess.SP↗

arXiv2020

Tractometry-based Anomaly Detection for Single-subject White Matter Analysis

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.

q-bio.QM↗

arXiv2020

Deep learning-based parameter mapping for joint relaxation and diffusion tensor MR Fingerprinting

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.

physics.med-ph↗

arXiv2018

q-Space Novelty Detection with Variational Autoencoders

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.

stat.ML↗

arXiv2018

Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

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.

physics.bio-ph↗