arXiv subjects

Chantal M. W. Tax

Publications and source records attributed to Chantal M. W. Tax.

13 recordsLinked to original sources

arXiv2026

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

Objective. To derive an exact analytical expression for the diffusion MRI signal arising from diffusion confined to a cylindrical surface under finite rectangular pulsed-gradient spin-echo (PGSE) gradients, and to develop computationally efficient strategies for repeated model evaluations. Approach. The Bloch-Torrey equation was solved using a spectral matrix formalism of the Laplace operator in the eigenbasis of the cylindrical surface. The resulting signal is expressed as a product of non-commuting matrix exponentials and is valid for arbitrary rectangular gradient durations and separations, without approximations to the diffusion propagator or spin phase distribution. A reduced real spectral basis was introduced to decrease the dimensionality of the problem. Accelerated implementations based on Strang splitting and Gauss-Legendre quadrature were developed for repeated signal evaluations and computation of the spherical mean. The analytical signal was validated against Monte Carlo diffusion simulations. Main results. The exact formulation showed excellent agreement with Monte Carlo simulations over a wide range of cylinder radii and acquisition parameters. The spectral expansion converged rapidly with mode order, and the reduced basis substantially decreased computational cost without loss of accuracy. The accelerated implementations provided large additional speed-ups while retaining controllable errors relative to the exact solution. Significance. The proposed framework extends exact finite-pulse solutions of the Bloch-Torrey equation to diffusion confined to cylindrical surfaces and provides practical implementations for directional and orientationally averaged diffusion MRI signals. It therefore offers an approximation-free reference for assessing faster signal approximations and for applications requiring large numbers of model evaluations.

physics.med-ph↗

arXiv2026

Diffusion MRI preprocessing affects ADC estimation and automatic PI-RADS v2.1 classification in bi-parametric prostate MRI

Diffusion-weighted imaging (DWI) is acquired as part of bi-parametric prostate MRI, but suffers from artifacts that degrade downstream quantitative and diagnostic performance. While DWI preprocessing is standard in brain imaging, its adoption in prostate imaging remains limited and lacks standardized pipelines. This study investigated the effect of different DWI preprocessing strategies on apparent diffusion coefficient (ADC) estimation and automatic Prostate Imaging Reporting and Data System (PI-RADS) classification. 268 cases were derived from the fastMRI prostate cohort by sequentially applying denoising, Gibbs-ringing correction, and diffeomorphic registration for susceptibility distortion correction. ADC maps were compared using linear least squares (LLS) and iteratively-weighted LLS (IWLLS). A 3-class DenseNet classifier was trained to predict PI-RADS scores from multi-channel MRI inputs. ADC analysis revealed statistically significant differences across preprocessing pipelines, with LLS and IWLLS producing numerically equivalent maps. Linear relationships between ADC values were preserved across most datasets (PCC ~0.99), while distortion correction realigned DWI to T2w anatomy and altered ADC values accordingly (PCC ~0.90). Classification showed the best AUROC and sensitivity for high-risk PI-RADS classes in the fully processed dataset. False-negative analysis revealed this dataset produced the least overconfident incorrect predictions on high-risk classes, which is a desirable property for clinical triage. DWI preprocessing, particularly distortion correction, enhances both ADC map quality and the predictive power of deep learning models for PI-RADS classification, supporting the need for optimized preprocessing pipelines in prostate MRI.

eess.IV↗

arXiv2026

Design of a double breast gradient coil with controlled anterior posterior gradient variation for diffusion weighted imaging

Introduction High performance gradients poses a promise for breast diffusion weighted imaging (DWI) but are restricted by physiological limits in whole body scanners. While local nonlinear coils offer higher amplitudes, they often suffer from severe gradient reduction near the chest wall. Methods We introduced an optimization framework incorporating a constraint to control anterior posterior gradient variation. A width based figure of merit was defined to evaluate performance regarding coil efficiency and minimum wire width. A prototype was constructed to validate the design methodology. Results The optimized coil achieved a 2.35 fold efficiency increase over standard linear coils. Compared to previous nonlinear designs, the new constraint reduced spatial variation by 35.7% and improved minimum efficiency near the chest wall by 2.6 fold. Experimental field maps matched simulations with errors under 8%. Discussion The proposed method effectively mitigates the trade-off between gradient strength and spatial uniformity along anterior posterior direction. By enhancing performance in the posterior breast region, the design addresses a critical limitation of previous local coils. Conclusion This framework enables the development of high performance, robust local gradient coils, facilitating the clinical implementation of advanced DWI protocols for breast cancer screening.

physics.med-ph↗

arXiv2026

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

Implicit neural representations for accurate estimation of the standard model of white matter

Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments. However, due to the model its high-dimensional nature, accurately estimating its parameters poses a complex problem and remains an active field of research, in which different (machine learning) strategies have been proposed. This work introduces an estimation framework based on implicit neural representations (INRs), which incorporate spatial regularization through the sinusoidal encoding of the input coordinates. The INR method is evaluated on both synthetic and in vivo datasets and compared to existing methods. Results demonstrate superior accuracy of the INR method in estimating SM parameters, particularly in low signal-to-noise conditions. Additionally, spatial upsampling of the INR can represent the underlying dataset anatomically plausibly in a continuous way. The INR is self-supervised, eliminating the need for labeled training data. It achieves fast inference, is robust to noise, supports joint estimation of SM kernel parameters and the fiber orientation distribution function with spherical harmonics orders up to at least 8, and accommodates gradient non-uniformity corrections. The combination of these properties positions INRs as a potentially important tool for analyzing and interpreting diffusion MRI data.

eess.IV↗

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↗

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↗

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

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

Automated characterization of noise distributions in diffusion MRI data

Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition process, which is usually not available. We introduce two new automated methods using the moments and maximum likelihood equations of the Gamma distribution to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the framework automatic and robust to artifacts. Simulations were created for two diffusion weightings with parallel imaging. Furthermore, MRI data of a water phantom with different combinations of parallel imaging were acquired. Finally, experiments on freely available datasets are used to assess reproducibility when limited information about the acquisition protocol is available. Additionally, we demonstrated the applicability of the proposed methods for a bias correction and denoising task on an in vivo dataset. A generalized version of the bias correction framework for non integer degrees of freedom is also introduced. The proposed framework is compared with three other algorithms with datasets from three vendors, employing different reconstruction methods. Simulations showed that assuming a Rician distribution can lead to misestimation of the noise distribution in parallel imaging. Results showed that signal leakage in multiband can also lead to a misestimation of the noise distribution. Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variability than compared methods. Results show that the proposed methods reduce the appearance of noise at high b-value. The proposed algorithms herein can estimate both parameters of the noise distribution automatically, are robust to signal leakage artifacts and perform best when used on acquired noise maps.

eess.IV↗

arXiv2020

Scanner Invariant Representations for Diffusion MRI Harmonization

Purpose: In the present work we describe the correction of diffusion-weighted MRI for site and scanner biases using a novel method based on invariant representation. Theory and Methods: Pooled imaging data from multiple sources are subject to variation between the sources. Correcting for these biases has become very important as imaging studies increase in size and multi-site cases become more common. We propose learning an intermediate representation invariant to site/protocol variables, a technique adapted from information theory-based algorithmic fairness; by leveraging the data processing inequality, such a representation can then be used to create an image reconstruction that is uninformative of its original source, yet still faithful to underlying structures. To implement this, we use a deep learning method based on variational auto-encoders (VAE) to construct scanner invariant encodings of the imaging data. Results: To evaluate our method, we use training data from the 2018 MICCAI Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our proposed method shows improvements on independent test data relative to a recently published baseline method on each subtask, mapping data from three different scanning contexts to and from one separate target scanning context. Conclusion: As imaging studies continue to grow, the use of pooled multi-site imaging will similarly increase. Invariant representation presents a strong candidate for the harmonization of these data.

q-bio.QM↗

arXiv2019

Multi-Stage Prediction Networks for Data Harmonization

In this paper, we introduce multi-task learning (MTL) to data harmonization (DH); where we aim to harmonize images across different acquisition platforms and sites. This allows us to integrate information from multiple acquisitions and improve the predictive performance and learning efficiency of the harmonization model. Specifically, we introduce the Multi Stage Prediction (MSP) Network, a MTL framework that incorporates neural networks of potentially disparate architectures, trained for different individual acquisition platforms, into a larger architecture that is refined in unison. The MSP utilizes high-level features of single networks for individual tasks, as inputs of additional neural networks to inform the final prediction, therefore exploiting redundancy across tasks to make the most of limited training data. We validate our methods on a dMRI harmonization challenge dataset, where we predict three modern platform types, from one obtained from an old scanner. We show how MTL architectures, such as the MSP, produce around 20\% improvement of patch-based mean-squared error over current state-of-the-art methods and that our MSP outperforms off-the-shelf MTL networks. Our code is available https://github.com/sbb-gh/ .

cs.LG↗

arXiv2018

Spherical Harmonic Residual Network for Diffusion Signal Harmonization

Diffusion imaging is an important method in the field of neuroscience, as it is sensitive to changes within the tissue microstructure of the human brain. However, a major challenge when using MRI to derive quantitative measures is that the use of different scanners, as used in multi-site group studies, introduces measurement variability. This can lead to an increased variance in quantitative metrics, even if the same brain is scanned. Contrary to the assumption that these characteristics are comparable and similar, small changes in these values are observed in many clinical studies, hence harmonization of the signals is essential. In this paper, we present a method that does not require additional preprocessing, such as segmentation or registration, and harmonizes the signal based on a deep learning residual network. For this purpose, a training database is required, which consist of the same subjects, scanned on different scanners. The results show that harmonized signals are significantly more similar to the ground truth signal compared to no harmonization, but also improve in comparison to another deep learning method. The same effect is also demonstrated in commonly used metrics derived from the diffusion MRI signal.

cs.CV↗