arXiv subjects

Jonathan Rafael-Patiño

Publications and source records attributed to Jonathan Rafael-Patiño.

5 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↗

arXiv2025

Spatially Regularized Super-Resolved Constrained Spherical Deconvolution (SR$^2$-CSD) of Diffusion MRI Data

Constrained Spherical Deconvolution (CSD) is widely used to estimate the white matter fiber orientation distribution (FOD) from diffusion MRI data. Its angular resolution depends on the maximum spherical harmonic order ($l_{max}$): low $l_{max}$ yields smooth but poorly resolved FODs, while high $l_{max}$, as in Super-CSD, enables resolving fiber crossings with small inter-fiber angles but increases sensitivity to noise. In this proof-of-concept study, we introduce Spatially Regularized Super-Resolved CSD (SR$^2$-CSD), a novel method that regularizes Super-CSD using a spatial FOD prior estimated via a self-calibrated total variation denoiser. We evaluated SR$^2$-CSD against CSD and Super-CSD across four datasets: (i) the HARDI-2013 challenge numerical phantom, assessing angular and peak number errors across multiple signal-to-noise ratio (SNR) levels and CSD variants (single-/multi-shell, single-/multi-tissue); (ii) the Sherbrooke in vivo dataset, evaluating spatial coherence of FODs; (iii) a six-subject test-retest dataset acquired with both full (96 gradient directions) and subsampled (45 directions) protocols, assessing reproducibility; and (iv) the DiSCo phantom, evaluating tractography accuracy under varying SNR levels and multiple noise repetitions. Across all evaluations, SR$^2$-CSD consistently reduced angular and peak number errors, improved spatial coherence, enhanced test-retest reproducibility, and yielded connectivity matrices more strongly correlated with ground-truth. Most improvements were statistically significant under multiple-comparison correction. These results demonstrate that incorporating spatial priors into CSD is feasible, mitigates estimation instability, and improves FOD reconstruction accuracy.

physics.med-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↗

arXiv2023

Why is the winner the best?

International benchmarking competitions have become fundamental for the comparative performance assessment of image analysis methods. However, little attention has been given to investigating what can be learnt from these competitions. Do they really generate scientific progress? What are common and successful participation strategies? What makes a solution superior to a competing method? To address this gap in the literature, we performed a multi-center study with all 80 competitions that were conducted in the scope of IEEE ISBI 2021 and MICCAI 2021. Statistical analyses performed based on comprehensive descriptions of the submitted algorithms linked to their rank as well as the underlying participation strategies revealed common characteristics of winning solutions. These typically include the use of multi-task learning (63%) and/or multi-stage pipelines (61%), and a focus on augmentation (100%), image preprocessing (97%), data curation (79%), and postprocessing (66%). The "typical" lead of a winning team is a computer scientist with a doctoral degree, five years of experience in biomedical image analysis, and four years of experience in deep learning. Two core general development strategies stood out for highly-ranked teams: the reflection of the metrics in the method design and the focus on analyzing and handling failure cases. According to the organizers, 43% of the winning algorithms exceeded the state of the art but only 11% completely solved the respective domain problem. The insights of our study could help researchers (1) improve algorithm development strategies when approaching new problems, and (2) focus on open research questions revealed by this work.

cs.CV↗

arXiv2020

A Signal Peak Separation Index for axisymmetric B-tensor encoding

Diffusion-weighted MRI (DW-MRI) has recently seen a rising interest in planar, spherical and general B-tensor encodings. Some of these sequences have aided traditional linear encoding in the estimation of white matter microstructural features, generally by making DW-MRI less sensitive to the orientation of axon fascicles in a voxel. However, less is known about their potential to make the signal more sensitive to fascicle orientation, especially in crossing-fascicle voxels. Although planar encoding has been commended for the resemblance of its signal with the voxel's orientation distribution function (ODF), linear encoding remains the near undisputed method of choice for orientation estimation. This paper presents a theoretical framework to gauge the sensitivity of axisymmetric B-tensors to fascicle orientations. A signal peak separation index (SPSI) is proposed, motivated by theoretical considerations on a simple multi-tensor model of fascicle crossing. Theory and simulations confirm the intuition that linear encoding, because it maximizes B-tensor anisotropy, possesses an intrinsic advantage over all other axisymmetric B-tensors. At identical SPSI however, oblate B-tensors yield higher signal and may be more robust to acquisition noise than their prolate counterparts. The proposed index relates the properties of the B-tensor to those of the tissue microstructure in a straightforward way and can thus guide the design of diffusion sequences for improved orientation estimation and tractography.

physics.med-ph↗