Revisiting the T2 spectrum imaging inverse problem: Bayesian regularized non-negative least squares

Canales-Rodríguez, Erick Jorge; Pizzolato, Marco; Yu, Thomas; Piredda, Gian Franco; Hilbert, Tom; Raduà, Joaquim; Kober, Tobias; Thiran, Jean‐Philippe

doi:10.1016/j.neuroimage.2021.118582

Cited by 10 publications

(15 citation statements)

References 65 publications

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“…Regularized NNLS could furthermore complicate the quantification of the intermediate fraction due to the relatively small intermediate range. New fitting techniques, such as Bayesian fitting or physics‐informed neural networks, show potential to overcome these limitations 24–26 . Optimized b ‐value strategies combined with these promising new fitting techniques could open up new possibilities for accurate and stable voxel‐wise fitting of the intermediate component.…”

Section: Discussionmentioning

confidence: 99%

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An optimized b‐value sampling for the quantification of interstitial fluid using diffusion‐weighted MRI, a genetic algorithm approach

Drenthen

Jansen

der

et al. 2023

Magnetic Resonance in Med

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Multi-b-value diffusion-weighted MRI techniques can simultaneously measure the parenchymal diffusivity, microvascular perfusion, and a third, intermediate diffusion component. This component is related to the interstitial fluid in the brain parenchyma. However, simultaneously estimating three diffusion components from multi-b-value data is difficult and has strong dependence on SNR and chosen b-values. As the number of acquired b-values is limited due to scanning time, it is important to know which b-values are most effective to be included. Therefore, this study evaluates an optimized b-value sampling for interstitial fluid estimation. Method:The optimized b-value sampling scheme is determined using a genetic algorithm. Subsequently, the performance of this optimized sampling is assessed by comparing it with a linear, logarithmic, and previously proposed sampling scheme, in terms of the RMS error (RMSE) for the intermediate component estimation. The in vivo performance of the optimized sampling is assessed using 7T data with 101 equally spaced b-values ranging from 0 to 1000 s/mm 2 . In this case, the RMSE was determined by comparing the fit that includes all b-values. Results: The optimized b-value sampling for estimating the intermediate component was reported to be [0, 30, 90, 210, 280, 350, 580, 620, 660, 680, 720, 760, 980, 990, 1000] s/mm 2 . For computer simulations, the optimized sampling had a lower RMSE, compared with the other samplings for varying levels of SNR. For the in vivo data, the voxel-wise RMSE of the optimized sampling was lower compared with other sampling schemes. Conclusion:The genetic algorithm-optimized b-value scheme improves the quantification of the diffusion component related to interstitial fluid in terms of a lower RMSE.

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Section: Discussionmentioning

confidence: 99%

“…New fitting techniques, such as Bayesian fitting or physics-informed neural networks, show potential to overcome these limitations. [24][25][26] Optimized b-value strategies combined with these promising new fitting techniques could open up new possibilities for accurate and stable voxel-wise fitting of the intermediate component.…”

Section: F I G U R Ementioning

confidence: 99%

An optimized b‐value sampling for the quantification of interstitial fluid using diffusion‐weighted MRI, a genetic algorithm approach

Drenthen

Jansen

der

et al. 2023

Magnetic Resonance in Med

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show abstract

“…This naturally comes at the cost of an additional, inevitable trade-off between bias and variance of the estimates. Such a trade-off could be optimized using adaptive regularization criteria such as those discussed, for instance, for 2 relaxometry (Canales-Rodríguez, Pizzolato, Piredda, Hilbert, Kunz, Pot, Yu, Salvador, Pomarol-Clotet, Kober et al, 2021a;Canales-Rodríguez, Pizzolato, Yu, Piredda, Hilbert, Radua, Kober and Thiran, 2021b). Moreover, in the future, the integration of necessary constraints (Haije, Özarslan and Feragen, 2020) while fitting the signal could ensure that the optimization of Eq.…”

Section: Discussionmentioning

confidence: 99%

Axial and radial axonal diffusivities from single encoding strongly diffusion-weighted MRI

Pizzolato¹,

Canales‐Rodríguez²,

Andersson³

et al. 2022

Preprint

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We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown orientation distribution of axons. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated. After revising existing theory, we introduce a new general method for the estimation of both axonal diffusivities at strong diffusion weightings based on zonal harmonics modeling. We additionally show how this could lead to estimates that are free from partial volume bias with, for instance, gray matter. We test the method on publicly available data from the MGH Adult Diffusion Human Connectome project dataset. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii. We address the estimation problem also from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

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“…To determine the whole radius distribution, future studies should generalize the used models to estimate distributions of diffusivities or T 2 times, respectively. [70][71][72][73][74][75][76][77] Fifth, all our analyses used raw diffusion-relaxation MRI data without preprocessing, so the Rician bias 78 may partially affect our results. Nevertheless, we verified that the SNR of our data was 34 and visually inspected the data to confirm our images were not dominated by noise.…”

Section: F I G U R Ementioning

confidence: 99%

Pore size estimation in axon‐mimicking microfibers with diffusion‐relaxation MRI

Canales‐Rodríguez,

Pizzolato,

Zhou

et al. 2024

Magnetic Resonance in Med

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PurposeThis study aims to evaluate two distinct approaches for fiber radius estimation using diffusion‐relaxation MRI data acquired in biomimetic microfiber 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 MethodsA 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.ResultsBoth methods show a linear relationship between effective radii estimated from MRI data and ground‐truth radii distributions, although some discrepancies were observed. The spherical mean power‐law method overestimated fiber radii. Conversely, the T2‐based method exhibited higher sensitivity to smaller fiber radii, but faced limitations in accurately estimating the radius in one particular phantom, possibly because of material‐specific relaxation changes.ConclusionThe study demonstrates the feasibility of both techniques to predict pore sizes of hollow microfibers. 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 fiber radius estimation, highlights the advantages and limitations of both methods, and provides datasets for reproducible research.

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Revisiting the T2 spectrum imaging inverse problem: Bayesian regularized non-negative least squares

Cited by 10 publications

References 65 publications

An optimized b‐value sampling for the quantification of interstitial fluid using diffusion‐weighted MRI, a genetic algorithm approach

An optimized b‐value sampling for the quantification of interstitial fluid using diffusion‐weighted MRI, a genetic algorithm approach

Axial and radial axonal diffusivities from single encoding strongly diffusion-weighted MRI

Pore size estimation in axon‐mimicking microfibers with diffusion‐relaxation MRI

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