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

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

PURPOSE

This 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 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, 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.

CONCLUSION

The 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.

An integrated Bayesian framework for multi-omics prediction and classification

With the growing commonality of multi-omics datasets, there is now increasing evidence that integrated omics profiles lead to more efficient discovery of clinically actionable biomarkers that enable better disease outcome prediction and patient stratification. Several methods exist to perform host phenotype prediction from cross-sectional, single-omics data modalities but decentralized frameworks that jointly analyze multiple time-dependent omics data to highlight the integrative and dynamic impact of repeatedly measured biomarkers are currently limited. In this article, we propose a novel Bayesian ensemble method to consolidate prediction by combining information across several longitudinal and cross-sectional omics data layers. Unlike existing frequentist paradigms, our approach enables uncertainty quantification in prediction as well as interval estimation for a variety of quantities of interest based on posterior summaries. We apply our method to four published multi-omics datasets and demonstrate that it recapitulates known biology in addition to providing novel insights while also outperforming existing methods in estimation, prediction, and uncertainty quantification. Our open-source software is publicly available at https://github.com/himelmallick/IntegratedLearner.

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/mm2) 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.

In Vivo Myelin Water Quantification Using Diffusion-Relaxation Correlation MRI: A Comparison of 1D and 2D Methods

Multidimensional Magnetic Resonance Imaging (MRI) is a versatile tool for microstructure mapping. We use a diffusion weighted inversion recovery spin echo (DW-IR-SE) sequence with spiral readouts at ultra-strong gradients to acquire a rich diffusion-relaxation data set with sensitivity to myelin water. We reconstruct 1D and 2D spectra with a two-step convex optimization approach and investigate a variety of multidimensional MRI methods, including 1D multi-component relaxometry, 1D multi-component diffusometry, 2D relaxation correlation imaging, and 2D diffusion-relaxation correlation spectroscopic imaging (DR-CSI), in terms of their potential to quantify tissue microstructure, including the myelin water fraction (MWF). We observe a distinct spectral peak that we attribute to myelin water in multi-component T1 relaxometry, T1-T2 correlation, T1-D correlation, and T2-D correlation imaging. Due to lower achievable echo times compared to diffusometry, MWF maps from relaxometry have higher quality. Whilst 1D multi-component T1 data allows much faster myelin mapping, 2D approaches could offer unique insights into tissue microstructure and especially myelin diffusion.

P2T2: A physically-primed deep-neural-network approach for robust T2 distribution estimation from quantitative T2-weighted MRI

Estimating T₂ relaxation time distributions from multi-echo T₂-weighted MRI (T₂W) data can provide valuable biomarkers for assessing inflammation, demyelination, edema, and cartilage composition in various pathologies, including neurodegenerative disorders, osteoarthritis, and tumors. Deep neural network (DNN) based methods have been proposed to address the complex inverse problem of estimating T₂ distributions from MRI data, but they are not yet robust enough for clinical data with low Signal-to-Noise ratio (SNR) and are highly sensitive to distribution shifts such as variations in echo-times (TE) used during acquisition. Consequently, their application is hindered in clinical practice and large-scale multi-institutional trials with heterogeneous acquisition protocols. We propose a physically-primed DNN approach, called P₂T₂, that incorporates the signal decay forward model in addition to the MRI signal into the DNN architecture to improve the accuracy and robustness of T₂ distribution estimation. We evaluated our P₂T₂ model in comparison to both DNN-based methods and classical methods for T₂ distribution estimation using 1D and 2D numerical simulations along with clinical data. Our model improved the baseline model's accuracy for low SNR levels (SNR<80) which are common in the clinical setting. Further, our model achieved a ∼35% improvement in robustness against distribution shifts in the acquisition process compared to previously proposed DNN models. Finally, Our P₂T₂ model produces the most detailed Myelin-Water fraction maps compared to baseline approaches when applied to real human MRI data. Our P₂T₂ model offers a reliable and precise means of estimating T₂ distributions from MRI data and shows promise for use in large-scale multi-institutional trials with heterogeneous acquisition protocols. Our source code is available at: https://github.com/Hben-atya/P2T2-Robust-T2-estimation.git.

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

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 only 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 distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

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

PURPOSE

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/mm² . 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/mm² . 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.

Variability and reproducibility of multi-echo T2 relaxometry: Insights from multi-site, multi-session and multi-subject MRI acquisitions

Quantitative magnetic resonance imaging (qMRI) can increase the specificity and sensitivity of conventional weighted MRI to underlying pathology by comparing meaningful physical or chemical parameters, measured in physical units, with normative values acquired in a healthy population. This study focuses on multi-echo T₂ relaxometry, a qMRI technique that probes the complex tissue microstructure by differentiating compartment-specific T₂ relaxation times. However, estimation methods are still limited by their sensitivity to the underlying noise. Moreover, estimating the model's parameters is challenging because the resulting inverse problem is ill-posed, requiring advanced numerical regularization techniques. As a result, the estimates from distinct regularization strategies are different. In this work, we aimed to investigate the variability and reproducibility of different techniques for estimating the transverse relaxation time of the intra- and extra-cellular space (T2IE) in gray (GM) and white matter (WM) tissue in a clinical setting, using a multi-site, multi-session, and multi-run T₂ relaxometry dataset. To this end, we evaluated three different techniques for estimating the T₂ spectra (two regularized non-negative least squares methods and a machine learning approach). Two independent analyses were performed to study the effect of using raw and denoised data. For both the GM and WM regions, and the raw and denoised data, our results suggest that the principal source of variance is the inter-subject variability, showing a higher coefficient of variation (CoV) than those estimated for the inter-site, inter-session, and inter-run, respectively. For all reconstruction methods studied, the CoV ranged between 0.32 and 1.64%. Interestingly, the inter-session variability was close to the inter-scanner variability with no statistical differences, suggesting that T2IE is a robust parameter that could be employed in multi-site neuroimaging studies. Furthermore, the three tested methods showed consistent results and similar intra-class correlation (ICC), with values superior to 0.7 for most regions. Results from raw data were slightly more reproducible than those from denoised data. The regularized non-negative least squares method based on the L-curve technique produced the best results, with ICC values ranging from 0.72 to 0.92.