Model-informed machine learning for multi-component T₂ relaxometry.

Recovering the T <sub>2</sub> distribution from multi-echo T <sub>2</sub> magnetic resonance (MR) signals is challenging but has high potential as it provides biomarkers characterizing the tissue micro-structure, such as the myelin water fraction (MWF). In this work, we propose to combine machine learning and aspects of parametric (fitting from the MRI signal using biophysical models) and non-parametric (model-free fitting of the T <sub>2</sub> distribution from the signal) approaches to T <sub>2</sub> relaxometry in brain tissue by using a multi-layer perceptron (MLP) for the distribution reconstruction. For training our network, we construct an extensive synthetic dataset derived from biophysical models in order to constrain the outputs with a priori knowledge of in vivo distributions. The proposed approach, called Model-Informed Machine Learning (MIML), takes as input the MR signal and directly outputs the associated T <sub>2</sub> distribution. We evaluate MIML in comparison to a Gaussian Mixture Fitting (parametric) and Regularized Non-Negative Least Squares algorithms (non-parametric) on synthetic data, an ex vivo scan, and high-resolution scans of healthy subjects and a subject with Multiple Sclerosis. In synthetic data, MIML provides more accurate and noise-robust distributions. In real data, MWF maps derived from MIML exhibit the greatest conformity to anatomical scans, have the highest correlation to a histological map of myelin volume, and the best unambiguous lesion visualization and localization, with superior contrast between lesions and normal appearing tissue. In whole-brain analysis, MIML is 22 to 4980 times faster than the non-parametric and parametric methods, respectively

Quantitative brain relaxation atlases for personalized detection and characterization of brain pathology.

To exploit the improved comparability and hardware independency of quantitative MRI, databases of MR physical parameters in healthy tissue are required, to which tissue properties of patients can be compared. In this work, normative values for longitudinal and transverse relaxation times in the brain were established and tested in single-subject comparisons for detection of abnormal relaxation times. Relaxometry maps of the brain were acquired from 52 healthy volunteers. After spatially normalizing the volumes into a common space, T <sub>1</sub> and T <sub>2</sub> inter-subject variability within the healthy cohort was modeled voxel-wise. A method for a single-subject comparison against the atlases was developed by computing z-scores with respect to the established healthy norms. The comparison was applied to two multiple sclerosis and one clinically isolated syndrome cases for a proof of concept. The established atlases exhibit a low variation in white matter structures (median RMSE of models equal to 32 ms for T <sub>1</sub> and 4 ms for T <sub>2</sub> ), indicating that relaxation times are in a narrow range for normal tissues. The proposed method for single-subject comparison detected relaxation time deviations from healthy norms in the example patient data sets. Relaxation times were found to be increased in brain lesions (mean z-scores >5). Moreover, subtle and confluent differences (z-scores ~2-4) were observed in clinically plausible regions (between lesions, corpus callosum). Brain T <sub>1</sub> and T <sub>2</sub> quantitative norms were derived voxel-wise with low variability in healthy tissue. Example patient deviation maps demonstrated good sensitivity of the atlases for detecting relaxation time alterations

Data-driven myelin water imaging based on T1 and T2 relaxometry.

Long acquisition times preclude the application of multiecho spin echo (MESE) sequences for myelin water fraction (MWF) mapping in daily clinical practice. In search of alternative methods, previous studies of interest explored the biophysical modeling of MWF from measurements of different tissue properties that can be obtained in scan times shorter than those required for the MESE. In this work, a novel data-driven estimation of MWF maps from fast relaxometry measurements is proposed and investigated. T <sub>1</sub> and T <sub>2</sub> relaxometry maps were acquired in a cohort of 20 healthy subjects along with a conventional MESE sequence. Whole-brain quantitative mapping was achieved with a fast protocol in 6 min 24 s. Reference MWF maps were derived from the MESE sequence (TA = 11 min 17 s) and their data-driven estimation from relaxometry measurements was investigated using three different modeling strategies: two general linear models (GLMs) with linear and quadratic regressors, respectively; a random forest regression model; and two deep neural network architectures, a U-Net and a conditional generative adversarial network (cGAN). Models were validated using a 10-fold crossvalidation. The resulting maps were visually and quantitatively compared by computing the root mean squared error (RMSE) between the estimated and reference MWF maps, the intraclass correlation coefficients (ICCs) between corresponding MWF values in different brain regions, and by performing Bland-Altman analysis. Qualitatively, the estimated maps appear to generally provide a similar, yet more blurred MWF contrast in comparison with the reference, with the cGAN model best capturing MWF variabilities in small structures. By estimating the average adjusted coefficient of determination of the GLM with quadratic regressors, we showed that 87% of the variability in the MWF values can be explained by relaxation times alone. Further quantitative analysis showed an average RMSE smaller than 0.1% for all methods. The ICC was greater than 0.81 for all methods, and the bias smaller than 2.19%. It was concluded that this work confirms the notion that relaxometry parameters contain a large part of the information on myelin water and that MWF maps can be generated from T <sub>1</sub> /T <sub>2</sub> data with minimal error. Among the investigated modeling approaches, the cGAN provided maps with the best trade-off between accuracy and blurriness. Fast relaxometry, like the 6 min 24 s whole-brain protocol used in this work in conjunction with machine learning, may thus have the potential to replace time-consuming MESE acquisitions

Fast and high-resolution myelin water imaging: Accelerating multi-echo GRASE with CAIPIRINHA.

Although several MRI methods have been explored to achieve in vivo myelin quantification, imaging the whole brain in clinically acceptable times and sufficiently high resolution remains challenging. To address this problem, this work investigates the acceleration of multi-echo T <sub>2</sub> acquisitions based on the multi-echo gradient and spin echo (GRASE) sequence using CAIPIRINHA undersampling and adapted k-space reordering patterns. A prototype multi-echo GRASE sequence supporting CAIPIRINHA parallel imaging was implemented. Multi-echo T <sub>2</sub> data were acquired from 12 volunteers using the implemented sequence (1.6 × 1.6 × 1.6 mm <sup>3</sup> , 84 slices, acquisition time [TA] = 10:30 min) and a multi-echo spin echo (MESE) sequence as reference (1.6 × 1.6 × 3.2 mm <sup>3</sup> , single-slice, TA = 5:41 min). Myelin water fraction (MWF) maps derived from both acquisitions were compared via correlation and Bland-Altman analyses. In addition, scan-rescan datasets were acquired to evaluate the repeatability of the derived maps. Resulting maps from the MESE and multi-echo GRASE sequences were found to be correlated (r = 0.83). The Bland-Altman analysis revealed a mean bias of -0.2% (P = .24) with the limits of agreement ranging from -3.7% to 3.3%. The Pearson's correlation coefficient among MWF values obtained from the scan-rescan datasets was found to be 0.95 and the mean bias equal to 0.11% (P = .32), indicating good repeatability of the retrieved maps. By combining a 3D multi-echo GRASE sequence with CAIPIRINHA sampling, whole-brain MWF maps were obtained in 10:30 min with 1.6 mm isotropic resolution. The good correlation with conventional MESE-based maps demonstrates that the implemented sequence may be a promising alternative to time-consuming MESE acquisitions

Comparison of non-parametric T₂ relaxometry methods for myelin water quantification.

Multi-component T <sub>2</sub> relaxometry allows probing tissue microstructure by assessing compartment-specific T <sub>2</sub> relaxation times and water fractions, including the myelin water fraction. Non-negative least squares (NNLS) with zero-order Tikhonov regularization is the conventional method for estimating smooth T <sub>2</sub> distributions. Despite the improved estimation provided by this method compared to non-regularized NNLS, the solution is still sensitive to the underlying noise and the regularization weight. This is especially relevant for clinically achievable signal-to-noise ratios. In the literature of inverse problems, various well-established approaches to promote smooth solutions, including first-order and second-order Tikhonov regularization, and different criteria for estimating the regularization weight have been proposed, such as L-curve, Generalized Cross-Validation, and Chi-square residual fitting. However, quantitative comparisons between the available reconstruction methods for computing the T <sub>2</sub> distribution, and between different approaches for selecting the optimal regularization weight, are lacking. In this study, we implemented and evaluated ten reconstruction algorithms, resulting from the individual combinations of three penalty terms with three criteria to estimate the regularization weight, plus non-regularized NNLS. Their performance was evaluated both in simulated data and real brain MRI data acquired from healthy volunteers through a scan-rescan repeatability analysis. Our findings demonstrate the need for regularization. As a result of this work, we provide a list of recommendations for selecting the optimal reconstruction algorithms based on the acquired data. Moreover, the implemented methods were packaged in a freely distributed toolbox to promote reproducible research, and to facilitate further research and the use of this promising quantitative technique in clinical practice

Periventricular gradient of T₁ tissue alterations in multiple sclerosis.

Pathology in multiple sclerosis is not homogenously distributed. Recently, it has been shown that structures adjacent to CSF are more severely affected. A gradient of brain tissue involvement was shown with more severe pathology in periventricular areas and in proximity to brain surfaces such as the subarachnoid spaces and ependyma, and hence termed the "surface-in" gradient. Here, we study whether (i) the surface-in gradient of periventricular tissue alteration measured by T <sub>1</sub> relaxometry is already present in early multiple sclerosis patients, (ii) how it differs between early and progressive multiple sclerosis patients, and (iii) whether the gradient-derived metrics in normal-appearing white matter and lesions correlate better with physical disability than conventional MRI-based metrics. Forty-seven patients with early multiple sclerosis, 52 with progressive multiple sclerosis, and 92 healthy controls were included in the study. Isotropic 3D T <sub>1</sub> relaxometry maps were obtained using the Magnetization-Prepared 2 Rapid Acquisition Gradient Echoes sequence at 3 T. After spatially normalizing the T <sub>1</sub> maps into a study-specific common space, T <sub>1</sub> inter-subject variability within the healthy cohort was modelled voxel-wise, yielding a normative T <sub>1</sub> atlas. Individual comparisons of each multiple sclerosis patient against the atlas were performed by computing z-scores. Equidistant bands of voxels were defined around the ventricles in the supratentorial white matter; the z-scores in these bands were analysed and compared between the early and progressive multiple sclerosis cohorts. Correlations between both conventional and z-score-gradient-derived MRI metrics and the Expanded Disability Status Scale were assessed. Patients with early and progressive multiple sclerosis demonstrated a periventricular gradient of T <sub>1</sub> relaxation time z-scores. In progressive multiple sclerosis, z-score-derived metrics reflecting the gradient of tissue abnormality in normal-appearing white matter were more strongly correlated with disability (maximal rho = 0.374) than the conventional lesion volume and count (maximal rho = 0.189 and 0.21 respectively). In early multiple sclerosis, the gradient of normal-appearing white matter volume with z-scores > 2 at baseline correlated with clinical disability assessed at two years follow-up. Our results suggest that the surface-in white matter gradient of tissue alteration is detectable with T1 relaxometry and is already present at clinical disease onset. The periventricular gradients correlate with clinical disability. The periventricular gradient in normal-appearing white matter may thus qualify as a promising biomarker for monitoring of disease activity from an early stage in all phenotypes of multiple sclerosis

Compressed sensing (CS) MP2RAGE versus standard MPRAGE: A comparison of derived brain volume measurements.

T1 Magnetization Prepared Two Rapid Acquisition Gradient Echo (MP2RAGE) with compress sensing (CS) has been proposed as an improvement of the standard MPRAGE sequence with multiple advantages including reduced acquisition time needed to provide a quantitative 3D anatomical image coupled with T1-map. Here we investigated the agreement between FreeSurfer-derived volume measurements obtained from MPRAGE and CS MP2RAGE acquisitions. MPRAGE and CS MP2RAGE images of 37 subjects (14 patients with neurodegenerative disorders and 23 healthy controls) were acquired on a 3 T MR scanner and grey matter volumes were extracted using standard FreeSurfer parcellation. Lin's concordance correlation coefficient (Lin's CCC), Bland-Altman analysis, Passing-Bablok regression and DICE similarity coefficient were calculated to assess the agreement between the two. We found a good correspondence for most of the regions examined, with 93.5 % of them showing a mean DICE index >0.70. Poorer results were found with Lin's CCC especially for subcortical labels across patients. The Bland-Altman analysis showed CS MP2RAGE tended to measure lower cortical volumes compared to MPRAGE but in most cases the difference wasn't statistically relevant. The Passing-Bablock regression indicated overall an absence of systematic constant and proportional bias when CS MP2RAGE was used instead of MPRAGE. We found a good concordance for volumes obtained from MPRAGE and CS MP2RAGE images using FreeSurfer, suggesting a possible role of CS MP2RAGE for structural analysis with significant advantages like shorter acquisition time and the possibility to simultaneously obtain quantitative T1-maps of the brain enriching the diagnostic power of this technique

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 T <sub>2</sub> relaxometry, a qMRI technique that probes the complex tissue microstructure by differentiating compartment-specific T <sub>2</sub> 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 ( ) in gray (GM) and white matter (WM) tissue in a clinical setting, using a multi-site, multi-session, and multi-run T <sub>2</sub> relaxometry dataset. To this end, we evaluated three different techniques for estimating the T <sub>2</sub> 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 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