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Purpose: To evaluate potential modeling paradigms and the impact of relaxation time effects on human blood-brain barrier (BBB) water exchange measurements using FEXI (BBB-FEXI), and to quantify the accuracy, precision, and repeatability of BBB-FEXI exchange rate estimates at 3 (Formula presented.). Methods: Three modeling paradigms were evaluated: (i) the apparent exchange rate (AXR) model; (ii) a two-compartment model ((Formula presented.)) explicitly representing intra- and extravascular signal components, and (iii) a two-compartment model additionally accounting for finite compartmental (Formula presented.) and (Formula presented.) relaxation times ((Formula presented.)). Each model had three free parameters. Simulations quantified biases introduced by the assumption of infinite relaxation times in the AXR and (Formula presented.) models, as well as the accuracy and precision of all three models. The scan–rescan repeatability of all paradigms was quantified for the first time in vivo in 10 healthy volunteers (age range 23–52 years; five female). Results: The assumption of infinite relaxation times yielded exchange rate errors in simulations up to 42%/14% in the AXR/ (Formula presented.) models, respectively. Accuracy was highest in the compartmental models; precision was best in the AXR model. Scan–rescan repeatability in vivo was good for all models, with negligible bias and repeatability coefficients in grey matter of (Formula presented.) (Formula presented.), (Formula presented.) (Formula presented.), and (Formula presented.) (Formula presented.). Conclusion: Compartmental modelling of BBB-FEXI signals can provide accurate and repeatable measurements of BBB water exchange; however, relaxation time and partial volume effects may cause model-dependent biases.

Optic neuropathy is a near ubiquitous feature of Friedreich's ataxia (FRDA). Previous studies have examined varying aspects of the anterior and posterior visual pathways but none so far have comprehensively evaluated the heterogeneity of degeneration across different areas of the retina, changes to the macula layers and combined these with volumetric MRI studies of the visual cortex and frataxin level.We investigated 62 genetically confirmed FRDA patients using an integrated approach as part of an observational cohort study. We included measurement of frataxin protein levels, clinical evaluation of visual and neurological function, optical coherence tomography to determine retinal nerve fibre layer thickness and macular layer volume and volumetric brain MRI.We demonstrate that frataxin level correlates with peripapillary retinal nerve fibre layer thickness and that retinal sectors differ in their degree of degeneration. We also shown that retinal nerve fibre layer is thinner in FRDA patients than controls and that this thinning is influenced by the AAO and GAA1. Furthermore we show that the ganglion cell and inner plexiform layers are affected in FRDA. Our MRI data indicate that there are borderline correlations between retinal layers and areas of the cortex involved in visual processing.Our study demonstrates the uneven distribution of the axonopathy in the retinal nerve fibre layer and highlight the relative sparing of the papillomacular bundle and temporal sectors. We show that thinning of the retinal nerve fibre layer is associated with frataxin levels, supporting the use the two biomarkers in future clinical trials design. © 2022 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

Nyquist ghost; Denoising; Diffusion Fantasma de Nyquist; Eliminación de ruido; Difusión Fantasma de Nyquist; Eliminació de soroll; Difusió Purpose To develop a robust reconstruction pipeline for EPI data that enables 2D Nyquist phase error correction using sensitivity encoding without incurring major noise artifacts in low SNR data. Methods SENSE with 2D phase error correction (PEC-SENSE) was combined with channel-wise noise removal using Marcenko–Pastur principal component analysis (MPPCA) to simultaneously eliminate Nyquist ghost artifacts in EPI data and mitigate the noise amplification associated with phase correction using parallel imaging. The proposed pipeline (coined SPECTRE) was validated in phantom DW-EPI data using the accuracy and precision of diffusion metrics; ground truth values were obtained from data acquired with a spin echo readout. Results from the SPECTRE pipeline were compared against PEC-SENSE reconstructions with three alternate denoising strategies: (i) no denoising; (ii) denoising of magnitude data after image formation; (iii) denoising of complex data after image formation. SPECTRE was then tested using high -value (i.e., low SNR) diffusion data (up to s/mm ) in four healthy subjects. Results Noise amplification associated with phase error correction incurred a 23% bias in phantom mean diffusivity (MD) measurements. Phantom MD estimates using the SPECTRE pipeline were within 8% of the ground truth value. In healthy volunteers, the SPECTRE pipeline visibly corrected Nyquist ghost artifacts and reduced associated noise amplification in high -value data. Conclusion The proposed reconstruction pipeline is effective in correcting low SNR data, and improves the accuracy and precision of derived diffusion metrics. EPSRC-funded UCL Centre for Doctoral Training in Medical Imaging, Grant/Award Number: EP/L016478/1

In a companion paper by Cohen-Adad et al. we introduce the spine generic quantitative MRI protocol that provides valuable metrics for assessing spinal cord macrostructural and microstructural integrity. This protocol was used to acquire a single subject dataset across 19 centers and a multi-subject dataset across 42 centers (for a total of 260 participants), spanning the three main MRI manufacturers: GE, Philips and Siemens. Both datasets are publicly available via git-annex. Data were analysed using the Spinal Cord Toolbox to produce normative values as well as inter/intra-site and inter/intra-manufacturer statistics. Reproducibility for the spine generic protocol was high across sites and manufacturers, with an average inter-site coefficient of variation of less than 5% for all the metrics. Full documentation and results can be found at https://spine-generic.rtfd.io/. The datasets and analysis pipeline will help pave the way towards accessible and reproducible quantitative MRI in the spinal cord., Measurement(s)spinal cordTechnology Type(s)magnetic resonance imagingFactor Type(s)manufacturer • siteSample Characteristic - OrganismHomo sapiensSample Characteristic - LocationCanada • Switzerland • Australia • United States of America • United Kingdom • Germany • French Republic • Czech Republic • Italy • Japan • Kingdom of Spain • China Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.14052269

PurposeTo compare different multi-echo combination methods for MRI quantitative susceptibility mapping (QSM). Given the current lack of consensus, we aimed to elucidate how to optimally combine multi-echo gradient-recalled echo (GRE) signal phase information, either before or after applying Laplacian-base methods (LBMs) for phase unwrapping or background field removal.MethodsMulti-echo GRE data were simulated in a numerical head phantom, and multiecho GRE images were acquired at 3 T in ten healthy volunteers. To enable image-based estimation of GRE signal noise, five volunteers were scanned twice in the same session without repositioning. Five QSM processing pipelines were designed: one applied nonlinear phase fitting over echo times (TEs) before LBMs; two applied LBMs to the TE-dependent phase and then combined multiple TEs via either TE-weighted or signal-to-noise ratio (SNR)-weighted averaging; two calculated TE-dependent susceptibility maps via either multi-step or single-step QSM and then combined multiple TEs via magnitude-weighted averaging. Results from different pipelines were compared using visual inspection; summary statistics of susceptibility in deep gray matter, white matter, and venous regions; phase noise maps (error propagation theory); and, in the healthy volunteers, regional fixed bias analysis (Bland-Altman) and regional differences between the means (nonparametric tests).ResultsNonlinearly fitting the multi-echo phase over TEs before applying LBMs provided the highest regional accuracy of χ and the lowest phase noise propagation compared to averaging the LBM-processed TE-dependent phase. This result was especially pertinent in high-susceptibility venous regions.ConclusionFor multi-echo QSM, we recommend combining the signal phase by nonlinear fitting before applying LBMs.

In a companion paper by Cohen-Adad et al. we introduce the spine generic quantitative MRI protocol that provides valuable metrics for assessing spinal cord macrostructural and microstructural integrity. This protocol was used to acquire a single subject dataset across 19 centers and a multi-subject dataset across 42 centers (for a total of 260 participants), spanning the three main MRI manufacturers: GE, Philips and Siemens. Both datasets are publicly available via git-annex. Data were analysed using the Spinal Cord Toolbox to produce normative values as well as inter/intra-site and inter/intra-manufacturer statistics. Reproducibility for the spine generic protocol was high across sites and manufacturers, with an average inter-site coefficient of variation of less than 5% for all the metrics. Full documentation and results can be found at https://spine-generic.rtfd.io/ . The datasets and analysis pipeline will help pave the way towards accessible and reproducible quantitative MRI in the spinal cord.

Quantitative Magnetic Resonance Imaging (qMRI) signal model fitting is traditionally performed via non-linear least square (NLLS) estimation. NLLS is slow and its performance can be affected by the presence of different local minima in the fitting objective function. Recently, machine learning techniques, including deep neural networks (DNNs), have been proposed as robust alternatives to NLLS. Here we present a deep learning implementation of qMRI model fitting, which uses DNNs to perform the inversion of the forward signal model. We compare two DNN training strategies, based on two alternative definitions of the loss function, since at present it is not known which definition leads to the most accurate, precise and robust parameter estimation. In strategy 1 we define the loss as the \(l^2\)-norm of tissue parameter prediction errors, while in strategy 2 as the \(l^2\)-norm of MRI signal prediction errors. We compare the two approaches on synthetic and 3T in vivo saturation inversion recovery (SIR) diffusion-weighted (DW) MRI data, using a model for joint diffusion-T1 mapping. Strategy 1 leads to lower tissue parameter root mean squared errors (RMSEs) when realistic noise distributions are considered (e.g. Rician versus Gaussian). However, strategy 2 offers lower signal reconstruction RMSE, and allows training to be performed on both synthetic and actual in vivo MRI measurements. In conclusion, for the qMRI model considered here both strategies are valid choices for DNN-based fitting. Strategy 2 is more practical, as it does not require pre-computation of reference tissue parameters, but may lead to worse parameter estimation.

Consider an (observable) random sample of size n from an infinite population of individuals, each individual being endowed with a finite set of "features" from a collection of features (F-j)(j>1) with unknown probabilities (p(j))(j>1), i.e., p(j) is the probability that an individual displays feature F-j. Under this feature sampling framework, in recent years there has been a growing interest in estimating the sum of the probability masses p(j)'s of features observed with frequency r >= 0 in the sample, here denoted by M-n,M-r. This is the natural feature sampling counterpart of the classical problem of estimating small probabilities in the species sampling framework, where each individual is endowed with only one feature (or "species"). In this paper we study the problem of consistent estimation of the small mass M-n,M-r. We first show that there do not exist universally consistent estimators, in the multiplicative sense, of the missing mass M-n,M-0. Then, we introduce an estimator of M-n,M-r and identify sufficient conditions under which the estimator is consistent. In particular, we propose a nonparametric estimator (M) over cap (n,r) of M-n,M-r which has the same analytic form of the celebrated Good-Turing estimator for small probabilities, with the sole difference that the two estimators have different ranges (supports). Then, we show that (M) over cap (n,r) is strongly consistent, in the multiplicative sense, under the assumption that (p(j))(j >= 1) has regularly varying heavy tails.

Etant donne un echantillon de taille n dans une population d’individus appartenant a differents types dont les proportions sont inconnues, comment estimer la probabilite de decouvrir un nouveau type au (n+1)-ieme tirage ? C’est un probleme classique en statistique, souvent appele le probleme de l’estimation de la masse manquante. Des resultats recents on montre : (i) l’impossibilite d’estimer la masse manquante sans imposer des hypotheses sur les proportions des types ; (ii) la convergence de l’estimateur de la masse manquante de Good–Turing sous l’hypothese que la queue des proportions des types decroit vers 0 comme une fonction reguliere de parametre α∈(0,1) ; (iii) la vitesse de convergence n−α/2 pour l’estimateur de Good–Turing pour la classe de probabilites a variation reguliere α∈(0,1). Dans cet article, nous proposons une preuve alternative, et remarquablement plus courte, de l’impossibilite de l’estimation de la masse manquante sans hypothese sur la distribution. Au dela de son interet propre, cette preuve alternative suggere une approche naturelle pour ameliorer et etendre les resultats de vitesse de convergence de l’estimateur de Good–Turing sous l’hypothese de proportions a variation reguliere α∈(0,1). En particulier, nous montrons que la vitesse de convergence n−α/2 est la meilleure que peut atteindre un estimateur, a une fonction a variation bornee pres. De plus, nous montrons qu’une borne inferieure a l’estimation du risque minimax est au moins d’echelle n−α/2, ce qui amene a la conjecture que l’estimateur de Good–Turing est l’estimateur minimax de vitesse optimale sous une hypothese de proportions a variation reguliere.

Quantitative Magnetic Resonance Imaging (qMRI) signal model fitting is traditionally performed via non-linear least square (NLLS) estimation. NLLS is slow and its performance can be affected by the presence of different local minima in the fitting objective function. Recently, machine learning techniques, including deep neural networks (DNNs), have been proposed as robust alternatives to NLLS. Here we present a deep learning implementation of qMRI model fitting, which uses DNNs to perform the inversion of the forward signal model. We compare two DNN training strategies, based on two alternative definitions of the loss function, since at present it is not known which definition leads to the most accurate, precise and robust parameter estimation. In strategy 1 we define the loss as the l2-norm of tissue parameter prediction errors, while in strategy 2 as the l2-norm of MRI signal prediction errors. We compare the two approaches on synthetic and 3T in vivo saturation inversion recovery (SIR) diffusion-weighted (DW) MRI data, using a model for joint diffusion-T1 mapping. Strategy 1 leads to lower tissue parameter root mean squared errors (RMSEs) when realistic noise distributions are considered (e.g. Rician vs Gaussian). However, strategy 2 offers lower signal reconstruction RMSE, and allows training to be performed on both synthetic and actual in vivo MRI measurements. In conclusion, both strategies are valid choices for DNN-based fitting. Strategy 2 is more practical, as it does not require pre-computation of reference tissue parameters, but may lead to worse parameter estimation.

Post randomization methods are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix M and a specified variable, an individual belonging to category i is changed to category j with probability $$M_{i,j}$$ M i , j . Every approach to choose the randomization matrix M has to balance between two desiderata: (1) preserving as much statistical information from the raw data as possible; (2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose M as the solution of a constrained maximization problems. Specifically, M is chosen as the solution of a constrained maximization problem, where we maximize the mutual information between raw and transformed data, given the constraint that the transformation satisfies the notion of differential privacy. For the general categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms.

Multi-parametric quantitative MRI (qMRI) of the spinal cord is a promising non-invasive tool to probe early microstructural damage in neurological disorders. It is usually performed by combining acquisitions with multiple signal readouts, which exhibit different thermal noise levels, geometrical distortions and susceptibility to physiological noise. This ultimately hinders joint multi-contrast modelling and makes the geometric correspondence of parametric maps challenging. We propose an approach to overcome these limitations, by implementing state-of-the-art microstructural MRI of the spinal cord with a unified signal readout. We base our acquisition on single-shot echo planar imaging with reduced field-of-view, and obtain data from two different vendors (vendor 1: Philips Achieva; vendor 2: Siemens Prisma). Importantly, the unified acquisition allows us to compare signal and noise across contrasts, thus enabling overall quality enhancement via Marchenko-Pastur (MP) Principal Component Analysis (PCA) denoising. MP-PCA is a recent method relying on redundant acquisitions, i.e. such that the number of measurements is much larger than the number of informative principal components. Here we used in vivo and synthetic data to test whether a unified readout enables more efficient denoising of less redundant acquisitions, since these can be denoised jointly with more redundant ones. We demonstrate that a unified readout provides robust multi-parametric maps, including diffusion and kurtosis tensors from diffusion MRI, myelin metrics from two-pool magnetisation transfer, and T1 and T2 from relaxometry. Moreover, we show that MP-PCA improves the quality of our multi-contrast acquisitions, since it reduces the coefficient of variation (i.e. variability) by up to 15% for mean kurtosis, 8% for bound pool fraction (BPF, myelin-sensitive), and 13% for T1, while enabling more efficient denoising of modalities limited in redundancy (e.g. relaxometry). In conclusion, multi-parametric spinal cord qMRI with unified readout is feasible and provides robust microstructural metrics with matched resolution and distortions, whose quality benefits from MP-PCA denoising, a useful pre-processing tool for spinal cord MRI.

Purpose: To translate the recently developed PRO‐QUEST (Progressive saturation for quantifying exchange rates using saturation times) sequence from preclinical 9.4T to 3T clinical magnetic field strength. Methods: Numerical simulations were performed to define the optimal saturation flip angles for PRO‐QUEST saturation pulses at 3T and demonstrate the effect of a ∆T 2 error on the exchange rate (k ex) estimation at various field strengths. Exchange‐dependent relaxation rate (R ex) was measured for glutamate solutions in various pH, healthy volunteers and patients with multiple sclerosis (MS). Additionally, concentration‐independent ratiometric R ex maps were produced to evaluate regional signal variations across the brain of human volunteers. Results: The calculated R ex significantly correlates with pH in glutamate samples, however, k ex values are underestimated as compared to those previously obtained at 9.4T. In the ratiometric R ex map of healthy volunteers, no significant differences are found between grey matter, white matter, and basal ganglia. In patients with MS, white matter lesions are visible in single saturation power R ex maps whereas only a periventricular lesion is apparent in the ratiometric R ex map. Conclusion: We demonstrate that quantification of pH sensitive indices using PRO‐QUEST is feasible at 3T within clinically acceptable acquisition times. Our initial findings in patients with MS show that pH sensitive indices varied with the type of lesion examined whereas no significant difference was found in healthy volunteers between tissue types, suggesting that it would be worthwhile to apply PRO‐QUEST in a larger cohort of patients to better understand its distinct imaging features relative to conventional techniques.

PURPOSE: To enable clinical applications of quantitative magnetization transfer (qMT) imaging by developing a fast method to map one of its fundamental model parameters, the bound pool fraction (BPF), in the human brain. THEORY AND METHODS: The theory of steady-state MT in the fast-exchange approximation is used to provide measurements of BPF, and bound pool transverse relaxation time ( T 2 B ). A sequence that allows sampling of the signal during steady-state MT saturation is used to perform BPF mapping with a 10-min-long fully echo planar imaging-based MRI protocol, including inversion recovery T1 mapping and B1 error mapping. The approach is applied in 6 healthy subjects and 1 multiple sclerosis patient, and validated against a single-slice full qMT reference acquisition. RESULTS: BPF measurements are in agreement with literature values using off-resonance MT, with average BPF of 0.114(0.100-0.128) in white matter and 0.068(0.054-0.085) in gray matter. Median voxel-wise percentage error compared with standard single slice qMT is 4.6%. Slope and intercept of linear regression between new and reference BPF are 0.83(0.81-0.85) and 0.013(0.11-0.16). Bland-Altman plot mean bias is 0.005. In the multiple sclerosis case, the BPF is sensitive to pathological changes in lesions. CONCLUSION: The method developed provides accurate BPF estimates and enables shorter scan time compared with currently available approaches, demonstrating the potential of bringing myelin sensitive measurement closer to the clinic.

Let (P1, …, PJ) denote J populations of animals from distinct regions. A priori, it is unknown which species are present in each region and what are their corresponding frequencies. Species are shared among populations and each species can be present in more than one region with its frequency varying across populations. In this article, we consider the problem of sequentially sampling these populations to observe the greatest number of different species. We adopt a Bayesian nonparametric approach and endow (P1, …, PJ) with a hierarchical Pitman–Yor process prior. As a consequence of the hierarchical structure, the J unknown discrete probability measures share the same support, that of their common random base measure. Given this prior choice, we propose a sequential rule that, at every time step, given the information available up to that point, selects the population from which to collect the next observation. Rather than picking the population with the highest posterior estimate of producing a new value, the proposed rule includes a Thompson sampling step to better balance the exploration–exploitation trade-off. We also propose an extension of the algorithm to deal with incidence data, where multiple observations are collected in a time period. The performance of the proposed algorithms is assessed through a simulation study and compared to three other strategies. Finally, we compare these algorithms using a dataset of species of trees, collected from different plots in South America. Supplementary materials for this article are available online.

Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we study the problem of estimating the missing mass $M_{n}$, namely the expected number hitherto unseen features that would be observed if one additional individual was sampled. This is motivated by numerous applied problems where the sampling procedure is expensive, in terms of time and/or financial resources allocated, and further samples can be only motivated by the possibility of recording new unobserved features. We introduce a simple, robust and theoretically sound nonparametric estimator $\hat{M}_{n}$ of $M_{n}$. $\hat{M}_{n}$ turns out to have the same analytic form of the popular Good-Turing estimator of the missing mass in species sampling models, with the difference that the two estimators have different ranges. We show that $\hat{M}_{n}$ admits a natural interpretation both as a jackknife estimator and as a nonparametric empirical Bayes estimator, we give provable guarantees for the performance of $\hat{M}_{n}$ in terms of minimax rate optimality, and we provide with an interesting connection between $\hat{M}_{n}$ and the Good-Turing estimator for species sampling. Finally, we derive non-asymptotic confidence intervals for $\hat{M}_{n}$, which are easily computable and do not rely on any asymptotic approximation. Our approach is illustrated with synthetic data and SNP data from the ENCODE sequencing genome project.

We characterize the class of exchangeable feature allocations assigning probability $V_{n,k}\prod_{l=1}^{k}W_{m_{l}}U_{n-m_{l}}$ to a feature allocation of $n$ individuals, displaying $k$ features with counts $(m_{1},\ldots,m_{k})$ for these features. Each element of this class is parametrized by a countable matrix $V$ and two sequences $U$ and $W$ of non-negative weights. Moreover, a consistency condition is imposed to guarantee that the distribution for feature allocations of $n-1$ individuals is recovered from that of $n$ individuals, when the last individual is integrated out. In Theorem 1.1, we prove that the only members of this class satisfying the consistency condition are mixtures of the Indian Buffet Process over its mass parameter $\gamma$ and mixtures of the Beta--Bernoulli model over its dimensionality parameter $N$. Hence, we provide a characterization of these two models as the only, up to randomization of the parameters, consistent exchangeable feature allocations having the required product form., Comment: 21 pages

PURPOSE To develop a fast and robust method for measuring T1 in the whole cervical spinal cord in vivo, and to assess its reproducibility. METHODS A spatially nonselective adiabatic inversion pulse is combined with zonally oblique-magnified multislice echo-planar imaging to produce a reduced field-of-view inversion-recovery echo-planar imaging protocol. Multi- inversion time data are obtained by cycling slice order throughout sequence repetitions. Measurement of T1 is performed using 12 inversion times for a total protocol duration of 7 min. Reproducibility of regional T1 estimates is assessed in a scan-rescan experiment on five heathy subjects. RESULTS Regional mean (standard deviation) T1 was: 1108.5 (±77.2) ms for left lateral column, 1110.1 (±83.2) ms for right lateral column, 1150.4 (±102.6) ms for dorsal column, and 1136.4 (±90.8) ms for gray matter. Regional T1 estimates showed good correlation between sessions (Pearson correlation coefficient = 0.89 (P value

A fundamental problem in Bayesian nonparametrics consists of selecting a prior distribution by assuming that the corresponding predictive probabilities obey certain properties. An early discussion of such a problem, although in a parametric framework, dates back to the seminal work by English philosopher W. E. Johnson, who introduced a noteworthy characterization for the predictive probabilities of the symmetric Dirichlet prior distribution. This is typically referred to as Johnson's "sufficientness" postulate. In this paper we review some nonparametric generalizations of Johnson's postulate for a class of nonparametric priors known as species sampling models. In particular we revisit and discuss the "sufficientness" postulate for the two parameter Poisson-Dirichlet prior within the more general framework of Gibbstype priors and their hierarchical generalizations.

MRI; Multi-echo QSM; Quantitative susceptibility mapping Imágen por resonancia magnética; QSM de ecos múltiples; Mapeo cuantitativo de susceptibilidad Imatge per ressonància magnètica; QSM de ressò múltiple; Mapeig quantitatiu de susceptibilitat Purpose To compare different multi-echo combination methods for MRI QSM. Given the current lack of consensus, we aimed to elucidate how to optimally combine multi-echo gradient-recalled echo signal phase information, either before or after applying Laplacian-base methods (LBMs) for phase unwrapping or background field removal. Methods Multi-echo gradient-recalled echo data were simulated in a numerical head phantom, and multi-echo gradient-recalled echo images were acquired at 3 Tesla in 10 healthy volunteers. To enable image-based estimation of gradient-recalled echo signal noise, 5 volunteers were scanned twice in the same session without repositioning. Five QSM processing pipelines were designed: 1 applied nonlinear phase fitting over TEs before LBMs; 2 applied LBMs to the TE-dependent phase and then combined multiple TEs via either TE-weighted or SNR-weighted averaging; and 2 calculated TE-dependent susceptibility maps via either multi-step or single-step QSM and then combined multiple TEs via magnitude-weighted averaging. Results from different pipelines were compared using visual inspection; summary statistics of susceptibility in deep gray matter, white matter, and venous regions; phase noise maps (error propagation theory); and, in the healthy volunteers, regional fixed bias analysis (Bland–Altman) and regional differences between the means (nonparametric tests). Results Nonlinearly fitting the multi-echo phase over TEs before applying LBMs provided the highest regional accuracy of and the lowest phase noise propagation compared to averaging the LBM-processed TE-dependent phase. This result was especially pertinent in high-susceptibility venous regions. Conclusion For multi-echo QSM, we recommend combining the signal phase by nonlinear fitting before applying LBMs. Supported by the UK Engineering and Physical Sciences Research Council (EPSRC), award number: 1489882 (e.b.); by the EPSRC-funded UCL Centre for Doctoral Training in Medical Imaging, grant EP/L016478/1 (a.k.), and the Department of Health's National Institute for Health Research funded Biomedical Research Centre at University College London Hospitals (a.k.); by the UCL Leonard Wolfson Experimental Neurology Centre, grant PR/ylr/18575 (d.l.t) The Queen Square MS Centre, where part of the MRI scans for this work were performed, is supported by grants from the UK MS Society and by the National Institute for Health Research University College London Hospitals Biomedical Research Centre (UCLH/BRC). F. Grussu was supported by PREdICT, a study at the Vall d'Hebron Institute of Oncology in Barcelona funded by AstraZeneca (f.g.), and funding from the postdoctoral fellowships program Beatriu de Pinós (2020 BP 00117), funded by the Secretary of Universities and Research, Government of Catalonia (f.g.)

Quantitative spinal cord (SC) magnetic resonance imaging (MRI) presents many challenges, including a lack of standardized imaging protocols. Here we present a prospectively harmonized quantitative MRI protocol, which we refer to as the spine generic protocol, for users of 3T MRI systems from the three main manufacturers: GE, Philips and Siemens. The protocol provides guidance for assessing SC macrostructural and microstructural integrity: T1-weighted and T2-weighted imaging for SC cross-sectional area computation, multi-echo gradient echo for gray matter cross-sectional area, and magnetization transfer and diffusion weighted imaging for assessing white matter microstructure. In a companion paper from the same authors, the spine generic protocol was used to acquire data across 42 centers in 260 healthy subjects. The key details of the spine generic protocol are also available in an open-access document that can be found at https://github.com/spine-generic/protocols . The protocol will serve as a starting point for researchers and clinicians implementing new SC imaging initiatives so that, in the future, inclusion of the SC in neuroimaging protocols will be more common. The protocol could be implemented by any trained MR technician or by a researcher/clinician familiar with MRI acquisition.