Non-negative least squares computation for in vivo myelin mapping using simulated multi-echo spin-echo T2 decay data

Magnetic resonance fingerprinting-based myelin water fraction mapping for the assessment of white matter maturation and integrity in typical development and leukodystrophies

A quantitative biomarker for myelination, such as myelin water fraction (MWF), would boost the understanding of normative and pathological neurodevelopment, improving patients' diagnosis and follow-up. We quantified the fraction of a rapidly relaxing pool identified as MW using multicomponent three-dimensional (3D) magnetic resonance fingerprinting (MRF) to evaluate white matter (WM) maturation in typically developing (TD) children and alterations in leukodystrophies (LDs). We acquired DTI and 3D MRF-based R1, R2 and MWF data of 15 TD children and 17 LD patients (9 months-12.5 years old) at 1.5 T. We computed normative maturation curves in corpus callosum and corona radiata and performed WM tract profile analysis, comparing MWF with R1, R2 and fractional anisotropy (FA). Normative maturation curves demonstrated a steep increase for all tissue parameters in the first 3 years of age, followed by slower growth for MWF while R1, R2R2 and FA reached a plateau. Unlike FA, MWF values were similar for regions of interest (ROIs) with different degrees of axonal packing, suggesting independence from fiber bundle macro-organization and higher myelin specificity. Tract profile analysis indicated a specific spatial pattern of myelination in the major fiber bundles, consistent across subjects. LD were better distinguished from TD by MWF rather than FA, showing reduced MWF with respect to age-matched controls in both ROI-based and tract analysis. In conclusion, MRF-based MWF provides myelin-specific WM maturation curves and is sensitive to alteration due to LDs, suggesting its potential as a biomarker for WM disorders. As MRF allows fast simultaneous acquisition of relaxometry and MWF, it can represent a valuable diagnostic tool to study and follow up developmental WM disorders in children.

Study of the collagen tissue nanostructure by analyzing the echo decay obtained using the MRI technique

The multicomponent relaxation observed in nuclear magnetic resonance experiments in biological tissues makes it difficult to establish a correlation between specific relaxation times and tissue structural parameters. The analysis of a nanostructure (the characteristic size of 10-1000 nm) is usually based on formulas for relaxation times which depend on structural parameters at the atomic or molecular levels in the size range of 0.1-5 nm. We have recently developed an analysis method in which relaxation times' anisotropy in a sample is explicitly related to its structure of nanocavities containing a liquid or gas. However, the method is based on the analysis of experimental data on the anisotropy of relaxation times obtained by using the standard NMR technique and rotating the sample relative to a magnetic field and requires a series of experiments. In the present study, to address this challenge, we develop a new method of analysis of a multi-exponential magnetic resonance signal that does not require determining relaxation times and eliminates the sample rotation and the necessity of a series of experiments. Using the magnetic resonance imaging (MRI) technique, the total signal from the whole sample was obtained as a sum of the signals (echo decays) from all voxels. In contrast to previous research, the volumes of nanocavities and their angular distribution can be obtained by analyzing a single total signal for the entire cartilage. In addition, within the framework of this approach, it is possible to identify the reason for the multicomponent nature of relaxation. The proposed method for analyzing a single multi-exponential signal (transverse relaxation) was implemented on cartilage. Using the signal, three anatomical zones of cartilage were studied, revealing significant structural differences between them. The proposed method not only avoids the need for sample rotation but also enables repeated application of layer-by-layer magnetic resonance imaging with micron resolution. The study results allow us to suggest that water molecules contributing to the echo decay are more likely located in nanocavities formed by the fibrillar structure rather than inside the fibrils.

The CALIPR framework for highly accelerated myelin water imaging with improved precision and sensitivity

Quantitative magnetic resonance imaging (MRI) techniques are powerful tools for the study of human tissue, but, in practice, their utility has been limited by lengthy acquisition times. Here, we introduce the Constrained, Adaptive, Low-dimensional, Intrinsically Precise Reconstruction (CALIPR) framework in the context of myelin water imaging (MWI); a quantitative MRI technique generally regarded as the most rigorous approach for noninvasive, in vivo measurement of myelin content. The CALIPR framework exploits data redundancy to recover high-quality images from a small fraction of an imaging dataset, which allowed MWI to be acquired with a previously unattainable sequence (fully sampled acquisition 2 hours:57 min:20 s) in 7 min:26 s (4.2% of the dataset, acceleration factor 23.9). CALIPR quantitative metrics had excellent precision (myelin water fraction mean coefficient of variation 3.2% for the brain and 3.0% for the spinal cord) and markedly increased sensitivity to demyelinating disease pathology compared to a current, widely used technique. The CALIPR framework facilitates drastically improved MWI and could be similarly transformative for other quantitative MRI applications.

Quantitative magnetic resonance imaging reflects different levels of histologically determined myelin densities in multiple sclerosis, including remyelination in inactive multiple sclerosis lesions

Magnetic resonance imaging (MRI) of focal or diffuse myelin damage or remyelination may provide important insights into disease progression and potential treatment efficacy in multiple sclerosis (MS). We performed post-mortem MRI and histopathological myelin measurements in seven progressive MS cases to evaluate the ability of three myelin-sensitive MRI scans to distinguish different stages of MS pathology, particularly chronic demyelinated and remyelinated lesions. At 3 Tesla, we acquired two different myelin water imaging (MWI) scans and magnetisation transfer ratio (MTR) data. Histopathology included histochemical stainings for myelin phospholipids (LFB) and iron as well as immunohistochemistry for myelin proteolipid protein (PLP), CD68 (phagocytosing microglia/macrophages) and BCAS1 (remyelinating oligodendrocytes). Mixed-effects modelling determined which histopathological metric best predicted MWF and MTR in normal-appearing and diffusely abnormal white matter, active/inactive, inactive, remyelinated and ischemic lesions. Both MWI measures correlated well with each other and histology across regions, reflecting the different stages of MS pathology. MTR data showed a considerable influence of components other than myelin and a strong dependency on tissue storage duration. Both MRI and histology revealed increased myelin densities in inactive compared with active/inactive lesions. Chronic inactive lesions harboured single scattered myelin fibres indicative of low-level remyelination. Mixed-effects modelling showed that smaller differences between white matter areas were linked to PLP densities and only to a small extent confounded by iron. MWI reflects differences in myelin lipids and proteins across various levels of myelin densities encountered in MS, including low-level remyelination in chronic inactive lesions.

Study of T2 mapping in quantifying and discriminating uterine lesions under different magnetic field strengths: 1.5 T vs. 3.0 T

BACKGROUND

MRI is the best imaging tool for the evaluation of uterine tumors, but conventional MRI diagnosis results rely on radiologists and contrast agents (if needed). As a new objective, reproducible and contrast-agent free quantification technique, T2 mapping has been applied to a number of diseases, but studies on the evaluation of uterine lesions and the influence of magnetic field strength are few. Therefore, the aim of this study was to systematically investigate and compare the performance of T2 mapping as a nonenhanced imaging tool in discriminating common uterine lesions between 1.5 T and 3.0 T MRI systems.

METHODS

A total of 50 healthy subjects and 126 patients with suspected uterine lesions were enrolled in our study, and routine uterine MRI sequences with additional T2 mapping sequences were performed. T2 maps were calculated by monoexponential fitting using a custom code in MATLAB. T2 values of normal uterine structures in the healthy group and lesions (benign: adenomyosis, myoma, endometrial polyps; malignant: cervical cancer, endometrial carcinoma) in the patient group were collected. The differences in T2 values between 1.5 T MRI and 3.0 T MRI in any normal structure or lesion were compared. The comparison of T2 values between benign and malignant lesions was also performed under each magnetic field strength, and the diagnostic efficacies of the T2 value obtained through receiver operating characteristic (ROC) analysis were compared between 1.5 T and 3.0 T.

RESULTS

The mean T2 value of any normal uterine structure or uterine lesion under 3.0 T MRI was significantly lower than that under 1.5 T MRI (p < 0.05). There were significant differences in T2 values between each lesion subgroup under both 1.5 T and 3.0 T MRI. Moreover, the T2 values of benign lesions (71.1 ± 22.0 ms at 1.5 T and 63.4 ± 19.1 ms at 3.0 T) were also significantly lower than those of malignant lesions (101.1 ± 4.5 ms at 1.5 T and 93.5 ± 5.1 ms at 3.0 T) under both field strengths. In the aspect of differentiating benign from malignant lesions, the area under the curve of the T2 value under 3.0 T (0.94) was significantly higher than that under 1.5 T MRI (0.90) (p = 0.02).

CONCLUSION

T2 mapping can be a potential tool for quantifying common uterine lesions, and it has better performance in distinguishing benign from malignant lesions under 3.0 T MRI.

Comparing myelin-sensitive magnetic resonance imaging measures and resulting g-ratios in healthy and multiple sclerosis brains

The myelin concentration and the degree of myelination of nerve fibers can provide valuable information on the integrity of human brain tissue. Magnetic resonance imaging (MRI) of myelin-sensitive parameters can help to non-invasively evaluate demyelinating diseases such as multiple sclerosis (MS). Several different myelin-sensitive MRI methods have been proposed to determine measures of the degree of myelination, in particular the g-ratio. However, variability in underlying physical principles and different biological models influence measured myelin concentrations, and consequently g-ratio values. We therefore investigated similarities and differences between five different myelin-sensitive MRI measures and their effects on g-ratio mapping in the brains of both MS patients and healthy volunteers. We compared two different estimates of the myelin water fraction (MWF) as well as the inhomogeneous magnetization transfer ratio (ihMTR), magnetization transfer saturation (MTsat), and macromolecular tissue volume (MTV) in 13 patients with MS and 14 healthy controls. In combination with diffusion-weighted imaging, we derived g-ratio parameter maps for each of the five different myelin measures. The g-ratio values calculated from different myelin measures varied strongly, especially in MS lesions. While, compared to normal-appearing white matter, MTsat and one estimate of the MWF resulted in higher g-ratio values within lesions, ihMTR, MTV, and the second MWF estimate resulted in lower lesion g-ratio values. As myelin-sensitive measures provide rough estimates of myelin content rather than absolute myelin concentrations, resulting g-ratio values strongly depend on the utilized myelin measure and model used for g-ratio mapping. When comparing g-ratio values, it is, thus, important to utilize the same MRI methods and models or to consider methodological differences. Particular caution is necessary in pathological tissue such as MS lesions.

Magic angle effect on diffusion tensor imaging in ligament and brain

PURPOSE

To evaluate the magic angle effect on diffusion tensor imaging (DTI) measurements in rat ligaments and mouse brains.

METHODS

Three rat knee joints and three mouse brains were scanned at 9.4 T using a modified 3D diffusion-weighted spin echo pulse sequence with the isotropic spatial resolution of 45 μm. The b value was 1000 s/mm2 for rat knee and 4000 s/mm2 for mouse brain. DTI model was used to investigate the quantitative metrics at different orientations with respect to the main magnetic field. The collagen fiber structure of the ligament was validated with polarized light microscopy (PLM) imaging.

RESULTS

The signal intensity, signal-to-noise ratio (SNR), and DTI metrics in the ligament were strongly dependent on the collagen fiber orientation with respect to the main magnetic field from both simulation and actual MRI scans. The variation of fractional anisotropy (FA) was about ~32%, and the variation of mean diffusivity (MD) was ~11%. These findings were further validated with the numerical simulation at different SNRs (~10.0 to 86.0). Compared to the ligament, the DTI metrics showed little orientation dependence in mouse brains.

CONCLUSION

Magic angle effect plays an important role in DTI measurements in the highly ordered collagen-rich tissues, while MD showed less orientation dependence than FA.

Myelin water fraction mapping from multiple echo spin echoes and an independent B1 + map

Purpose

Myelin water fraction (MWF) is often obtained from a multiple echo spin echo (MESE) sequence using multi‐component T₂ fitting with non‐negative least squares. This process fits many unknowns including B₁⁺ to produce a T₂ spectrum for each voxel. Presented is an alternative using a rapid B₁⁺ mapping sequence to supply B₁⁺ for the MWF fitting procedure.

Methods

Effects of B₁⁺ errors on MWF calculations were modeled for 2D and 3D MESE using Bloch and extended phase graph simulations, respectively. Variations in SNR and relative refocusing widths were tested. Human brain experiments at 3 T used 2D MESE and an independent B₁⁺ map. MWF maps were produced with the standard approach and with the use of the independent B₁⁺ map. Differences in B₁⁺ and mean MWF in specific brain regions were compared.

Results

For 2D MESE, MWF with the standard method was strongly affected by B₁⁺ misestimations arising from limited SNR and response asymmetry around 180°, which decreased with increasing relative refocusing width. Using an independent B₁⁺ map increased mean MWF and decreased coefficient of variation. Notable differences in vivo in 2D MESE were in areas of high B₁⁺ such as thalamus and splenium where mean MWF increased by 88% and 31%, respectively (P < 0.001). Simulations also demonstrated the advantages of this approach for 3D MESE when SNR is <500.

Conclusion

For 2D MESE, because of increased complexity of decay curves and limited SNR, supplying B₁⁺ improves MWF results in peripheral and central brain regions where flip angles differ substantially from 180°.

Subsecond accurate myelin water fraction reconstruction from FAST-T2 data with 3D UNET

PURPOSE

To develop a 3D UNET convolutional neural network for rapid extraction of myelin water fraction (MWF) maps from six-echo fast acquisition with spiral trajectory and T₂ -prep data and to evaluate its accuracy in comparison with multilayer perceptron (MLP) network.

METHODS

The MWF maps were extracted from 138 patients with multiple sclerosis using an iterative three-pool nonlinear least-squares algorithm (NLLS) without and with spatial regularization (srNLLS), which were used as ground-truth labels to train, validate, and test UNET and MLP networks as a means to accelerate data fitting. Network testing was performed in 63 patients with multiple sclerosis and a numerically simulated brain phantom at SNR of 200, 100 and 50.

RESULTS

Simulations showed that UNET reduced the MWF mean absolute error by 30.1% to 56.4% and 16.8% to 53.6% over the whole brain and by 41.2% to 54.4% and 21.4% to 49.4% over the lesions for predicting srNLLS and NLLS MWF, respectively, compared to MLP, with better performance at lower SNRs. UNET also outperformed MLP for predicting srNLLS MWF in the in vivo multiple-sclerosis brain data, reducing mean absolute error over the whole brain by 61.9% and over the lesions by 67.5%. However, MLP yielded 41.1% and 51.7% lower mean absolute error for predicting in vivo NLLS MWF over the whole brain and the lesions, respectively, compared with UNET. The whole-brain MWF processing time using a GPU was 0.64 seconds for UNET and 0.74 seconds for MLP.

CONCLUSION

Subsecond whole-brain MWF extraction from fast acquisition with spiral trajectory and T₂ -prep data using UNET is feasible and provides better accuracy than MLP for predicting MWF output of srNLLS algorithm.

Model-based multi-parameter mapping

Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2*) or magnetisation-transfer saturation (MTsat), involves inverting a highly non-linear function. Many methods for deriving parameter maps assume perfect measurements and do not consider how noise is propagated through the estimation procedure, resulting in needlessly noisy maps. Instead, we propose a probabilistic generative (forward) model of the entire dataset, which is formulated and inverted to jointly recover (log) parameter maps with a well-defined probabilistic interpretation (e.g., maximum likelihood or maximum a posteriori). The second order optimisation we propose for model fitting achieves rapid and stable convergence thanks to a novel approximate Hessian. We demonstrate the utility of our flexible framework in the context of recovering more accurate maps from data acquired using the popular multi-parameter mapping protocol. We also show how to incorporate a joint total variation prior to further decrease the noise in the maps, noting that the probabilistic formulation allows the uncertainty on the recovered parameter maps to be estimated. Our implementation uses a PyTorch backend and benefits from GPU acceleration. It is available at https://github.com/balbasty/nitorch.

Continuous diffusion spectrum computation for diffusion-weighted magnetic resonance imaging of the kidney tubule system

Background

The use of rigid multi-exponential models (with a priori predefined numbers of components) is common practice for diffusion-weighted MRI (DWI) analysis of the kidney. This approach may not accurately reflect renal microstructure, as the data are forced to conform to the a priori assumptions of simplified models. This work examines the feasibility of less constrained, data-driven non-negative least squares (NNLS) continuum modelling for DWI of the kidney tubule system in simulations that include emulations of pathophysiological conditions.

Methods

Non-linear least squares (LS) fitting was used as reference for the simulations. For performance assessment, a threshold of 5% or 10% for the mean absolute percentage error (MAPE) of NNLS and LS results was used. As ground truth, a tri-exponential model using defined volume fractions and diffusion coefficients for each renal compartment (tubule system: D_tubules , f_tubules ; renal tissue: D_tissue , f_tissue ; renal blood: D_blood , f_blood ;) was applied. The impact of: (I) signal-to-noise ratio (SNR) =40-1,000, (II) number of b-values (n=10-50), (III) diffusion weighting (b-range_small =0-800 up to b-range_large =0-2,180 s/mm²), and (IV) fixation of the diffusion coefficients D_tissue and D_blood was examined. NNLS was evaluated for baseline and pathophysiological conditions, namely increased tubular volume fraction (ITV) and renal fibrosis (10%: grade I, mild) and 30% (grade II, moderate).

Results

NNLS showed the same high degree of reliability as the non-linear LS. MAPE of the tubular volume fraction (f_tubules ) decreased with increasing SNR. Increasing the number of b-values was beneficial for f_tubules precision. Using the b-range_large led to a decrease in MAPE _ftubules compared to b-range_small. The use of a medium b-value range of b=0-1,380 s/mm² improved f_tubules precision, and further b_max increases beyond this range yielded diminishing improvements. Fixing D_blood and D_tissue significantly reduced MAPE _ftubules and provided near perfect distinction between baseline and ITV conditions. Without constraining the number of renal compartments in advance, NNLS was able to detect the (fourth) fibrotic compartment, to differentiate it from the other three diffusion components, and to distinguish between 10% vs. 30% fibrosis.

Conclusions

This work demonstrates the feasibility of NNLS modelling for DWI of the kidney tubule system and shows its potential for examining diffusion compartments associated with renal pathophysiology including ITV fraction and different degrees of fibrosis.

Towards in vivo g-ratio mapping using MRI: Unifying myelin and diffusion imaging

BACKGROUND

The g-ratio, quantifying the comparative thickness of the myelin sheath encasing an axon, is a geometrical invariant that has high functional relevance because of its importance in determining neuronal conduction velocity. Advances in MRI data acquisition and signal modelling have put in vivo mapping of the g-ratio, across the entire white matter, within our reach. This capacity would greatly increase our knowledge of the nervous system: how it functions, and how it is impacted by disease.

NEW METHOD

This is the second review on the topic of g-ratio mapping using MRI.

RESULTS

This review summarizes the most recent developments in the field, while also providing methodological background pertinent to aggregate g-ratio weighted mapping, and discussing pitfalls associated with these approaches.

COMPARISON WITH EXISTING METHODS

Using simulations based on recently published data, this review reveals caveats to the state-of-the-art calibration methods that have been used for in vivo g-ratio mapping. It highlights the need to estimate both the slope and offset of the relationship between these MRI-based markers and the true myelin volume fraction if we are really to achieve the goal of precise, high sensitivity g-ratio mapping in vivo. Other challenges discussed in this review further evidence the need for gold standard measurements of human brain tissue from ex vivo histology.

CONCLUSIONS

We conclude that the quest to find the most appropriate MRI biomarkers to enable in vivo g-ratio mapping is ongoing, with the full potential of many novel techniques yet to be investigated.

Comparison of multi echo T2 relaxation and steady state approaches for myelin imaging in the central nervous system

The traditional approach for measuring myelin-associated water with quantitative magnetic resonance imaging (MRI) uses multi-echo T₂ relaxation data to calculate the myelin water fraction (MWF). A fundamentally different approach, abbreviated “mcDESPOT”, uses a more efficient steady-state acquisition to generate an equivalent metric (f_M). Although previous studies have demonstrated inherent instability and bias in the complex mcDESPOT analysis procedure, f_M has often been used as a surrogate for MWF. We produced and compared multivariate atlases of MWF and f_M in healthy human brain and cervical spinal cord (available online) and compared their ability to detect multiple sclerosis pathology. A significant bias was found in all regions (p < 10^–5), albeit reversed for spinal cord (f_M-MWF =  − 3.4%) compared to brain (+ 6.2%). MWF and f_M followed an approximately linear relationship for regions with MWF <  ~ 10%. For MWF >  ~ 10%, the relationship broke down and f_M no longer increased in tandem with MWF. For multiple sclerosis patients, MWF and f_M Z score maps showed overlapping areas of low Z score and similar trends between patients and brain regions, although those of f_M generally had greater spatial extent and magnitude of severity. These results will guide future choice of myelin-sensitive quantitative MRI and improve interpretation of studies using either myelin imaging approach.

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

Multi-component T₂ relaxometry allows probing tissue microstructure by assessing compartment-specific T₂ 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 T₂ 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 T₂ 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.