Fast and robust quantification of uncertainty in non-linear diffusion MRI models

Diffusion MRI (dMRI) allows for non-invasive investigation of brain tissue microstructure. By fitting a model to the dMRI signal, various quantitative measures can be derived from the data, such as fractional anisotropy, neurite density and axonal radii maps. We investigate the Fisher Information Matrix (FIM) and uncertainty propagation as a generally applicable method for quantifying the parameter uncertainties in linear and non-linear diffusion MRI models. In direct comparison with Markov Chain Monte Carlo (MCMC) sampling, the FIM produces similar uncertainty estimates at much lower computational cost. Using acquired and simulated data, we then list several characteristics that influence the parameter variances, including data complexity and signal-to-noise ratio. For practical purposes we investigate a possible use of uncertainty estimates in decreasing intra-group variance in group statistics by uncertainty-weighted group estimates. This has potential use cases for detection and suppression of imaging artifacts.

Fiber-orientation independent component of R2* obtained from single-orientation MRI measurements in simulations and a post-mortem human optic chiasm

The effective transverse relaxation rate (R2*) is sensitive to the microstructure of the human brain like the g-ratio which characterises the relative myelination of axons. However, the fibre-orientation dependence of R2* degrades its reproducibility and any microstructural derivative measure. To estimate its orientation-independent part (R2,iso*) from single multi-echo gradient-recalled-echo (meGRE) measurements at arbitrary orientations, a second-order polynomial in time model (hereafter M2) can be used. Its linear time-dependent parameter, β1, can be biophysically related to R2,iso* when neglecting the myelin water (MW) signal in the hollow cylinder fibre model (HCFM). Here, we examined the performance of M2 using experimental and simulated data with variable g-ratio and fibre dispersion. We found that the fitted β1 can estimate R2,iso* using meGRE with long maximum-echo time (TEmax ≈ 54 ms), but not accurately captures its microscopic dependence on the g-ratio (error 84%). We proposed a new heuristic expression for β1 that reduced the error to 12% for ex vivo compartmental R2 values. Using the new expression, we could estimate an MW fraction of 0.14 for fibres with negligible dispersion in a fixed human optic chiasm for the ex vivo compartmental R2 values but not for the in vivo values. M2 and the HCFM-based simulations failed to explain the measured R2*-orientation-dependence around the magic angle for a typical in vivo meGRE protocol (with TEmax ≈ 18 ms). In conclusion, further validation and the development of movement-robust in vivo meGRE protocols with TEmax ≈ 54 ms are required before M2 can be used to estimate R2,iso* in subjects.

Magnetic resonance imaging at 9.4 T: the Maastricht journey

The 9.4 T scanner in Maastricht is a whole-body magnet with head gradients and parallel RF transmit capability. At the time of the design, it was conceptualized to be one of the best fMRI scanners in the world, but it has also been used for anatomical and diffusion imaging. 9.4 T offers increases in sensitivity and contrast, but the technical ultra-high field (UHF) challenges, such as field inhomogeneities and constraints set by RF power deposition, are exacerbated compared to 7 T. This article reviews some of the 9.4 T work done in Maastricht. Functional imaging experiments included blood oxygenation level-dependent (BOLD) and blood-volume weighted (VASO) fMRI using different readouts. BOLD benefits from shorter T₂* at 9.4 T while VASO from longer T₁. We show examples of both ex vivo and in vivo anatomical imaging. For many applications, pTx and optimized coils are essential to harness the full potential of 9.4 T. Our experience shows that, while considerable effort was required compared to our 7 T scanner, we could obtain high-quality anatomical and functional data, which illustrates the potential of MR acquisitions at even higher field strengths. The practical challenges of working with a relatively unique system are also discussed.

BUDA-MESMERISE: Rapid acquisition and unsupervised parameter estimation for T1 , T2 , M0 , B0 , and B1 maps

PURPOSE

Rapid acquisition scheme and parameter estimation method are proposed to acquire distortion-free spin- and stimulated-echo signals and combine the signals with a physics-driven unsupervised network to estimate T₁ , T₂ , and proton density (M₀ ) parameter maps, along with B₀ and B₁ information from the acquired signals.

THEORY AND METHODS

An imaging sequence with three 90° RF pulses is utilized to acquire spin- and stimulated-echo signals. We utilize blip-up/-down acquisition to eliminate geometric distortion incurred by the effects of B₀ inhomogeneity on rapid EPI acquisitions. For multislice imaging, echo-shifting is applied to utilize dead time between the second and third RF pulses to encode information from additional slice positions. To estimate parameter maps from the spin- and stimulated-echo signals with high fidelity, 2 estimation methods, analytic fitting and a novel unsupervised deep neural network method, are developed.

RESULTS

The proposed acquisition provided distortion-free T₁ , T₂ , relative proton density (M0), B₀ , and B₁ maps with high fidelity both in phantom and in vivo brain experiments. From the rapidly acquired spin- and stimulated-echo signals, analytic fitting and the network-based method were able to estimate T₁ , T₂ , M₀ , B₀ , and B₁ maps with high accuracy. Network estimates demonstrated noise robustness owing to the fact that the convolutional layers take information into account from spatially adjacent voxels.

CONCLUSION

The proposed acquisition/reconstruction technique enabled whole-brain acquisition of coregistered, distortion-free, T₁ , T₂ , M₀ , B₀ , and B₁ maps at 1 × 1 × 5 mm³ resolution in 50 s. The proposed unsupervised neural network provided noise-robust parameter estimates from this rapid acquisition.

The Influence of Radio-Frequency Transmit Field Inhomogeneities on the Accuracy of G-ratio Weighted Imaging

G-ratio weighted imaging is a non-invasive, in-vivo MRI-based technique that aims at estimating an aggregated measure of relative myelination of axons across the entire brain white matter. The MR g-ratio and its constituents (axonal and myelin volume fraction) are more specific to the tissue microstructure than conventional MRI metrics targeting either the myelin or axonal compartment. To calculate the MR g-ratio, an MRI-based myelin-mapping technique is combined with an axon-sensitive MR technique (such as diffusion MRI). Correction for radio-frequency transmit (B1+) field inhomogeneities is crucial for myelin mapping techniques such as magnetization transfer saturation. Here we assessed the effect of B1+ correction on g-ratio weighted imaging. To this end, the B1+ field was measured and the B1+ corrected MR g-ratio was used as the reference in a Bland-Altman analysis. We found a substantial bias (≈-89%) and error (≈37%) relative to the dynamic range of g-ratio values in the white matter if the B1+ correction was not applied. Moreover, we tested the efficiency of a data-driven B1+ correction approach that was applied retrospectively without additional reference measurements. We found that it reduced the bias and error in the MR g-ratio by a factor of three. The data-driven correction is readily available in the open-source hMRI toolbox (www.hmri.info) which is embedded in the statistical parameter mapping (SPM) framework.

MESMERISED: Super-accelerating T1 relaxometry and diffusion MRI with STEAM at 7 T for quantitative multi-contrast and diffusion imaging

There is an increasing interest in quantitative imaging of T₁, T₂ and diffusion contrast in the brain due to greater robustness against bias fields and artifacts, as well as better biophysical interpretability in terms of microstructure. However, acquisition time constraints are a challenge, particularly when multiple quantitative contrasts are desired and when extensive sampling of diffusion directions, high b-values or long diffusion times are needed for multi-compartment microstructure modeling. Although ultra-high fields of 7 T and above have desirable properties for many MR modalities, the shortening T₂ and the high specific absorption rate (SAR) of inversion and refocusing pulses bring great challenges to quantitative T₁, T₂ and diffusion imaging. Here, we present the MESMERISED sequence (Multiplexed Echo Shifted Multiband Excited and Recalled Imaging of STEAM Encoded Diffusion). MESMERISED removes the dead time in Stimulated Echo Acquisition Mode (STEAM) imaging by an echo-shifting mechanism. The echo-shift (ES) factor is independent of multiband (MB) acceleration and allows for very high multiplicative (ESxMB) acceleration factors, particularly under moderate and long mixing times. This results in super-acceleration and high time efficiency at 7 T for quantitative T₁ and diffusion imaging, while also retaining the capacity to perform quantitative T₂ and B₁ mapping. We demonstrate the super-acceleration of MESMERISED for whole-brain T₁ relaxometry with total acceleration factors up to 36 at 1.8 mm isotropic resolution, and up to 54 at 1.25 mm resolution qT₁ imaging, corresponding to a 6x and 9x speedup, respectively, compared to MB-only accelerated acquisitions. We then demonstrate highly efficient diffusion MRI with high b-values and long diffusion times in two separate cases. First, we show that super-accelerated multi-shell diffusion acquisitions with 370 whole-brain diffusion volumes over 8 b-value shells up to b = 7000 s/mm² can be generated at 2 mm isotropic in under 8 minutes, a data rate of almost a volume per second, or at 1.8 mm isotropic in under 11 minutes, achieving up to 3.4x speedup compared to MB-only. A comparison of b = 7000 s/mm² MESMERISED against standard MB pulsed gradient spin echo (PGSE) diffusion imaging shows 70% higher SNR efficiency and greater effectiveness in supporting complex diffusion signal modeling. Second, we demonstrate time-efficient sampling of different diffusion times with 1.8 mm isotropic diffusion data acquired at four diffusion times up to 290 ms, which supports both Diffusion Tensor Imaging (DTI) and Diffusion Kurtosis Imaging (DKI) at each diffusion time. Finally, we demonstrate how adding quantitative T₂ and B₁⁺ mapping to super-accelerated qT₁ and diffusion imaging enables efficient quantitative multi-contrast mapping with the same MESMERISED sequence and the same readout train. MESMERISED extends possibilities to efficiently probe T₁, T₂ and diffusion contrast for multi-component modeling of tissue microstructure.

Robust and fast nonlinear optimization of diffusion MRI microstructure models

Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of run time, fit, accuracy and precision. Parameter initialization approaches were found to be relevant especially for more complex models, such as those involving several fiber orientations per voxel. For these, a fitting cascade initializing or fixing parameter values in a later optimization step from simpler models in an earlier optimization step further improved run time, fit, accuracy and precision compared to a single step fit. This establishes and makes available standards by which robust fit and accuracy can be achieved in shorter run times. This is especially relevant for the use of diffusion microstructure modeling in large group or population studies and in combining microstructure parameter maps with tractography results.

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Evaluate robustness of fit, accuracy, precision for diffusion microstructure models

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Test three optimization algorithms and three parameter initialization strategies

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GPU implementation removes run time constraints; whole brain fit within minutes

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Powell conjugate-direction algorithm has superior fit, accuracy, precision

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Initialization approaches are important for crossing fiber microstructure models

High resolution anatomical and quantitative MRI of the entire human occipital lobe ex vivo at 9.4T

Several magnetic resonance imaging (MRI) contrasts are sensitive to myelin content in gray matter in vivo which has ignited ambitions of MRI-based in vivo cortical histology. Ultra-high field (UHF) MRI, at fields of 7 T and beyond, is crucial to provide the resolution and contrast needed to sample contrasts over the depth of the cortex and get closer to layer resolved imaging. Ex vivo MRI of human post mortem samples is an important stepping stone to investigate MRI contrast in the cortex, validate it against histology techniques applied in situ to the same tissue, and investigate the resolutions needed to translate ex vivo findings to in vivo UHF MRI. Here, we investigate key technology to extend such UHF studies to large human brain samples while maintaining high resolution, which allows investigation of the layered architecture of several cortical areas over their entire 3D extent and their complete borders where architecture changes. A 16 channel cylindrical phased array radiofrequency (RF) receive coil was constructed to image a large post mortem occipital lobe sample (~80×80×80 mm³) in a wide-bore 9.4 T human scanner with the aim of achieving high-resolution anatomical and quantitative MR images. Compared with a human head coil at 9.4 T, the maximum Signal-to-Noise ratio (SNR) was increased by a factor of about five in the peripheral cortex. Although the transmit profile with a circularly polarized transmit mode at 9.4 T is relatively inhomogeneous over the large sample, this challenge was successfully resolved with parallel transmit using the kT-points method. Using this setup, we achieved 60μm anatomical images for the entire occipital lobe showing increased spatial definition of cortical details compared to lower resolutions. In addition, we were able to achieve sufficient control over SNR, B₀ and B₁ homogeneity and multi-contrast sampling to perform quantitative T₂* mapping over the same volume at 200 μm. Markov Chain Monte Carlo sampling provided maximum posterior estimates of quantitative T₂* and their uncertainty, allowing delineation of the stria of Gennari over the entire length and width of the calcarine sulcus. We discuss how custom RF receive coil arrays built to specific large post mortem sample sizes can provide a platform for UHF cortical layer-specific quantitative MRI over large fields of view.

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Custom-built 16 channel 9.4 T RF-coil to image large post mortem samples at high resolution.

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Parallel transmit techniques allow homogenization of B₁⁺ for 3D GRE imaging at UHF.

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60 μm anatomical MRI of the entire human occipital lobe.

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200 μm isotropic quantitative T₂^* mapping of the entire human occipital lobe.

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A platform for future UHF cortical layer specific qMRI over large FoVs.

Lymphocyte subsets and their proliferation in a model for a delayed-type hypersensitivity reaction in the skin

A delayed-type hypersensitivity (DTH) reaction was induced in the skin of young pigs, by local injection of phytohaemagglutinin, and evaluation was carried out on the resulting accumulation of lymphocyte subsets and lymphocyte production by incorporation of bromodeoxyuridine in the skin and the draining lymph node. There was a rapid increase in mononuclear cells, which were found in clusters around venules. These included very few B lymphocytes, and CD8+ lymphocytes far outnumbered CD4+ cells. Underlining the importance of determining absolute numbers, the relative and absolute numbers of lymphocyte subsets showed quite different patterns during the development of the skin reaction. Lymphocytes in the normal skin incorporated the DNA precursor bromodeoxyuridine at higher rates than have been found for peripheral lymphoid organs. After intradermal phytohaemagglutinin injections, all subsets showed high proliferation rates in the skin, with kinetics which differed from the reaction in the draining lymph node. The labelling indexes of cells labelled with bromodeoxyuridine in vitro and in vivo were comparable. The phytohaemagglutinin injections also caused a marked and rapid increase in the proliferation of the cells in the basal layer of the epidermis. This model DTH-like reaction in skin with major CD8+ T-cell accumulation and proliferation locally and in the lymph nodes provides a reliable model for study of such reactions and for investigation of the regulatory role of cytokines.

Proliferation of macrophage subpopulations in the adult rat: comparison of various lymphoid organs

Adult male Lewis rats received a single intravenous injection of 5-bromo-2'-deoxyuridine (BRDU) to label all proliferating cells in the S-phase of the cell cycle. Various lymphoid organs were removed 1 and 24 hr after injection to assess local proliferation and migration of newly formed cells, respectively. In cell suspensions, surface staining was performed for macrophage subsets (ED1, ED2, ED3), and the DNA label BRDU was detected by a monoclonal antibody. Local proliferation of ED1+ macrophages occurred in all organs investigated with the exception of the blood. Bone marrow outweighed the other organs by far; in addition to the proliferating ED1+ promonocytes, the bone marrow also contained BRDU-labeled ED2+ macrophages. Newly formed ED1+ monocytes migrated into lymphoid organs such as the mesenteric lymph nodes and spleen where they comprised about 90% of newly formed macrophages. In the spleen, ED3+ macrophages seemed to be renewed by local proliferation, whereas in the mesenteric lymph nodes these cells were replaced by immigration. The heterogeneity of macrophages was further demonstrated by the different renewal of splenic macrophages. ED1+ and ED3+ cells were replaced in a matter of days, whereas it would probably take several months to renew ED2+ cells.

Proliferation of lymphocyte subsets in the adult rat: a comparison of different lymphoid organs

Adult, male Lewis rats received a single injection of 5-bromo-2'-deoxyuridine (BrdUrd) i.v. to label proliferating cells in the S phase of the cell cycle. After 1 and 24 h the thymus, bone marrow, blood, spleen, peripheral, cervical and mesenteric lymph nodes as well as Peyer's patches were removed. In cell suspensions surface staining was performed for B, T, T helper (Th) and cytotoxic/suppressor (Tc/s) T lymphocytes by identifying kappa light chain, CD5+, CD4+ and CD8+ cells, respectively. On the same slide the DNA label BrdUrd was demonstrated by a monoclonal antibody. B, T, Th and Tc/s lymphocytes proliferate locally both in central lymphoid organs such as the thymus and the bone marrow, and in peripheral lymphoid organs such as the spleen, lymph nodes and Peyer's patches. Within an organ the amount of proliferation among the lymphocyte subsets is similar, differing not more than threefold. Although concerning only a small fraction of cells within the organ, an unexpected finding is the high percentage of BrdUrd-labeled cells among B lymphocytes in the thymus (3%) and among T lymphocytes in the bone marrow (3%). One day after injection of BrdUrd the thymus contains 25% BrdUrd+ T lymphocytes, while the other organs investigated do not show more than about 2% BrdUrd+ B and T lymphocytes. Many of the newly formed lymphocyte subsets leave their organ of birth within 24 h. Thus the amount of proliferation in the lymphocyte subsets investigated is very similar and the differences between central (thymus and bone marrow) and peripheral lymphoid organs are much smaller than expected.

The mucosa of the male genital tract; part of the common mucosal secretory immune system?

The selective migration of mucosal-derived lymphoid blasts to other mucosal organs is taken to be an essential part of the common secretory immune system. In rats, proliferating lymphoid cells from mesenteric lymph nodes (mLN) and peripheral lymph nodes (pLN) were labeled in vitro using two different techniques, in order to test the hypothesis that the mucosa of the male genital tract is a preferential site for mLN lymphoid blasts to home to. A low but significant migration to male genital organs was found, but with no difference between blasts from pLN and mLN. Thus there is no evidence to include the male genital tract in the common mucosal secretory immune system. Recirculating lymphocytes from the thoracic duct entered the male genital organs with a similar distribution to the pattern of lymphoid blasts. There is probably an exchange between these immigrating lymphocytes and the different subsets, which are localized in the epithelium (T suppressor) and interstitial tissue (T helper) in male genital organs. The lymphoid cells in the male genital tract might play an important role in the immune function of seminal fluid and in sexually transmissible diseases.

Migration pattern of lymphocyte subsets in the normal rat and the influence of splenic tissue

Lymphocyte subsets leave the blood and appear in the thoracic duct of normal rats at different rates. The aim of the present study was to investigate their migration pattern through blood, spleen, bone marrow, mesenteric lymph nodes, and Peyer's patches in normal Lewis rats and to study the role of the spleen using splenectomized and spleen-transplanted animals. Fluorescein isothiocyanate (FITC)-labelled thoracic duct lymphocytes (TDL) were injected intravenously into rats and after 15 min, 1, 6, and 24 h the percentages of B, T, T helper (TH) and T-cytotoxic/suppressor (TC/S) lymphocytes in the FITC+ cells were determined in cell suspensions by means of monoclonal antibodies. B and T lymphocytes are preferentially localized in different organs, e.g. B cells in Peyer's patches and T cells in mesenteric lymph nodes. The migration of TH lymphocytes differed from that of TC/S lymphocytes in all the organs investigated. In the late phase after injection the migration of B and TH lymphocytes was influenced by the spleen, since after splenectomy the number of injected B lymphocytes increased and that of TH lymphocytes decreased in all organs investigated except the bone marrow. Splenic autotransplantation could not normalize the disturbed migration.

Numbers and heterogeneity of mast cells in the male genital tract of the rat

Normal adult rats were used to quantitate and characterize mast cells in the male genital tract. The tissues were either fixed in a fixative containing formalin (Schaffer solution) or with basic lead acetate (BLA) to identify 'connective-tissue mast cells' and 'mucosal mast cells', respectively. In the epididymis and seminal vesicle small numbers of mast cells were identified without any obvious heterogeneity. In the prostate, however, a mean of 45.1 +/- 9.3 and 23.0 +/- 4.0 mast cells/mm2 was found after BLA and Schaffer fixation, respectively. This difference might be of functional and clinical significance.

Postnatal development and lymphocyte production of jejunal and ileal Peyer's patches in normal and gnotobiotic pigs

The development of the number, size, structure and proliferative capacity of Peyer's patches (PP) in the jejunum and ileum has been studied during the early postnatal period of conventional and germ-free pigs. A mean of 15 discrete PP in the jejunum and upper ileum (jejPP) were counted at birth, and the number increased only gradually. A continuous PP is located in the terminal ileum (ileal PP). The length of both jejPP and ileal PP increased with age due to the increase in follicle size and in the number of follicles in the ileal PP. In older pigs, only the ileal PP regressed to small scattered follicles. In germ-free piglets at 39 and 59 days of age, longer PP were found than in normal new-born piglets, but they were significantly shorter than in age-matched controls. Lymphocyte production was studied by the metaphase-arrest technique using vincristine. Lymphocyte production in follicles increased dramatically with age, while in other compartments, such as the inter-follicular and dome area, a low age-independent production of lymphocytes was found. There were no differences in lymphocytopoiesis between jejPP and ileal PP. The present data show major differences in the development, structure and function of PP in pigs in comparison to other species. These species-specific aspects are important for future studies on the immunological function of PP.

Comparison of lymphocyte production in lymphoid organs and their compartments using the metaphase-arrest technique

Lymphocyte proliferation was studied in normal young anesthetized pigs by the metaphase-arrest technique using vincristine (VCR). In each animal biopsies were taken simultaneously from the thymus, mesenteric lymph nodes, spleen, palatine tonsil and Peyer's patches from the ileum and jejunum. After taking the first samples, 0.25 mg VCR/kg body weight was injected i.v. and then four more biopsies were excised for up to 3.5 h after VCR. Imprints of the lymphoid organs were evaluated as an overall index for each organ, and histological sections were used to determine the mitotic index in typical B- and T-lymphocyte areas in these organs. In follicles of mesenteric lymph nodes, tonsils and the two types of Peyer's patches a comparable increase in the mitotic index was found, 3.62% per hour. In the corona the increase was also comparable but much lower, 0.43% per hour and in the interfollicular area similarly 0.38% per hour. In the spleen the mitotic rate was 0.69% for the white pulp and 0.42% per hour for the red pulp. In the thymic cortex the mitotic index increased by 0.49% and in the medulla by a surprisingly high value of 0.32% per hour. The metaphase-arrest technique in larger animals enables a comparison of lymphocyte production among organs and their different compartments, and demonstrates the important contribution of peripheral lymphoid organs to the renewal of the lymphocyte pools.