High-resolution quantitative and functional MRI indicate lower myelination of thin and thick stripes in human secondary visual cortex.

The characterization of cortical myelination is essential for the study of structure-function relationships in the human brain. However, knowledge about cortical myelination is largely based on post-mortem histology, which generally renders direct comparison to function impossible. The repeating pattern of pale-thin-pale-thick stripes of cytochrome oxidase (CO) activity in the primate secondary visual cortex (V2) is a prominent columnar system, in which histology also indicates different myelination of thin/thick versus pale stripes. We used quantitative magnetic resonance imaging (qMRI) in conjunction with functional magnetic resonance imaging (fMRI) at ultra-high field strength (7 T) to localize and study myelination of stripes in four human participants at sub-millimeter resolution in vivo. Thin and thick stripes were functionally localized by exploiting their sensitivity to color and binocular disparity, respectively. Resulting functional activation maps showed robust stripe patterns in V2 which enabled further comparison of quantitative relaxation parameters between stripe types. Thereby, we found lower longitudinal relaxation rates (R1) of thin and thick stripes compared to surrounding gray matter in the order of 1-2%, indicating higher myelination of pale stripes. No consistent differences were found for effective transverse relaxation rates (R2*). The study demonstrates the feasibility to investigate structure-function relationships in living humans within one cortical area at the level of columnar systems using qMRI.

Quantitative MRI maps of human neocortex explored using cell type-specific gene expression analysis.

Quantitative magnetic resonance imaging (qMRI) allows extraction of reproducible and robust parameter maps. However, the connection to underlying biological substrates remains murky, especially in the complex, densely packed cortex. We investigated associations in human neocortex between qMRI parameters and neocortical cell types by comparing the spatial distribution of the qMRI parameters longitudinal relaxation rate (${R_{1}}$), effective transverse relaxation rate (${R_{2}}^{\ast }$), and magnetization transfer saturation (MTsat) to gene expression from the Allen Human Brain Atlas, then combining this with lists of genes enriched in specific cell types found in the human brain. As qMRI parameters are magnetic field strength-dependent, the analysis was performed on MRI data at 3T and 7T. All qMRI parameters significantly covaried with genes enriched in GABA- and glutamatergic neurons, i.e. they were associated with cytoarchitecture. The qMRI parameters also significantly covaried with the distribution of genes enriched in astrocytes (${R_{2}}^{\ast }$ at 3T, ${R_{1}}$ at 7T), endothelial cells (${R_{1}}$ and MTsat at 3T), microglia (${R_{1}}$ and MTsat at 3T, ${R_{1}}$ at 7T), and oligodendrocytes and oligodendrocyte precursor cells (${R_{1}}$ at 7T). These results advance the potential use of qMRI parameters as biomarkers for specific cell types.

B 1 + $$ {B}_1

PURPOSE: Magnetization transfer saturation ( MTsat $$ \mathrm{MTsat} $$ ) is a useful marker to probe tissue macromolecular content and myelination in the brain. The increased B 1 + $$ {B}_1^{+} $$ -inhomogeneity at ≥ 7 $$ \ge 7 $$ T and significantly larger saturation pulse flip angles which are often used for postmortem studies exceed the limits where previous MTsat $$ \mathrm{MTsat} $$ B 1 + $$ {B}_1^{+} $$ correction methods are applicable. Here, we develop a calibration-based correction model and procedure, and validate and evaluate it in postmortem 7T data of whole chimpanzee brains. THEORY: The B 1 + $$ {B}_1^{+} $$ dependence of MTsat $$ \mathrm{MTsat} $$ was investigated by varying the off-resonance saturation pulse flip angle. For the range of saturation pulse flip angles applied in typical experiments on postmortem tissue, the dependence was close to linear. A linear model with a single calibration constant C $$ C $$ is proposed to correct bias in MTsat $$ \mathrm{MTsat} $$ by mapping it to the reference value of the saturation pulse flip angle. METHODS: C $$ C $$ was estimated voxel-wise in five postmortem chimpanzee brains. "Individual-based global parameters" were obtained by calculating the mean C $$ C $$ within individual specimen brains and "group-based global parameters" by calculating the means of the individual-based global parameters across the five brains. RESULTS: The linear calibration model described the data well, though C $$ C $$ was not entirely independent of the underlying tissue and B 1 + $$ {B}_1^{+} $$ . Individual-based correction parameters and a group-based global correction parameter ( C = 1 . 2 $$ C=1.2 $$ ) led to visible, quantifiable reductions of B 1 + $$ {B}_1^{+} $$ -biases in high-resolution MTsat $$ \mathrm{MTsat} $$ maps. CONCLUSION: The presented model and calibration approach effectively corrects for B 1 + $$ {B}_1^{+} $$ inhomogeneities in postmortem 7T data.

Brain structure and function: a multidisciplinary pipeline to study hominoid brain evolution.

To decipher the evolution of the hominoid brain and its functions, it is essential to conduct comparative studies in primates, including our closest living relatives. However, strong ethical concerns preclude in vivo neuroimaging of great apes. We propose a responsible and multidisciplinary alternative approach that links behavior to brain anatomy in non-human primates from diverse ecological backgrounds. The brains of primates observed in the wild or in captivity are extracted and fixed shortly after natural death, and then studied using advanced MRI neuroimaging and histology to reveal macro- and microstructures. By linking detailed neuroanatomy with observed behavior within and across primate species, our approach provides new perspectives on brain evolution. Combined with endocranial brain imprints extracted from computed tomographic scans of the skulls these data provide a framework for decoding evolutionary changes in hominin fossils. This approach is poised to become a key resource for investigating the evolution and functional differentiation of hominoid brains.

Error quantification in multi-parameter mapping facilitates robust estimation and enhanced group level sensitivity.

Multi-Parameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of PD, R1, and MTsat maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the model-based signal-to-noise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental raw-image-based SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from PD to R1 and decreased from PD to MTsat by a factor of 3-4. Exploring the artefact-sensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisition-specific errors to down-weight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their single-repeat or averaged counterparts. The error and mSNR maps may better inform power-calculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the open-source hMRI toolbox.

Combining navigator and optical prospective motion correction for high-quality 500 µm resolution quantitative multi-parameter mapping at 7T.

PURPOSE: High-resolution quantitative multi-parameter mapping shows promise for non-invasively characterizing human brain microstructure but is limited by physiological artifacts. We implemented corrections for rigid head movement and respiration-related B0-fluctuations and evaluated them in healthy volunteers and dementia patients. METHODS: Camera-based optical prospective motion correction (PMC) and FID navigator correction were implemented in a gradient and RF-spoiled multi-echo 3D gradient echo sequence for mapping proton density (PD), longitudinal relaxation rate (R1) and effective transverse relaxation rate (R2*). We studied their effectiveness separately and in concert in young volunteers and then evaluated the navigator correction (NAVcor) with PMC in a group of elderly volunteers and dementia patients. We used spatial homogeneity within white matter (WM) and gray matter (GM) and scan-rescan measures as quality metrics. RESULTS: NAVcor and PMC reduced artifacts and improved the homogeneity and reproducibility of parameter maps. In elderly participants, NAVcor improved scan-rescan reproducibility of parameter maps (coefficient of variation decreased by 14.7% and 11.9% within WM and GM respectively). Spurious inhomogeneities within WM were reduced more in the elderly than in the young cohort (by 9% vs. 2%). PMC increased regional GM/WM contrast and was especially important in the elderly cohort, which moved twice as much as the young cohort. We did not find a significant interaction between the two corrections. CONCLUSION: Navigator correction and PMC significantly improved the quality of PD, R1, and R2* maps, particularly in less compliant elderly volunteers and dementia patients.

The variability of MR axon radii estimates in the human white matter.

The noninvasive quantification of axonal morphology is an exciting avenue for gaining understanding of the function and structure of the central nervous system. Accurate non-invasive mapping of micron-sized axon radii using commonly applied neuroimaging techniques, that is, diffusion-weighted MRI, has been bolstered by recent hardware developments, specifically MR gradient design. Here the whole brain characterization of the effective MR axon radius is presented and the inter- and intra-scanner test-retest repeatability and reproducibility are evaluated to promote the further development of the effective MR axon radius as a neuroimaging biomarker. A coefficient-of-variability of approximately 10% in the voxelwise estimation of the effective MR radius is observed in the test-retest analysis, but it is shown that the performance can be improved fourfold using a customized along-tract analysis.

Mapping Short Association Fibers in the Early Cortical Visual Processing Stream Using In Vivo Diffusion Tractography.

Short association fibers (U-fibers) connect proximal cortical areas and constitute the majority of white matter connections in the human brain. U-fibers play an important role in brain development, function, and pathology but are underrepresented in current descriptions of the human brain connectome, primarily due to methodological challenges in diffusion magnetic resonance imaging (dMRI) of these fibers. High spatial resolution and dedicated fiber and tractography models are required to reliably map the U-fibers. Moreover, limited quantitative knowledge of their geometry and distribution makes validation of U-fiber tractography challenging. Submillimeter resolution diffusion MRI-facilitated by a cutting-edge MRI scanner with 300 mT/m maximum gradient amplitude-was used to map U-fiber connectivity between primary and secondary visual cortical areas (V1 and V2, respectively) in vivo. V1 and V2 retinotopic maps were obtained using functional MRI at 7T. The mapped V1-V2 connectivity was retinotopically organized, demonstrating higher connectivity for retinotopically corresponding areas in V1 and V2 as expected. The results were highly reproducible, as demonstrated by repeated measurements in the same participants and by an independent replication group study. This study demonstrates a robust U-fiber connectivity mapping in vivo and is an important step toward construction of a more complete human brain connectome.

Biophysically motivated efficient estimation of the spatially isotropic R2* component from a single gradient-recalled echo measurement.

PURPOSE: To propose and validate an efficient method, based on a biophysically motivated signal model, for removing the orientation-dependent part of R2* using a single gradient-recalled echo (GRE) measurement. METHODS: The proposed method utilized a temporal second-order approximation of the hollow-cylinder-fiber model, in which the parameter describing the linear signal decay corresponded to the orientation-independent part of R2* . The estimated parameters were compared to the classical, mono-exponential decay model for R2* in a sample of an ex vivo human optic chiasm (OC). The OC was measured at 16 distinct orientations relative to the external magnetic field using GRE at 7T. To show that the proposed signal model can remove the orientation dependence of R2* , it was compared to the established phenomenological method for separating R2* into orientation-dependent and -independent parts. RESULTS: Using the phenomenological method on the classical signal model, the well-known separation of R2* into orientation-dependent and -independent parts was verified. For the proposed model, no significant orientation dependence in the linear signal decay parameter was observed. CONCLUSIONS: Since the proposed second-order model features orientation-dependent and -independent components at distinct temporal orders, it can be used to remove the orientation dependence of R2* using only a single GRE measurement.

Microstructural imaging of human neocortex in vivo.

The neocortex of the human brain is the seat of higher brain function. Modern imaging techniques, chief among them magnetic resonance imaging (MRI), allow non-invasive imaging of this important structure. Knowledge of the microstructure of the neocortex has classically come from post-mortem histological studies of human tissue, and extrapolations from invasive animal studies. From these studies, we know that the scale of important neocortical structure spans six orders of magnitude, ranging from the size of axonal diameters (microns), to the size of cortical areas responsible for integrating sensory information (centimetres). MRI presents an opportunity to move beyond classical methods, because MRI is non-invasive and MRI contrast is sensitive to neocortical microstructure over all these length scales. MRI thus allows inferences to be made about neocortical microstructure in vivo, i.e. MRI-based in vivo histology. We review recent literature that has applied and developed MRI-based in vivo histology to probe the microstructure of the human neocortex, focusing specifically on myelin, iron, and neuronal fibre mapping. We find that applications such as cortical parcellation (using [Formula: see text] maps as proxies for myelin content) and investigation of cortical iron deposition with age (using [Formula: see text] maps) are already contributing to the frontiers of knowledge in neuroscience. Neuronal fibre mapping in the cortex remains challenging in vivo, but recent improvements in diffusion MRI hold promise for exciting applications in the near future. The literature also suggests that utilising multiple complementary quantitative MRI maps could increase the specificity of inferences about neocortical microstructure relative to contemporary techniques, but that further investment in modelling is required to appropriately combine the maps. In vivo histology of human neocortical microstructure is undergoing rapid development. Future developments will improve its specificity, sensitivity, and clinical applicability, granting an ever greater ability to investigate neuroscientific and clinical questions about the human neocortex.

NODDI-DTI: Estimating Neurite Orientation and Dispersion Parameters from a Diffusion Tensor in Healthy White Matter.

The NODDI-DTI signal model is a modification of the NODDI signal model that formally allows interpretation of standard single-shell DTI data in terms of biophysical parameters in healthy human white matter (WM). The NODDI-DTI signal model contains no CSF compartment, restricting application to voxels without CSF partial-volume contamination. This modification allowed derivation of analytical relations between parameters representing axon density and dispersion, and DTI invariants (MD and FA) from the NODDI-DTI signal model. These relations formally allow extraction of biophysical parameters from DTI data. NODDI-DTI parameters were estimated by applying the proposed analytical relations to DTI parameters estimated from the first shell of data, and compared to parameters estimated by fitting the NODDI-DTI model to both shells of data (reference dataset) in the WM of 14 in vivo diffusion datasets recorded with two different protocols, and in simulated data. The first two datasets were also fit to the NODDI-DTI model using only the first shell (as for DTI) of data. NODDI-DTI parameters estimated from DTI, and NODDI-DTI parameters estimated by fitting the model to the first shell of data gave similar errors compared to two-shell NODDI-DTI estimates. The simulations showed the NODDI-DTI method to be more noise-robust than the two-shell fitting procedure. The NODDI-DTI method gave unphysical parameter estimates in a small percentage of voxels, reflecting voxelwise DTI estimation error or NODDI-DTI model invalidity. In the course of evaluating the NODDI-DTI model, it was found that diffusional kurtosis strongly biased DTI-based MD values, and so, making assumptions based on healthy WM, a novel heuristic correction requiring only DTI data was derived and used to mitigate this bias. Since validations were only performed on healthy WM, application to grey matter or pathological WM would require further validation. Our results demonstrate NODDI-DTI to be a promising model and technique to interpret restricted datasets acquired for DTI analysis in healthy white matter with greater biophysical specificity, though its limitations must be borne in mind.

Conformational analysis of small organic molecules using NOE and RDC data: A discussion of strychnine and α-methylene-γ-butyrolactone.

To understand the properties and/or reactivity of an organic molecule, an understanding of its three-dimensional structure is necessary. Simultaneous determination of configuration and conformation often poses a daunting challenge. Thus, the more information accessible for a given molecule, the better. Additionally to (3)J-couplings, two sources of information, quantitative NOE and more recently also RDCs, are used for conformational analysis by NMR spectroscopy. In this paper, we compare these sources of conformational information in two molecules: the configurationally well-characterized strychnine 1, and the only recently configurationally and conformationally characterized α-methylene-γ-butyrolactone 2. We discuss possible sources of error in the measurement and analysis process, and how to exclude them. By this means, we are able to bolster the previously proposed flexibility for these two molecules.

Quantum mechanical NMR simulation algorithm for protein-size spin systems.

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch-Redfield-Wangsness theory) on isotopically enriched human ubiquitin - a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.

Simulation of coherence selection by pulsed field gradients in liquid-state NMR using an auxiliary matrix formalism.

An algorithm for simulating coherence selection due to a pulse sequence element consisting of two pulsed field gradients separated by a short collection of pulses and delays is introduced. This algorithm involves computation of the matrix exponential of an auxiliary matrix twice the size of the system Liouvillian, a dimensional increase smaller than is required with other known computational methods. Approximations valid for most simulations of liquid-state NMR spectra are involved in the derivation. Diffusion is omitted, but could be treated in an approximate way as a damping over the pulse sequence element. Several NMR pulse sequences using gradients for coherence selection have been implemented, making use of the functionality of Spinach (http://spindynamics.org/Spinach.php). Example simulations testing these implementations are presented, and the extent to which the formal dimensional reduction can lead to a speedup in simulation time discussed. It is found that the previously known methods can be made competitive with the auxiliary matrix method by making use of their embarrassingly parallel nature. Cases where the relative dimensional reduction of the auxiliary matrix method is very large, or where efficient parallelization of the simulation independent of the nature of the algorithm used exists, are found to lead to situations beneficial for the auxiliary matrix algorithm in this comparison.

Grid-free powder averages: on the applications of the Fokker-Planck equation to solid state NMR.

We demonstrate that Fokker-Planck equations in which spatial coordinates are treated on the same conceptual level as spin coordinates yield a convenient formalism for treating magic angle spinning NMR experiments. In particular, time dependence disappears from the background Hamiltonian (sample spinning is treated as an interaction), spherical quadrature grids are avoided completely (coordinate distributions are a part of the formalism) and relaxation theory with any linear diffusion operator is easily adopted from the Stochastic Liouville Equation theory. The proposed formalism contains Floquet theory as a special case. The elimination of the spherical averaging grid comes at the cost of increased matrix dimensions, but we show that this can be mitigated by the use of state space restriction and tensor train techniques. It is also demonstrated that low correlation order basis sets apparently give accurate answers in powder-averaged MAS simulations, meaning that polynomially scaling simulation algorithms do exist for a large class of solid state NMR experiments.

Parallel density matrix propagation in spin dynamics simulations.

Several methods for density matrix propagation in parallel computing environments are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.

Quantum mechanical simulation of solid effect dynamic nuclear polarisation using Krylov-Bogolyubov time averaging and a restricted state-space.

A strategy is described for simulations of solid effect dynamic nuclear polarisation that reduces substantially the dimension of the quantum mechanical problem. Averaging the Hamiltonian in the doubly rotating frame is used to confine the active space to the zero quantum coherence subspace. A further restriction of the Liouville space is made by truncating higher spin order states, which are weakly populated due to the presence of relaxation processes. Based on a dissipative transport equation, which is used to estimate the transport of the magnetisation starting from single spin order to higher spin order states, a minimal spin order for the states is calculated that needs to be taken into account for the spin dynamics simulation. The strategy accelerates individual spin calculations by orders of magnitude, thus making it possible to simulate the polarisation dynamics of systems with up to 25 nuclear spins.

On the accuracy of the state space restriction approximation for spin dynamics simulations.

We present an algebraic foundation for the state space restriction approximation in spin dynamics simulations and derive applicability criteria as well as minimal basis set requirements for practically encountered simulation tasks. The results are illustrated with nuclear magnetic resonance (NMR), electron spin resonance (ESR), dynamic nuclear polarization (DNP), and spin chemistry simulations. It is demonstrated that state space restriction yields accurate results in systems where the time scale of spin relaxation processes approximately matches the time scale of the experiment. Rigorous error bounds and basis set requirements are derived.

Destination state screening of active spaces in spin dynamics simulations.

We propose a novel avenue for state space reduction in time domain Liouville space spin dynamics simulations, using detectability as a selection criterion--only those states that evolve into or affect other detectable states are kept in the simulation. This basis reduction procedure (referred to as destination state screening) is formally exact and can be applied on top of the existing state space restriction techniques. As demonstrated below, in many cases this results in further reduction of matrix dimension, leading to considerable acceleration of many spin dynamics simulation types. Destination state screening is implemented in the latest version of the Spinach library (http://spindynamics.org).