Intra-axonal diffusivity in brain white matter.

Biophysical modeling lies at the core of evaluating tissue cellular structure using diffusion-weighted MRI, albeit with shortcomings. The challenges lie not only in the complexity of the diffusion phenomenon, but also in the need to know the diffusion-specific properties of diverse cellular compartments in vivo. The likelihood function obtained from the commonly acquired Stejskal-Tanner diffusion-weighted MRI data is degenerate with different parameter constellations explaining the signal equally well, thereby hindering an unambiguous parameter estimation. The aim of this study is to measure the intra-axonal water diffusivity which is one of the central parameters of white matter models. Estimating intra-axonal diffusivity is complicated by (i) the presence of other compartments, and (ii) the orientation dispersion of axons. Our measurement involves an efficient signal suppression of water in extra-axonal space and all cellular processes oriented outside a narrow cone around the principal fiber direction. This is achieved using a planar water mobility filter that suppresses signal from all molecules that are mobile in the plane transverse to the fiber bundle. After the planar filter, the diffusivity of the remaining intra-axonal signal is measured using linear and spherical diffusion encoding. We find the average intra-axonal diffusivity D0=2.25±0.03µm2/ms for the timing of the applied gradients, which gives D0(∞)≈2.0µm2/ms when extrapolated to infinite diffusion time. The result imposes a strong limitation on the parameter selection for biophysical modeling of diffusion-weighted MRI.

A unique analytical solution of the white matter standard model using linear and planar encodings.

PURPOSE: It is known that white matter modeling based on commonly used linear diffusion encoding is an ill-posed problem. We analyze the additional information gained from a double pulsed diffusion encoding. METHODS: Zeroth (spherical means) and second-order (harmonic powers) rotation invariant signal features are used to factor micro- and mesoscopic contributions. The b-value dependency up to second-order of the features form 6 nonlinear equations, which are analyzed. RESULTS: The 6 derived equations can be uniquely solved for all relevant biophysical parameters. No assumptions about the form of the mesoscopic contribution (fiber dispersion) is necessary. Under certain conditions the solution still shows a certain degeneracy which is inherent to model. It is further shown that a combination of second-order information from single and spherical diffusion encoding is not enough to solve the problem. CONCLUSIONS: A combination of single and double pulsed diffusion encodings is sufficient to solve the full 3 compartment white matter model uniquely.

The absence of restricted water pool in brain white matter.

Understanding diffusion-weighted MR signal in brain white matter (WM) has been a long-sought-after goal. Modern research pursues this goal by focusing on the biological compartments that contributes essentially to the signal. In this study, we experimentally address the apparent presence of a compartment in which water motion is restricted in all spatial directions. Using isotropic diffusion encoding, we establish an upper bound on the fraction of such a compartment, which is shown to be about 2% of the unweighted signal for moderate diffusion times. This helps to eliminate such a compartment that have been assumed in literature on biophysical modeling. We also used the diffusion decay curve obtained from the isotropic encoding to establish a lower limit on the mean diffusivities of either of intra- or extra-axonal compartment as a function of their relative water fraction.

Modelfree global tractography.

Tractography based on diffusion-weighted MRI investigates the large scale arrangement of the neurite fibers in brain white matter. It is usually assumed that the signal is a convolution of a fiber specific response function (FRF) with a fiber orientation distribution (FOD). The FOD is the focus of tractography. While in the past the FRF was estimated beforehand and was usually assumed to be fix, more recent approaches estimate the response function during tractography. This work proposes a novel objective function independent of the FRF, just aiming for FOD reconstruction. The objective is integrated into global tractography showing promising results.

Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach.

Diffusion-sensitized magnetic resonance imaging probes the cellular structure of the human brain, but the primary microstructural information gets lost in averaging over higher-level, mesoscopic tissue organization such as different orientations of neuronal fibers. While such averaging is inevitable due to the limited imaging resolution, we propose a method for disentangling the microscopic cell properties from the effects of mesoscopic structure. We further avoid the classical fitting paradigm and use supervised machine learning in terms of a Bayesian estimator to estimate the microstructural properties. The method finds detectable parameters of a given microstructural model and calculates them within seconds, which makes it suitable for a broad range of neuroscientific applications.

Temperature dependence of water diffusion pools in brain white matter.

Water diffusion in brain tissue can now be easily investigated using magnetic resonance (MR) techniques, providing unique insights into cellular level microstructure such as axonal orientation. The diffusive motion in white matter is known to be non-Gaussian, with increasing evidence for more than one water-containing tissue compartment. In this study, freshly excised porcine brain white matter was measured using a 125-MHz MR spectrometer (3T) equipped with gradient coils providing magnetic field gradients of up to 35,000 mT/m. The sample temperature was varied between -14 and +19 °C. The hypothesis tested was that white matter contains two slowly exchanging pools of water molecules with different diffusion properties. A Stejskal-Tanner diffusion sequence with very short gradient pulses and b-factors up to 18.8 ms/µm(2) was used. The dependence on b-factor of the attenuation due to diffusion was robustly fitted by a biexponential function, with comparable volume fractions for each component. The diffusion coefficient of each component follows Arrhenius behavior, with significantly different activation energies. The measured volume fractions are consistent with the existence of three water-containing compartments, the first comprising relatively free cytoplasmic and extracellular water molecules, the second of water molecules in glial processes, and the third comprising water molecules closely associated with membranes, as for example, in the myelin sheaths and elsewhere. The activation energy of the slow diffusion pool suggests proton hopping at the surface of membranes by a Grotthuss mechanism, mediated by hydrating water molecules.

Gibbs-ringing artifact removal based on local subvoxel-shifts.

PURPOSE: To develop a fast and stable method for correcting the gibbs-ringing artifact. METHODS: Gibbs-ringing is a well-known artifact which manifests itself as spurious oscillations in the vicinity of sharp image gradients at tissue boundaries. The origin can be seen in the truncation of k-space during MRI data-acquisition. Correction techniques like Gegenbauer reconstruction or extrapolation methods aim at recovering these missing data. Here, we present a simple and robust method which exploits a different view on the Gibbs-phenomenon: The truncation in k-space can be interpreted as a convolution of the underlying image with a sinc-function. As the image is reconstructed on a discretized grid, the severity of the ringing artifacts depends on how this grid is located with respect to the edge and the oscillation pattern of the function. We propose to reinterpolate the image based on local, subvoxel-shifts to sample the ringing pattern at the zero-crossings of the oscillating sinc-function. RESULTS: With the proposed method, the artifact can simply, effectively, and robustly be removed with a minimal amount of image smoothing. CONCLUSIONS: The robustness of the method suggests it as a suitable candidate for an implementation in the standard image processing pipeline in clinical routine. Magn Reson Med 76:1574-1581, 2016. © 2015 International Society for Magnetic Resonance in Medicine.

Layer-specific intracortical connectivity revealed with diffusion MRI.

In this work, we show for the first time that the tangential diffusion component is orientationally coherent at the human cortical surface. Using diffusion magnetic resonance imaging (dMRI), we have succeeded in tracking intracortical fiber pathways running tangentially within the cortex. In contrast with histological methods, which reveal little regarding 3-dimensional organization in the human brain, dMRI delivers additional understanding of the layer dependence of the fiber orientation. A postmortem brain block was measured at very high angular and spatial resolution. The dMRI data had adequate resolution to allow analysis of the fiber orientation within 4 notional cortical laminae. We distinguished a lamina at the cortical surface where diffusion was tangential along the surface, a lamina below the surface where diffusion was mainly radial, an internal lamina covering the Stria of Gennari, where both strong radial and tangential diffusion could be observed, and a deep lamina near the white matter, which also showed mainly radial diffusion with a few tangential compartments. The measurement of the organization of the tangential diffusion component revealed a strong orientational coherence at the cortical surface.

Fast accurate MR thermometry using phase referenced asymmetric spin-echo EPI at high field.

PURPOSE: A novel highly accurate method for MR thermometry, effective at high field, is introduced and validated, which corrects for slow and fast field fluctuations by means of reference images. METHODS: An asymmetric spin-echo echo planar imaging sequence was made frequency-selective to water or a reference substance by controlling the slice-select gradient polarity and the duration of the excitation and refocusing radiofrequency pulses. Images were acquired pairwise, and the temperature-sensitive water images were corrected for field fluctuations using the reference images. In a phantom radiofrequency heating experiment, dissolved dimethyl sulfoxide was used as a reference substance. Temperature stability was tested in vivo on the human brain, referenced using subcutaneous scalp fat. Water and fat phase images were acquired only 50 ms apart. Bloch simulations validated the frequency selection accuracy. RESULTS: Asymmetric spin-echo imaging using a simple frequency selection method provides highly accurate referenced MR thermometry in phantoms and in vivo at 7 T. Effects of field fluctuations caused by field drift, breathing, and heart beat were corrected. The technique is highly robust against B1 inhomogeneities. CONCLUSION: Frequency selection using gradient-reversal can enable fast accurate referenced in vivo MR thermometry, assisting thermal characterization of radiofrequency coils and possibly in vivo SAR monitoring.

The Gini coefficient: a methodological pilot study to assess fetal brain development employing postmortem diffusion MRI.

BACKGROUND: Diffusion-weighted imaging (DWI) is important in the assessment of fetal brain development. However, it is clinically challenging and time-consuming to prepare neuromorphological examinations to assess real brain age and to detect abnormalities. OBJECTIVE: To demonstrate that the Gini coefficient can be a simple, intuitive parameter for modelling fetal brain development. MATERIALS AND METHODS: Postmortem fetal specimens(n = 28) were evaluated by diffusion-weighted imaging (DWI) on a 3-T MRI scanner using 60 directions, 0.7-mm isotropic voxels and b-values of 0, 150, 1,600 s/mm(2). Constrained spherical deconvolution (CSD) was used as the local diffusion model. Fractional anisotropy (FA), apparent diffusion coefficient (ADC) and complexity (CX) maps were generated. CX was defined as a novel diffusion metric. On the basis of those three parameters, the Gini coefficient was calculated. RESULTS: Study of fetal brain development in postmortem specimens was feasible using DWI. The Gini coefficient could be calculated for the combination of the three diffusion parameters. This multidimensional Gini coefficient correlated well with age (Adjusted R(2) = 0.59) between the ages of 17 and 26 gestational weeks. CONCLUSIONS: We propose a new method that uses an economics concept, the Gini coefficient, to describe the whole brain with one simple and intuitive measure, which can be used to assess the brain's developmental state.

Effects of air susceptibility on proton resonance frequency MR thermometry.

OBJECT: The temperature dependence of the proton resonance frequency (PRF) is often used in MR thermometry. However, this method is prone to even very small changes in local magnetic field strength. Here, we report on the effects of susceptibility changes of surrounding air on the magnetic field inside an object and their inferred effect on the measured MR temperature. MATERIALS AND METHODS: MR phase thermometry was performed on spherical agar phantoms enclosed in cylindrical containers at 7 T. The air susceptibility inside the cylindrical container was changed by both heating the air and changing the gas composition. RESULTS: Changing the temperature of surrounding air from 23 to 69°C caused an apparent MR temperature error of 2 K. When ambient air was displaced by 100% oxygen, the MR temperature error increased to 40 K. The magnetic field shift and therefore error in inferred MR temperature scales linearly with volume susceptibility change and has a strong and nontrivial dependence on the experimental configuration. CONCLUSION: Air susceptibility changes associated with oxygen concentration changes greatly affect PRF MR thermometry measurements. Air temperature changes can also affect these measurements, but to a smaller degree. For uncalibrated MR thermometry, air susceptibility changes may be a significant source of error.

After over 200 years, 7 T magnetic resonance imaging reveals the foliate structure of the human corpus callosum in vivo.

OBJECTIVE: A fine structure of the corpus callosum (CC), consisting of radial lines, is seen in historical anatomical atlases as far back as that of Vicq d'Azyr (1786). This study examines a similar pattern observed in vivo using high-resolution MR images at 7 T. METHODS: 8 healthy subjects were examined with 7.0-T MRI. Anatomical images were collected with a gradient echo scan with 0.5-mm isotropic resolution, which were rated for visibility of the radial pattern. In addition, the second eigenvector of the diffusion tensor images was examined. RESULTS: The fine radial lines are detected not only in the sagittal view but also in the axial view of the in vivo MR images. From this, it is likely that these structures are two-dimensional ribbons. Interestingly, and confirming the structural nature of these stripes, the second eigenvector of the diffusion tensor imaging data shows an extremely similar pattern of oriented foliate structure. A similar modular structure involving transient septa has been observed previously in histological sections of human fetal CC. CONCLUSION: The separate sets of data-the atlas of Klingler, anatomical images and second eigenvector images-all indicate a ribbon-like arrangement of the fibres in the CC. As such, they closely match the structures shown in the drawn atlases of as old as 1786. Advances in knowledge: This ribbon arrangement of fibres in the CC, previously unseen in CT or lower field MRI, can now be observed in vivo. This appears to match over two centuries of ex vivo observations.

Parametric effects of numerical distance on the intraparietal sulcus during passive viewing of rapid numerosity changes.

A number of functional neuroimaging studies have revealed that regions in and around the intraparietal sulcus (IPS) are parametrically modulated by numerical distance, whereby there is an inverse relationship between distance and levels of activation. These areas are thus thought to contain the internal representation of numerical magnitude. Nevertheless, it has also been suggested that the IPS is involved in response selection during number comparison tasks rather than the representation of numerical magnitude per se. In order to test the independence of the effect of distance on cortical regions, we employed a passive viewing paradigm. Sixteen right-handed male participants viewed rapidly changing slides containing arrays of squares. By varying the distance between the numerosity presented in separate blocks (8 vs. 8, 8 vs. 12, and 8 vs. 16), we examined which regions exhibit a parametric effect of numerical distance. This analysis revealed such effects in the superior part of the IPS bilaterally as well as the superior parietal lobule and the supramarginal gyrus. In contrast, slides rapidly changing in area but not number (Area constant, Area x 1, and Area x 2) did not yield a parametric effect of distance in these regions. Instead, a reverse effect of area was found in a region of the calcarine sulcus. These findings suggest that areas in and around the IPS are involved in numerical magnitude discrimination in the absence of an explicit task and response requirements.

Neural correlates of symbolic number processing in children and adults.

Using functional magnetic resonance imaging, we examined developmental differences in the functional neuroanatomy underlying symbolic number processing. Twelve adults and 12 children had to judge the relative magnitude of two single-digit Arabic numerals. We investigated which brain areas were significantly (P<0.005, uncorrected) more activated during processing of number pairs with small relative to large numerical distances. In the adult group, symbolic distance modulated bilateral parietal regions. In contrast, the group of children primarily engaged frontal regions. We conclude that the functional neuroanatomy underlying symbolic numerical magnitude processing undergoes an ontogenetic shift towards greater parietal engagement. This change may reflect maturation of underlying representations and increasing automaticity in mapping between numerical symbols and the magnitudes they represent.

Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study.

Numerical magnitude processing is an essential everyday skill. Functional brain imaging studies with human adults have repeatedly revealed that bilateral regions of the intraparietal sulcus are correlated with various numerical and mathematical skills. Surprisingly little, however, is known about the development of these brain representations. In the present study, we used functional neuroimaging to compare the neural correlates of nonsymbolic magnitude judgments between children and adults. Although behavioral performance was similar across groups, in comparison to the group of children the adult participants exhibited greater effects of numerical distance on the left intraparietal sulcus. Our findings are the first to reveal that even the most basic aspects of numerical cognition are subject to age-related changes in functional neuroanatomy. We propose that developmental impairments of number may be associated with atypical specialization of cortical regions underlying magnitude processing.

Dissociating response conflict from numerical magnitude processing in the brain: an event-related fMRI study.

Functional neuroimaging studies of numerical cognition have repeatedly associated activation of the intraparietal sulcus (IPS) with number processing. During number comparison, the IPS has been found to be modulated by the numerical distance. This has lead to the contention that the IPS houses the internal representation of numerical magnitude. However, this theory has been challenged by the argument that IPS activation may reflect domain-general response selection. In the present study, we used the numerical size congruity paradigm to further elucidate the role played by the IPS in number comparison. In an event-related, functional magnetic resonance imaging (fMRI) study, participants judged which of two number words was numerically larger. In addition to the numerical distance, physical stimulus size was varied such that physical size and numerical magnitude were either (a) congruent (e.g., numerically smaller number printed in smaller font) or (b) incongruent (e.g., numerically larger number printed in smaller font). This allowed for the study of both the main effects and the interaction of numerical distance and stimulus congruency. A main effect of numerical distance was found in bilateral regions of the IPS. However, these parietal areas were not significantly modulated by congruency or the interaction of distance and congruency. Instead, the main effect of congruency and an interaction of distance and congruency were observed in anterior cingulate and prefrontal cortices. These findings suggest some degree of independence between the processing of numerical distance and size congruity, lending support for the hypothesis that distance effects in IPS reflect the underlying representation of numerical magnitude.