High b-value q-space diffusion MRS of nerves: structural information and comparison with histological evidence

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

Beyond the diffusion standard model in fixed rat spinal cord with combined linear and planar encoding

Information about tissue on the microscopic and mesoscopic scales can be accessed by modelling diffusion MRI signals, with the aim of extracting microstructure-specific biomarkers. The standard model (SM) of diffusion, currently the most broadly adopted microstructural model, describes diffusion in white matter (WM) tissues by two Gaussian components, one of which has zero radial diffusivity, to represent diffusion in intra- and extra-axonal water, respectively. Here, we reappraise these SM assumptions by collecting comprehensive double diffusion encoded (DDE) MRI data with both linear and planar encodings, which was recently shown to substantially enhance the ability to estimate SM parameters. We find however, that the SM is unable to account for data recorded in fixed rat spinal cord at an ultrahigh field of 16.4 T, suggesting that its underlying assumptions are violated in our experimental data. We offer three model extensions to mitigate this problem: first, we generalize the SM to accommodate finite radii (axons) by releasing the constraint of zero radial diffusivity in the intra-axonal compartment. Second, we include intracompartmental kurtosis to account for non-Gaussian behaviour. Third, we introduce an additional (third) compartment. The ability of these models to account for our experimental data are compared based on parameter feasibility and Bayesian information criterion. Our analysis identifies the three-compartment description as the optimal model. The third compartment exhibits slow diffusion with a minor but non-negligible signal fraction (∼12%). We demonstrate how failure to take the presence of such a compartment into account severely misguides inferences about WM microstructure. Our findings bear significance for microstructural modelling at large and can impact the interpretation of biomarkers extracted from the standard model of diffusion.

Constant gradient FEXSY: A time-efficient method for measuring exchange

Filter-Exchange NMR Spectroscopy (FEXSY) is a method for measurement of apparent transmembranal water exchange rates. The experiment is comprised of two co-linear sequential pulsed-field gradient (PFG) blocks, separated by a mixing period in which exchange takes place. The first block remains constant and serves as a diffusion-based filter that removes signal coming from fast-diffusing water. The mixing time and the gradient area (q-value) of the second block are varied on repeated iterations to produce a 2D data set that is analyzed using a bi-compartmental model which assumes that intra- and extra-cellular water are slow and fast diffusing, respectively. Here we suggest a variant of the FEXSY method in which measurements for different mixing times are taken at a constant gradient. This Constant Gradient FEXSY (CG-FEXSY) allows for the determination of the exchange rate by using a smaller 1D data set, so that the same information can be gathered during a considerably shorter scan time. Furthermore, in the limit of high diffusion weighting, such that the extra-cellular water signal is removed while the intra-cellular signal is retained, CG-FEXSY also allows for determination of the intra-cellular mean residence time (MRT). The theoretical results are validated on a living yeast cells sample and on a fixed porcine optic nerve, where the values obtained from the two methods are shown to be in agreement.

Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

Effects of nongaussian diffusion on "isotropic diffusion" measurements: An ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.

What dominates the time dependence of diffusion transverse to axons: Intra- or extra-axonal water?

Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo diffusion MRI uniquely sensitive to the cellular features about three orders of magnitude below imaging resolution. However, there is a longstanding debate, regarding which contribution - intra- or extra-cellular - is more relevant in the overall time-dependence of the MRI-derived diffusion metrics. Here we resolve this debate in the human brain white matter. By varying not just the diffusion time, but also the gradient pulse duration of a standard diffusion MRI sequence, we identify a functional form of the measured time-dependent diffusion coefficient transverse to white matter tracts in 10 healthy volunteers. This specific functional form is shown to originate from the extra-axonal space, and provides estimates of the fiber packing correlation length for axons in a bundle. Our results offer a metric for the outer axonal diameter, a promising candidate marker for demyelination in neurodegenerative diseases. From the methodological perspective, our analysis demonstrates how competing models, which describe different physics yet interpolate standard measurements equally well, can be distinguished based on their prediction for an independent "orthogonal" measurement.

Can we detect the effect of spines and leaflets on the diffusion of brain intracellular metabolites?

Prior models used to clarify which aspects of tissue microstructure mostly affect intracellular diffusion and corresponding diffusion-weighted magnetic resonance (DW-MR) signal have focused on relatively simple geometrical descriptions of the cellular microenvironment (spheres, randomly oriented cylinders, etc…), neglecting finer morphological details which may have an important role. Some types of neurons present high density of spines; and astrocytes and macroglial cells processes present leaflets, which may all impact the diffusion process. Here, we use Monte-Carlo simulations of many particles diffusing in cylindrical compartments with secondary structures mimicking spines and leaflets of neuronal and glial cell fibers, to investigate to what extent the diffusion-weighted signal of intracellular molecules is sensitive to spines/leaflets density and length. In order to study the specificity of DW-MR signal to these kinds of secondary structures, beading-like geometry is simulated as "control" deviation from smooth cylinder too. Results suggest that: a) the estimated intracellular tortuosity increases as spines/leaflets density or length (beading amplitude) increase; b) the tortuosity limit is reached for diffusion time t_d>200 ms for metabolites and t_d>70 ms for water molecules, suggesting that the effects of these finer morphological details are negligible at t_d longer than these threshold values; c) fiber diameter is overestimated, while intracellular diffusivity is underestimated, when simple geometrical models based on hollow smooth cylinders are used; d) apparent surface-to-volume, S/V, ratio estimated by linear fit of high frequency OG data appears to be an excellent estimation of the actual S/V ratio, even in the presence of secondary structures, and it increases as spines and leaflets density or length increase (while decreasing as beadings amplitude increases). Comparison between numerical simulations and multimodal metabolites DW-MRS experiments in vivo in mouse brain shows that these fine structures may affect the DW-MRS signal and the derived diffusion metrics consistently with their expected density and geometrical features. This work suggests that finer structures of cell morphology have non-negligible effects on intracellular molecules' diffusion that may be measured by using multimodal DW-MRS approaches, stimulating future developments and applications.

Demonstration of Non-Gaussian Restricted Diffusion in Tumor Cells Using Diffusion Time-Dependent Diffusion-Weighted Magnetic Resonance Imaging Contrast

The diffusion-weighted magnetic resonance imaging (DWI) technique enables quantification of water mobility for probing microstructural properties of biological tissue and has become an effective tool for collecting information about the underlying pathology of cancerous tissue. Measurements using multiple b-values have indicated biexponential signal attenuation, ascribed to “fast” (high ADC) and “slow” (low ADC) diffusion components. In this empirical study, we investigate the properties of the diffusion time (Δ)-dependent components of the diffusion-weighted (DW) signal in a constant b-value experiment. A xenograft gliobastoma mouse was imaged using Δ = 11 ms, 20 ms, 40 ms, 60 ms, and b = 500–4000 s/mm² in intervals of 500 s/mm². Data were corrected for EPI distortions, and the Δ-dependence on the DW-signal was measured within three regions of interest [intermediate- and high-density tumor regions and normal-appearing brain (NAB) tissue regions]. In this study, we verify the assumption that the slow decaying component of the DW-signal is non-Gaussian and dependent on Δ, consistent with restricted diffusion of the intracellular space. As the DW-signal is a function of Δ and is specific to restricted diffusion, manipulating Δ at constant b-value (cb) provides a complementary and direct approach for separating the restricted from the hindered diffusion component. We found that Δ-dependence is specific to the tumor tissue signal. Based on an extended biexponential model, we verified the interpretation of the diffusion time-dependent contrast and successfully estimated the intracellular restricted ADC, signal volume fraction, and cell size within each ROI.

Differentiation of Low- and High-Grade Gliomas Using High b-Value Diffusion Imaging with a Non-Gaussian Diffusion Model

BACKGROUND AND PURPOSE

Imaging-based tumor grading is highly desirable but faces challenges in sensitivity, specificity, and diagnostic accuracy. A recently proposed diffusion imaging method by using a fractional order calculus model offers a set of new parameters to probe not only the diffusion process itself but also intravoxel tissue structures, providing new opportunities for noninvasive tumor grading. This study aimed to demonstrate the feasibility of using the fractional order calculus model to differentiate low- from high-grade gliomas in adult patients and illustrate its improved performance over a conventional diffusion imaging method using ADC (or D).

MATERIALS AND METHODS

Fifty-four adult patients (18-70 years of age) with histology-proved gliomas were enrolled and divided into low-grade (n = 24) and high-grade (n = 30) groups. Multi-b-value diffusion MR imaging was performed with 17 b-values (0-4000 s/mm(2)) and was analyzed by using a fractional order calculus model. Mean values and SDs of 3 fractional order calculus parameters (D, β, and μ) were calculated from the normal contralateral thalamus (as a control) and the tumors, respectively. On the basis of these values, the low- and high-grade glioma groups were compared by using a Mann-Whitney U test. Receiver operating characteristic analysis was performed to assess the performance of individual parameters and the combination of multiple parameters for low- versus high-grade differentiation.

RESULTS

Each of the 3 fractional order calculus parameters exhibited a statistically higher value (P ≤ .011) in the low-grade than in the high-grade gliomas, whereas there was no difference in the normal contralateral thalamus (P ≥ .706). The receiver operating characteristic analysis showed that β (area under the curve = 0.853) produced a higher area under the curve than D (0.781) or μ (0.703) and offered a sensitivity of 87.5%, specificity of 76.7%, and diagnostic accuracy of 82.1%.

CONCLUSIONS

The study demonstrated the feasibility of using a non-Gaussian fractional order calculus diffusion model to differentiate low- and high-grade gliomas. While all 3 fractional order calculus parameters showed statistically significant differences between the 2 groups, β exhibited a better performance than the other 2 parameters, including ADC (or D).

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Differentiation of Low- and High-Grade Pediatric Brain Tumors with High b-Value Diffusion-weighted MR Imaging and a Fractional Order Calculus Model

PURPOSE

To demonstrate that a new set of parameters (D, β, and μ) from a fractional order calculus (FROC) diffusion model can be used to improve the accuracy of MR imaging for differentiating among low- and high-grade pediatric brain tumors.

MATERIALS AND METHODS

The institutional review board of the performing hospital approved this study, and written informed consent was obtained from the legal guardians of pediatric patients. Multi-b-value diffusion-weighted magnetic resonance (MR) imaging was performed in 67 pediatric patients with brain tumors. Diffusion coefficient D, fractional order parameter β (which correlates with tissue heterogeneity), and a microstructural quantity μ were calculated by fitting the multi-b-value diffusion-weighted images to an FROC model. D, β, and μ values were measured in solid tumor regions, as well as in normal-appearing gray matter as a control. These values were compared between the low- and high-grade tumor groups by using the Mann-Whitney U test. The performance of FROC parameters for differentiating among patient groups was evaluated with receiver operating characteristic (ROC) analysis.

RESULTS

None of the FROC parameters exhibited significant differences in normal-appearing gray matter (P ≥ .24), but all showed a significant difference (P < .002) between low- (D, 1.53 μm(2)/msec ± 0.47; β, 0.87 ± 0.06; μ, 8.67 μm ± 0.95) and high-grade (D, 0.86 μm(2)/msec ± 0.23; β, 0.73 ± 0.06; μ, 7.8 μm ± 0.70) brain tumor groups. The combination of D and β produced the largest area under the ROC curve (0.962) in the ROC analysis compared with individual parameters (β, 0.943; D,0.910; and μ, 0.763), indicating an improved performance for tumor differentiation.

CONCLUSION

The FROC parameters can be used to differentiate between low- and high-grade pediatric brain tumor groups. The combination of FROC parameters or individual parameters may serve as in vivo, noninvasive, and quantitative imaging markers for classifying pediatric brain tumors.

Modeling of the diffusion MR signal in calibrated model systems and nerves

Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.

Advanced MRI strategies for assessing spinal cord injury

Advanced magnetic resonance (MR) approaches permit the noninvasive quantification of macromolecular, functional, and physiological properties of biological tissues. In this chapter, we review the application of advanced MR techniques to the spinal cord. Macromolecular properties of the spinal cord can be studied using magnetization transfer (MT) MR, diffusion tensor imaging (DTI), Q-space diffusion spectroscopy, and selective detection of myelin water. The functional and metabolic status of the spinal cord can be studied using functional MRI (fMRI), perfusion imaging, and magnetic resonance spectroscopy (MRS). Finally, we consider the outlook for advanced MR studies in persons in whom metal hardware has been implanted to stabilize the cord. In spite of the spinal cord's diminutive size, its location deep within the body, and constant motion, recent work shows that the spinal cord can be studied using these advanced MR approaches.

White matter maturation in the brains of Long Evans shaker myelin mutant rats by ex-vivo QSI and DTI

The brains of Long Evans shaker (les) rats, a model of dysmyelination, and their age- matched controls were studied by ex-vivo q-space diffusion imaging (QSI) and diffusion tensor imaging (DTI). The QSI and DTI indices were computed from the same acquisition. The les and the control brains were studied at different stages of maturation and disease progression. The mean displacement, the probability for zero displacement and kurtosis were computed from QSI data while the fractional anisotropy (FA) and the eigenvalues were computed from DTI. It was found that all QSI indices detect the les pathology, at all stages of maturation, while only some of the DTI indices could detect the les pathology. The QSI mean displacement was larger in the les group as compared with their age-matched controls while the probability for zero displacement and the kurtosis were both lower all indicating higher degree of restriction in the control brains. Since all the DTI eigenvalues were higher in the les brains as compared to controls, the less efficient DTI measure for discerning the les pathology was found to be the FA. Clearly, the most sensitive DTI parameter to the les pathology is λ3, i.e., the minimal diffusivity. Since the QSI and DTI data were obtained from the same acquisition, despite the somewhat higher SNR of the QSI data compared to the DTI data, it seems that the higher diagnostic capacity of the QSI data in this experimental model of dysmyelination, originates mainly from the higher diffusing weighting of the QSI data.

The role of tissue microstructure and water exchange in biophysical modelling of diffusion in white matter

Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.

Noninvasive mapping of water diffusional exchange in the human brain using filter-exchange imaging

We present the first in vivo application of the filter-exchange imaging protocol for diffusion MRI. The protocol allows noninvasive mapping of the rate of water exchange between microenvironments with different self-diffusivities, such as the intracellular and extracellular spaces in tissue. Since diffusional water exchange across the cell membrane is a fundamental process in human physiology and pathophysiology, clinically feasible and noninvasive imaging of the water exchange rate would offer new means to diagnose disease and monitor treatment response in conditions such as cancer and edema. The in vivo use of filter-exchange imaging was demonstrated by studying the brain of five healthy volunteers and one intracranial tumor (meningioma). Apparent exchange rates in white matter range from 0.8±0.08 s(-1) in the internal capsule, to 1.6±0.11 s(-1) for frontal white matter, indicating that low values are associated with high myelination. Solid tumor displayed values of up to 2.9±0.8 s(-1). In white matter, the apparent exchange rate values suggest intra-axonal exchange times in the order of seconds, confirming the slow exchange assumption in the analysis of diffusion MRI data. We propose that filter-exchange imaging could be used clinically to map the water exchange rate in pathologies. Filter-exchange imaging may also be valuable for evaluating novel therapies targeting the function of aquaporins.

WITHDRAWN: First observation of diffusion-diffraction pattern in neuronal tissue by double-pulsed-field-gradient NMR

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Accurate noninvasive measurement of cell size and compartment shape anisotropy in yeast cells using double-pulsed field gradient MR

The accurate characterization of pore morphology is of great interest in a wide range of scientific disciplines. Conventional single-pulsed field gradient (s-PFG) diffusion MR can yield compartmental size and shape only when compartments are coherently ordered using q-space approaches that necessitate strong gradients. However, double-PFG (d-PFG) methodology can provide novel microstructural information even when specimens are characterized by polydispersity in size and shape, and even when anisotropic compartments are randomly oriented. In this study, for the first time, we show that angular d-PFG experiments can be used to accurately measure cellular size and shape anisotropy of fixed yeast cells employing relatively weak gradients. The cell size, as measured by light microscopy, was found to be 5.32 ± 0.83 µm, whereas the results from noninvasive angular d-PFG experiments yielded a cell size of 5.46 ± 0.45 µm. Moreover, the low compartment shape anisotropy of the cells could be inferred from experiments conducted at long mixing times. Finally, similar experiments were conducted in a phantom comprising anisotropic compartments that were randomly oriented, showing that angular d-PFG MR provides novel information on compartment eccentricity that could not be accessed using conventional methods. Angular d-PFG methodology seems to be promising for the accurate estimation of compartment size and compartment shape anisotropy in heterogeneous systems in general, and biological cells and tissues in particular.

Advanced MRI strategies for assessing spinal cord injury

Advanced magnetic resonance (MR) approaches permit the noninvasive quantification of macromolecular, functional, and physiological properties of biological tissues. In this chapter, we review the application of advanced MR techniques to the spinal cord. Macromolecular properties of the spinal cord can be studied using magnetization transfer (MT) MR, diffusion tensor imaging (DTI), Q-space diffusion spectroscopy, and selective detection of myelin water. The functional and metabolic status of the spinal cord can be studied using functional MRI (fMRI), perfusion imaging, and magnetic resonance spectroscopy (MRS). Finally, we consider the outlook for advanced MR studies in persons in whom metal hardware has been implanted to stabilize the cord. In spite of the spinal cord's diminutive size, its location deep within the body, and constant motion, recent work shows that the spinal cord can be studied using these advanced MR approaches.

Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus

PURPOSE

To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence.

MATERIALS AND METHODS

The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2600 s/mm(2). For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β, and μ values and the goodness-of-fit in three specific regions of interest (ROIs) in white matter, gray matter, and cerebrospinal fluid, respectively, were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively.

RESULTS

The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents.

CONCLUSION

The diffusion-induced signal attenuation in a TRSE pulse sequence can be described by an FC diffusion model at high b-values. This model performs equally well for data acquired from the human brain tissues with a TRSE pulse sequence or a conventional Stejskal-Tanner sequence.

High b-value q-space analyzed diffusion-weighted MRI using 1.5 tesla clinical scanner; determination of displacement parameters in the brains of normal versus multiple sclerosis and low-grade glioma subjects

PURPOSE

We aimed to determine the displacement parameters in the brains of normal individuals relative to brain parenchymal abnormalities, such as multiple sclerosis (MS) and low-grade glioma, by q-space imaging (QSI) using 1.5-T magnetic resonance (MR) scanner.

MATERIALS AND METHODS

Thirty-five normal, three pathologically proven low-grade glioma, and five MS subjects were imaged by a 1.5-T MR unit for QSI (b-values, 0-12,000 s/mm(2)). Mean displacement (MD) values in white matter (WM), gray matter (GM), and lateral ventricle (cerebrospinal fluid [CSF]) of normal subjects, plaques, and normal appearing WM (NAWM) of MS subjects and glioma lesions were calculated. Mann-Whitney U test was used for comparison.

RESULTS

In normal subjects, MD values were 6.6 ± 0.2, 8.44 ± 0.41, and 17.08 ± 0.80 μm for WM, GM, and CSF, respectively, while those for NAWM and WM plaques in MS, and glioma lesions were significantly higher at 7.0 ± 0.17, 9.3 ± 2.3, and 9.6 ± 0.40 μm, respectively, compared to WM in normal subjects.

CONCLUSION

We propose that the relative values of MD obtained by QSI in control and diseased tissues can be useful for diagnosing various WM abnormalities.

q-space and conventional diffusion imaging of axon and myelin damage in the rat spinal cord after axotomy

Parallel and perpendicular diffusion properties of water in the rat spinal cord were investigated 3 and 30 days after dorsal root axotomy, a specific insult resulting in early axonal degeneration followed by later myelin damage in the dorsal column white matter. Results from q-space analysis (i.e., the diffusion probability density function) obtained with strong diffusion weighting were compared to conventional anisotropy and diffusivity measurements at low b-values, as well as to histology for axon and myelin damage. q-Space contrasts included the height (return to zero displacement probability), full width at half maximum, root mean square displacement, and kurtosis excess of the probability density function, which quantifies the deviation from gaussian diffusion. Following axotomy, a significant increase in perpendicular diffusion (with decreased kurtosis excess) and decrease in parallel diffusion (with increased kurtosis excess) were found in lesions relative to uninjured white matter. Notably, a significant change in abnormal parallel diffusion was detected from 3 to 30 days with full width at half maximum, but not with conventional diffusivity. Also, directional full width at half maximum and root mean square displacement measurements exhibited different sensitivities to white matter damage. When compared to histology, the increase in perpendicular diffusion was not specific to demyelination, whereas combined reduced parallel diffusion and increased perpendicular diffusion was associated with axon damage.

From single-pulsed field gradient to double-pulsed field gradient MR: gleaning new microstructural information and developing new forms of contrast in MRI

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

MR diffusion kurtosis imaging for neural tissue characterization

In conventional diffusion tensor imaging (DTI), water diffusion distribution is described as a 2nd-order three-dimensional (3D) diffusivity tensor. It assumes that diffusion occurs in a free and unrestricted environment with a Gaussian distribution of diffusion displacement, and consequently that diffusion weighted (DW) signal decays with diffusion factor (b-value) monoexponentially. In biological tissue, complex cellular microstructures make water diffusion a highly hindered or restricted process. Non-monoexponential decays are experimentally observed in both white matter and gray matter. As a result, DTI quantitation is b-value dependent and DTI fails to fully utilize the diffusion measurements that are inherent to tissue microstructure. Diffusion kurtosis imaging (DKI) characterizes restricted diffusion and can be readily implemented on most clinical scanners. It provides a higher-order description of water diffusion process by a 2nd-order 3D diffusivity tensor as in conventional DTI together with a 4th-order 3D kurtosis tensor. Because kurtosis is a measure of the deviation of the diffusion displacement profile from a Gaussian distribution, DKI analyses quantify the degree of diffusion restriction or tissue complexity without any biophysical assumption. In this work, the theory of diffusion kurtosis and DKI including the directional kurtosis analysis is revisited. Several recent rodent DKI studies from our group are summarized, and DKI and DTI compared for their efficacy in detecting neural tissue alterations. They demonstrate that DKI offers a more comprehensive approach than DTI in describing the complex water diffusion process in vivo. By estimating both diffusivity and kurtosis, it may provide improved sensitivity and specificity in MR diffusion characterization of neural tissues.

Detecting diffusion-diffraction patterns in size distribution phantoms using double-pulsed field gradient NMR: Theory and experiments

NMR observable nuclei undergoing restricted diffusion within confining pores are important reporters for microstructural features of porous media including, inter-alia, biological tissues, emulsions and rocks. Diffusion NMR, and especially the single-pulsed field gradient (s-PFG) methodology, is one of the most important noninvasive tools for studying such opaque samples, enabling extraction of important microstructural information from diffusion-diffraction phenomena. However, when the pores are not monodisperse and are characterized by a size distribution, the diffusion-diffraction patterns disappear from the signal decay, and the relevant microstructural information is mostly lost. A recent theoretical study predicted that the diffusion-diffraction patterns in double-PFG (d-PFG) experiments have unique characteristics, such as zero-crossings, that make them more robust with respect to size distributions. In this study, we theoretically compared the signal decay arising from diffusion in isolated cylindrical pores characterized by lognormal size distributions in both s-PFG and d-PFG methodologies using a recently presented general framework for treating diffusion in NMR experiments. We showed the gradual loss of diffusion-diffraction patterns in broadening size distributions in s-PFG and the robustness of the zero-crossings in d-PFG even for very large standard deviations of the size distribution. We then performed s-PFG and d-PFG experiments on well-controlled size distribution phantoms in which the ground-truth is well-known a priori. We showed that the microstructural information, as manifested in the diffusion-diffraction patterns, is lost in the s-PFG experiments, whereas in d-PFG experiments the zero-crossings of the signal persist from which relevant microstructural information can be extracted. This study provides a proof of concept that d-PFG may be useful in obtaining important microstructural features in samples characterized by size distributions.

Observation of restricted diffusion in the presence of a free diffusion compartment: single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion-diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.

On high b diffusion imaging in the human brain: ruminations and experimental insights

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.

Enhanced detection of diffusion reductions in Creutzfeldt-Jakob disease at a higher B factor

BACKGROUND AND PURPOSE

Diffusion-weighted imaging (DWI) is sensitive to the cerebral manifestations of human prion diseases. The magnitude of diffusion weighting, termed "b factor," has only been evaluated at the standard b = 1000 s/mm(2). This is the first rigorous evaluation of b = 2000 s/mm(2) in Creutzfeldt-Jakob Disease (CJD).

MATERIALS AND METHODS

We compared DWI characteristics of 13 patients with CJD and 15 healthy controls at b = 1000 s/mm(2) and b = 2000 s/mm(2). Apparent diffusion coefficients (ADC) were computed and analyzed for the whole brain by voxel-wise analysis (by SPM5) as well as in anatomically defined volumes of interest (by FSL FIRST).

RESULTS

Measured ADC was significantly lower (by approximately 5%-15%) at b = 2000 s/mm(2) than at b = 1000 s/mm(2) and significantly lower in patients than in controls. The differences between patients and controls were greater and more extensive at b = 2000 s/mm(2) than at b = 1000 s/mm(2) in the expected regions (thalamus, putamen, and caudate nucleus).

CONCLUSIONS

Because higher b factors change the absolute value of observed ADC, as well as lesion detection, care should be taken when combining studies using different b factors. While the clinical application of high b factors is currently limited by a low signal intensity-to-noise ratio, it may offer more information in questionable cases, and our results confirm and extend the central role of diffusion imaging in human prion diseases.

Neurite density from magnetic resonance diffusion measurements at ultrahigh field: comparison with light microscopy and electron microscopy

Due to its unique sensitivity to tissue microstructure, diffusion-weighted magnetic resonance imaging (MRI) has found many applications in clinical and fundamental science. With few exceptions, a more precise correspondence between physiological or biophysical properties and the obtained diffusion parameters remain uncertain due to lack of specificity. In this work, we address this problem by comparing diffusion parameters of a recently introduced model for water diffusion in brain matter to light microscopy and quantitative electron microscopy. Specifically, we compare diffusion model predictions of neurite density in rats to optical myelin staining intensity and stereological estimation of neurite volume fraction using electron microscopy. We find that the diffusion model describes data better and that its parameters show stronger correlation with optical and electron microscopy, and thus reflect myelinated neurite density better than the more frequently used diffusion tensor imaging (DTI) and cumulant expansion methods. Furthermore, the estimated neurite orientations capture dendritic architecture more faithfully than DTI diffusion ellipsoids.

QSI and DTI of excised brains of the myelin-deficient rat

High b-value q-space diffusion imaging (QSI) and conventional DTI methodologies were used to study the MRI diffusion characteristics of excised brains of 21-day-old myelin-deficient (md) rats and their age-matched controls. Three different indices were calculated from the QSI data, i.e., Displacement, Probability and Kurtosis, for the purpose of evaluating the effect of the myelin sheaths on the MR diffusion characteristics in white matter (WM) ROIs of the md versus control brains. The examined WM ROIs were the corpus callosum, the external capsule, and the internal capsule. In all examined WM ROIs, significant differences were observed between the md and control brains for all QSI indices. These differences reveal that myelin sheaths surrounding the axons in WM ROIs mostly affect the component exhibiting restricted diffusion, which is manifested by low mean displacement values and high probability and kurtosis values. Such differences were found to be more pronounced in long diffusion times, i.e., Delta=200 ms. Conventional DTI performed with relatively low b-values (b<1500 s/mm2) was also used to study md versus control brains. Interestingly, the fractional anisotropy (FA) index, which was calculated from DTI data, did not reveal any significant difference between the groups in the examined WM ROIs. However, some distinctions were revealed by the three eigenvalues (lambda1, lambda2, and lambda3) obtained from the tensor analysis. These findings were supported by Voxel-based analysis using SPM. Finally, MRI-guided histology showed very good agreement between myelin-stained regions and regions with highly restricted diffusion detected by QSI.

Measuring small compartmental dimensions with low-q angular double-PGSE NMR: The effect of experimental parameters on signal decay

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.

Erythrocyte-shape evolution recorded with fast-measurement NMR diffusion-diffraction

PURPOSE

To monitor red blood cell (RBC) shape evolution by (1)H(2)O diffusion-diffraction NMR in time steps comparable to those required for the acquisition of a (31)P NMR spectrum; thus, to correlate RBC mean diameter with ATP concentration after poisoning with NaF.

MATERIALS AND METHODS

Pulsed-field gradient-stimulated echo (PFGSTE) diffusion experiments were recorded on (1)H(2)O in RBC suspensions. Under conditions of restricted diffusion, q-space experiments report on mean RBC diameter. To decrease experiment time, the phase cycling of radiofrequency (RF) pulses was cut to two transients by using unbalanced pairs of gradient pulses. Data processing used a recent digital filter. Differential interference contrast (DIC) light microscopy also recorded shape changes. (31)P NMR spectroscopy gave estimates of mean ATP concentration.

RESULTS

NaF caused RBC-shape evolution from discocytes, through various forms of echinocytes, to spherocytes, over approximately 6 h and approximately 10 h at 37 degrees C and 25 degrees C, respectively. ATP declined to approximately 0.5 its normal concentration before the first stage of discocyte transformation; the concentration was 0.0 after approximately 1.5 h and 3.0 h, respectively, at the two temperatures.

CONCLUSION

RBC shape was readily monitored by NMR with a temporal resolution that was useful for correlations with both DIC microscopy and (31)P NMR spectra.

The effect of experimental parameters on the signal decay in double-PGSE experiments: negative diffractions and enhancement of structural information

Double pulsed gradient spin echo (d-PGSE) experiment has been recently suggested for detecting microscopic anisotropy in macroscopically isotropic samples. This sequence is complex and has many variables, including, intra alia, combinations of directions and amplitudes of the pulsed gradients, diffusion times in each of the encoding periods and the mixing time period. The effect of these experimental parameters of the d-PGSE sequence was studied in an array of water filled microcapillaries of micron diameters. We found that negative diffractions occur, as indeed predicted by recently published simulations. We also found differential effects of prolongation of the mixing time between collinear and orthogonal d-PGSE experiments. The d-PGSE experiment in the collinear direction perpendicular to the long axis of the cylinder exhibited a marked dependence on the mixing time, while the orthogonal d-PGSE experiment exhibited no such dependence at all. Interestingly, one of the most important predictions by the simulations was that the d-PGSE sequence could potentially discriminate between compartments of different sizes better than the single PGSE (s-PGSE) and it seems that our experimental results indeed corroborate these predictions.

Compartment-specific q-space analysis of diffusion-weighted data from isolated rhesus optic and sciatic nerves

We investigated compartment-specific water diffusion properties in two widely structurally different isolated bovine nerves. Sciatic and optic nerves were immersed in saline containing Gd-DTPA(2+). Consequently, T(1) became non-monoexponential and fit well to a biexponential function. q-Space diffusion data were collected for each component. In the sciatic nerve, the slow-decaying component (T(1s)) was considerably more restricted and directional than the fast-decaying component (T(1f)). In the optic nerve, fractional anisotropy of both components was comparable and similar to that of the total H(2)O signal. The root mean square of the displacement distribution functions of T(1s) correlated well with the widely different axonal diameters of both nerves. Possibly, the source of T(1s) is the intra-axonal compartment and that of T(1f) is associated with the inter-axonal space. The compartment specificity of the method shown makes it useful for the investigation of the contribution of each nerve compartment to diffusion tensor imaging measurements and other diffusion-based methods.

High b-value q-space diffusion-weighted MRI of the human cervical spinal cord in vivo: feasibility and application to multiple sclerosis

Q-space analysis is an alternative analysis technique for diffusion-weighted imaging (DWI) data in which the probability density function (PDF) for molecular diffusion is estimated without the need to assume a Gaussian shape. Although used in the human brain, q-space DWI has not yet been applied to study the human spinal cord in vivo. Here we demonstrate the feasibility of performing q-space imaging in the cervical spinal cord of eight healthy volunteers and four patients with multiple sclerosis. The PDF was computed and water displacement and zero-displacement probability maps were calculated from the width and height of the PDF, respectively. In the dorsal column white matter, q-space contrasts showed a significant (P < 0.01) increase in the width and a decrease in the height of the PDF in lesions, the result of increased diffusion. These q-space contrasts, which are sensitive to the slow diffusion component, exhibited improved detection of abnormal diffusion compared to perpendicular apparent diffusion constant measurements. The conspicuity of lesions compared favorably with magnetization transfer (MT)-weighted images and quantitative CSF-normalized MT measurements. Thus, q-space DWI can be used to study water diffusion in the human spinal cord in vivo and is well suited to assess white matter damage.

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.