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

Extra-axonal contribution to double diffusion encoding-based pore size estimates in the corticospinal tract

OBJECTIVE

To study the origin of compartment size overestimation in double diffusion encoding MRI (DDE) in vivo experiments in the human corticospinal tract. Here, the extracellular space is hypothesized to be the origin of the DDE signal. By exploiting the DDE sensitivity to pore shape, it could be possible to identify the origin of the measured signal. The signal difference between parallel and perpendicular diffusion gradient orientation can indicate if a compartment is regular or eccentric in shape. As extracellular space can be considered an eccentric compartment, a positive difference would mean a high contribution to the compartment size estimates.

MATERIALS AND METHODS

Computer simulations using MISST and in vivo experiments in eight healthy volunteers were performed. DDE experiments using a double spin-echo preparation with eight perpendicular directions were measured in vivo. The difference between parallel and perpendicular gradient orientations was analyzed using a Wilcoxon signed-rank test and a Mann-Whitney U test.

RESULTS

Simulations and MR experiments showed a statistically significant difference between parallel and perpendicular diffusion gradient orientation signals ([Formula: see text]).

CONCLUSION

The results suggest that the DDE-based size estimate may be considerably influenced by the extra-axonal compartment. However, the experimental results are also consistent with purely intra-axonal contributions in combination with a large fiber orientation dispersion.

Diffusion pore imaging in the presence of extraporal water

Diffusion-weighted imaging (DWI) is a powerful, non-invasive tool which is widely used in clinical routine. Mostly, apparent diffusion coefficient maps are acquired, which cannot be related directly to cellular structure. More recently it was shown that DWI is able to reconstruct pore shapes using a specialized magnetic field gradient scheme so that cell size distributions may be obtained. So far, artificial systems have been used for experimental demonstration without extraporal signal components and relatively low gradient amplitudes. The aim of this study was to investigate the feasibility of diffusion pore imaging in the presence of extraporal fluids and to develop correction methods for the effects arising from extraporal signal contributions. Monte Carlo simulations and validation experiments on a 14.1 T NMR spectrometer equipped with a dedicated diffusion probe head were performed. Both by using a filter gradient approach suppressing extraporal signal components as well as by using post-processing methods relying on the Gaussian phase approximation, it was possible to reconstruct pore space functions in the presence of extraporal fluids with little to no deviations from the expectations. These results may be a significant step towards application of diffusion pore imaging to biological samples.

In vivo Correlation Tensor MRI reveals microscopic kurtosis in the human brain on a clinical 3T scanner

Diffusion MRI (dMRI) has become one of the most important imaging modalities for noninvasively probing tissue microstructure. Diffusional Kurtosis MRI (DKI) quantifies the degree of non-gaussian diffusion, which in turn has been shown to increase sensitivity towards, e.g., disease and orientation mapping in neural tissue. However, the specificity of DKI is limited as different sources can contribute to the total intravoxel diffusional kurtosis, including: variance in diffusion tensor magnitudes (K_iso), variance due to diffusion anisotropy (K_aniso), and microscopic kurtosis (μK) related to restricted diffusion, microstructural disorder, and/or exchange. Interestingly, μK is typically ignored in diffusion MRI signal modeling as it is assumed to be negligible in neural tissues. However, recently, Correlation Tensor MRI (CTI) based on Double-Diffusion-Encoding (DDE) was introduced for kurtosis source separation, revealing non negligible μK in preclinical imaging. Here, we implemented CTI for the first time on a clinical 3T scanner and investigated the sources of total kurtosis in healthy subjects. A robust framework for kurtosis source separation in humans is introduced, followed by estimation of μK (and the other kurtosis sources) in the healthy brain. Using this clinical CTI approach, we find that μK significantly contributes to total diffusional kurtosis both in gray and white matter tissue but, as expected, not in the ventricles. The first μK maps of the human brain are presented, revealing that the spatial distribution of μK provides a unique source of contrast, appearing different from isotropic and anisotropic kurtosis counterparts. Moreover, group average templates of these kurtosis sources have been generated for the first time, which corroborated our findings at the underlying individual-level maps. We further show that the common practice of ignoring μK and assuming the multiple gaussian component approximation for kurtosis source estimation introduces significant bias in the estimation of other kurtosis sources and, perhaps even worse, compromises their interpretation. Finally, a twofold acceleration of CTI is discussed in the context of potential future clinical applications. We conclude that CTI has much potential for future in vivo microstructural characterizations in healthy and pathological tissue.

Elucidating the complex organization of neural micro-domains in the locust Schistocerca gregaria using dMRI

To understand brain function it is necessary to characterize both the underlying structural connectivity between neurons and the physiological integrity of these connections. Previous research exploring insect brain connectivity has typically used electron microscopy techniques, but this methodology cannot be applied to living animals and so cannot be used to understand dynamic physiological processes. The relatively large brain of the desert locust, Schistercera gregaria (Forksȧl) is ideal for exploring a novel methodology; micro diffusion magnetic resonance imaging (micro-dMRI) for the characterization of neuronal connectivity in an insect brain. The diffusion-weighted imaging (DWI) data were acquired on a preclinical system using a customised multi-shell diffusion MRI scheme optimized to image the locust brain. Endogenous imaging contrasts from the averaged DWIs and Diffusion Kurtosis Imaging (DKI) scheme were applied to classify various anatomical features and diffusion patterns in neuropils, respectively. The application of micro-dMRI modelling to the locust brain provides a novel means of identifying anatomical regions and inferring connectivity of large tracts in an insect brain. Furthermore, quantitative imaging indices derived from the kurtosis model that include fractional anisotropy (FA), mean diffusivity (MD) and kurtosis anisotropy (KA) can be extracted. These metrics could, in future, be used to quantify longitudinal structural changes in the nervous system of the locust brain that occur due to environmental stressors or ageing.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

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.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties

PURPOSE

A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented.

METHODS

This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods.

RESULTS

Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition.

CONCLUSIONS

The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

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.

Imaging brain microstructure with diffusion MRI: practicality and applications

This article gives an overview of microstructure imaging of the brain with diffusion MRI and reviews the state of the art. The microstructure-imaging paradigm aims to estimate and map microscopic properties of tissue using a model that links these properties to the voxel scale MR signal. Imaging techniques of this type are just starting to make the transition from the technical research domain to wide application in biomedical studies. We focus here on the practicalities of both implementing such techniques and using them in applications. Specifically, the article summarizes the relevant aspects of brain microanatomy and the range of diffusion-weighted MR measurements that provide sensitivity to them. It then reviews the evolution of mathematical and computational models that relate the diffusion MR signal to brain tissue microstructure, as well as the expanding areas of application. Next we focus on practicalities of designing a working microstructure imaging technique: model selection, experiment design, parameter estimation, validation, and the pipeline of development of this class of technique. The article concludes with some future perspectives on opportunities in this topic and expectations on how the field will evolve in the short-to-medium term.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

Microscopic anisotropy misestimation in spherical-mean single diffusion encoding MRI

Purpose

Microscopic fractional anisotropy (µFA) can disentangle microstructural information from orientation dispersion. While double diffusion encoding (DDE) MRI methods are widely used to extract accurate µFA, it has only recently been proposed that powder‐averaged single diffusion encoding (SDE) signals, when coupled with the diffusion standard model (SM) and a set of constraints, could be used for µFA estimation. This study aims to evaluate µFA as derived from the spherical mean technique (SMT) set of constraints, as well as more generally for powder‐averaged SM signals.

Methods

SDE experiments were performed at 16.4 T on an ex vivo mouse brain (Δ/δ = 12/1.5 ms). The µFA maps obtained from powder‐averaged SDE signals were then compared to maps obtained from DDE‐MRI experiments (Δ/τ/δ = 12/12/1.5 ms), which allow a model‐free estimation of µFA. Theory and simulations that consider different types of heterogeneity are presented for corroborating the experimental findings.

Results

µFA, as well as other estimates derived from powder‐averaged SDE signals produced large deviations from the ground truth in both gray and white matter. Simulations revealed that these misestimations are likely a consequence of factors not considered by the underlying microstructural models (such as intercomponent and intracompartmental kurtosis).

Conclusion

Powder‐averaged SMT and (2‐component) SM are unable to accurately report µFA and other microstructural parameters in ex vivo tissues. Improper model assumptions and constraints can significantly compromise parameter specificity. Further developments and validations are required prior to implementation of these models in clinical or preclinical research.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.

Double diffusion encoding MRI for the clinic

PURPOSE

The purpose of this study is to develop double diffusion encoding (DDE) MRI methods for clinical use. Microscopic diffusion anisotropy measurements from DDE promise greater specificity to changes in tissue microstructure compared with conventional diffusion tensor imaging, but implementation of DDE sequences on whole-body MRI scanners is challenging because of the limited gradient strengths and lengthy acquisition times.

METHODS

A custom single-refocused DDE sequence was implemented on a 3T whole-body scanner. The DDE gradient orientation scheme and sequence parameters were optimized based on a Gaussian diffusion assumption. Using an optimized 5-min DDE acquisition, microscopic fractional anisotropy (μFA) maps were acquired for the first time in multiple sclerosis patients.

RESULTS

Based on simulations and in vivo human measurements, six parallel and six orthogonal diffusion gradient pairs were found to be the minimum number of diffusion gradient pairs necessary to produce a rotationally invariant measurement of μFA. Simulations showed that optimal precision and accuracy of μFA measurements were obtained using b-values between 1500 and 3000 s/mm² . The μFA maps showed improved delineation of multiple sclerosis lesions compared with conventional fractional anisotropy and distinct contrast from T₂ -weighted fluid attenuated inversion recovery and T₁ -weighted imaging.

CONCLUSION

The μFA maps can be measured using DDE in a clinical setting and may provide new opportunities for characterizing multiple sclerosis lesions and other types of tissue degeneration. Magn Reson Med 80:507-520, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Distinguishing neuronal from astrocytic subcellular microstructures using in vivo Double Diffusion Encoded 1H MRS at 21.1 T

Measuring cellular microstructures non-invasively and achieving specificity towards a cell-type population within an interrogated in vivo tissue, remains an outstanding challenge in brain research. Magnetic Resonance Spectroscopy (MRS) provides an opportunity to achieve cellular specificity via the spectral resolution of metabolites such as N-Acetylaspartate (NAA) and myo-Inositol (mI), which are considered neuronal and astrocytic markers, respectively. Yet the information typically obtained with MRS describes metabolic concentrations, diffusion coefficients or relaxation rates rather than microstructures. Understanding how these metabolites are compartmentalized is a challenging but important goal, which so far has been mainly addressed using diffusion models. Here, we present direct in vivo evidence for the confinement of NAA and mI within sub-cellular components, namely, the randomly oriented process of neurons and astrocytes, respectively. Our approach applied Relaxation Enhanced MRS at ultrahigh (21.1 T) field, and used its high ¹H sensitivity to measure restricted diffusion correlations for NAA and mI using a Double Diffusion Encoding (DDE) filter. While very low macroscopic anisotropy was revealed by spatially localized Diffusion Tensor Spectroscopy, DDE displayed characteristic amplitude modulations reporting on confinements in otherwise randomly oriented anisotropic microstructures for both metabolites. This implies that for the chosen set of parameters, the DDE measurements had a biased sensitivity towards NAA and mI sited in the more confined environments of neurites and astrocytic branches, than in the cell somata. These measurements thus provide intrinsic diffusivities and compartment diameters, and revealed subcellular neuronal and astrocytic morphologies in normal in vivo rat brains. The relevance of these measurements towards human applications—which could in turn help understand CNS plasticity as well as diagnose brain diseases—is discussed.

In vivo imaging of cancer cell size and cellularity using temporal diffusion spectroscopy

PURPOSE

A temporal diffusion MRI spectroscopy based approach has been developed to quantify cancer cell size and density in vivo.

METHODS

A novel imaging microstructural parameters using limited spectrally edited diffusion (IMPULSED) method selects a specific limited diffusion spectral window for an accurate quantification of cell sizes ranging from 10 to 20 μm in common solid tumors. In practice, it is achieved by a combination of a single long diffusion time pulsed gradient spin echo (PGSE) and three low-frequency oscillating gradient spin echo (OGSE) acquisitions. To validate our approach, hematoxylin and eosin staining and immunostaining of cell membranes, in concert with whole slide imaging, were used to visualize nuclei and cell boundaries, and hence, enabled accurate estimates of cell size and cellularity.

RESULTS

Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes were obtained in vivo for three types of human colon cancers. The IMPULSED-derived apparent cellularities showed a stronger correlation (r = 0.81; P < 0.0001) with histology-derived cellularities than conventional ADCs (r = -0.69; P < 0.03).

CONCLUSION

The IMPULSED approach samples a specific region of temporal diffusion spectra with enhanced sensitivity to length scales of 10-20 μm, and enables measurements of cell sizes and cellularities in solid tumors in vivo. Magn Reson Med 78:156-164, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Impact of transcytolemmal water exchange on estimates of tissue microstructural properties derived from diffusion MRI

PURPOSE

To investigate the influence of transcytolemmal water exchange on estimates of tissue microstructural parameters derived from diffusion MRI using conventional PGSE and IMPULSED methods.

METHODS

Computer simulations were performed to incorporate a broad range of intracellular water life times τin (50-∞ ms), cell diameters d (5-15 μm), and intrinsic diffusion coefficient Din (0.6-2 μm2 /ms) for different values of signal-to-noise ratio (SNR) (10 to 50). For experiments, murine erythroleukemia (MEL) cancer cells were cultured and treated with saponin to selectively change cell membrane permeability. All fitted microstructural parameters from simulations and experiments in vitro were compared with ground-truth values.

RESULTS

Simulations showed that, for both PGSE and IMPULSED methods, cell diameter d can be reliably fit with sufficient SNR (≥ 50), whereas intracellular volume fraction fin is intrinsically underestimated due to transcytolemmal water exchange. Din can be reliably fit only with sufficient SNR and using the IMPULSED method with short diffusion times. These results were confirmed with those obtained in the cell culture experiments in vitro.

CONCLUSION

For the sequences and models considered in this study, transcytolemmal water exchange has minor effects on the fittings of d and Din with physiologically relevant membrane permeabilities if the SNR is sufficient (> 50), but fin is intrinsically underestimated. Magn Reson Med 77:2239-2249, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Studying microstructure and microstructural changes in plant tissues by advanced diffusion magnetic resonance imaging techniques

As sessile organisms, plants must respond to the environment by adjusting their growth and development. Most of the plant body is formed post-embryonically by continuous activity of apical and lateral meristems. The development of lateral adventitious roots is a complex process, and therefore the development of methods that can visualize, non-invasively, the plant microstructure and organ initiation that occur during growth and development is of paramount importance. In this study, relaxation-based and advanced diffusion magnetic resonance imaging (MRI) methods including diffusion tensor (DTI), q-space diffusion imaging (QSI), and double-pulsed-field-gradient (d-PFG) MRI, at 14.1 T, were used to characterize the hypocotyl microstructure and the microstructural changes that occurred during the development of lateral adventitious roots in tomato. Better contrast was observed in relaxation-based MRI using higher in-plane resolution but this also resulted in a significant reduction in the signal-to-noise ratio of the T2-weighted MR images. Diffusion MRI revealed that water diffusion is highly anisotropic in the vascular cylinder. QSI and d-PGSE MRI showed that in the vascular cylinder some of the cells have sizes in the range of 6-10 μm. The MR images captured cell reorganization during adventitious root formation in the periphery of the primary vascular bundles, adjacent to the xylem pole that broke through the cortex and epidermis layers. This study demonstrates that MRI and diffusion MRI methods allow the non-invasive study of microstructural features of plants, and enable microstructural changes associated with adventitious root formation to be followed.

Model-based estimation of microscopic anisotropy using diffusion MRI: a simulation study

Non-invasive estimation of cell size and shape is a key challenge in diffusion MRI. This article presents a model-based approach that provides independent estimates of pore size and eccentricity from diffusion MRI data. The technique uses a geometric model of finite cylinders with gamma-distributed radii to represent pores of various sizes and elongations. We consider both macroscopically isotropic substrates and substrates of semi-coherently oriented anisotropic pores and we use Monte Carlo simulations to generate synthetic data. We compare the sensitivity of single and double diffusion encoding (SDE and DDE) sequences to the size distribution and eccentricity, and further analyse different protocols of DDE sequences with parallel and/or perpendicular pairs of gradients. We show that explicitly accounting for size distribution is necessary for accurate microstructural parameter estimates, and a model that assumes a single size yields biased eccentricity values. We also find that SDE sequences support estimates, although DDE sequences with mixed parallel and perpendicular gradients enhance accuracy. In the case of macroscopically anisotropic substrates, this model-based approach can be extended to a rotationally invariant framework to provide features of pore shape (specifically eccentricity) in the presence of size distribution and orientation dispersion.

Two-Dimensional Correlation of Isotropic and Directional Diffusion Using NMR

Diffusion nuclear magnetic resonance (NMR) is a powerful technique for studying porous media, but yields ambiguous results when the sample comprises multiple regions with different pore sizes, shapes, and orientations. Inspired by solid-state NMR techniques for correlating isotropic and anisotropic chemical shifts, we propose a diffusion NMR method to resolve said ambiguity. Numerical data inversion relies on sparse representation of the data in a basis of radial and axial diffusivities. Experiments are performed on a composite sample with a cell suspension and a liquid crystal.

Eddy current compensated double diffusion encoded (DDE) MRI

PURPOSE

Eddy currents might lead to image distortions in diffusion-weighted echo planar imaging. A method is proposed to reduce their effects on double diffusion encoding (DDE) MRI experiments and the thereby derived microscopic fractional anisotropy (μFA).

METHODS

The twice-refocused spin echo scheme was adapted for DDE measurements. To assess the effect of individual diffusion encodings on the image distortions, measurements of a grid of plastic rods in water were performed. The effect of eddy current compensation on μFA measurements was evaluated in the brains of six healthy volunteers.

RESULTS

The use of an eddy current compensation reduced the signal variation. As expected, the distortions caused by the second encoding were larger than those of the first encoding, entailing a stronger need to compensate for them. For an optimal result, however, both encodings had to be compensated. The artifact reduction strongly improved the measurement of the μFA in ventricles and gray matter by reducing the overestimation. An effect of the compensation on absolute μFA values in white matter was not observed.

CONCLUSION

It is advisable to compensate both encodings in DDE measurements for eddy currents. Magn Reson Med 77:328-335, 2017. © 2015 Wiley Periodicals, Inc.

Model-Based Estimation of Microscopic Anisotropy in Macroscopically Isotropic Substrates Using Diffusion MRI

Non-invasive estimation of cell size and shape is a key challenge in diffusion MRI. Changes in cell size and shape discriminate functional areas in the brain and can highlight different degrees of malignancy in cancer tumours. Consequently various methods have emerged recently that aim to measure the microscopic anisotropy of porous media such as biological tissue and aim to reflect pore eccentricity, the simplest shape feature. However, current methods assume a substrate of identical pores, and are strongly influenced by non-trivial size distribution. This paper presents a model-based approach that provides estimates of pore size and shape from diffusion MRI data. The technique uses a geometric model of randomly oriented finite cylinders with gamma distributed radii. We use Monte Carlo simulation to generate synthetic data in substrates consisting of randomly oriented cuboids with various size distributions and eccentricities. We compare the sensitivity of single and double pulsed field gradient (sPFG and dPFG) sequences to the size distribution and eccentricity and further compare different protocols of dPFG sequences with parallel and/or perpendicular pairs of gradients. The key result demonstrates that this model-based approach can provide features of pore shape (specifically eccentricity) that are independent of the size distribution unlike previous attempts to characterise microscopic anisotropy. We show further that explicitly accounting for size distribution is necessary for accurate estimates of average size and eccentricity, and a model that assumes a single size fails to recover the ground truth values. We find the most accurate parameter estimates for dPFG sequences with mixed parallel and perpendicular gradients, nevertheless all other sequences, including sPFG, show sensitivity as well.

Size Distribution Imaging by Non-Uniform Oscillating-Gradient Spin Echo (NOGSE) MRI

Objects making up complex porous systems in Nature usually span a range of sizes. These size distributions play fundamental roles in defining the physicochemical, biophysical and physiological properties of a wide variety of systems - ranging from advanced catalytic materials to Central Nervous System diseases. Accurate and noninvasive measurements of size distributions in opaque, three-dimensional objects, have thus remained long-standing and important challenges. Herein we describe how a recently introduced diffusion-based magnetic resonance methodology, Non-Uniform-Oscillating-Gradient-Spin-Echo (NOGSE), can determine such distributions noninvasively. The method relies on its ability to probe confining lengths with a (length)6 parametric sensitivity, in a constant-time, constant-number-of-gradients fashion; combined, these attributes provide sufficient sensitivity for characterizing the underlying distributions in μm-scaled cellular systems. Theoretical derivations and simulations are presented to verify NOGSE's ability to faithfully reconstruct size distributions through suitable modeling of their distribution parameters. Experiments in yeast cell suspensions - where the ground truth can be determined from ancillary microscopy - corroborate these trends experimentally. Finally, by appending to the NOGSE protocol an imaging acquisition, novel MRI maps of cellular size distributions were collected from a mouse brain. The ensuing micro-architectural contrasts successfully delineated distinctive hallmark anatomical sub-structures, in both white matter and gray matter tissues, in a non-invasive manner. Such findings highlight NOGSE's potential for characterizing aberrations in cellular size distributions upon disease, or during normal processes such as development.

Quantification of cell size using temporal diffusion spectroscopy

PURPOSE

A new approach has been developed to quantify cell sizes and intracellular volume fractions using temporal diffusion spectroscopy with diffusion-weighted acquisitions.

METHODS

Temporal diffusion spectra may be used to characterize tissue microstructure by measuring the effects of restrictions over a range of diffusion times. Oscillating gradients have been used previously to probe variations on cellular and subcellular scales, but their ability to accurately measure cell sizes larger than 10 μm is limited. By combining measurements made using oscillating gradient spin echo (OGSE) and a conventional pulsed gradient spin echo (PGSE) acquisition with a single, relatively long diffusion time, we can accurately quantify cell sizes and intracellular volume fractions.

RESULTS

Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes and intracellular volume fractions were obtained in vitro for (i) different cell types with sizes ranging from 10 to 20 μm, (ii) different cell densities, and (iii) before and after anticancer treatment.

CONCLUSION

Hybrid OGSE-PGSE acquisitions sample a larger region of temporal diffusion spectra and can accurately quantify cell sizes over a wide range. Moreover, the maximum gradient strength used was lower than 15 G/cm, suggesting that this approach is translatable to practical MR imaging.

Microscopic diffusion anisotropy in the human brain: reproducibility, normal values, and comparison with the fractional anisotropy

Human neuroimaging of tissue microstructure, such as axonal density and integrity, is key in clinical and neuroscience research. Most studies rely on diffusion tensor imaging (DTI) and the measures derived from it, most prominently fractional anisotropy (FA). However, FA also depends on fiber orientation distribution, a more macroscopic tissue property. Recently introduced measures of so-called microscopic diffusion anisotropy, diffusion anisotropy on a cellular or microscopic level, overcome this limitation because they are independent of the orientation distributions of axons and fibers. In this study, we evaluate the feasibility of two measures of microscopic diffusion anisotropy I(MA) and MA indices, for human neuroscience and clinical research. Both indices reflect the eccentricity of the cells but while I(MA) also depends on the cell size, MA is independent of the cell size and, like FA, scaled between 0 and 1. In whole-brain measurements of a group of 19 healthy volunteers, we measured average values and variability, evaluated their reproducibility, both within and between sessions, and compared MA to FA values in selected regions-of-interest (ROIs). The within- and between-session comparison did not show substantial differences but the reproducibility was much better for the MA than I(MA) (coefficient of variation between sessions 10.5% vs. 28.9%). The reproducibility was less for MA than FA overall, but comparable in the defined ROIs and the average group sizes required for between-group comparisons was similar (about 60 participants for a relative difference of 5%). Group-averaged values of MA index were generally larger and showed less variation across white-matter brain ROIs than FA (mean ± standard deviation of seven ROIs 0.83 ± 0.10 vs. 0.58 ± 0.13). Even in some gray-matter ROIs, MA values comparable to those of white matter ROIs were observed. Furthermore, the within-group variation of the values in white matter ROIs was lower for the MA compared to the FA (mean standard deviation over volunteers 0.038 vs. 0.049) which could be due to significant variability in the distribution of fiber orientation contributing to FA. These results indicate that MA (i) should be preferred to I(MA), (ii) has a reproducibility and group-size requirements comparable to those of FA; (iii) is less sensitive to the fiber orientation distribution than FA; and (iv) could be more sensitive to differences or changes of the tissue microstructure than FA. R1.1.

Nonparametric pore size distribution using d-PFG: comparison to s-PFG and migration to MRI

Here we present the successful translation of a pore size distribution (PSD) estimation method from NMR to MRI. This approach is validated using a well-characterized MRI phantom consisting of stacked glass capillary arrays (GCA) having different diameters. By employing a double pulsed-field gradient (d-PFG) MRI sequence, this method overcomes several important theoretical and experimental limitations of previous single-PFG (s-PFG) based MRI methods by allowing the relative diffusion gradients' direction to vary. This feature adds an essential second dimension in the parameters space, which can potentially improve the reliability and stability of the PSD estimation. To infer PSDs from the MRI data in each voxel an inverse linear problem is solved in conjunction with the multiple correlation function (MCF) framework, which can account for arbitrary experimental parameters (e.g., long diffusion pulses). This scheme makes no a priori assumptions about the functional form of the underlying PSD. Creative use of region of interest (ROI) analysis allows us to create different underlying PSDs using the same GCA MRI phantom. We show that an s-PFG experiment on the GCA phantom fails to accurately reconstruct the size distribution, thus demonstrating the superiority of the d-PFG experiment. In addition, signal simulations corrupted by different noise levels were used to generate continuous and complex PSDs, which were then successfully reconstructed. Finally, owing to the reduced q- or b- values required to measure microscopic PSDs via d-PFG MRI, this method will be better suited to biomedical and clinical applications, in which gradient strength of scanners is limited.

Orientationally invariant metrics of apparent compartment eccentricity from double pulsed field gradient diffusion experiments

Pulsed field gradient diffusion sequences (PFG) with multiple diffusion encoding blocks have been indicated to offer new microstructural tissue information, such as the ability to detect nonspherical compartment shapes in macroscopically isotropic samples, i.e. samples with negligible directional signal dependence on diffusion gradients in standard diffusion experiments. However, current acquisition schemes are not rotationally invariant in the sense that the derived metrics depend on the orientation of the sample, and are affected by the interplay of sampling directions and compartment orientation dispersion when applied to macroscopically anisotropic systems. Here we propose a new framework, the d-PFG 5-design, to enable rotationally invariant estimation of double wave vector diffusion metrics (d-PFG). The method is based on the idea that an appropriate orientational average of the signal emulates the signal from a powder preparation of the same sample, where macroscopic anisotropy is absent by construction. Our approach exploits the theory of exact numerical integration (quadrature) of polynomials on the rotation group, and we exemplify the general procedure with a set consisting of 60 pairs of diffusion wave vectors (the d-PFG 5-design) facilitating a theoretically exact determination of the fourth order Taylor or cumulant expansion of the orientationally averaged signal. The d-PFG 5-design is evaluated with numerical simulations and ex vivo high field diffusion MRI experiments in a nonhuman primate brain. Specifically, we demonstrate rotational invariance when estimating compartment eccentricity, which we show offers new microstructural information, complementary to that of fractional anisotropy (FA) from diffusion tensor imaging (DTI). The imaging observations are supported by a new theoretical result, directly relating compartment eccentricity to FA of individual pores.

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.

Efficient parallel Levenberg-Marquardt model fitting towards real-time automated parametric imaging microscopy

We present a fast, accurate and robust parallel Levenberg-Marquardt minimization optimizer, GPU-LMFit, which is implemented on graphics processing unit for high performance scalable parallel model fitting processing. GPU-LMFit can provide a dramatic speed-up in massive model fitting analyses to enable real-time automated pixel-wise parametric imaging microscopy. We demonstrate the performance of GPU-LMFit for the applications in superresolution localization microscopy and fluorescence lifetime imaging microscopy.

Mapping average axon diameters in porcine spinal cord white matter and rat corpus callosum using d-PFG MRI

Knowledge of microstructural features of nerve fascicles, such as their axon diameter, is crucial for understanding normal function in the central and peripheral nervous systems as well as assessing changes due to pathologies. In this study double-pulsed field gradient (d-PFG) filtered MRI was used to map the average axon diameter (AAD) in porcine spinal cord, which was then compared to AADs measured with optical microscopy of the same specimen, as a way to further validate this new MRI method. A novel 3D d-PFG acquisition scheme was used to obtain AADs in each voxel of a coronal slice of rat brain corpus callosum. AAD measurements were also acquired using optical microscopy performed on histological sections and validated using a glass capillary array phantom.

Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI

Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghan's matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation frequency and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients.

Isotropic diffusion weighting in PGSE NMR by magic-angle spinning of the q-vector

When PGSE NMR is applied to water in microheterogeneous materials such as liquid crystals, foodstuffs, porous rocks, and biological tissues, the signal attenuation is often multi-exponential, indicating the presence of pores having a range of sizes or anisotropic domains having a spread of orientations. Here we modify the standard PGSE experiment by introducing low-amplitude harmonically modulated gradients, which effectively make the q-vector perform magic-angle spinning (MAS) about an axis fixed in the laboratory frame. With this new technique, denoted q-MAS PGSE, the signal attenuation depends on the isotropic average of the local diffusion tensor. The capability of q-MAS PGSE to distinguish between pore size and domain orientation dispersion is demonstrated by experiments on a yeast cell suspension and a polydomain anisotropic liquid crystal. In the latter case, the broad distribution of apparent diffusivities observed with PGSE is narrowed to its isotropic average with q-MAS PGSE in a manner that is analogous to the narrowing of chemical shift anisotropy powder patterns using magic-angle sample spinning in solid-state NMR. The new q-MAS PGSE technique could be useful for resolving size/orientation ambiguities in the interpretation of PGSE data from, e.g., water confined within the axons of human brain tissue.

In vivo detection of microscopic anisotropy using quadruple pulsed-field gradient (qPFG) diffusion MRI on a clinical scanner

We report our design and implementation of a quadruple pulsed-field gradient (qPFG) diffusion MRI pulse sequence on a whole-body clinical scanner and demonstrate its ability to non-invasively detect restriction-induced microscopic anisotropy in human brain tissue. The microstructural information measured using qPFG diffusion MRI in white matter complements that provided by diffusion tensor imaging (DTI) and exclusively characterizes diffusion of water trapped in microscopic compartments with unique measures of average cell geometry. We describe the effect of white matter fiber orientation on the expected MR signal and highlight the importance of incorporating such information in the axon diameter measurement using a suitable mathematical framework. Integration of qPFG diffusion-weighted images (DWI) with fiber orientations measured using high-resolution DTI allows the estimation of average axon diameters in the corpus callosum of healthy human volunteers. Maps of inter-hemispheric average axon diameters reveal an anterior-posterior variation in good topographical agreement with anatomical measurements reported in previous post-mortem studies. With further technical refinements and additional clinical validation, qPFG diffusion MRI could provide a quantitative whole-brain histological assessment of white and gray matter, enabling a wide range of neuroimaging applications for improved diagnosis of neurodegenerative pathologies, monitoring neurodevelopmental processes, and mapping brain connectivity.

Equivalence of double and single wave vector diffusion contrast at low diffusion weighting

Multiple pulsed field gradient diffusion sequences have received renewed interest in recent years as a potentially new type of MRI contrast. This attention is largely a result of the ability to measure pore sizes using low-amplitude diffusion gradients, and to distinguish between macroscopically isotropic systems of anisotropic pores and systems of isotropic pores. In this article, it is shown that, under many circumstances, the same type of information can be obtained by combining two or more standard single pulse diffusion-weighted experiments acquired at different diffusion times. Similarly, information from multiple pulsed field gradient diffusion can be reconstructed from several single pulsed diffusion experiments. This possibility is rooted in the information contained in the time dependence of the diffusion tensor, which provides a complete description of the diffusion-weighted MR signal at low gradient amplitudes. The new information arising at the fourth order in the cumulant expansion is discussed. The coupling of the wave vectors at long mixing times is found to be controlled by the variance of the single pore mean displacement tensor. In particular, a discussion is given concerning the way in which the sensitivity of the fourth-order term to the pore shape anisotropy is modulated by pore orientation anisotropy and vanishes in coherently oriented homogeneous ensembles. For macroscopically isotropic systems, a new index of pore shape anisotropy is proposed.