PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study

Modeling conduction delays in the corpus callosum using MRI-measured g-ratio

Conduction of action potentials along myelinated axons is affected by their structural features, such as the axonal g-ratio, the ratio between the inner and outer diameters of the myelin sheath surrounding the axon. The effect of g-ratio variance on conduction properties has been quantitatively evaluated using single-axon models. It has recently become possible to estimate a g-ratio weighted measurement in vivo using quantitative MRI. Nevertheless, it is still unclear whether the variance in the g-ratio in the healthy human brain leads to significant differences in conduction velocity. In this work we tested whether the g-ratio MRI measurement can be used to predict conduction delays in the corpus callosum. We present a comprehensive framework in which the structural properties of fibers (i.e. length and g-ratio, measured using MRI), are incorporated in a biophysical model of axon conduction, to model conduction delays of long-range white matter fibers. We applied this framework to the corpus callosum, and found conduction delay estimates that are compatible with previously estimated values of conduction delays. We account for the variance in the velocity given the axon diameter distribution in the splenium, mid-body and genu, to further compare the fibers within the corpus callosum. Conduction delays have been suggested to increase with age. Therefore, we investigated whether there are differences in the g-ratio and the fiber length between young and old adults, and whether this leads to a difference in conduction speed and delays. We found very small differences between the predicted delays of the two groups in the motor fibers of the corpus callosum. We also found that the motor fibers of the corpus callosum have the fastest conduction estimates. Using the axon diameter distributions, we found that the occipital fibers have the slowest estimations, while the frontal and motor fiber tracts have similar estimates. Our study provides a framework for predicting conduction latencies in vivo. The framework could have major implications for future studies of white matter diseases and large range network computations. Our results highlight the need for improving additional in vivo measurements of white matter microstructure.

Towards microstructure fingerprinting: Estimation of tissue properties from a dictionary of Monte Carlo diffusion MRI simulations

Many closed-form analytical models have been proposed to relate the diffusion-weighted magnetic resonance imaging (DW-MRI) signal to microstructural features of white matter tissues. These models generally make assumptions about the tissue and the diffusion processes which often depart from the biophysical reality, limiting their reliability and interpretability in practice. Monte Carlo simulations of the random walk of water molecules are widely recognized to provide near groundtruth for DW-MRI signals. However, they have mostly been limited to the validation of simpler models rather than used for the estimation of microstructural properties. This work proposes a general framework which leverages Monte Carlo simulations for the estimation of physically interpretable microstructural parameters, both in single and in crossing fascicles of axons. Monte Carlo simulations of DW-MRI signals, or fingerprints, are pre-computed for a large collection of microstructural configurations. At every voxel, the microstructural parameters are estimated by optimizing a sparse combination of these fingerprints. Extensive synthetic experiments showed that our approach achieves accurate and robust estimates in the presence of noise and uncertainties over fixed or input parameters. In an in vivo rat model of spinal cord injury, our approach provided microstructural parameters that showed better correspondence with histology than five closed-form models of the diffusion signal: MMWMD, NODDI, DIAMOND, WMTI and MAPL. On whole-brain in vivo data from the human connectome project (HCP), our method exhibited spatial distributions of apparent axonal radius and axonal density indices in keeping with ex vivo studies. This work paves the way for microstructure fingerprinting with Monte Carlo simulations used directly at the modeling stage and not only as a validation tool.

Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI

The key component of a microstructural diffusion MRI 'super-scanner' is a dedicated high-strength gradient system that enables stronger diffusion weightings per unit time compared to conventional gradient designs. This can, in turn, drastically shorten the time needed for diffusion encoding, increase the signal-to-noise ratio, and facilitate measurements at shorter diffusion times. This review, written from the perspective of the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure, an initiative to establish a shared 300 mT/m-gradient facility amongst the microstructural imaging community, describes ten advantages of ultra-strong gradients for microstructural imaging. Specifically, we will discuss how the increase of the accessible measurement space compared to a lower-gradient systems (in terms of Δ, b-value, and TE) can accelerate developments in the areas of 1) axon diameter distribution mapping; 2) microstructural parameter estimation; 3) mapping micro-vs macroscopic anisotropy features with gradient waveforms beyond a single pair of pulsed-gradients; 4) multi-contrast experiments, e.g. diffusion-relaxometry; 5) tractography and high-resolution imaging in vivo and 6) post mortem; 7) diffusion-weighted spectroscopy of metabolites other than water; 8) tumour characterisation; 9) functional diffusion MRI; and 10) quality enhancement of images acquired on lower-gradient systems. We finally discuss practical barriers in the use of ultra-strong gradients, and provide an outlook on the next generation of 'super-scanners'.

Relevance of time-dependence for clinically viable diffusion imaging of the spinal cord

Purpose

Time‐dependence is a key feature of the diffusion‐weighted (DW) signal, knowledge of which informs biophysical modelling. Here, we study time‐dependence in the human spinal cord, as its axonal structure is specific and different from the brain.

Methods

We run Monte Carlo simulations using a synthetic model of spinal cord white matter (WM) (large axons), and of brain WM (smaller axons). Furthermore, we study clinically feasible multi‐shell DW scans of the cervical spinal cord (b = 0; b = 711 s mm⁻²; b = 2855 s mm⁻²), obtained using three diffusion times (Δ of 29, 52 and 76 ms) from three volunteers.

Results

Both intra‐/extra‐axonal perpendicular diffusivities and kurtosis excess show time‐dependence in our synthetic spinal cord model. This time‐dependence is reflected mostly in the intra‐axonal perpendicular DW signal, which also exhibits strong decay, unlike our brain model. Time‐dependence of the total DW signal appears detectable in the presence of noise in our synthetic spinal cord model, but not in the brain. In WM in vivo, we observe time‐dependent macroscopic and microscopic diffusivities and diffusion kurtosis, NODDI and two‐compartment SMT metrics. Accounting for large axon calibers improves fitting of multi‐compartment models to a minor extent.

Conclusions

Time‐dependence of clinically viable DW MRI metrics can be detected in vivo in spinal cord WM, thus providing new opportunities for the non‐invasive estimation of microstructural properties. The time‐dependence of the perpendicular DW signal may feature strong intra‐axonal contributions due to large spinal axon caliber. Hence, a popular model known as “stick” (zero‐radius cylinder) may be sub‐optimal to describe signals from the largest spinal axons.

Recent advances in diffusion neuroimaging: applications in the developing preterm brain

Measures obtained from diffusion-weighted imaging provide objective indices of white matter development and injury in the developing preterm brain. To date, diffusion tensor imaging (DTI) has been used widely, highlighting differences in fractional anisotropy (FA) and mean diffusivity (MD) between preterm infants at term and healthy term controls; altered white matter development associated with a number of perinatal risk factors; and correlations between FA values in the white matter in the neonatal period and subsequent neurodevelopmental outcome. Recent developments, including neurite orientation dispersion and density imaging (NODDI) and fixel-based analysis (FBA), enable white matter microstructure to be assessed in detail. Constrained spherical deconvolution (CSD) enables multiple fibre populations in an imaging voxel to be resolved and allows delineation of fibres that traverse regions of fibre-crossings, such as the arcuate fasciculus and cerebellar–cortical pathways. This review summarises DTI findings in the preterm brain and discusses initial findings in this population using CSD, NODDI, and FBA.

Validation of diffusion MRI estimates of compartment size and volume fraction in a biomimetic brain phantom using a human MRI scanner with 300 mT/m maximum gradient strength

Diffusion microstructural imaging techniques have attracted great interest in the last decade due to their ability to quantify axon diameter and volume fraction in healthy and diseased human white matter. The estimates of compartment size and volume fraction continue to be debated, in part due to the lack of a gold standard for validation and quality control. In this work, we validate diffusion MRI estimates of compartment size and volume fraction using a novel textile axon ("taxon") phantom constructed from hollow polypropylene yarns with distinct intra- and extra-taxonal compartments to mimic white matter in the brain. We acquired a comprehensive set of diffusion MRI measurements in the phantom using multiple gradient directions, diffusion times and gradient strengths on a human MRI scanner equipped with maximum gradient strength (G_max) of 300 mT/m. We obtained estimates of compartment size and restricted volume fraction through a straightforward extension of the AxCaliber/ActiveAx frameworks that enables estimation of mean compartment size in fiber bundles of arbitrary orientation. The voxel-wise taxon diameter estimates of 12.2 ± 0.9 μm were close to the manufactured inner diameter of 11.8 ± 1.2 μm with G_max = 300 mT/m. The estimated restricted volume fraction demonstrated an expected decrease along the length of the fiber bundles in accordance with the known construction of the phantom. When G_max was restricted to 80 mT/m, the taxon diameter was overestimated, and the estimates for taxon diameter and packing density showed greater uncertainty compared to data with G_max = 300 mT/m. In conclusion, the compartment size and volume fraction estimates resulting from diffusion measurements on a human scanner were validated against ground truth in a phantom mimicking human white matter, providing confidence that this method can yield accurate estimates of parameters in simplified but realistic microstructural environments. Our work also demonstrates the importance of a biologically analogous phantom that can be applied to validate a variety of diffusion microstructural imaging methods in human scanners and be used for standardization of diffusion MRI protocols for neuroimaging research.

Studying neuroanatomy using MRI

The study of neuroanatomy using imaging enables key insights into how our brains function, are shaped by genes and environment, and change with development, aging and disease. Developments in MRI acquisition, image processing and data modeling have been key to these advances. However, MRI provides an indirect measurement of the biological signals we aim to investigate. Thus, artifacts and key questions of correct interpretation can confound the readouts provided by anatomical MRI. In this review we provide an overview of the methods for measuring macro- and mesoscopic structure and for inferring microstructural properties; we also describe key artifacts and confounds that can lead to incorrect conclusions. Ultimately, we believe that, although methods need to improve and caution is required in interpretation, structural MRI continues to have great promise in furthering our understanding of how the brain works.

Assessing the validity of the approximation of diffusion-weighted-MRI signals from crossing fascicles by sums of signals from single fascicles

PURPOSE

To assess the validity of the superposition approximation for crossing fascicles, i.e., the assumption that the total diffusion-weighted MRI signal is the sum of the signals arising from each fascicle independently, even when the fascicles intermingle in a voxel.

METHODS

Monte Carlo simulations were used to study the impact of the approximation on the diffusion-weighted MRI signal and to assess whether this approximate model allows microstructural features of interwoven fascicles to be accurately estimated, despite signal differences.

RESULTS

Small normalized signal differences were observed, typically 10-3-10-2. The use of the approximation had little impact on the estimation of the crossing angle, the axonal density index, and the radius index in clinically realistic scenarios wherein the acquisition noise was the predominant source of errors. In the absence of noise, large systematic errors due to the superposition approximation only persisted for the radius index, mainly driven by a low sensitivity of diffusion-weighted MRI signals to small radii in general.

CONCLUSION

The use of the superposition approximation rather than a model of interwoven fascicles does not adversely impact the estimation of microstructural features of interwoven fascicles in most current clinical settings. Magn Reson Med 79:2332-2345, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Resolution limit of cylinder diameter estimation by diffusion MRI: The impact of gradient waveform and orientation dispersion

Diffusion MRI has been proposed as a non-invasive technique for axonal diameter mapping. However, accurate estimation of small diameters requires strong gradients, which is a challenge for the transition of the technique from preclinical to clinical MRI scanners, since these have weaker gradients. In this work, we develop a framework to estimate the lower bound for accurate diameter estimation, which we refer to as the resolution limit. We analyse only the contribution from the intra-axonal space and assume that axons can be represented by impermeable cylinders. To address the growing interest in using techniques for diffusion encoding that go beyond the conventional single diffusion encoding (SDE) sequence, we present a generalised analysis capable of predicting the resolution limit regardless of the gradient waveform. Using this framework, waveforms were optimised to minimise the resolution limit. The results show that, for parallel cylinders, the SDE experiment is optimal in terms of yielding the lowest possible resolution limit. In the presence of orientation dispersion, diffusion encoding sequences with square-wave oscillating gradients were optimal. The resolution limit for standard clinical MRI scanners (maximum gradient strength 60-80 mT/m) was found to be between 4 and 8 μm, depending on the noise levels and the level of orientation dispersion. For scanners with a maximum gradient strength of 300 mT/m, the limit was reduced to between 2 and 5 μm.

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.

Validation of surface-to-volume ratio measurements derived from oscillating gradient spin echo on a clinical scanner using anisotropic fiber phantoms

A diffusion measurement in the short-time surface-to-volume ratio (S/V) limit (Mitra et al., Phys Rev Lett. 1992;68:3555) can disentangle the free diffusion coefficient from geometric restrictions to diffusion. Biophysical parameters, such as the S/V of tissue membranes, can be used to estimate microscopic length scales non-invasively. However, due to gradient strength limitations on clinical MRI scanners, pulsed gradient spin echo (PGSE) measurements are impractical for probing the S/V limit. To achieve this limit on clinical systems, an oscillating gradient spin echo (OGSE) sequence was developed. Two phantoms containing 10 fiber bundles, each consisting of impermeable aligned fibers with different packing densities, were constructed to achieve a range of S/V values. The frequency-dependent diffusion coefficient, D(ω), was measured in each fiber bundle using OGSE with different gradient waveforms (cosine, stretched cosine, and trapezoidal), while D(t) was measured from PGSE and stimulated-echo measurements. The S/V values derived from the universal high-frequency behavior of D(ω) were compared against those derived from quantitative proton density measurements using single spin echo (SE) with varying echo times, and from magnetic resonance fingerprinting (MRF). S/V estimates derived from different OGSE waveforms were similar and demonstrated excellent correlation with both SE- and MRF-derived S/V measures (ρ  ≥  0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using teffS/V=9/64f, rather than the commonly used t_eff  = 1/(4f), validating the specific frequency/diffusion time conversion for this regime. Our well-characterized fiber phantom can be used for the calibration of OGSE and diffusion modeling techniques, as the S/V ratio can be measured independently using other MR modalities. Moreover, our calibration experiment offers an exciting perspective of mapping tissue S/V on clinical systems.

1D and 2D diffusion pore imaging on a preclinical MR system using adaptive rephasing: Feasibility and pulse sequence comparison

Diffusion pore imaging (DPI) has recently been proposed as a means to acquire images of the average pore shape in an image voxel or region of interest. The highly asymmetric gradient scheme of its sequence makes it substantially demanding in terms of the hardware of the NMR system. The aim of this work is to show the feasibility of DPI on a preclinical 9.4T animal scanner. Using water-filled capillaries with an inner radius of 10μm, four different variants of the DPI sequence were compared in 1D and 2D measurements. The pulse sequences applied cover the basic implementation using one long and one temporally narrow gradient pulse, a CPMG-like variant with multiple refocusing RF pulses as well as two variants splitting up the long gradient and distributing it on either side of the refocusing pulse. Substantial differences between the methods were found in terms of signal-to-noise ratio, contrast, blurring, deviations from the expected results and sensitivity to gradient imperfections. Each of the tested sequences was found to produce characteristic gradient mismatches dependent on the absolute value, direction and sign of the applied q-value. Read gradients were applied to compensate these mismatches translating them into time shifts, which enabled 1D DPI yielding capillary radius estimations within the tolerances specified by the manufacturer. For a successful DPI application in 2D, a novel gradient amplitude adaption scheme was implemented to correct for the occurring time shifts. Using this adaption, higher conformity to the expected pore shape, reduced blurring and enhanced contrast were achieved. Images of the phantom's pore shape could be acquired with a nominal resolution of 2.2μm.

Machine learning based compartment models with permeability for white matter microstructure imaging

Some microstructure parameters, such as permeability, remain elusive because mathematical models that express their relationship to the MR signal accurately are intractable. Here, we propose to use computational models learned from simulations to estimate these parameters. We demonstrate the approach in an example which estimates water residence time in brain white matter. The residence time τ_i of water inside axons is a potentially important biomarker for white matter pathologies of the human central nervous system, as myelin damage is hypothesised to affect axonal permeability, and thus τ_i. We construct a computational model using Monte Carlo simulations and machine learning (specifically here a random forest regressor) in order to learn a mapping between features derived from diffusion weighted MR signals and ground truth microstructure parameters, including τ_i. We test our numerical model using simulated and in vivo human brain data. Simulation results show that estimated parameters have strong correlations with the ground truth parameters (R²={0.88,0.95,0.82,0.99}) for volume fraction, residence time, axon radius and diffusivity respectively), and provide a marked improvement over the most widely used Kärger model (R²={0.75,0.60,0.11,0.99}). The trained model also estimates sensible microstructure parameters from in vivo human brain data acquired from healthy controls, matching values found in literature, and provides better reproducibility than the Kärger model on both the voxel and ROI level. Finally, we acquire data from two Multiple Sclerosis (MS) patients and compare to the values in healthy subjects. We find that in the splenium of corpus callosum (CC-S) the estimate of the residence time is 0.57±0.05s for the healthy subjects, while in the MS patient with a lesion in CC-S it is 0.33±0.12s in the normal appearing white matter (NAWM) and 0.19±0.11s in the lesion. In the corticospinal tracts (CST) the estimate of the residence time is 0.52±0.09s for the healthy subjects, while in the MS patient with a lesion in CST it is 0.56±0.05s in the NAWM and 0.13±0.09s in the lesion. These results agree with our expectations that the residence time in lesions would be lower than in NAWM because the loss of myelin should increase permeability. Overall, we find parameter estimates in the two MS patients consistent with expectations from the pathology of MS lesions demonstrating the clinical potential of this new technique.

Investigating white matter fibre density and morphology using fixel-based analysis

Voxel-based analysis of diffusion MRI data is increasingly popular. However, most white matter voxels contain contributions from multiple fibre populations (often referred to as crossing fibres), and therefore voxel-averaged quantitative measures (e.g. fractional anisotropy) are not fibre-specific and have poor interpretability. Using higher-order diffusion models, parameters related to fibre density can be extracted for individual fibre populations within each voxel ('fixels'), and recent advances in statistics enable the multi-subject analysis of such data. However, investigating within-voxel microscopic fibre density alone does not account for macroscopic differences in the white matter morphology (e.g. the calibre of a fibre bundle). In this work, we introduce a novel method to investigate the latter, which we call fixel-based morphometry (FBM). To obtain a more complete measure related to the total number of white matter axons, information from both within-voxel microscopic fibre density and macroscopic morphology must be combined. We therefore present the FBM method as an integral piece within a comprehensive fixel-based analysis framework to investigate measures of fibre density, fibre-bundle morphology (cross-section), and a combined measure of fibre density and cross-section. We performed simulations to demonstrate the proposed measures using various transformations of a numerical fibre bundle phantom. Finally, we provide an example of such an analysis by comparing a clinical patient group to a healthy control group, which demonstrates that all three measures provide distinct and complementary information. By capturing information from both sources, the combined fibre density and cross-section measure is likely to be more sensitive to certain pathologies and more directly interpretable.

Double oscillating diffusion encoding and sensitivity to microscopic anisotropy

Purpose

To introduce a novel diffusion pulse sequence, namely double oscillating diffusion encoding (DODE), and to investigate whether it adds sensitivity to microscopic diffusion anisotropy (µA) compared to the well‐established double diffusion encoding (DDE) methodology.

Methods

We simulate measurements from DODE and DDE sequences for different types of microstructures exhibiting restricted diffusion. First, we compare the effect of varying pulse sequence parameters on the DODE and DDE signal. Then, we analyse the sensitivity of the two sequences to the microstructural parameters (pore diameter and length) which determine µA. Finally, we investigate specificity of measurements to particular substrate configurations.

Results

Simulations show that DODE sequences exhibit similar signal dependence on the relative angle between the two gradients as DDE sequences, however, the effect of varying the mixing time is less pronounced. The sensitivity analysis shows that in substrates with elongated pores and various orientations, DODE sequences increase the sensitivity to pore diameter, while DDE sequences are more sensitive to pore length. Moreover, DDE and DODE sequence parameters can be tailored to enhance/suppress the signal from a particular range of substrates.

Conclusions

A combination of DODE and DDE sequences maximize sensitivity to µA, compared to using just the DDE method. Magn Reson Med 78:550–564, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Assessing the accuracy of using oscillating gradient spin echo sequences with AxCaliber to infer micron-sized axon diameters

OBJECTIVE

Current magnetic resonance imaging (MRI) axon diameter measurements rely on the pulsed gradient spin-echo sequence, which is unable to provide diffusion times short enough to measure small axon diameters. This study combines the AxCaliber axon diameter fitting method with data generated from Monte Carlo simulations of oscillating gradient spin-echo sequences (OGSE) to infer micron-sized axon diameters, in order to determine the feasibility of using MRI to infer smaller axon diameters in brain tissue.

MATERIALS AND METHODS

Monte Carlo computer simulation data were synthesized from tissue geometries of cylinders of different diameters using a range of gradient frequencies in the cosine OGSE sequence . Data were fitted to the AxCaliber method modified to allow the new pulse sequence. Intra- and extra-axonal water were studied separately and together.

RESULTS

The simulations revealed the extra-axonal model to be problematic. Rather than change the model, we found that restricting the range of gradient frequencies such that the measured apparent diffusion coefficient was constant over that range resulted in more accurate fitted diameters. Thus a careful selection of frequency ranges is needed for the AxCaliber method to correctly model extra-axonal water, or adaptations to the method are needed. This restriction helped reduce the necessary gradient strengths for measurements that could be performed with parameters feasible for a Bruker BG6 gradient set. For these experiments, the simulations inferred diameters as small as 0.5 μm on square-packed and randomly packed cylinders. The accuracy of the inferred diameters was found to be dependent on the signal-to-noise ratio (SNR), with smaller diameters more affected by noise, although all diameter distributions were distinguishable from one another for all SNRs tested.

CONCLUSION

The results of this study indicate the feasibility of using MRI with OGSE on preclinical scanners to infer small axon diameters.

Multi-compartment microscopic diffusion imaging

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay.

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.

The Effect of Microcirculatory Flow on Oscillating Gradient Diffusion MRI and Diffusion Encoding with Dual-Frequency Orthogonal Gradients (DEFOG)

PURPOSE

We investigated the effect of microcirculatory flow on oscillating gradient spin echo (OGSE) diffusion MRI at low b-values and developed a diffusion preparation method called diffusion encoding with dual-frequency orthogonal gradients (DEFOG) to suppress the effect.

METHODS

Compared to conventional OGSE sequences, DEFOG adds a pulsed gradient that is orthogonal to the oscillating gradient and has a moderate diffusion weighting (e.g., 300 s/mm² ). In vivo MRI data were acquired from adult mouse brains (n = 5) on an 11.7 Tesla scanner, with diffusion times from 23.2 to 0.83 ms and b-values from 50 to 700 s/mm² .

RESULTS

Apparent diffusion coefficients (ADCs) measured using a conventional OGSE sequence at low b-values (< 200 mm² /s) were significantly higher than those measured at moderate b-values (> 300 mm² /s), potentially due to contributions from microcirculatory flow. In comparison, OGSE ADCs measured using the DEFOG method at low b-values were comparable to those measured at moderate b-values. The effect of microcirculatory flow on diffusion signals was diffusion time-dependent, and this dependency may reflect the capillary geometry and blood flow velocity in the mouse cortex.

CONCLUSION

Microcirculatory flow affects OGSE diffusion MRI measurements at low b-values, and this effect can be suppressed using the DEFOG method. Magn Reson Med 77:1583-1592, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter

Axonal density and diameter are two fundamental properties of brain white matter. Recently, advanced diffusion MRI techniques have made these two parameters accessible in vivo. However, the techniques available to estimate such parameters are still under development. For example, current methods to map axonal diameters capture relative trends over different structures, but consistently over-estimate absolute diameters. Axonal density estimates are more accessible experimentally, but different modeling approaches exist and the impact of the experimental parameters has not been thoroughly quantified, potentially leading to incompatibility of results obtained in different studies using different techniques. Here, we characterise the impact of diffusion time on axonal density and diameter estimates using Monte Carlo simulations and STEAM diffusion MRI at 7 T on 9 healthy volunteers. We show that axonal density and diameter estimates strongly depend on diffusion time, with diameters almost invariably overestimated and density both over and underestimated for some commonly used models. Crucially, we also demonstrate that these biases are reduced when the model accounts for diffusion time dependency in the extra-axonal space. For axonal density estimates, both upward and downward bias in different situations are removed by modeling extra-axonal time-dependence, showing increased accuracy in these estimates. For axonal diameter estimates, we report increased accuracy in ground truth simulations and axonal diameter estimates decreased away from high values given by earlier models and towards known values in the human corpus callosum when modeling extra-axonal time-dependence. Axonal diameter feasibility under both advanced and clinical settings is discussed in the light of the proposed advances.