Surface-to-volume ratio with oscillating gradients

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

Diffusion time dependency of extracellular diffusion

PURPOSE

To quantify the variations of the power-law dependences on diffusion time t or gradient frequencyf $$ f $$ of extracellular water diffusion measured by diffusion MRI (dMRI).

METHODS

Model cellular systems containing only extracellular water were used to investigate thet / f $$ t/f $$ dependence ofD ex $$ {D}_{ex} $$ , the extracellular diffusion coefficient. Computer simulations used a randomly packed tissue model with realistic intracellular volume fractions and cell sizes. DMRI measurements were performed on samples consisting of liposomes containing heavy water(D2 O, deuterium oxide) dispersed in regular water (H2 O).D ex $$ {D}_{ex} $$ was obtained over a broadt $$ t $$ range (∼1-1000 ms) and then fit power-law equationsD ex ( t ) = D const + const · t - ϑ t $$ {D}_{ex}(t)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {t}^{-{\vartheta}_t} $$ andD ex ( f ) = D const + const · f ϑ f $$ {D}_{ex}(f)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {f}^{\vartheta_f} $$ .

RESULTS

Both simulated and experimental results suggest that no single power-law adequately describes the behavior ofD ex $$ {D}_{ex} $$ over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limitedt $$ t $$ ranges; for example,θ t = θ f = - 1 2 $$ {\theta}_t={\theta}_f=-\frac{1}{2} $$ is valid only for short times, whereasθ t = 1 $$ {\theta}_t=1 $$ orθ f = 3 2 $$ {\theta}_f=\frac{3}{2} $$ is valid only for long times but cannot describe other ranges simultaneously. For the specifict $$ t $$ range of 5-70 ms used in typical human dMRI measurements,θ t = θ f = 1 $$ {\theta}_t={\theta}_f=1 $$ matches the data well empirically.

CONCLUSION

The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or longt $$ t $$ limits cannot be applied to typical dMRI measurements in human cancer or liver. It is essential to determine the appropriate diffusion time range when modeling extracellular diffusion in dMRI-based quantitative microstructural imaging.

Tuned bipolar oscillating gradients for mapping frequency dispersion of diffusion kurtosis in the human brain

PURPOSE

Oscillating gradient spin-echo (OGSE) sequences have demonstrated an ability to probe time-dependent microstructural features, although they often suffer from low SNR due to increased TEs. In this work we introduce frequency-tuned bipolar (FTB) gradients as a variation of oscillating gradients with reduced TE and demonstrate their utility by mapping the frequency dispersion of kurtosis in human subjects.

METHODS

An FTB oscillating gradient waveform is presented that provides encoding of 1.5 net oscillation periods, thereby reducing the TE of the acquisition. Simulations were performed to determine an optimal protocol based on the SNR of kurtosis frequency dispersion-defined as the difference in kurtosis between pulsed and oscillating gradient acquisitions. Healthy human subjects were scanned at 7T using pulsed gradient and an optimized 23 Hz FTB protocol, which featured a maximum b-value of 2500 s/mm² . In addition, to directly compare existing methods, measurements using traditional cosine OGSE were also acquired.

RESULTS

FTB oscillating gradients demonstrated equivalent frequency-dependent diffusion measurements compared with cosine-modulated OGSE while enabling a significant reduction in TE. Optimization and in vivo results suggest that FTB gradients provide increased SNR of kurtosis dispersion maps compared with traditional cosine OGSE. The optimized FTB gradient protocol demonstrated consistent reductions in apparent kurtosis values and increased diffusivity in generated frequency dispersion maps.

CONCLUSIONS

This work presents an alternative to traditional cosine OGSE sequences, enabling more time-efficient acquisitions of frequency-dependent diffusion quantities as demonstrated through in vivo kurtosis frequency dispersion maps.

Rat Brain Global Ischemia-Induced Diffusion Changes Revisited: Biophysical Modeling of the Water and NAA MR "Diffusion Signal"

PURPOSE

To assess changes in intracellular diffusion as a mechanism for the reduction in water ADC that accompanies brain injury. Using NAA as a marker of neuronal cytoplasmic diffusion, NAA diffusion was measured before and after global ischemia (immediately postmortem) in the female Sprague-Dawley rat.

METHODS

Diffusion-weighted PRESS spectra, with diffusion encoding in a single direction, were acquired from large voxels of rat brain gray matter in vivo and postischemia employing either pairs of pulsed half-sine-shaped gradients (in vivo and postischemia, b_max  = 19 ms/μm² ) or sinusoidal oscillating gradients (in vivo only) with frequencies of 99.2-250 Hz. A 2D randomly oriented cylinder (neurite) model gave estimates of longitudinal and transverse diffusivities (D_L and D_T , respectively). In this model, D_L represents the "free" diffusivity of NAA, whereas D_T reflects highly restricted diffusion. Using oscillating gradients, the frequency dependence of D_T [D_T (ω)] gave estimates of the cylinder (axon/dendrite) radius.

RESULTS

A 10% decrease in D_L,NAA followed global ischemia, dropping from 0.391 ± 0.012 μm² /ms to 0.350 ± 0.009 μm² /ms. Modeling D_T,NAA (ω) provided an estimate of the neurite radius of 1.0 ± 0.6 μm.

CONCLUSION

Whereas the increase in apparent intraneuronal viscosity suggested by changes in D_L,NAA may contribute to the overall reduction in water ADC associated with brain injury, it is not sufficient to be the sole explanation. Estimates of neurite radius based on D_T (ω) were consistent with literature values.

Combined diffusion-relaxometry microstructure imaging: Current status and future prospects

Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, T 1 , T 2 , and T 2 ∗ . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.

Feasibility of oscillating and pulsed gradient diffusion MRI to assess neonatal hypoxia-ischemia on clinical systems

Diffusion-time- (t_d) dependent diffusion MRI (dMRI) extends our ability to characterize brain microstructure by measuring dMRI signals at varying t_d. The use of oscillating gradient (OG) is essential for accessing short t_d but is technically challenging on clinical MRI systems. This study aims to investigate the clinical feasibility and value of t_d-dependent dMRI in neonatal hypoxic-ischemic encephalopathy (HIE). Eighteen HIE neonates and six normal term-born neonates were scanned on a 3 T scanner, with OG-dMRI at an oscillating frequency of 33 Hz (equivalent t_d ≈ 7.5 ms) and pulsed gradient (PG)-dMRI at a t_d of 82.8 ms and b-value of 700 s/mm². The t_d-dependence, as quantified by the difference in apparent diffusivity coefficients between OG- and PG-dMRI (ΔADC), was observed in the normal neonatal brains, and the ΔADC was higher in the subcortical white matter than the deep grey matter. In HIE neonates with severe and moderate injury, ΔADC significantly increased in the basal ganglia (BG) compared to the controls (23.7% and 10.6%, respectively). In contrast, the conventional PG-ADC showed a 12.6% reduction only in the severe HIE group. White matter edema regions also demonstrated increased ΔADC, where PG-ADC did not show apparent changes. Our result demonstrated that t_d-dependent dMRI provided high sensitivity in detecting moderate-to-severe HIE.

Oscillating-gradient spin-echo diffusion-weighted imaging (OGSE-DWI) with a limited number of oscillations: I. Signal equation

The oscillating-gradient spin-echo (OGSE) sequence has been promoted as a promising diffusion-weighted magnetic resonance imaging (DWI) technique for probing in vivo tissue microstructure in the frequency domain. However, due to practical restrictions on the duration and number of oscillations that a motion-probing gradient can have, the technique has limited spectral resolution and range. This work re-examines the OGSE-DWI method to clarify how these limitations are reflected in the signal model. There are several aspects of the revised framework that distinguish it from the conventional description employed for OGSE DWI. In particular, while the conventional OGSE signal model implies that the spectral density of molecular diffusion may be directly sampled in experiments, in practice information about the spectral density can be only indirectly obtained.

Time-dependent diffusion MRI probes cerebellar microstructural alterations in a mouse model of Down syndrome

The cerebellum is a complex system with distinct cortical laminar organization. Alterations in cerebellar microstructure are common and associated with many factors such as genetics, cancer and ageing. Diffusion MRI (dMRI) provides a non-invasive tool to map the brain structural organization, and the recently proposed diffusion-time (td )-dependent dMRI further improves its capability to probe the cellular and axonal/dendritic microstructures by measuring water diffusion at multiple spatial scales. The td -dependent diffusion profile in the cerebellum and its utility in detecting cerebellar disorders, however, are not yet elucidated. Here, we first deciphered the spatial correspondence between dMRI contrast and cerebellar layers, based on which the cerebellar layer-specific td -dependent dMRI patterns were characterized in both euploid and Ts65Dn mice, a mouse model of Down syndrome. Using oscillating gradient dMRI, which accesses diffusion at short td 's by modulating the oscillating frequency, we detected subtle changes in the apparent diffusivity coefficient of the cerebellar internal granular layer and Purkinje cell layer of Ts65Dn mice that were not detectable by conventional pulsed gradient dMRI. The detection sensitivity of oscillating gradient dMRI increased with the oscillating frequency at both the neonatal and adult stages. The td -dependence, quantified by ΔADC map, was reduced in Ts65Dn mice, likely associated with the reduced granule cell density and abnormal dendritic arborization of Purkinje cells as revealed from histological evidence. Our study demonstrates superior sensitivity of short-td diffusion using oscillating gradient dMRI to detect cerebellar microstructural changes in Down syndrome, suggesting the potential application of this technique in cerebellar disorders.

A single-shot measurement of time-dependent diffusion over sub-millisecond timescales using static field gradient NMR

Time-dependent diffusion behavior is probed over sub-millisecond timescales in a single shot using a nuclear magnetic resonance static gradient time-incremented echo train acquisition (SG-TIETA) framework. The method extends the Carr-Purcell-Meiboom-Gill cycle under a static field gradient by discretely incrementing the π-pulse spacings to simultaneously avoid off-resonance effects and probe a range of timescales (50-500 µs). Pulse spacings are optimized based on a derived ruleset. The remaining effects of pulse inaccuracy are examined and found to be consistent across pure liquids of different diffusivities: water, decane, and octanol-1. A pulse accuracy correction is developed. Instantaneous diffusivity, Dinst(t), curves (i.e., half of the time derivative of the mean-squared displacement in the gradient direction) are recovered from pulse accuracy-corrected SG-TIETA decays using a model-free log-linear least squares inversion method validated by Monte Carlo simulations. A signal-averaged 1-min experiment is described. A flat Dinst(t) is measured on pure dodecamethylcyclohexasiloxane, whereas decreasing Dinst(t) is measured on yeast suspensions, consistent with the expected short-time Dinst(t) behavior for confining microstructural barriers on the order of micrometers.

Probing neural tissues at small scales: Recent progress of oscillating gradient spin echo (OGSE) neuroimaging in humans

The detection sensitivity of diffusion MRI (dMRI) is dependent on diffusion times. A shorter diffusion time can increase the sensitivity to smaller length scales. However, the conventional dMRI uses the pulse gradient spin echo (PGSE) sequence that probes relatively long diffusion times only. To overcome this, the oscillating gradient spin echo (OGSE) sequence has been developed to probe much shorter diffusion times with hardware limitations on preclinical and clinical MRI systems. The OGSE sequence has been previously used on preclinical animal MRI systems. Recently, several studies have translated the OGSE sequence to humans on clinical MRI systems and achieved new information that is invisible using conventional PGSE sequence. This paper provides an overview of the recent progress of the OGSE neuroimaging in humans, including the technical improvements in the translation of the OGSE sequence to human imaging and various applications in different neurological disorders and stroke. Some possible future directions of the OGSE sequence are also discussed.

Microstructure with diffusion MRI: what scale we are sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructure MRI (μMRI) aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal-Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

The impact of realistic axonal shape on axon diameter estimation using diffusion MRI

To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D_⊥(t) and kurtosis K_⊥(t), to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D_⊥(t) is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K_⊥∣_t→∞ deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.

Diffusion-prepared 3D gradient spin-echo sequence for improved oscillating gradient diffusion MRI

PURPOSE

Oscillating gradient (OG) enables the access of short diffusion times for time-dependent diffusion MRI (dMRI); however, it poses several technical challenges for clinical use. This study proposes a 3D oscillating gradient-prepared gradient spin-echo (OGprep-GRASE) sequence to improve SNR and shorten acquisition time for OG dMRI on clinical scanners.

METHODS

The 3D OGprep-GRASE sequence consisted of global saturation, diffusion encoding, fat saturation, and GRASE readout modules. Multiplexed sensitivity-encoding reconstruction was used to correct the phase errors between multiple shots. We compared the scan time and SNR of the proposed sequence and the conventional 2D-EPI sequence for OG dMRI at 30-90-mm slice coverage. We also examined the time-dependent diffusivity changes with OG dMRI acquired at frequencies of 50 Hz and 25 Hz and pulsed-gradient dMRI at diffusion times of 30 ms and 60 ms.

RESULTS

The OGprep-GRASE sequence reduced the scan time by a factor of 1.38, and increased the SNR by 1.74-2.27 times compared with 2D EPI for relatively thick slice coverage (60-90 mm). The SNR gain led to improved diffusion-tensor reconstruction in the multishot protocols. Image distortion in 2D-EPI images was also reduced in GRASE images. Diffusivity measurements from the pulsed-gradient dMRI and OG dMRI showed clear diffusion-time dependency in the white matter and gray matter of the human brain, using both the GRASE and EPI sequences.

CONCLUSION

The 3D OGprep-GRASE sequence improved scan time and SNR and reduced image distortion compared with the 2D multislice acquisition for OG dMRI on a 3T clinical system, which may facilitate the clinical translation of time-dependent dMRI.

Diffusion-time dependence of diffusional kurtosis in the mouse brain

PURPOSE

To investigate diffusion-time dependency of diffusional kurtosis in the mouse brain using pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE) sequences.

METHODS

3D PGSE and OGSE kurtosis tensor data were acquired from ex vivo brains of adult, cuprizone-treated, and age-matched control mice with diffusion-time (t_D ) ~ 20 ms and frequency (f) = 70 Hz, respectively. Further, 2D acquisitions were performed at multiple times/frequencies ranging from f = 140 Hz to t_D = 30 ms with b-values up to 4000 s/mm² . Monte Carlo simulations were used to investigate the coupled effects of varying restriction size and permeability on time/frequency-dependence of kurtosis with both diffusion-encoding schemes. Simulations and experiments were further performed to investigate the effect of varying number of cycles in OGSE waveforms.

RESULTS

Kurtosis and diffusivity maps exhibited significant region-specific changes with diffusion time/frequency across both gray and white matter areas. PGSE- and OGSE-based kurtosis maps showed reversed contrast between gray matter regions in the cerebellar and cerebral cortex. Localized time/frequency-dependent changes in kurtosis tensor metrics were found in the splenium of the corpus callosum in cuprizone-treated mouse brains, corresponding to regional demyelination seen with histological assessment. Monte Carlo simulations showed that kurtosis estimates with pulsed- and oscillating-gradient waveforms differ in their sensitivity to exchange. Both simulations and experiments showed dependence of kurtosis on number of cycles in OGSE waveforms for non-zero permeability.

CONCLUSION

The results show significant time/frequency-dependency of diffusional kurtosis in the mouse brain, which can provide sensitivity to probe intrinsic cellular heterogeneity and pathological alterations in gray and white matter.

Diffusion dispersion imaging: Mapping oscillating gradient spin-echo frequency dependence in the human brain

PURPOSE

Oscillating gradient spin-echo (OGSE) diffusion MRI provides information about the microstructure of biological tissues by means of the frequency dependence of the apparent diffusion coefficient (ADC). ADC dependence on OGSE frequency has been explored in numerous rodent studies, but applications in the human brain have been limited and have suffered from low contrast between different frequencies, long scan times, and a limited exploration of the nature of the ADC dependence on frequency.

THEORY AND METHODS

Multiple frequency OGSE acquisitions were acquired in healthy subjects at 7T to explore the power-law frequency dependence of ADC, the "diffusion dispersion." Furthermore, a method for optimizing the estimation of the ADC difference between different OGSE frequencies was developed, which enabled the design of a highly efficient protocol for mapping diffusion dispersion.

RESULTS

For the first time, evidence of a linear dependence of ADC on the square root of frequency in healthy human white matter was obtained. Using the optimized protocol, high-quality, full-brain maps of apparent diffusion dispersion rate were also demonstrated at an isotropic resolution of 2 mm in a scan time of 6 min.

CONCLUSIONS

This work sheds light on the nature of diffusion dispersion in the healthy human brain and introduces full-brain diffusion dispersion mapping at clinically relevant scan times. These advances may lead to new biomarkers of pathology or improved microstructural modeling.

Probing Surface-to-Volume Ratio of an Anisotropic Medium by Diffusion NMR with General Gradient Encoding

Since the seminal paper by Mitra et al., diffusion MR has been widely used in order to estimate surface-to-volume ratios. In this paper, we generalize Mitra's formula for arbitrary diffusion encoding waveforms, including recently developed q-space trajectory encoding sequences. We show that the surface-to-volume ratio can be significantly misestimated using the original Mitra's formula without taking into account the applied gradient profile. In order to obtain more accurate estimation in anisotropic samples, we propose an efficient and robust optimization algorithm to design diffusion gradient waveforms with prescribed features. Our results are supported by Monte Carlo simulations.

Evidence of the diffusion time dependence of intravoxel incoherent motion in the brain

PURPOSE

To investigate the diffusion time (T_D ) dependence of intravoxel incoherent motion (IVIM) signals in the brain.

METHODS

A 3-compartment IVIM model was proposed to characterize 2 types of microcirculatory flows in addition to tissue water in the brain: flows that cross multiple vascular segments (pseudo-diffusive) and flows that stay in 1 segment (ballistic) within T_D . The model was first evaluated using simulated flow signals. Experimentally, flow-compensated (FC) pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE) sequences were tested using a flow phantom and then used to examine IVIM signals in the mouse brain with T_D ranging from ~2.5 ms to 40 ms on an 11.7T scanner.

RESULTS

By fitting the model to simulated flow signals, we demonstrated the T_D dependency of the estimated fraction of pseudo-diffusive flow and the pseudo-diffusion coefficient (D*), which were dictated by the characteristic timescale of microcirculatory flow (τ). Flow phantom experiments validated that the OGSE and FC-PGSE sequences were not susceptible to the change in flow velocity. In vivo mouse brain data showed that both the estimated fraction of pseudo-diffusive flow and D* increased significantly as T_D increased.

CONCLUSION

We demonstrated that IVIM signals measured in the brain are T_D -dependent, potentially because more microcirculatory flows approach the pseudo-diffusive limit as T_D increases with respect to τ. Measuring the T_D dependency of IVIM signals may provide additional information on microvascular flows in the brain.

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.

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.

Concise derivation of oscillating-gradient-derived ADC

The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion-sensitizing gradients in the high-frequency regime. We provide a concise derivation of the analytical expression for the ADC for an arbitrary number of gradient oscillations N and initial phase φ. It is demonstrated that an ultimate goal - to determine the surface-to-volume ratio (S/V) from MR measurements by using oscillating gradients - can be achieved with cosine-type gradients (φ = 0) for an arbitrary N. However, to determine S/V employing gradients with φ ≠ 0 (including the sine-type gradients) and arbitrary N additionally requires prior knowledge of the time-dependent diffusion coefficient D(t). The latter is rarely known a priori but can be estimated under certain limiting conditions: (i) in the short time regime, when the total diffusion time of the measurements, t, is smaller than the characteristic diffusion time of the microstructural system of interest, an analytical expression for D(t) is available (Mitra's expression) and this allows S/V to be determined in the short time regime with sine-type gradients; (ii) in the important case of purely restricted diffusion, D(t) → 0 at sufficiently long time, the signal becomes independent of φ and behaves as for the cosine-type gradients, thus, allowing determination of S/V.

Effects of mesoscopic susceptibility and transverse relaxation on diffusion NMR

Measuring molecular diffusion is based on the spatial encoding of spin-carrying molecules using external Larmor frequency gradients. Intrinsic variations of the Larmor frequency and of the local relaxation rate, commonly present in structurally complex samples, interfere with the external gradients, confounding the NMR-measured diffusion propagator. Here we consider, analytically and numerically, the effects of the mesoscopic magnetic structure (local susceptibility and transverse relaxation rate) on the NMR-measured "apparent" diffusion coefficient (ADC). We show that in the fast diffusion regime, when molecules spread past the correlation length of the magnetic structure, the deviation of ADC from the genuine diffusion coefficient increases as a power law of diffusion time. The effect of mesoscopically varying transverse relaxation rate is sequence-independent and always leads to the decrease of ADC with time, whereas the effect sign for the mesoscopic Larmor frequency variations depends on the presence of refocussing pulses in the diffusion sequence. We connect this unexpectedly diverging with time ADC discrepancy to the spatial statistics of the mesocopic magnetic structure. Our results establish a novel kind of NMR contrast tied to the microstructural complexity, and can be applied to discern the mesoscopic effects of hindrances to molecular diffusion, susceptibility variations, and varying local relaxation rate, on the measured diffusion propagator. In particular, we numerically show that the susceptibility effect of a microvascular network is sufficient to explain the observed ADC decrease due to superparamagnetic iron-oxide contrast injection in monkeys.

Oscillating gradient diffusion kurtosis imaging of normal and injured mouse brains

Recent advances in diffusion MRI employ multiple diffusion encoding schemes with varying diffusion direction, weighting, and diffusion time to investigate specific microstructural properties in biological tissues. In this study, we examined time-dependent diffusion kurtosis contrast in adult mouse brains and in neonatal mouse brains after hypoxic-ischemic (HI) injury. In vivo diffusion kurtosis maps were acquired with a short diffusion time using an oscillating gradient spin echo (OGSE) sequence at 100 Hz and with a relatively long diffusion time (20 ms) using a pulsed gradient spin echo (PGSE) sequence. In the adult mouse brain, we found that the cortex and hippocampus showed larger differences between OGSE kurtosis and PGSE kurtosis than major white matter tracts. In neonatal mouse brains with unilateral HI injury, the OGSE kurtosis map overall provided stronger edema contrast than the PGSE kurtosis map, and the differences between OGSE and PGSE kurtosis measurements in the edema region reflected heterogeneity of injury. This is the first in vivo study that has demonstrated multi-direction OGSE kurtosis contrasts in the mouse brain. Comparing PGSE and OGSE kurtosis measures may provide additional information on microstructural changes after ischemic stroke.

On modeling

Mapping tissue microstructure with MRI holds great promise as a noninvasive window into tissue organization at the cellular level. Having originated within the realm of diffusion NMR in the late 1970s, this field is experiencing an exponential growth in the number of publications. At the same time, model-based approaches are also increasingly incorporated into advanced MRI acquisition and reconstruction techniques. However, after about two decades of intellectual and financial investment, microstructural mapping has yet to find a single commonly accepted clinical application. Here, we suggest that slow progress in clinical translation may signify unresolved fundamental problems. We outline such problems and related practical pitfalls, as well as review strategies for developing and validating tissue microstructure models, to provoke a discussion on how to bridge the gap between our scientific aspirations and the clinical reality. We argue for recalibrating the efforts of our community toward a more systematic focus on fundamental research aimed at identifying relevant degrees of freedom affecting the measured MR signal. Such a focus is essential for realizing the truly revolutionary potential of noninvasive three-dimensional in vivo microstructural mapping.

Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue

Molecular diffusion measured with diffusion weighted MRI (DWI) offers a probe for tissue microstructure. However, inferring microstructural properties from conventional DWI data is a complex inverse problem and has to account for heterogeneity in sizes, shapes and orientations of the tissue compartments contained within an imaging voxel. Alternative experimental means for disentangling the signal signatures of such features could provide a stronger link between the data and its interpretation. Double diffusion encoding (DDE) offers the possibility to factor out variation in compartment shapes from orientational dispersion of anisotropic domains by measuring the correlation between diffusivity in multiple directions. Time dependence of the diffusion is another effect reflecting the dimensions and distributions of barriers. In this paper we extend on DDE with a modified version of the oscillating gradient spin echo (OGSE) experiment, giving a basic contrast mechanism closely linked to both the temporal diffusion spectrum and the compartment anisotropy. We demonstrate our new method on post mortem brain tissue and show that we retrieve the correct temporal diffusion tensor spectrum in synthetic data from Monte Carlo simulations of random walks in a range of disordered geometries of different sizes and shapes.

Brain Metabolite Diffusion from Ultra-Short to Ultra-Long Time Scales: What Do We Learn, Where Should We Go?

In vivo diffusion-weighted MR spectroscopy (DW-MRS) allows measuring diffusion properties of brain metabolites. Unlike water, most metabolites are confined within cells. Hence, their diffusion is expected to purely reflect intracellular properties, opening unique possibilities to use metabolites as specific probes to explore cellular organization and structure. However, interpretation and modeling of DW-MRS, and more generally of intracellular diffusion, remains difficult. In this perspective paper, we will focus on the study of the time-dependency of brain metabolite apparent diffusion coefficient (ADC). We will see how measuring ADC over several orders of magnitude of diffusion times, from less than 1 ms to more than 1 s, allows clarifying our understanding of brain metabolite diffusion, by firmly establishing that metabolites are neither massively transported by active mechanisms nor massively confined in subcellular compartments or cell bodies. Metabolites appear to be instead diffusing in long fibers typical of neurons and glial cells such as astrocytes. Furthermore, we will evoke modeling of ADC time-dependency to evaluate the effect of, and possibly quantify, some structural parameters at various spatial scales, departing from a simple model of hollow cylinders and introducing additional complexity, either short-ranged (such as dendritic spines) or long-ranged (such as cellular fibers ramification). Finally, we will discuss the experimental feasibility and expected benefits of extending the range of diffusion times toward even shorter and longer values.

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

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

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.

Fundamentals of diffusion MRI physics

Diffusion MRI is commonly considered the "engine" for probing the cellular structure of living biological tissues. The difficulty of this task is threefold. First, in structurally heterogeneous media, diffusion is related to structure in quite a complicated way. The challenge of finding diffusion metrics for a given structure is equivalent to other problems in physics that have been known for over a century. Second, in most cases the MRI signal is related to diffusion in an indirect way dependent on the measurement technique used. Third, finding the cellular structure given the MRI signal is an ill-posed inverse problem. This paper reviews well-established knowledge that forms the basis for responding to the first two challenges. The inverse problem is briefly discussed and the reader is warned about a number of pitfalls on the way.

Pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE) in mouse gliomas

Solid tumor microstructure is related to the aggressiveness of the tumor, interstitial pressure and drug delivery pathways, which are closely associated with treatment response, metastatic spread and prognosis. In this study, we introduce a novel diffusion MRI data analysis framework, pulsed and oscillating gradient MRI for assessment of cell size and extracellular space (POMACE), and demonstrate its feasibility in a mouse tumor model. In vivo and ex vivo POMACE experiments were performed on mice bearing the GL261 murine glioma model (n = 8). Since the complete diffusion time dependence is in general non-analytical, the tumor microstructure was modeled in an appropriate time/frequency regime by impermeable spheres (radius Rcell , intracellular diffusivity Dics ) surrounded by extracellular space (ECS) (approximated by constant apparent diffusivity Decs in volume fraction ECS). POMACE parametric maps (ECS, Rcell , Dics , Decs ) were compared with conventional diffusion-weighted imaging metrics, electron microscopy (EM), alternative ECS determination based on effective medium theory (EMT), and optical microscopy performed on the same samples. It was shown that Decs can be approximated by its long time tortuosity limit in the range [1/(88 Hz)-31 ms]. ECS estimations (44 ± 7% in vivo and 54 ± 11% ex vivo) were in agreement with EMT-based ECS and literature on brain gliomas. Ex vivo, ECS maps correlated well with optical microscopy. Cell sizes (Rcell  = 4.8 ± 1.3 in vivo and 4.3 ± 1.4 µm ex vivo) were consistent with EM measurements (4.7 ± 1.8 µm). In conclusion, Rcell and ECS can be quantified and mapped in vivo and ex vivo in brain tumors using the proposed POMACE method. Our experimental results support the view that POMACE provides a way to interpret the frequency or time dependence of the diffusion coefficient in tumors in terms of objective biophysical parameters of neuronal tissue, which can be used for non-invasive monitoring of preclinical cancer studies and treatment efficacy. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry

The time-dependent apparent diffusion coefficient as measured by pulsed gradient NMR can be used to estimate parameters of porous structures including the surface-to-volume ratio and the mean curvature of pores. In this work, the short-time diffusion limit and in particular the influence of the temporal profile of diffusion gradients on the expansion as proposed by Mitra et al. (1993) is investigated. It is shown that flow-compensated waveforms, i.e. those whose first moment is zero, are blind to the term linear in observation time, which is the term that is proportional to mean curvature and surface permeability. A gradient waveform that smoothly interpolates between flow-compensated and bipolar waveform is proposed and the degree of flow-compensation is used as a second experimental dimension. This two-dimensional ansatz is shown to yield an improved precision when characterizing the confining domain. This technique is demonstrated with simulations and in experiments performed with cylindrical capillaries of 100 μm radius.

Surface-to-volume ratio mapping of tumor microstructure using oscillating gradient diffusion weighted imaging

PURPOSE

To disentangle the free diffusivity (D0 ) and cellular membrane restrictions, by means of their surface-to-volume ratio (S/V), using the frequency-dependence of the diffusion coefficient D(ω), measured in brain tumors in the short diffusion-time regime using oscillating gradients (OGSE).

METHODS

In vivo and ex vivo OGSE experiments were performed on mice bearing the GL261 murine glioma model (n = 10) to identify the relevant time/frequency (t/ω) domain where D(ω) linearly decreases with ω(-1/2) . Parametric maps (S/V, D0 ) are compared with conventional DWI metrics. The impact of frequency range and temperature (20°C versus 37°C) on S/V and D0 is investigated ex vivo.

RESULTS

The validity of the short diffusion-time regime is demonstrated in vivo and ex vivo. Ex vivo measurements confirm that the purely geometric restrictions embodied in S/V are independent from temperature and frequency range, while the temperature dependence of the free diffusivity D0 is similar to that of pure water.

CONCLUSION

Our results suggest that D(ω) in the short diffusion-time regime can be used to uncouple the purely geometric restriction effect, such as S/V, from the intrinsic medium diffusivity properties, and provides a nonempirical and objective way to interpret frequency/time-dependent diffusion changes in tumors in terms of objective biophysical tissue parameters. Magn Reson Med 76:237-247, 2016. © 2015 Wiley Periodicals, Inc.

Mesoscopic structure of neuronal tracts from time-dependent diffusion

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (ln t)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the asymptotically linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques.

Oscillating gradient diffusion MRI reveals unique microstructural information in normal and hypoxia-ischemia injured mouse brains

PURPOSE

We investigated whether oscillating gradient diffusion MRI (dMRI) can provide information on brain microstructural changes after formaldehyde fixation and after hypoxic-ischemic (HI) injury beyond that provided by conventional dMRI.

METHODS

Pulsed gradient spin echo (PGSE) and oscillating gradient spin echo (OGSE) dMRI of the adult mouse brain was performed in vivo (50-200 Hz, b = 600 mm(2)/s), and a similar protocol was applied to neonatal mouse brains at 24 h after unilateral hypoxia-ischemia. Animals were perfusion fixed with 4% paraformaldehyde for ex vivo dMRI and histology.

RESULTS

Apparent diffusion coefficients (ADCs) measured in the live adult mouse brain presented tissue-dependent frequency-dependence. In vivo OGSE-ADC maps at high oscillating frequencies (>100 Hz) showed clear contrast between the molecular layer and granule cell layer in the adult mouse cerebellum. Formaldehyde fixation significantly altered the temporal diffusion spectra in several brain regions. In neonatal mouse brains with HI injury, in vivo ADC measurements from edema regions showed diminished edema contrasts at 200 Hz compared with the PGSE results. Histology showed severe tissue swelling and necrosis in the edema regions.

CONCLUSION

The results demonstrate the unique ability of OGSE-dMRI in delineating tissue microstructures at different spatial scales.

A model for extra-axonal diffusion spectra with frequency-dependent restriction

PURPOSE

In the brain, there is growing interest in using the temporal diffusion spectrum to characterize axonal geometry in white matter because of the potential to be more sensitive to small pores compared to conventional time-dependent diffusion. However, analytical expressions for the diffusion spectrum of particles have only been derived for simple, restricting geometries such as cylinders, which are often used as a model for intra-axonal diffusion. The extra-axonal space is more complex, but the diffusion spectrum has largely not been modeled. We propose a model for the extra-axonal space, which can be used for interpretation of experimental data.

THEORY AND METHODS

An empirical model describing the extra-axonal space diffusion spectrum was compared with simulated spectra. Spectra were simulated using Monte Carlo methods for idealized, regularly and randomly packed axons over a wide range of packing densities and spatial scales. The model parameters are related to the microstructural properties of tortuosity, axonal radius, and separation for regularly packed axons and pore size for randomly packed axons.

RESULTS

Forward model predictions closely matched simulations. The model fitted the simulated spectra well and accurately estimated microstructural properties.

CONCLUSIONS

This simple model provides expressions that relate the diffusion spectrum to biologically relevant microstructural properties.

Revealing mesoscopic structural universality with diffusion

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

Exact analytical results for ADC with oscillating diffusion sensitizing gradients

The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion sensitizing gradients. Exact analytical expressions are obtained in the high-frequency expansion of the ADC for an arbitrary number of oscillations N. These expressions are universal and valid for arbitrary system geometry. The validity conditions of the high-frequency expansion of ADC are obtained in the framework of a simple 1D model of restricted diffusion. These conditions are shown to be substantially different for cos- and sin-type gradients: for the cos-type gradients, the high-frequency expansion is valid when the period of a single oscillation is smaller than the characteristic diffusion time, the frequency dependence of ADC being practically the same for any N. In contrast, for the sin-type gradients, the high-frequency regime can be achieved only when the total diffusion time is smaller than the characteristic diffusion time, the frequency dependence of ADC being different for different N.

In vivo investigation of restricted diffusion in the human brain with optimized oscillating diffusion gradient encoding

PURPOSE

Previous studies in phantoms and animals using animal MR systems have shown promising results in using oscillating gradient spin echo (OGSE) diffusion acquisition to depict microstructure information. The OGSE approach has also been shown to be a sensitive biomarker of tumor treatment response and white matter-related diseases. Translating these studies to a human MR scanner faces multiple challenges due to the much weaker gradient system. The goals of this study are to optimize the OGSE acquisition for a human MR system and investigate its applicability in the in vivo human brain.

METHODS

An analytical analysis of the OGSE modulation spectrum was provided. Based on this analysis and thorough simulation experiments, the OGSE acquisition was optimized in terms of diffusion waveform shape, waveform timing, and sequence timing-to achieve higher diffusion sensitivity and better sampling of the diffusion spectrum.

RESULTS

The trapezoid-cosine waveform was found to be the optimal OGSE waveform. At the three employed peak encoding frequencies of 18 Hz, 44 Hz, and 63 Hz, the waveform polarity for the least blurry sampling of the diffusion spectrum was 90+/180-, 90+/180+, and 90+/180+, respectively. For the highest diffusion-to-noise ratio at 63 Hz, the b-value was 200 s/mm(2) and the echo time was 116 ms. Using the optimized sequence, a frequency dependence of the measured apparent diffusion coefficients was observed in white matter-dominant regions such as the corpus callosum.

CONCLUSION

The obtained results demonstrate, for the first time, the potential of using an OGSE acquisition for investigating microstructure information on a human MR system.

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.

Random walk with barriers

Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented membranes (d - 1 dimensional planes in d dimensions) and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence for any d. Its origin lies in the strong structural fluctuations introduced by the spatially extended random restrictions, representing a novel universality class of the structural disorder. Our results agree well with Monte Carlo simulations in two dimensions. They can be used to identify permeable barriers as restrictions to transport, and to quantify their permeability and surface area.