Temporal diffusion spectroscopy: theory and implementation in restricted systems using oscillating gradients

Restricted diffusion characteristics in oscillating gradient spin echo with mesoscopic phantom

In diffusion magnetic resonance imaging, oscillating gradient spin echo (OGSE) has an extremely short diffusion time if motion probing gradient (MPG) is applied to the waveform. Further, it can detect microstructural specificity. OGSE changes sensitivity to spin displacement velocity based on the MPG phase. The current study aimed to investigate the restricted diffusion characteristics of each OGSE waveform using the capillary phantom with various b-values, frequencies, and MPG phases. We performed OGSE (b-value = 300, 500, 800, 1200, 1600, and 2000 s/mm2) for the sine and cosine waveforms using the capillary phantom (6, 12, 25, 50, and 100 μm and free water) with a 9.4-T experimental magnetic resonance imaging system and a solenoid coil. We evaluated the axial and radial diffusivity (AD, RD) of each structure size. The output current of the MPG was assessed with an oscilloscope and analyzed with the gradient modulation power spectra by fast Fourier transform. In sine, the sidelobe spectrum was enhanced with increasing frequency, and the central spectrum slightly increased. The difference in RD was detected at 6 and 12 μm; however, it did not depend on the structure scale at 50 or 100 μm and free water. In cosine, the diffusion spectrum was enhanced, whereas the central spectrum decreased with increasing frequency. Both AD and RD in cosine had a frequency dependence, and AD and RD increased with a higher frequency regardless of structure size. AD and RD in either sine or cosine had no evident b-value dependence. We evaluated the OGSE-restricted diffusion characteristics. The measurements obtained diffusion information similar to the pulsed gradient spin echo. Hence, the cosine measurements indicated that a higher frequency could capture faster diffusion within the diffusion phenomena.

Revealing tumor microstructure with oscillating diffusion encoding MRI in pre-surgical and post-treatment glioma patients

PURPOSE

We hypothesized that the time-dependent diffusivity at short diffusion times, as measured by oscillating gradient spin echo (OGSE) diffusion MRI, can characterize tissue microstructures in glioma patients.

THEORY AND METHODS

Five adult patients with known diffuse glioma, including two pre-surgical and three with new enhancing lesions after treatment for high-grade glioma, were scanned in an ultra-high-performance gradient 3.0T MRI system. OGSE diffusion MRI at 30-100 Hz and pulsed gradient spin echo diffusion imaging (approximated as 0 Hz) were obtained. The ADC and trace-diffusion-weighted image at each acquired frequency were calculated, that is, ADC (f) and TraceDWI (f).

RESULTS

In pre-surgical patients, biopsy-confirmed solid enhancing tumor in a high-grade glioblastoma showed higherADC ( f ) ADC ( 0 Hz ) $$ \frac{\mathrm{ADC}\ (f)}{\mathrm{ADC}\ \left(0\ \mathrm{Hz}\right)} $$ and lowerTraceDWI ( f ) TraceDWI ( 0 Hz ) $$ \frac{\mathrm{TraceDWI}\ (f)}{\mathrm{TraceDWI}\ \left(0\ \mathrm{Hz}\right)} $$ , compared to that at same OGSE frequency in a low-grade astrocytoma. In post-treatment patients, the enhancing lesions of two patients who were diagnosed with tumor progression contained more voxels with highADC ( f ) ADC ( 0 Hz ) $$ \frac{\mathrm{ADC}\ (f)}{\mathrm{ADC}\ \left(0\ \mathrm{Hz}\right)} $$ and lowTraceDWI ( f ) TraceDWI ( 0 Hz ) $$ \frac{\mathrm{TraceDWI}\left(\mathrm{f}\right)}{\mathrm{TraceDWI}\left(0\ \mathrm{Hz}\right)} $$ , compared to the enhancing lesions of a patient who was diagnosed with treatment effect. Non-enhancing T2 signal abnormality lesions in both the pre-surgical high-grade glioblastoma and post-treatment tumor progressions showed regions with highADC ( f ) ADC ( 0 Hz ) $$ \frac{\mathrm{ADC}\ (f)}{\mathrm{ADC}\ \left(0\ \mathrm{Hz}\right)} $$ and lowTraceDWI ( f ) TraceDWI ( 0 Hz ) $$ \frac{\mathrm{TraceDWI}\ \left(\mathrm{f}\right)}{\mathrm{TraceDWI}\ \left(0\ \mathrm{Hz}\right)} $$ , consistent with infiltrative tumor. The solid tumor of the glioblastoma, the enhancing lesions of post-treatment tumor progressions, and the suspected infiltrative tumors showed high diffusion time-dependency from 30 to 100 Hz, consistent with high intra-tumoral volume fraction (cellular density).

CONCLUSION

Different characteristics of OGSE-based time-dependent diffusivity can reveal heterogenous tissue microstructures that indicate cellular density in glioma patients.

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.

Asymmetry in three-site relaxation exchange NMR

The asymmetry of peak integrals in 2D relaxation maps of exchange between three sites indicates circular flow between the relaxation sites. This disagrees with the detailed balance according to which the exchange between any pair of sites must be balanced in terms of thermodynamic equilibrium. Confined diffusion of particles jumping randomly on a 2D checkerboard grid to any of their eight neighbor positions and confined gas diffusion were modeled in Monte Carlo simulations to explore the impact of topological constraints on particle exchange between three pools. Both models produce density variations across the pore and reveal that up to 1 % of the molecules move in circular paths between the relaxation pools. This motion is driven by different features of either algorithm. It is silent in terms of thermodynamic equilibrium, confirming that multi-site exchange maps are symmetric in this case. The coherent flux is argued to result from stochastic pore resonance related to diffusion eigenmodes. If it can be driven experimentally by external time-varying electric, magnetic, or ultrasonic fields, this may be a way to enhance heterogeneous catalysis.

Fourier transform temporal diffusion spectroscopy

Temporal diffusion spectroscopy (TDS) currently uses the oscillating gradient spin echo (OGSE) experiment to measure the spectral density of translational velocity autocorrelation at single frequencies. Due to timing restrictions imposed by the transverse relaxation, the frequency selectivity and the sampling density of OGSE are limited, especially at low frequencies. We propose to overcome this problem by adopting the principles of Fourier transform spectroscopy. The new method of Fourier transform TDS (FTDS) uses two broadband gradient waveforms with different relative delays to make the spin echo attenuation sensitive to a broad range of diffusion frequencies with different harmonic modulations and calculates the spectrum by discrete Fourier transform. The method was validated by a measurement of diffusion spectra in highly restrictive tissues of a celery stalk and provided results consistent with OGSE, however, on a denser frequency grid.

A new perspective of molecular diffusion by nuclear magnetic resonance

The diffusion-weighted NMR signal acquired using Pulse Field Gradient (PFG) techniques, allows for extrapolating microstructural information from porous materials and biological tissues. In recent years there has been a multiplication of diffusion models expressed by parametric functions to fit the experimental data. However, clear-cut criteria for the model selection are lacking. In this paper, we develop a theoretical framework for the interpretation of NMR attenuation signals in the case of Gaussian systems with stationary increments. The full expression of the Stejskal-Tanner formula for normal diffusing systems is devised, together with its extension to the domain of anomalous diffusion. The range of applicability of the relevant parametric functions to fit the PFG data can be fully determined by means of appropriate checks to ascertain the correctness of the fit. Furthermore, the exact expression for diffusion weighted NMR signals pertaining to Brownian yet non-Gaussian processes is also derived, accompanied by the proper check to establish its contextual relevance. The analysis provided is particularly useful in the context of medical MRI and clinical practise where the hardware limitations do not allow the use of narrow pulse gradients.

IMPULSED model based cytological feature estimation with U-Net: Application to human brain tumor at 3T

PURPOSE

This work introduces and validates a deep-learning-based fitting method, which can rapidly provide accurate and robust estimation of cytological features of brain tumor based on the IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) model fitting with diffusion-weighted MRI data.

METHODS

The U-Net was applied to rapidly quantify extracellular diffusion coefficient (D_ex ), cell size (d), and intracellular volume fraction (v_in ) of brain tumor. At the training stage, the image-based training data, synthesized by randomizing quantifiable microstructural parameters within specific ranges, was used to train U-Net. At the test stage, the pre-trained U-Net was applied to estimate the microstructural parameters from simulated data and the in vivo data acquired on patients at 3T. The U-Net was compared with conventional non-linear least-squares (NLLS) fitting in simulations in terms of estimation accuracy and precision.

RESULTS

Our results confirm that the proposed method yields better fidelity in simulations and is more robust to noise than the NLLS fitting. For in vivo data, the U-Net yields obvious quality improvement in parameter maps, and the estimations of all parameters are in good agreement with the NLLS fitting. Moreover, our method is several orders of magnitude faster than the NLLS fitting (from about 5 min to <1 s).

CONCLUSION

The image-based training scheme proposed herein helps to improve the quality of the estimated parameters. Our deep-learning-based fitting method can estimate the cell microstructural parameters fast and accurately.

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.

Axon diameter inferences in the human corpus callosum using oscillating gradient spin echo sequences

Previous methods used to infer axon diameter distributions using magnetic resonance imaging (MRI) primarily use single diffusion encoding sequences such as pulsed gradient spin echo (PGSE) and are thus sensitive to axons of diameters >5 μm. We applied oscillating gradient spin echo (OGSE) sequences to study human axons in the 1-2 μm range in the corpus callosum, which include the majority of axons constituting cortical connections. The ActiveAx model was applied to calculate the fitted mean effective diameter for axons (AxD) and was compared with values found using histology. Axon diameters from histological data were calculated using three different datasets; true diameters (minimum diameter), a combination of minimum and maximum diameters, and diameters measured across a consistent diffusion direction. The AxD estimates from MRI were 1.8 ± 0.1 μm to 2.34 ± 0.04 μm with an average of 2.0 ± 0.2 μm for the ActiveAx model. The histology AxD values were 1.43 ± 0.02 μm when using the true minimum axon diameters, 5.52 ± 0.02 μm when using the combination of minimum and maximum axon diameters, and 2.20 ± 0.02 μm when collecting measurements across a consistent diffusion direction. This experiment demonstrates the first known usage of OGSE to calculate axon diameters in the human corpus callosum on a 1-2 μm scale. The importance for the model to account for axonal orientation dispersion is indicated by histological results which more closely match the MRI model results depending on the direction of axon diameter measurements. These initial steps using this non-invasive imaging method can be applied to future methodology to develop in vivo axon diameter measurements in human brain tissue.

Diffusion-Weighted Imaging: Recent Advances and Applications

Quantitative diffusion imaging techniques enable the characterization of tissue microstructural properties of the human brain "in vivo", and are widely used in neuroscientific and clinical contexts. In this review, we present the basic physical principles behind diffusion imaging and provide an overview of the current diffusion techniques, including standard and advanced techniques as well as their main clinical applications. Standard diffusion tensor imaging (DTI) offers sensitivity to changes in microstructure due to diseases and enables the characterization of single fiber distributions within a voxel as well as diffusion anisotropy. Nonetheless, its inability to represent complex intravoxel fiber topologies and the limited biological specificity of its metrics motivated the development of several advanced diffusion MRI techniques. For example, high-angular resolution diffusion imaging (HARDI) techniques enabled the characterization of fiber crossing areas and other complex fiber topologies in a single voxel and supported the development of higher-order signal representations aiming to decompose the diffusion MRI signal into distinct microstructure compartments. Biophysical models, often known by their acronym (e.g., CHARMED, WMTI, NODDI, DBSI, DIAMOND) contributed to capture the diffusion properties from each of such tissue compartments, enabling the computation of voxel-wise maps of axonal density and/or morphology that hold promise as clinically viable biomarkers in several neurological and neuroscientific applications; for example, to quantify tissue alterations due to disease or healthy processes. Current challenges and limitations of state-of-the-art models are discussed, including validation efforts. Finally, novel diffusion encoding approaches (e.g., b-tensor or double diffusion encoding) may increase the biological specificity of diffusion metrics towards intra-voxel diffusion heterogeneity in clinical settings, holding promise in neurological applications.

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.

Diffusion Tensor Imaging of Skeletal Muscle Contraction Using Oscillating Gradient Spin Echo

Diffusion tensor imaging (DTI) measures water diffusion in skeletal muscle tissue and allows for muscle assessment in a broad range of neuromuscular diseases. However, current DTI measurements, typically performed using pulsed gradient spin echo (PGSE) diffusion encoding, are limited to the assessment of non-contracted musculature, therefore providing limited insight into muscle contraction mechanisms and contraction abnormalities. In this study, we propose the use of an oscillating gradient spin echo (OGSE) diffusion encoding strategy for DTI measurements to mitigate the effect of signal voids in contracted muscle and to obtain reliable diffusivity values. Two OGSE sequences with encoding frequencies of 25 and 50 Hz were tested in the lower leg of five healthy volunteers with relaxed musculature and during active dorsiflexion and plantarflexion, and compared with a conventional PGSE approach. A significant reduction of areas of signal voids using OGSE compared with PGSE was observed in the tibialis anterior for the scans obtained in active dorsiflexion and in the soleus during active plantarflexion. The use of PGSE sequences led to unrealistically elevated axial diffusivity values in the tibialis anterior during dorsiflexion and in the soleus during plantarflexion, while the corresponding values obtained using the OGSE sequences were significantly reduced. Similar findings were seen for radial diffusivity, with significantly higher diffusivity measured in plantarflexion in the soleus muscle using the PGSE sequence. Our preliminary results indicate that DTI with OGSE diffusion encoding is feasible in human musculature and allows to quantitatively assess diffusion properties in actively contracting skeletal muscle. OGSE holds great potential to assess microstructural changes occurring in the skeletal muscle during contraction, and for non-invasive assessment of contraction abnormalities in patients with muscle diseases.

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.

Double diffusion encoding and applications for biomedical imaging

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

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.

Sequential Diffusion Spectra as a Tool for Studying Time-Dependent Translational Molecular Dynamics: A Cement Hydration Study

The translational molecular dynamics in porous materials are affected by the presence of the porous structure that presents an obstacle for diffusing molecules in longer time scales, but not as much in shorter time scales. The characteristic time scales have equivalent frequency ranges of molecular dynamics, where longer time scales correspond to lower frequencies while the shorter time scales correspond to higher frequencies of molecular dynamics. In this study, a novel method for direct measurement of diffusion at a given frequency of translational molecular dynamics is exploited to measure the diffusion spectra, i.e., distribution of diffusion in a wide range of frequencies. This method utilizes NMR modulated gradient spin-echo (MGSE) pulse sequence to measure the signal attenuation during the train of spin-echoes formed in the presence of a constant gradient. From attenuation, the diffusion coefficient at the frequency equal to the inverse double inter-echo time is calculated. The method was employed to study the white cement hydration process by the sequential acquisition of the diffusion spectra. The measured spectra were also analyzed by the diffusion spectra model to obtain the time-dependence of the best-fit model parameters. The presented method can also be applied to study other similar systems with the time evolution of porous structure.

Comparison of pulsed and oscillating gradient diffusion-weighted MRI for characterizing hepatocellular nodules in liver cirrhosis: ex vivo study in a rat model

BACKGROUND

In contrast to classical pulsed gradient diffusion-weighted MRI, oscillating gradient diffusion-weighted MR imaging (DWI) is sensitive to short distance diffusion changes at the intracellular level.

PURPOSE

To compare the diagnostic performance of pulsed and oscillating DWI for characterizing hepatocellular nodules in a rat model of hepatic cirrhosis.

STUDY TYPE

Prospective, experimental study.

ANIMAL MODEL

Cirrhosis was induced by weekly intraperitoneal injection of diethylnitrosamine in Wistar rats.

FIELD STRENGTH/SEQUENCE

Ex vivo liver MRI was performed at 7T with T₁ -weighted, T₂ -weighted, pulsed, and oscillating gradient diffusion-weighted sequences.

ASSESSMENT

Apparent diffusion coefficient from pulsed (ADC_pulsed ) and oscillating gradient (ADC_oscillating ) sequences was calculated in 82 nodules identified on the T₁ /T₂ -weighted images and on pathological examination. Two pathologists classified the nodules in three categories: benign (regenerative and low-grade dysplastic nodules), with intermediate malignancy (high-grade dysplastic nodules and early hepatocellular carcinomas) and overtly malignant (progressed hepatocellular carcinomas).

STATISTICAL TESTS

Differences between groups were assessed with Kruskal-Wallis and Mann-Whitney tests.

RESULTS

ADC, mainly ADC_oscillating , increased in the group of nodules with intermediate malignancy (ADC_pulsed : 0.75 ± 0.25 × 10^-3 mm² /s vs. 0.64 ± 0.07 × 10^-3 mm² /s in benign nodules, P = 0.025; ADC_oscillating : 0.81 ± 0.20 × 10^-3 mm² /s vs. 0.65 ± 0.13 × 10^-3 mm² /s, P = 0.0008) and ADC_pulsed decreased in the group of progressed hepatocellular carcinomas (ADC_pulsed : 0.60 ± 0.08 × 10^-3 mm² /s, P = 0.042; ADC_oscillating : 0.68 ± 0.08 × 10^-3 mm² /s, P = 0.1).

DATA CONCLUSION

ADC during hepatocarcinogenesis in rats increased in nodules with intermediate malignancy and decreased in progressed hepatocellular carcinomas. Our results suggest that oscillating gradient DWI is more sensitive to the early steps of hepatocarcinogenesis and might be useful for differentiating between high-grade dysplastic nodules / early hepatocellular carcinomas and regenerating nodules / low-grade dysplastic nodules.

LEVEL OF EVIDENCE

2 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2020;51:1065-1074.

Oscillating-gradient diffusion magnetic resonance imaging detects acute subcellular structural changes in the mouse forebrain after neonatal hypoxia-ischemia

The recently developed oscillating-gradient diffusion MRI (OG-dMRI) technique extends our ability to examine brain structures at different spatial scales. In this study, we investigated the sensitivity of OG-dMRI in detecting cellular and subcellular structural changes in a mouse model of neonatal hypoxia ischemia (HI). Neonatal mice received unilateral HI injury or sham injury at postnatal day 10, followed by in vivo T₂-weighted and diffusion MRI of the brains at 3-6 h and 24 h after HI. Apparent diffusion coefficient (ADC) maps were acquired using conventional pulsed-gradient dMRI (PG-dMRI) and OG-dMRI with oscillating frequencies from 50 to 200 Hz. Pathology at cellular and subcellular levels was evaluated using neuronal, glial, and mitochondrial markers. We found significantly higher rates of ADC increase with oscillating frequencies (Δ_fADC) in the ipsilateral edema region, compared to the contralateral side, starting as early as 3 h after HI. Even in injured regions that showed no apparent change in PG-ADC or pseudo-normalized PG-ADC measurements, Δ_fADC remained significantly elevated. Histopathology showed swelling of sub-cellular structures in these regions with no apparent whole-cell level change. These results suggest that OG-dMRI is sensitive to subcellular structural changes in the brain after HI and is less susceptible to pseudo-normalization than PG-dMRI.

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.

Inferring diameters of spheres and cylinders using interstitial water

OBJECT

Most early methods to infer axon diameter distributions using magnetic resonance imaging (MRI) used single diffusion encoding sequences such as pulsed gradient spin echo (SE) and are thus sensitive to axons of diameters > 5 μm. We previously simulated oscillating gradient (OG) SE sequences for diffusion spectroscopy to study smaller axons including the majority constituting cortical connections. That study suggested the model of constant extra-axonal diffusion breaks down at OG accessible frequencies. In this study we present data from phantoms to test a time-varying interstitial apparent diffusion coefficient.

MATERIALS AND METHODS

Diffusion spectra were measured in four samples from water packed around beads of diameters 3, 6 and 10 μm; and 151 μm diameter tubes. Surface-to-volume ratios, and diameters were inferred.

RESULTS

The bead pore radii estimates were 0.60±0.08 μm, 0.54±0.06 μm and 1.0±0.1 μm corresponding to bead diameters ranging from 2.9±0.4 μm to 5.3±0.7 μm, 2.6±0.3 μm to 4.8±0.6 μm, and 4.9±0.7 μm to 9±1 μm. The tube surface-to-volume ratio estimate was 0.06±0.02 μm^-1 corresponding to a tube diameter of 180±70 μm.

CONCLUSION

Interstitial models with OG inferred 3-10 μm bead diameters from 0.54±0.06 μm to 1.0±0.1 μm pore radii and 151 μm tube diameters from 0.06±0.02 μm^-1 surface-to-volume ratios.

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.

Presence of time-dependent diffusion in the brachial plexus

PURPOSE

This work describes the development of a method to measure the variation of apparent diffusion coefficient (ADC) with diffusion time (Δ) in the brachial plexus, as a potential method of probing microstructure.

METHODS

Diffusion-weighted MRI with body signal suppression was used to highlight the nerves from surrounding tissues, and sequence parameters were optimized for sensitivity to change with diffusion time. A porous media-restricted diffusion model based on the Latour-Mitra equation was fitted to the diffusion time-dependent ADC data from the brachial plexus nerves and cord.

RESULTS

The ADC was observed to reduce at long diffusion times, confirming that diffusion was restricted in the nerves and cord in healthy subjects. T2 of the nerves was measured to be 80 ± 5 ms, the diffusion coefficient was found to vary from (1.5 ± 0.1) × 10^-3 mm² /s at a diffusion time of 18.3 ms to (1.0 ± 0.2) × 10^-3 mm² /s at a diffusion time of 81.3 ms.

CONCLUSION

A novel method of probing restricted diffusion in the brachial plexus was developed. Resulting parameters were comparable with values obtained previously on biological systems. Magn Reson Med 79:789-795, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

In vivo diffusion MRS investigation of non-water molecules in biological tissues

Diffusion MRS of non-water molecules offers great potential in directly revealing various tissue microstructures and physiology at both cellular and subcellular levels. In brain, ¹ H diffusion MRS has been demonstrated as a new tool for probing normal tissue microstructures and their pathological changes. In skeletal muscle, ¹ H diffusion MRS could characterize slow and restricted intramyocellular lipid diffusion, providing a sensitive marker for metabolic alterations, while ³¹ P diffusion MRS can measure ATP and PCr diffusion, which may reflect the capacity of cellular energy transport, complementing the information from frequently used ³¹ P MRS in muscle. In intervertebral disk, ¹ H diffusion MRS can directly monitor extracellular matrix integrity by quantifying the mobility of macromolecules such as proteoglycans and collagens. In tumor tissue, ¹³ C diffusion MRS could probe intracellular glycolytic metabolism, while ¹ H diffusion MRS may separate the spectrally overlapped lactate and lipid resonances. In this review, recent diffusion MRS studies of these biologically relevant non-water molecules under normal and diseased conditions will be presented. Technical considerations for diffusion MRS experiments will be discussed. With advances in MRI hardware and diffusion methodology, diffusion MRS of non-water molecules is expected to provide increasingly valuable and biologically specific information on tissue microstructures and physiology, complementing the traditional diffusion MRI of small and ubiquitous water molecules. Copyright © 2016 John Wiley & Sons, Ltd.

Probing metabolite diffusion at ultra-short time scales in the mouse brain using optimized oscillating gradients and "short"-echo-time diffusion-weighted MRS

Measuring diffusion at ultra-short time scales may yield information about short-range intracellular structure and cytosol viscosity. However, reaching such time scales usually requires oscillating gradients, which in turn imply long echo times T_E . Here we propose a new kind of stretched oscillating gradient that allows us to increase diffusion-weighting b while preserving spectral and temporal properties of the gradient modulation. We used these optimized gradients to measure metabolite diffusion in the mouse brain down to effective diffusion times of 1 ms while keeping T_E relatively short (60 ms). At such T_E , a significant macromolecule signal could still be observed and used as an internal reference of approximately null diffusivity, which proved critical to discard datasets corrupted by some motion artifact. The methods introduced here may be useful to improve the accuracy and precision of metabolite apparent diffusion coefficient measurements with oscillating gradients.

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.

Effects of off-resonance spins on the performance of the modulated gradient spin echo sequence

Translational molecular dynamics in various materials can also be studied by diffusion spectra. These can be measured by a constant gradient variant of the modulated gradient spin echo (MGSE) sequence which is composed of a CPMG RF pulse train superimposed to a constant magnetic field gradient. The application of the RF train makes the effective gradient oscillating thus enabling measurements of diffusion spectra in a wide range of frequencies. However, seemingly straightforward implementation of the MGSE sequence proved to be complicated and can give overestimated results for diffusion if not interpreted correctly. In this study, unrestricted diffusion in water and other characteristic materials was analyzed by the MGSE sequence in the frequency range 50-3000Hz using a 6T/m diffusion probe. First, it was shown that the MGSE echo train acquired from the entire sample decays faster than the train acquired only from a narrow band at zero frequency of the sample. Then, it was shown that the decay rate is dependent on the band's off-resonance characterized by the ratio Δω0/ω1 and that with higher off-resonances the decay is faster. The faster decay therefore corresponds to a higher diffusion coefficient if the diffusion is calculated using standard Stejskal-Tanner formula. The result can be explained by complex coherence pathways contributing to the MGSE echo signals when |Δω0|/ω1>0. In a magnetic field gradient, all the pathways are more diffusion attenuated than the direct coherence pathway and therefore decay faster, which leads to an overestimation of the diffusion coefficient. A solution to this problem was found in an efficient off-resonance signal reduction by using only zero frequency filtered MGSE echo train signals.

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.

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.

Structural information revealed by the dispersion of ADC with frequency

Diffusion MRI provides a non-invasive means to characterize tissue microstructure at varying length scales. Temporal diffusion spectra reveal how the apparent diffusion coefficient (ADC) varies with frequency. When measured using oscillating gradient spin echo sequences, the manner in which ADC disperses with gradient frequency (which is related to the reciprocal of diffusion time) provides information on the characteristic dimensions of restricting structures within the medium. For example, the dispersion of ADC with oscillating gradient frequency (ΔfADC) has been shown to correlate with axon sizes in white matter and provide novel tissue contrast in images of mouse hippocampus and cerebellum. However, despite increasing interest in applying frequency-dependent ADC to derive novel information on tissue, the interpretations of ADC spectra are not always clear. In this study, the relation between ADC spectra and restricting dimensions are further elucidated and used to derive novel image contrast related to the sizes of intrinsic microstructures.

Diffusion-weighted imaging in cancer: physical foundations and applications of restriction spectrum imaging

Diffusion-weighted imaging (DWI) has been at the forefront of cancer imaging since the early 2000s. Before its application in clinical oncology, this powerful technique had already achieved widespread recognition due to its utility in the diagnosis of cerebral infarction. Following this initial success, the ability of DWI to detect inherent tissue contrast began to be exploited in the field of oncology. Although the initial oncologic applications for tumor detection and characterization, assessing treatment response, and predicting survival were primarily in the field of neurooncology, the scope of DWI has since broadened to include oncologic imaging of the prostate gland, breast, and liver. Despite its growing success and application, misconceptions about the underlying physical basis of the DWI signal exist among researchers and clinicians alike. In this review, we provide a detailed explanation of the biophysical basis of diffusion contrast, emphasizing the difference between hindered and restricted diffusion, and elucidating how diffusion parameters in tissue are derived from the measurements via the diffusion model. We describe one advanced DWI modeling technique, called restriction spectrum imaging (RSI). This technique offers a more direct in vivo measure of tumor cells, due to its ability to distinguish separable pools of water within tissue based on their intrinsic diffusion characteristics. Using RSI as an example, we then highlight the ability of advanced DWI techniques to address key clinical challenges in neurooncology, including improved tumor conspicuity, distinguishing actual response to therapy from pseudoresponse, and delineation of white matter tracts in regions of peritumoral edema. We also discuss how RSI, combined with new methods for correction of spatial distortions inherent in diffusion MRI scans, may enable more precise spatial targeting of lesions, with implications for radiation oncology and surgical planning. See all articles in this Cancer Research section, "Physics in Cancer Research."

Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy

Mapping mean axon diameter and intra-axonal volume fraction may have significant clinical potential because nerve conduction velocity is directly dependent on axon diameter, and several neurodegenerative diseases affect axons of specific sizes and alter axon counts. Diffusion-weighted MRI methods based on the pulsed gradient spin echo (PGSE) sequence have been reported to be able to assess axon diameter and volume fraction non-invasively. However, due to the relatively long diffusion times used, e.g. >20ms, the sensitivity to small axons (diameter<2μm) is low, and the derived mean axon diameter has been reported to be overestimated. In the current study, oscillating gradient spin echo (OGSE) diffusion sequences with variable frequency gradients were used to assess rat spinal white matter tracts with relatively short effective diffusion times (1-5ms). In contrast to previous PGSE-based methods, the extra-axonal diffusion cannot be modeled as hindered (Gaussian) diffusion when short diffusion times are used. Appropriate frequency-dependent rates are therefore incorporated into our analysis and validated by histology-based computer simulation of water diffusion. OGSE data were analyzed to derive mean axon diameters and intra-axonal volume fractions of rat spinal white matter tracts (mean axon diameter of ~1.27-5.54μm). The estimated values were in good agreement with histology, including the small axon diameters (<2.5μm). This study establishes a framework for the quantification of nerve morphology using the OGSE method with high sensitivity to small axons.

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.

Fast and robust measurement of microstructural dimensions using temporal diffusion spectroscopy

Mapping axon sizes non-invasively is of interest for neuroscientists and may have significant clinical potential because nerve conduction velocity is directly dependent on axon size. Current approaches to measuring axon sizes using diffusion-weighted MRI, e.g. q-space imaging with pulsed gradient spin echo (PGSE) sequences usually require long scan times and high q-values to detect small axons (diameter <2μm). The oscillating gradient spin echo (OGSE) method has been shown to be able to achieve very short diffusion times and hence may be able to detect smaller axons with high sensitivity. In the current study, OGSE experiments were performed to measure the inner diameters of hollow microcapillaries with a range of sizes (∼1.5-19.3μm) that mimic axons in the human central nervous system. The results suggest that OGSE measurements, even with only moderately high frequencies, are highly sensitive to compartment sizes, and a minimum of two ADC values with different frequencies may be sufficient to extract the microcapillary size accurately. This suggests that the OGSE method may serve as a fast and robust measurement method for mapping axon sizes non-invasively.

Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo (NOGSE) NMR

Noninvasive measurements of microstructure in materials, cells, and in biological tissues, constitute a unique capability of gradient-assisted NMR. Diffusion-diffraction MR approaches pioneered by Callaghan demonstrated this ability; Oscillating-Gradient Spin-Echo (OGSE) methodologies tackle the demanding gradient amplitudes required for observing diffraction patterns by utilizing constant-frequency oscillating gradient pairs that probe the diffusion spectrum, D(ω). Here we present a new class of diffusion MR experiments, termed Non-uniform Oscillating-Gradient Spin-Echo (NOGSE), which dynamically probe multiple frequencies of the diffusion spectral density at once, thus affording direct microstructural information on the compartment's dimension. The NOGSE methodology applies N constant-amplitude gradient oscillations; N-1 of these oscillations are spaced by a characteristic time x, followed by a single gradient oscillation characterized by a time y, such that the diffusion dynamics is probed while keeping (N-1)x+y≡TNOGSE constant. These constant-time, fixed-gradient-amplitude, multi-frequency attributes render NOGSE particularly useful for probing small compartment dimensions with relatively weak gradients - alleviating difficulties associated with probing D(ω) frequency-by-frequency or with varying relaxation weightings, as in other diffusion-monitoring experiments. Analytical descriptions of the NOGSE signal are given, and the sequence's ability to extract small compartment sizes with a sensitivity towards length to the sixth power, is demonstrated using a microstructural phantom. Excellent agreement between theory and experiments was evidenced even upon applying weak gradient amplitudes. An MR imaging version of NOGSE was also implemented in ex vivo pig spinal cords and mouse brains, affording maps based on compartment sizes. The effects of size distributions on NOGSE are also briefly analyzed.

Imaging neurodegeneration in the mouse hippocampus after neonatal hypoxia-ischemia using oscillating gradient diffusion MRI

PURPOSE

To investigate if frequency-dependent contrasts using oscillating gradient diffusion MRI (dMRI) can detect hypoxia-ischemia (HI) -induced neurodegeneration in the neonatal mouse hippocampus.

METHODS

Pulsed- and oscillating-gradient dMR images (at 50, 100, and 150 Hz) were acquired from postmortem fixed brains of mice exposed to neonatal HI using the Rice-Vanucci model. MRI data were acquired at 1, 4, and 8 days following HI, and compared with histological data from the same mice for in situ histological validation of the MRI findings.

RESULTS

The rate of change of apparent diffusion coefficient with gradient frequency (Δf ADC) revealed unique layer-specific contrasts in the neonatal mouse hippocampus. Δf ADC measurements were found to show a significant decrease in response to neonatal HI injury, in the pyramidal (Py) and granule (GrDG) cell layers compared with contralateral regions. The areas of reduced intensity in the Δf ADC maps corresponded to regional neurodegeneration seen with H&E and Fluoro-Jade C stainings, indicating that alterations in Δf ADC contrasts are sensitive to early microstructural changes due to HI-induced neurodegeneration in the studied regions.

CONCLUSION

The findings show that the frequency-dependence of ADC measurements with oscillating-gradient dMRI can provide a sensitive contrast to detect HI-induced neurodegeneration in neuronal layers of the neonatal mouse hippocampus.

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.