Diffusion MRI with pulsed and free gradient waveforms: Effects of restricted diffusion and exchange

Diffusion MRI with double diffusion encoding and variable mixing times disentangles water exchange from transient kurtosis

Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic kurtosis. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the transient kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as tMGE (MGE incorporating transient kurtosis) that accounts for both effects by exploiting the distinct signatures of exchange and transient kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while transient kurtosis arguably has a much faster dependence. We find that applying tMGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may enable estimation of the exchange rate as well as isotropic, anisotropic, and transient kurtosis.

Revealing membrane integrity and cell size from diffusion kurtosis time dependence

PURPOSE

The nonmonotonic dependence of diffusion kurtosis on diffusion time has been observed in biological tissues, yet its relation to membrane integrity and cellular geometry remains to be clarified. Here we establish and explain the characteristic asymmetric shape of the kurtosis peak. We also derive the relation between the peak timet peak $$ {t}_{\mathrm{peak}} $$ , when kurtosis reaches its maximum, and tissue parameters.

METHODS

The peak shape and its positiont peak $$ {t}_{\mathrm{peak}} $$ qualitatively follow from the adiabatic extension of the Kärger model onto the case of intra-cellular diffusivity time-dependence. This intuition is corroborated by the effective medium theory-based calculation, as well as by Monte Carlo simulations of diffusion and exchange in randomly and densely packed spheres for various values of permeability, cell fractions and sizes, and intrinsic diffusivity.

RESULTS

We establish thatt peak $$ {t}_{\mathrm{peak}} $$ is proportional to the geometric mean of two characteristic time scales: extra-cellular correlation time (determined by cell size) and intra-cellular residence time (determined by membrane permeability). When exchange is barrier-limited, the peak shape approaches a universal scaling form determined by the ratiot / t peak $$ t/{t}_{\mathrm{peak}} $$ .

CONCLUSION

Numerical simulations and theory provide an interpretation of a specific feature of kurtosis time-dependence, offering a potential biomarker for in vivo evaluation of pathology by disentangling the functional (permeability) and structural (cell size) integrity in tissues. This is relevant as the time-dependent diffusion cumulants are sensitive to pathological changes in membrane integrity and cellular structure in diseases, such as ischemic stroke, tumors, and Alzheimer's disease.

Assessing tumor microstructure with time-dependent diffusion imaging: Considerations and feasibility on clinical MRI and MRI-Linac

BACKGROUND

Quantitative imaging biomarkers (QIBs) can characterize tumor heterogeneity and provide information for biological guidance in radiotherapy (RT). Time-dependent diffusion MRI (TDD-MRI) derived parameters are promising QIBs, as they describe tissue microstructure with more specificity than traditional diffusion-weighted MRI (DW-MRI). Specifically, TDD-MRI can provide information about both restricted diffusion and diffusional exchange, which are the two time-dependent effects affecting diffusion in tissue, and relevant in tumors. However, exhaustive modeling of both effects can require long acquisitions and complex model fitting. Furthermore, several introduced TDD-MRI measurements can require high gradient strengths and/or complex gradient waveforms that are possibly not available in RT settings.

PURPOSE

In this study, we investigated the feasibility of a simple analysis framework for the detection of restricted diffusion and diffusional exchange effects in the TDD-MRI signal. To promote the clinical applicability, we use standard gradient waveforms on a conventional 1.5 T MRI system with moderate gradient strength (Gmax = 45 mT/m), and on a hybrid 1.5 T MRI-Linac system with low gradient strength (Gmax = 15 mT/m).

METHODS

Restricted diffusion and diffusional exchange were simulated in geometries mimicking tumor microstructure to investigate the DW-MRI signal behavior and to determine optimal experimental parameters. TDD-MRI was implemented using pulsed field gradient spin echo with the optimized parameters on a conventional MRI system and a MRI-Linac. Experiments in green asparagus and 10 patients with brain lesions were performed to evaluate the time-dependent diffusion (TDD) contrast in the source DW-images.

RESULTS

Simulations demonstrated how the TDD contrast was able to differentiate only dominating diffusional exchange in smaller cells from dominating restricted diffusion in larger cells. The maximal TDD contrast in simulations with typical cancer cell sizes and in asparagus measurements exceeded 5% on the conventional MRI but remained below 5% on the MRI-Linac. In particular, the simulated TDD contrast in typical cancer cell sizes (r = 5-10 µm) remained below or around 2% with the MRI-Linac gradient strength. In patients measured with the conventional MRI, we found sub-regions reflecting either dominating restricted diffusion or dominating diffusional exchange in and around brain lesions compared to the noisy appearing white matter.

CONCLUSIONS

On the conventional MRI system, the TDD contrast maps showed consistent tumor sub-regions indicating different dominating TDD effects, potentially providing information on the spatial tumor heterogeneity. On the MRI-Linac, the available TDD contrast measured in asparagus showed the same trends as with the conventional MRI but remained close to typical measurement noise levels when simulated in common cancer cell sizes. On conventional MRI systems with moderate gradient strengths, the TDD contrast could potentially be used as a tool to identify which time-dependent effects to include when choosing a biophysical model for more specific tumor characterization.

Tuned exchange imaging: Can the filter exchange imaging pulse sequence be adapted for applications with thin slices and restricted diffusion?

Filter exchange imaging (FEXI) is a double diffusion-encoding (DDE) sequence that is specifically sensitive to exchange between sites with different apparent diffusivities. FEXI uses a diffusion-encoding filtering block followed by a detection block at varying mixing times to map the exchange rate. Long mixing times enhance the sensitivity to exchange, but they pose challenges for imaging applications that require a stimulated echo sequence with crusher gradients. Thin imaging slices require strong crushers, which can introduce significant diffusion weighting and bias exchange rate estimates. Here, we treat the crushers as an additional encoding block and consider FEXI as a triple diffusion-encoding sequence. This allows the bias to be corrected in the case of multi-Gaussian diffusion, but not easily in the presence of restricted diffusion. Our approach addresses challenges in the presence of restricted diffusion and relies on the ability to independently gauge sensitivities to exchange and restricted diffusion for arbitrary gradient waveforms. It follows two principles: (i) the effects of crushers are included in the forward model using signal cumulant expansion; and (ii) timing parameters of diffusion gradients in filter and detection blocks are adjusted to maintain the same level of restriction encoding regardless of the mixing time. This results in the tuned exchange imaging (TEXI) protocol. The accuracy of exchange mapping with TEXI was assessed through Monte Carlo simulations in spheres of identical sizes and gamma-distributed sizes, and in parallel hexagonally packed cylinders. The simulations demonstrate that TEXI provides consistent exchange rates regardless of slice thickness and restriction size, even with strong crushers. However, the accuracy depends on b-values, mixing times, and restriction geometry. The constraints and limitations of TEXI are discussed, including suggestions for protocol adaptations. Further studies are needed to optimize the precision of TEXI and assess the approach experimentally in realistic, heterogeneous substrates.

Restriction-induced time-dependent transcytolemmal water exchange: Revisiting the Kӓrger exchange model

The Kӓrger model and its derivatives have been widely used to incorporate transcytolemmal water exchange rate, an essential characteristic of living cells, into analyses of diffusion MRI (dMRI) signals from tissues. The Kӓrger model consists of two homogeneous exchanging components coupled by an exchange rate constant and assumes measurements are made with sufficiently long diffusion time and slow water exchange. Despite successful applications, it remains unclear whether these assumptions are generally valid for practical dMRI sequences and biological tissues. In particular, barrier-induced restrictions to diffusion produce inhomogeneous magnetization distributions in relatively large-sized compartments such as cancer cells, violating the above assumptions. The effects of this inhomogeneity are usually overlooked. We performed computer simulations to quantify how restriction effects, which in images produce edge enhancements at compartment boundaries, influence different variants of the Kӓrger-model. The results show that the edge enhancement effect will produce larger, time-dependent estimates of exchange rates in e.g., tumors with relatively large cell sizes (>10 μm), resulting in overestimations of water exchange as previously reported. Moreover, stronger diffusion gradients, longer diffusion gradient durations, and larger cell sizes, all cause more pronounced edge enhancement effects. This helps us to better understand the feasibility of the Kärger model in estimating water exchange in different tissue types and provides useful guidance on signal acquisition methods that may mitigate the edge enhancement effect. This work also indicates the need to correct the overestimated transcytolemmal water exchange rates obtained assuming the Kärger-model.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence (s) or signal model (s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (∼2-500ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points: τk=17±4ms, fNG=0.72±0.01, Reff=1.05±0.01μm, and κeff=0.19±0.04μm/ms, which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈t-2.4, which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence(s) or signal model(s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (~ 2-500 ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points:τ k = 17 ± 4 m s ,f N G = 0.71 ± 0.01 ,R e f f = 1.10 ± 0.01 μ m , andκ eff = 0.21 ± 0.06 μ m / m s , which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with ≈ t - 2.4 , which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.

DPP: deep phase prior for parallel imaging with wave encoding

Objective.In Magnetic Resonance (MR) parallel imaging with virtual channel-expanded Wave encoding, limitations are imposed on the ability to comprehensively and accurately characterize the background phase. These limitations are primarily attributed to the calibration process relying solely on center low-frequency Auto-Calibration Signals (ACS) data for calibration.Approach.To tackle the challenge of accurately estimating the background phase in wave encoding, a novel deep neural network model guided by deep phase priors is proposed with integrated virtual conjugate coil (VCC) extension. Concretely, within the proposed framework, the background phase is implicitly characterized by employing a carefully designed decoder convolutional neural network, leveraging the inherent characteristics of phase smoothness and compact support in the transformed domain. Furthermore, the proposed model with wave encoding benefits from additional priors, which incorporate transmission sparsity of the latent image and coil sensitivity smoothness.Main results.Ablation experiments were conducted to ascertain the proposed method's capability to implicitly represent CSM and the background phase. Subsequently, the superiority of the proposed method is demonstrated through confidence comparisons with competing methods, employing 4-fold and 5-fold acceleration experiments. In achieving 4-fold and 5-fold acceleration, the optimal quantitative metrics (PSNR/SSIM/NMSE) are 44.1359 dB/0.9863/0.0008 (4-fold) and 41.2074/0.9846/0.0017 (5-fold), respectively. Furthermore, the generalizability of the proposed method is further validated by conducting acceleration experiments with T1, T2, T2*, and various undersampling patterns. In addition, the DPP delivered much better performance than the conventional methods by exploring accelerated phase-sensitive SWI imaging. In SWI accelerated imaging, it also surpasses the optimal competing method in terms of (PSNR/SSIM/NMSE) with 0.096%/0.009%/0.0017%.Significance.The proposed method enables precise characterization of the background phase in the integrated VCC and wave encoding framework, supported via theoretical analysis and empirical findings. Our code is available at:https://github.com/sober235/DPP.

Diffusional kurtosis time dependence and the water exchange rate for the multi-compartment Kärger model

PURPOSE

To demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate.

THEORY AND METHODS

The general formula for the kurtosis is derived from a power series solution for the multi-compartment KM. A lower bound on the exchange rate is established from the observation that the kurtosis is always a logarithmically convex function of time. Both the kurtosis time dependence and the lower bound are illustrated with numerical calculations. The lower bound is also applied to previously published data for the time dependence of the kurtosis in both brain and tumors.

RESULTS

The kurtosis for the multi-compartment KM is given by a sum in which each term is associated with an eigenvector of the exchange rate matrix. The lower bound is determined from the most negative value for the logarithmic derivative of the kurtosis with respect to time. In the cerebral cortex, the lower bound is found to vary from 15 to 76 s-1 , depending on the experimental details, while for the tumors considered, it varies from 2 to 4 s-1 .

CONCLUSION

The time dependence of the kurtosis for the multi-compartment KM has a simple analytic solution that allows a lower bound for the mean KM water exchange rate to be determined directly from experiment. This may be useful in tissues with complex microstructure that is difficult to model explicitly.

Ultra-strong diffusion-weighted MRI reveals cerebellar grey matter abnormalities in movement disorders

Structural brain MRI has proven invaluable in understanding movement disorder pathophysiology. However, most work has focused on grey/white matter volumetric (macrostructural) and white matter microstructural effects, limiting understanding of frequently implicated grey matter microstructural differences. Using ultra-strong spherical tensor encoding diffusion-weighted MRI, a persistent MRI signal was seen in healthy cerebellar grey matter even at high diffusion-weightings (b ​≥ 10,000 s/mm2). Quantifying the proportion of this signal (denoted fs), previously ascertained to originate from inside small spherical spaces, provides a potential proxy for cell body density. In this work, this approach was applied for the first time to a clinical cohort, including patients with diagnosed movement disorders in which the cerebellum has been implicated in symptom pathophysiology. Five control participants (control group 1, median age 24.5 years (20-39 years), imaged at two timepoints, demonstrated consistency in measurement of all three measures - MD (Mean Diffusivity) fs, and Ds (dot diffusivity)- with intraclass correlation coefficients (ICC) of 0.98, 0.86 and 0.76, respectively. Comparison with an older control group (control group 2 (n = 5), median age 51 years (43-58 years)) found no significant differences, neither with morphometric nor microstructural (MD (p = 0.36), fs (p = 0.17) and Ds (p = 0.22)) measures. The movement disorder cohort (Parkinson's Disease, n = 5, dystonia, n = 5. Spinocerebellar Ataxia 6, n = 5) when compared to the age-matched control cohort (Control Group 2) identified significantly lower MD (p < 0.0001 and p < 0.0001) and higher fs values (p < 0.0001 and p < 0.0001) in SCA6 and dystonia cohorts respectively. Lobar division of the cerebellum found these same differences in the superior and inferior posterior lobes, while no differences were seen in either the anterior lobes or with Ds measurements. In contrast to more conventional measures from diffusion tensor imaging, this framework provides enhanced specificity to differences in restricted spherical spaces in grey matter (including small cells) by eliminating signals from cerebrospinal fluid and axons. In the context of human and animal histopathology studies, these findings potentially implicate the cerebellar Purkinje and granule cells as contributors to the observed signal differences, with both cell types having been implicated in several neurological disorders through both postmortem and animal model studies. This novel microstructural imaging approach shows promise for improving movement disorder diagnosis, prognosis, and treatment.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms that are selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of gradient waveforms with different sensitivities to restricted diffusion and exchange (150 samples), our results reveal unique time-dependence signatures in grey and white matter, where the former is characterised by both restricted diffusion and exchange and the latter predominantly exhibits restricted diffusion. Furthermore, we show that gradient waveforms with independently varying sensitivities to restricted diffusion and exchange can be used to map exchange in the human brain. We consistently find that exchange in grey matter is at least twice as fast as in white matter, across all subjects and all gradient strengths. The shortest exchange times observed in this study were in the cerebellar cortex (115 ms). We also assess the feasibility of future clinical applications of the method used in this work, where we find that the grey-white matter exchange contrast obtained with a 25-minute 300 mT/m protocol is preserved by a 4-minute 300 mT/m and a 10-minute 80 mT/m protocol. Our work underlines the utility of free waveforms for detecting time-dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

Meningioma microstructure assessed by diffusion MRI: An investigation of the source of mean diffusivity and fractional anisotropy by quantitative histology

BACKGROUND

Mean diffusivity (MD) and fractional anisotropy (FA) from diffusion MRI (dMRI) have been associated with cell density and tissue anisotropy across tumors, but it is unknown whether these associations persist at the microscopic level.

PURPOSE

To quantify the degree to which cell density and anisotropy, as determined from histology, account for the intra-tumor variability of MD and FA in meningioma tumors. Furthermore, to clarify whether other histological features account for additional intra-tumor variability of dMRI parameters.

MATERIALS AND METHODS

We performed ex-vivo dMRI at 200 μm isotropic resolution and histological imaging of 16 excised meningioma tumor samples. Diffusion tensor imaging (DTI) was used to map MD and FA, as well as the in-plane FA (FA_IP). Histology images were analyzed in terms of cell nuclei density (CD) and structure anisotropy (SA; obtained from structure tensor analysis) and were used separately in a regression analysis to predict MD and FA_IP, respectively. A convolutional neural network (CNN) was also trained to predict the dMRI parameters from histology patches. The association between MRI and histology was analyzed in terms of out-of-sample (R²_OS) on the intra-tumor level and within-sample R² across tumors. Regions where the dMRI parameters were poorly predicted from histology were analyzed to identify features apart from CD and SA that could influence MD and FA_IP, respectively.

RESULTS

Cell density assessed by histology poorly explained intra-tumor variability of MD at the mesoscopic level (200 μm), as median R²_OS = 0.04 (interquartile range 0.01-0.26). Structure anisotropy explained more of the variation in FA_IP (median R²_OS = 0.31, 0.20-0.42). Samples with low R²_OS for FA_IP exhibited low variations throughout the samples and thus low explainable variability, however, this was not the case for MD. Across tumors, CD and SA were clearly associated with MD (R² = 0.60) and FA_IP (R² = 0.81), respectively. In 37% of the samples (6 out of 16), cell density did not explain intra-tumor variability of MD when compared to the degree explained by the CNN. Tumor vascularization, psammoma bodies, microcysts, and tissue cohesivity were associated with bias in MD prediction based solely on CD. Our results support that FA_IP is high in the presence of elongated and aligned cell structures, but low otherwise.

CONCLUSION

Cell density and structure anisotropy account for variability in MD and FA_IP across tumors but cell density does not explain MD variations within the tumor, which means that low or high values of MD locally may not always reflect high or low tumor cell density. Features beyond cell density need to be considered when interpreting MD.