Correlation Tensor MRI deciphers underlying kurtosis sources in stroke

Tensor-valued diffusion MRI of human acute stroke

PURPOSE

Tensor-valued diffusion encoding can disentangle orientation dispersion and subvoxel anisotropy, potentially offering insight into microstructural changes after cerebral ischemia. The purpose was to evaluate tensor-valued diffusion MRI in human acute ischemic stroke, assess potential confounders from diffusion time dependencies, and compare to Monte Carlo diffusion simulations of axon beading.

METHODS

Linear (LTE) and spherical (STE) b-tensor encoding with inherently different effective diffusion times were acquired in 21 acute ischemic stroke patients between 3 and 57 h post-onset at 3 T in 2.5 min. In an additional 10 patients, STE with 2 LTE yielding different effective diffusion times were acquired for comparison. Diffusional variance decomposition (DIVIDE) was used to estimate microscopic anisotropy (μFA), as well as anisotropic, isotropic, and total diffusional variance (MKA , MKI , MKT ). DIVIDE parameters, and diffusion tensor imaging (DTI)-derived mean diffusivity and fractional anisotropy (FA) were compared in lesion versus contralateral white matter. Monte Carlo diffusion simulations of various cylindrical geometries for all b-tensor protocols were used to interpret parameter measurements.

RESULTS

MD was ˜40% lower in lesions for all LTE/STE protocols. The DIVIDE parameters varied with effective diffusion time: higher μFA and MKA in lesion versus contralateral white matter for STE with longer effective diffusion time LTE, whereas the shorter effective diffusion time LTE protocol yielded lower μFA and MKA in lesions. Both protocols, regardless of diffusion time, were consistent with simulations of greater beading amplitude and intracellular volume fraction.

CONCLUSION

DIVIDE parameters depend on diffusion time in acute stroke but consistently indicate neurite beading and larger intracellular volume fraction.

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

OBJECTIVE

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

MATERIALS AND METHODS

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

RESULTS

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

CONCLUSION

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

Differentiation of white matter histopathology using b-tensor encoding and machine learning

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a non-invasive technique that is sensitive to microstructural geometry in neural tissue and is useful for the detection of neuropathology in research and clinical settings. Tensor-valued diffusion encoding schemes (b-tensor) have been developed to enrich the microstructural data that can be obtained through DW-MRI. These advanced methods have proven to be more specific to microstructural properties than conventional DW-MRI acquisitions. Additionally, machine learning methods are particularly useful for the study of multidimensional data sets. In this work, we have tested the reach of b-tensor encoding data analyses with machine learning in different histopathological scenarios. We achieved this in three steps: 1) We induced different levels of white matter damage in rodent optic nerves. 2) We obtained ex vivo DW-MRI data with b-tensor encoding schemes and calculated quantitative metrics using Q-space trajectory imaging. 3) We used a machine learning model to identify the main contributing features and built a voxel-wise probabilistic classification map of histological damage. Our results show that this model is sensitive to characteristics of microstructural damage. In conclusion, b-tensor encoded DW-MRI data analyzed with machine learning methods, have the potential to be further developed for the detection of histopathology and neurodegeneration.

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

Optimal experimental design and estimation for q-space trajectory imaging

Tensor-valued diffusion encoding facilitates data analysis by q-space trajectory imaging. By modeling the diffusion signal of heterogeneous tissues with a diffusion tensor distribution (DTD) and modulating the encoding tensor shape, this novel approach allows disentangling variations in diffusivity from microscopic anisotropy, orientation dispersion, and mixtures of multiple isotropic diffusivities. To facilitate the estimation of the DTD parameters, a parsimonious acquisition scheme coupled with an accurate and precise estimation of the DTD is needed. In this work, we create two precision-optimized acquisition schemes: one that maximizes the precision of the raw DTD parameters, and another that maximizes the precision of the scalar measures derived from the DTD. The improved precision of these schemes compared to a naïve sampling scheme is demonstrated in both simulations and real data. Furthermore, we show that the weighted linear least squares (WLLS) estimator that uses the squared reciprocal of the noisy signal as weights can be biased, whereas the iteratively WLLS estimator with the squared reciprocal of the predicted signal as weights outperforms the conventional unweighted linear LS and nonlinear LS estimators in terms of accuracy and precision. Finally, we show that the use of appropriate constraints can considerably increase the precision of the estimator with only a limited decrease in accuracy.

Comparison of two types of microscopic diffusion anisotropy in mouse brain

Two distinct types of microscopic diffusion anisotropy (MA) are compared in brain for both normal control and transgenic (3xTg-AD) mice, which develop Alzheimer's disease pathology. The first type of MA is the commonly used microscopic fractional anisotropy (μFA), and the second is a new MA measure referred to as μFA'. These two MA parameters have different symmetry properties that are central to their physical interpretations. Specifically, μFA is invariant with respect to local rotations of compartmental diffusion tensors while μFA' is invariant with respect to global diffusion tensor deformations. A key distinction between μFA and μFA' is that μFA is affected by the same type of orientationally coherent diffusion anisotropy as the conventional fractional anisotropy (FA) while μFA' is not. Furthermore, μFA can be viewed as having independent contributions from FA and μFA', as is quantified by an equation relating all three anisotropies. The normal control and transgenic mice are studied at ages ranging from 2 to 15 months, with double diffusion encoding MRI being used to estimate μFA and μFA'. μFA and μFA' are nearly identical in low FA brain regions, but they show notable differences when FA is large. In particular, μFA and FA are found to be strongly correlated in the fimbria, but μFA' and FA are not. In addition, both μFA and μFA' are seen to increase with age in the corpus callosum and external capsule, and modest differences between normal control and transgenic mice are observed for μFA and μFA' in the corpus callosum and for μFA in the fimbria. The triad of FA, μFA, and μFA' is proposed as a useful combination of parameters for assessing diffusion anisotropy in brain.

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

Monitoring time dependence with diffusion MRI yields observables sensitive to compartment sizes (restricted diffusion) and membrane permeability (water exchange). However, restricted diffusion and exchange have opposite effects on the diffusion-weighted signal, which can lead to errors in parameter estimates. In this work, we propose a signal representation that incorporates the effects of both restricted diffusion and exchange up to second order in b-value and is compatible with gradient waveforms of arbitrary shape. The representation features mappings from a gradient waveform to two scalars that separately control the sensitivity to restriction and exchange. We demonstrate that these scalars span a two-dimensional space that can be used to choose waveforms that selectively probe restricted diffusion or exchange, eliminating the correlation between the two phenomena. We found that waveforms with specific but unconventional shapes provide an advantage over conventional pulsed and oscillating gradient acquisitions. We also show that parametrization of waveforms into a two-dimensional space can be used to understand protocols from other approaches that probe restricted diffusion and exchange. For example, we found that the variation of mixing time in filter-exchange imaging corresponds to variation of our exchange-weighting scalar at a fixed value of the restriction-weighting scalar. The proposed signal representation was evaluated using Monte Carlo simulations in identical parallel cylinders with hexagonal and random packing as well as parallel cylinders with gamma-distributed radii. Results showed that the approach is sensitive to sizes in the interval 4-12 μm and exchange rates in the simulated range of 0 to 20 s - 1 , but also that there is a sensitivity to the extracellular geometry. The presented theory constitutes a simple and intuitive description of how restricted diffusion and exchange influence the signal as well as a guide to protocol design capable of separating the two effects.

COnstrained Reference frame diffusion TEnsor Correlation Spectroscopic (CORTECS) MRI: A practical framework for high-resolution diffusion tensor distribution imaging

High-resolution imaging studies have consistently shown that in cortical tissue water diffuses preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if the relative contributions from microscopic water pools to the net voxel signal vary across experiments that use different diffusion times, b-values, TEs, and TRs. With this in mind, we propose a practical new framework for imaging non-parametric diffusion tensor distributions (DTDs) by constraining the microscopic diffusion tensors of the DTD to be diagonalized using the same orthonormal reference frame of the mesoscopic voxel. In each voxel, the constrained DTD (cDTD) is completely determined by the correlation spectrum of the microscopic principal diffusivities associated with the axes of the voxel reference frame. Consequently, all cDTDs are inherently limited to the domain of positive definite tensors and can be reconstructed efficiently using Inverse Laplace Transform methods. Moreover, the cDTD reconstruction can be performed using only data acquired efficiently with single diffusion encoding, although it also supports datasets with multiple diffusion encoding. In tissues with a well-defined architecture, such as the cortex, we can further constrain the cDTD to contain only cylindrically symmetric diffusion tensors and measure the 2D correlation spectra of principal diffusivities along the radial and tangential orientation with respect to the cortical surface. To demonstrate this framework, we perform numerical simulations and analyze high-resolution dMRI data from a fixed macaque monkey brain. We estimate 2D cDTDs in the cortex and derive, in each voxel, the marginal distributions of the microscopic principal diffusivities, the corresponding distributions of the microscopic fractional anisotropies and mean diffusivities along with their 2D correlation spectra to quantify the cDTD shape-size characteristics. Signal components corresponding to specific bands in these cDTD-derived spectra show high specificity to cortical laminar structures observed with histology. Our framework drastically simplifies the measurement of non-parametric DTDs in high-resolution datasets with mesoscopic voxel sizes much smaller than the radius of curvature of the underlying anatomy, e.g., cortical surface, and can be applied retrospectively to analyze existing diffusion MRI data from fixed cortical tissues.

MR Fingerprinting with b-Tensor Encoding for Simultaneous Quantification of Relaxation and Diffusion in a Single Scan

PURPOSE

Although both relaxation and diffusion imaging are sensitive to tissue microstructure, studies have reported limited sensitivity and robustness of using relaxation or conventional diffusion alone to characterize tissue microstructure. Recently, it has been shown that tensor-valued diffusion encoding and joint relaxation-diffusion quantification enable more reliable quantification of compartment-specific microstructural properties. However, scan times to acquire such data can be prohibitive. Here, we aim to simultaneously quantify relaxation and diffusion using MR fingerprinting (MRF) and b-tensor encoding in a clinically feasible time.

METHODS

We developed multidimensional MRF scans (mdMRF) with linear and spherical b-tensor encoding (LTE and STE) to simultaneously quantify T1, T2, and ADC maps from a single scan. The image quality, accuracy, and scan efficiency were compared between the mdMRF using LTE and STE. Moreover, we investigated the robustness of different sequence designs to signal errors and their impact on the maps.

RESULTS

T1 and T2 maps derived from the mdMRF scans have consistently high image quality, while ADC maps are sensitive to different sequence designs. Notably, the fast imaging steady state precession (FISP)-based mdMRF scan with peripheral pulse gating provides the best ADC maps that are free of image distortion and shading artifacts.

CONCLUSION

We demonstrated the feasibility of quantifying T1, T2, and ADC maps simultaneously from a single mdMRF scan in around 24 s/slice. The map quality and quantitative values are consistent with the reference scans.

Nonparametric 5D D-R2 distribution imaging with single-shot EPI at 21.1 T: Initial results for in vivo rat brain

In vivo human diffusion MRI is by default performed using single-shot EPI with greater than 50-ms echo times and associated signal loss from transverse relaxation. The individual benefits of the current trends of increasing B₀ to boost SNR and employing more advanced signal preparation schemes to improve the specificity for selected microstructural properties eventually may be cancelled by increased relaxation rates at high B₀ and echo times with advanced encoding. Here, initial attempts to translate state-of-the-art diffusion-relaxation correlation methods from 3 T to 21.1 T are made to identify hurdles that need to be overcome to fulfill the promises of both high SNR and readily interpretable microstructural information.

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

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