The link between diffusion MRI and tumor heterogeneity: Mapping cell eccentricity and density by diffusional variance decomposition (DIVIDE)

On the potential for mapping apparent neural soma density via a clinically viable diffusion MRI protocol

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B-tensor encoding enables estimation of spherical cellular structures in the brain.

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Spherical compartments may provide markers for apparent neural soma density.

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Model parameters can be estimated in a fast and robust way using deep learning.

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Practical acquisition times are achievable on widely available clinical scanners.

Diffusion MRI is a valuable tool for probing tissue microstructure in the brain noninvasively. Today, model-based techniques are widely available and used for white matter characterisation where their development is relatively mature. Conversely, tissue modelling in grey matter is more challenging, and no generally accepted models exist. With advances in measurement technology and modelling efforts, a clinically viable technique that reveals salient features of grey matter microstructure, such as the density of quasi-spherical cell bodies and quasi-cylindrical cell projections, is an exciting prospect. As a step towards capturing the microscopic architecture of grey matter in clinically feasible settings, this work uses a biophysical model that is designed to disentangle the diffusion signatures of spherical and cylindrical structures in the presence of orientation heterogeneity, and takes advantage of B-tensor encoding measurements, which provide additional sensitivity compared to standard single diffusion encoding sequences. For the fast and robust estimation of microstructural parameters, we leverage recent advances in machine learning and replace conventional fitting techniques with an artificial neural network that fits complex biophysical models within seconds. Our results demonstrate apparent markers of spherical and cylindrical geometries in healthy human subjects, and in particular an increased volume fraction of spherical compartments in grey matter compared to white matter. We evaluate the extent to which spherical and cylindrical geometries may be interpreted as correlates of neural soma and neural projections, respectively, and quantify parameter estimation errors in the presence of various departures from the modelling assumptions. While further work is necessary to translate the ideas presented in this work to the clinic, we suggest that biomarkers focussing on quasi-spherical cellular geometries may be valuable for the enhanced assessment of neurodevelopmental disorders and neurodegenerative diseases.

Whole-Brain Imaging of Subvoxel T1-Diffusion Correlation Spectra in Human Subjects

T1 relaxation and water mobility generate eloquent MRI tissue contrasts with great diagnostic value in many neuroradiological applications. However, conventional methods do not adequately quantify the microscopic heterogeneity of these important biophysical properties within a voxel, and therefore have limited biological specificity. We describe a new correlation spectroscopic (CS) MRI method for measuring how T1 and mean diffusivity (MD) co-vary in microscopic tissue environments. We develop a clinical pulse sequence that combines inversion recovery (IR) with single-shot isotropic diffusion encoding (IDE) to efficiently acquire whole-brain MRIs with a wide range of joint T1-MD weightings. Unlike conventional diffusion encoding, the IDE preparation ensures that all subvoxel water pools are weighted by their MDs regardless of the sizes, shapes, and orientations of their corresponding microscopic diffusion tensors. Accordingly, IR-IDE measurements are well-suited for model-free, quantitative spectroscopic analysis of microscopic water pools. Using numerical simulations, phantom experiments, and data from healthy volunteers we demonstrate how IR-IDE MRIs can be processed to reconstruct maps of two-dimensional joint probability density functions, i.e., correlation spectra, of subvoxel T1-MD values. In vivo T1-MD spectra show distinct cerebrospinal fluid and parenchymal tissue components specific to white matter, cortical gray matter, basal ganglia, and myelinated fiber pathways, suggesting the potential for improved biological specificity. The one-dimensional marginal distributions derived from the T1-MD correlation spectra agree well with results from other relaxation spectroscopic and quantitative MRI studies, validating the T1-MD contrast encoding and the spectral reconstruction. Mapping subvoxel T1-diffusion correlations in patient populations may provide a more nuanced, comprehensive, sensitive, and specific neuroradiological assessment of the non-specific changes seen on fluid-attenuated inversion recovery (FLAIR) and diffusion-weighted MRIs (DWIs) in cancer, ischemic stroke, or brain injury.

Mapping prostatic microscopic anisotropy using linear and spherical b-tensor encoding: A preliminary study

Purpose:

Tensor-valued diffusion encoding provides more specific information than conventional diffusion-weighted imaging (DWI), but has mainly been applied in neuroimaging studies. This study aimed to assess its potential for the imaging of prostate cancer (PCa).

Methods:

Seventeen patients with histologically proven PCa were enrolled. DWI of the prostate was performed with linear and spherical tensor encoding using a maximal b-value of 1.5 ms/μm² and a voxel size of 3 × 3 × 4 mm³. The gamma-distribution model was used to estimate the mean diffusivity (MD), the isotropic kurtosis (MK_I), and the anisotropic kurtosis (MK_A). Regions of interest were placed in MR-defined cancerous tissues, as well as in apparently healthy tissues in the peripheral and transitional zones (PZs and TZs).

Results:

DWI with linear and spherical encoding yielded different image contrasts at high b-values, which enabled the estimation of MK_A and MK_I. Compared with healthy tissue (PZs and TZs combined) the cancers displayed a significantly lower MD (P < .05), higher MK_I (P < 10⁻⁵), and lower MK_A (P < .05). Compared with the TZ, tissue in the PZ showed lower MD (P < 10⁻³) and higher MK_A (P < 10⁻³). No significant differences were found between cancers of different Gleason scores, possibly because of the limited sample size.

Conclusion:

Tensor-valued diffusion encoding enabled mapping of MK_A and MK_I in the prostate. The elevated MK_I in PCa compared with normal tissues suggests an elevated heterogeneity in the cancers. Increased in-plane resolution could improve tumor delineation in future studies.

Q-space trajectory imaging with positivity constraints (QTI+)

Q-space trajectory imaging (QTI) enables the estimation of useful scalar measures indicative of the local tissue structure. This is accomplished by employing generalized gradient waveforms for diffusion sensitization alongside a diffusion tensor distribution (DTD) model. The first two moments of the underlying DTD are made available by acquisitions at low diffusion sensitivity (b-values). Here, we show that three independent conditions have to be fulfilled by the mean and covariance tensors associated with distributions of symmetric positive semidefinite tensors. We introduce an estimation framework utilizing semi-definite programming (SDP) to guarantee that these conditions are met. Applying the framework on simulated signal profiles for diffusion tensors distributed according to non-central Wishart distributions demonstrates the improved noise resilience of QTI+ over the commonly employed estimation methods. Our findings on a human brain data set also reveal pronounced improvements, especially so for acquisition protocols featuring few number of volumes. Our method’s robustness to noise is expected to not only improve the accuracy of the estimates, but also enable a meaningful interpretation of contrast in the derived scalar maps. The technique’s performance on shorter acquisitions could make it feasible in routine clinical practice.

Rapid microscopic fractional anisotropy imaging via an optimized linear regression formulation

Water diffusion anisotropy in the human brain is affected by disease, trauma, and development. Microscopic fractional anisotropy (μFA) is a diffusion MRI (dMRI) metric that can quantify water diffusion anisotropy independent of neuron fiber orientation dispersion. However, there are several different techniques to estimate μFA and few have demonstrated full brain imaging capabilities within clinically viable scan times and resolutions. Here, we present an optimized spherical tensor encoding (STE) technique to acquire μFA directly from the 2nd order cumulant expansion of the powder averaged dMRI signal obtained from direct linear regression (i.e. diffusion kurtosis) which requires fewer powder-averaged signals than other STE fitting techniques and can be rapidly computed. We found that the optimal dMRI parameters for white matter μFA imaging were a maximum b-value of 2000 s/mm² and a ratio of STE to LTE tensor encoded acquisitions of 1.7 for our system specifications. We then compared two implementations of the direct regression approach to the well-established gamma model in 4 healthy volunteers on a 3 Tesla system. One implementation used mean diffusivity (D) obtained from a 2nd order fit of the cumulant expansion, while the other used a linear estimation of D from the low b-values. Both implementations of the direct regression approach showed strong linear correlations with the gamma model (ρ = 0.97 and ρ = 0.90) but mean biases of -0.11 and - 0.02 relative to the gamma model were also observed, respectively. All three μFA measurements showed good test-retest reliability (ρ ≥ 0.79 and bias = 0). To demonstrate the potential scan time advantage of the direct approach, 2 mm isotropic resolution μFA was demonstrated over a 10 cm slab using a subsampled data set with fewer powder-averaged signals that would correspond to a 3.3-min scan. Accordingly, our results introduce an optimization procedure that has enabled nearly full brain μFA in only several minutes.

Glioma grading, molecular feature classification, and microstructural characterization using MR diffusional variance decomposition (DIVIDE) imaging

OBJECTIVE

To evaluate the potential of diffusional variance decomposition (DIVIDE) for grading, molecular feature classification, and microstructural characterization of gliomas.

MATERIALS AND METHODS

Participants with suspected gliomas underwent DIVIDE imaging, yielding parameter maps of fractional anisotropy (FA), mean diffusivity (MD), anisotropic mean kurtosis (MK_A), isotropic mean kurtosis (MK_I), total mean kurtosis (MK_T), MK_A/MK_T, and microscopic fractional anisotropy (μFA). Tumor type and grade, isocitrate dehydrogenase (IDH) 1/2 mutant status, and the Ki-67 labeling index (Ki-67 LI) were determined after surgery. Statistical analysis included 33 high-grade gliomas (HGG) and 17 low-grade gliomas (LGG). Tumor diffusion metrics were compared between HGG and LGG, among grades, and between wild and mutated IDH types using appropriate tests according to normality assessment results. Receiver operating characteristic and Spearman correlation analysis were also used for statistical evaluations.

RESULTS

FA, MD, MK_A, MK_I, MK_T, μFA, and MK_A/MK_T differed between HGG and LGG (FA: p = 0.047; MD: p = 0.037, others p < 0.001), and among glioma grade II, III, and IV (FA: p = 0.048; MD: p = 0.038, others p < 0.001). All diffusion metrics differed between wild-type and mutated IDH tumors (MK_I: p = 0.003; others: p < 0.001). The metrics that best discriminated between HGG and LGGs and between wild-type and mutated IDH tumors were MK_T and FA respectively (area under the curve 0.866 and 0.881). All diffusion metrics except FA showed significant correlation with Ki-67 LI, and MK_I had the highest correlation coefficient (r_s = 0.618).

CONCLUSION

DIVIDE is a promising technique for glioma characterization and diagnosis.

KEY POINTS

• DIVIDE metrics MK_I is related to cell density heterogeneity while MK_A and μFA are related to cell eccentricity. • DIVIDE metrics can effectively differentiate LGG from HGG and IDH mutation from wild-type tumor, and showed significant correlation with the Ki-67 labeling index. • MK_I was larger than MK_A which indicates predominant cell density heterogeneity in gliomas. • MK_A and MK_I increased with grade or degree of malignancy, however with a relatively larger increase in the cell eccentricity metric MK_A in relation to the cell density heterogeneity metric MK_I.

Investigating the relationship between diffusion kurtosis tensor imaging (DKTI) and histology within the normal human brain

Measurements of water diffusion with MRI have been used as a biomarker of tissue microstructure and heterogeneity. In this study, diffusion kurtosis tensor imaging (DKTI) of the brain was undertaken in 10 healthy volunteers at a clinical field strength of 3 T. Diffusion and kurtosis metrics were measured in regions-of-interest on the resulting maps and compared with quantitative analysis of normal post-mortem tissue histology from separate age-matched donors. White matter regions showed low diffusion (0.60 ± 0.04 × 10-3 mm2/s) and high kurtosis (1.17 ± 0.06), consistent with a structured heterogeneous environment comprising parallel neuronal fibres. Grey matter showed intermediate diffusion (0.80 ± 0.02 × 10-3 mm2/s) and kurtosis (0.82 ± 0.05) values. An important finding is that the subcortical regions investigated (thalamus, caudate and putamen) showed similar diffusion and kurtosis properties to white matter. Histological staining of the subcortical nuclei demonstrated that the predominant grey matter was permeated by small white matter bundles, which could account for the similar kurtosis to white matter. Quantitative histological analysis demonstrated higher mean tissue kurtosis and vector standard deviation values for white matter (1.08 and 0.81) compared to the subcortical regions (0.34 and 0.59). Mean diffusion on DKTI was positively correlated with tissue kurtosis (r = 0.82, p < 0.05) and negatively correlated with vector standard deviation (r = -0.69, p < 0.05). This study demonstrates how DKTI can be used to study regional structural variations in the cerebral tissue microenvironment and could be used to probe microstructural changes within diseased tissue in the future.

In vivo tensor-valued diffusion MRI of focal demyelination in white and deep grey matter of rodents

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We performed in-vivo tensor-valued diffusion MRI in demyelinating rodents.

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Lysolecithin was injected in white and deep grey matter to cause focal demyelination.

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Focal demyelination reduced microscopic fractional anisotropy (µFA).

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Isotropic kurtosis may be particularly sensitive to deep grey matter lesions.

Background

Multiple sclerosis (MS) is a chronic inflammatory demyelinating disease leading to damage of white matter (WM) and grey matter (GM). Magnetic resonance imaging (MRI) is the modality of choice to assess brain damage in MS, but there is an unmet need in MRI for achieving higher sensitivity and specificity to MS-related microstructural alterations in WM and GM.

Objective

To explore whether tensor-valued diffusion MRI (dMRI) can yield sensitive microstructural read-outs for focal demyelination in cerebral WM and deep GM (DGM).

Methods

Eight rats underwent L-α-Lysophosphatidylcholine (LPC) injections in the WM and striatum to introduce focal demyelination. Multimodal MRI was performed at 7 Tesla after 7 days. Tensor-valued dMRI was complemented by diffusion tensor imaging, quantitative MRI and proton magnetic resonance spectroscopy (MRS).

Results

Quantitative MRI and MRS confirmed that LPC injections caused inflammatory demyelinating lesions in WM and DGM. Tensor-valued dMRI illustrated a significant decline of microscopic fractional anisotropy (µFA) in both LPC-treated WM and DGM (P < 0.005) along with a marked increase of isotropic kurtosis (MK_I) in DGM (P < 0.0001).

Conclusion

Tensor-valued dMRI bears considerable potential for microstructural imaging in MS, suggesting a regional µFA decrease may be a sensitive indicator of MS lesions, while a regional MK_I increase may be particularly sensitive in detecting DGM lesions of MS.

Microstructure Modeling of High b-Value Diffusion-Weighted Images in Glioblastoma

Apparent diffusion coefficient has limits to differentiate solid tumor from normal tissue or edema in glioblastoma (GBM). This study investigated a microstructure model (MSM) in GBM using a clinically available diffusion imaging technique. The MSM was modified to integrate with bi-polar diffusion gradient waveforms, and applied to 30 patients with newly diagnosed GBM. Diffusion-weighted (DW) images acquired on a 3 T scanner with b-values from 0 to 2500 s/mm² were fitted in volumes of interest (VOIs) of solid tumor to obtain the apparent restriction size of intracellular water (ARS), the fractional volume of intracellular water (V_in), and extracellular (D_ex) water diffusivity. The parameters in solid tumor were compared with those of other tissue types by Students’ t test. For comparison, DW images were fitted by conventional mono-exponential and bi-exponential models. ARS, D_ex, and V_in from the MSM in tumor VOIs were significantly greater than those in WM, GM, and edema (P values of .01–.001). ARS values in solid tumors (from 21.6 to 34.5 um) had absolutely no overlap with those in all other tissue types (from 0.9 to 3.5 um). V_in values showed a descending order from solid tumor (from 0.32 to 0.52) to WM, GM, and edema (from 0.05 to 0.25), consisting with the descending cellularity in these tissue types. The parameters from mono-exponential and bi-exponential models could not significantly differentiate solid tumor from all other tissue types, particularly from edema. Further development and histopathological validation of the MSM will warrant its role in clinical management of GBM.

Quartile histogram assessment of glioma malignancy using high b-value diffusion MRI with a continuous-time random-walk model

The purpose of this study is to investigate the feasibility of using a continuous-time random-walk (CTRW) diffusion model, together with a quartile histogram analysis, for assessing glioma malignancy by probing tissue heterogeneity as well as cellularity. In this prospective study, 91 patients (40 females, 51 males) with histopathologically proven gliomas underwent MRI at 3 T. The cohort included 42 grade II (GrII), 19 grade III (GrIII) and 29 grade IV (GrIV) gliomas. Echo-planar diffusion-weighted imaging was conducted using 17 b-values (0-4000 s/mm² ). Three CTRW model parameters, including an anomalous diffusion coefficient D_m , and two parameters related to temporal and spatial diffusion heterogeneity α and β, respectively, were obtained. The mean parameter values within the tumor regions of interest (ROIs) were computed by utilizing the first quartile of the histograms as well as the full ROI for comparison. A Bonferroni-Holm-corrected Mann-Whitney U-test was used for the group comparisons. Individual and combinations of the CTRW parameters were evaluated for the characterization of gliomas with a receiver operating characteristic analysis. All first-quartile mean CTRW parameters yielded significant differences (p-values < 0.05) between pair-wise comparisons of GrII (D_m : 1.14 ± 0.37 μm² /ms; α: 0.904 ± 0.03, β: 0.913 ± 0.06), GrIII (D_m : 0.88 ± 0.21 μm² /ms; α: 0.888 ± 0.01, β: 0.857 ± 0.06) and GrIV gliomas (D_m : 0.73 ± 0.22 μm² /ms; α: 0.878 ± 0.01; β: 0.791 ± 0.07). The highest sensitivity, specificity, accuracy and area-under-the-curve of using the combinations of the first-quartile parameters were 84.2%, 78.5%, 75.4% and 0.76 for GrII and GrIII classification; 86.2%, 89.4%, 75% and 0.76 for GrIII and GrIV classification; and 86.2%, 85.7%, 84.5% and 0.90 for GrII and GrIV classification, respectively. Quartile-based analysis produced higher accuracy and area-under-the-curve than the full ROI-based analysis in all classifications. The CTRW diffusion model, together with a quartile-based histogram analysis, offers a new way for probing tumor structural heterogeneity at a subvoxel level, and has potential for in vivo assessment of glioma malignancy to complement histopathology.

Multidimensional Diffusion Magnetic Resonance Imaging for Characterization of Tissue Microstructure in Breast Cancer Patients: A Prospective Pilot Study

Diffusion-weighted imaging is a non-invasive functional imaging modality for breast tumor characterization through apparent diffusion coefficients. Yet, it has so far been unable to intuitively inform on tissue microstructure. In this IRB-approved prospective study, we applied novel multidimensional diffusion (MDD) encoding across 16 patients with suspected breast cancer to evaluate its potential for tissue characterization in the clinical setting. Data acquired via custom MDD sequences was processed using an algorithm estimating non-parametric diffusion tensor distributions. The statistical descriptors of these distributions allow us to quantify tissue composition in terms of metrics informing on cell densities, shapes, and orientations. Additionally, signal fractions from specific cell types, such as elongated cells (bin1), isotropic cells (bin2), and free water (bin3), were teased apart. Histogram analysis in cancers and healthy breast tissue showed that cancers exhibited lower mean values of "size" (1.43 ± 0.54 × 10-3 mm2/s) and higher mean values of "shape" (0.47 ± 0.15) corresponding to bin1, while FGT (fibroglandular breast tissue) presented higher mean values of "size" (2.33 ± 0.22 × 10-3 mm2/s) and lower mean values of "shape" (0.27 ± 0.11) corresponding to bin3 (p < 0.001). Invasive carcinomas showed significant differences in mean signal fractions from bin1 (0.64 ± 0.13 vs. 0.4 ± 0.25) and bin3 (0.18 ± 0.08 vs. 0.42 ± 0.21) compared to ductal carcinomas in situ (DCIS) and invasive carcinomas with associated DCIS (p = 0.03). MDD enabled qualitative and quantitative evaluation of the composition of breast cancers and healthy glands.

Time dependence in diffusion MRI predicts tissue outcome in ischemic stroke patients

Purpose:

Reperfusion therapy enables effective treatment of ischemic stroke presenting within 4–6 hours. However, tissue progression from ischemia to infarction is variable, and some patients benefit from treatment up until 24 hours. Improved imaging techniques are needed to identify these patients. Here, it was hypothesized that time dependence in diffusion MRI may predict tissue outcome in ischemic stroke.

Methods:

Diffusion MRI data were acquired with multiple diffusion times in five non-reperfused patients at 2, 9, and 100 days after stroke onset. Maps of “rate of kurtosis change” (k), mean kurtosis, ADC, and fractional anisotropy were derived. The ADC maps defined lesions, normal-appearing tissue, and the lesion tissue that would either be infarcted or remain viable by day 100. Diffusion parameters were compared (1) between lesions and normal-appearing tissue, and (2) between lesion tissue that would be infarcted or remain viable.

Results:

Positive values of k were observed within stroke lesions on day 2 (P = .001) and on day 9 (P = .023), indicating diffusional exchange. On day 100, high ADC values indicated infarction of 50 ± 20% of the lesion volumes. Tissue infarction was predicted by high k values both on day 2 (P = .026) and on day 9 (P = .046), by low mean kurtosis values on day 2 (P = .043), and by low fractional anisotropy values on day 9 (P = .029), but not by low ADC values.

Conclusions:

Diffusion time dependence predicted tissue outcome in ischemic stroke more accurately than the ADC, and may be useful for predicting reperfusion benefit.

Improving the characterization of meningioma microstructure in proton therapy from conventional apparent diffusion coefficient measurements using Monte Carlo simulations of diffusion MRI

PURPOSE

Proton therapy could benefit from noninvasively gaining tumor microstructure information, at both planning and monitoring stages. The anatomical location of brain tumors, such as meningiomas, often hinders the recovery of such information from histopathology, and conventional noninvasive imaging biomarkers, like the apparent diffusion coefficient (ADC) from diffusion-weighted MRI (DW-MRI), are nonspecific. The aim of this study was to retrieve discriminative microstructural markers from conventional ADC for meningiomas treated with proton therapy. These markers were employed for tumor grading and tumor response assessment.

METHODS

DW-MRIs from patients affected by meningioma and enrolled in proton therapy were collected before (n = 35) and 3 months after (n = 25) treatment. For the latter group, the risk of an adverse outcome was inferred by their clinical history. Using Monte Carlo methods, DW-MRI signals were simulated from packings of synthetic cells built with well-defined geometrical and diffusion properties. Patients' ADC was modeled as a weighted sum of selected simulated signals. The weights that best described a patient's ADC were determined through an optimization procedure and used to estimate a set of markers of tumor microstructure: diffusion coefficient (D), volume fraction (vf), and radius (R). Apparent cellularity (ρ_app ) was estimated from vf and R for an easier clinical interpretability. Differences between meningothelial and atypical subtypes, and low- and high-grade meningiomas were assessed with nonparametric statistical tests, whereas sensitivity and specificity with ROC analyses. Similar analyses were performed for patients showing low or high risk of an adverse outcome to preliminary evaluate response to treatment.

RESULTS

Significant (P < 0.05) differences in median ADC, D, vf, R, and ρ_app values were found when comparing meningiomas' subtypes and grades. ROC analyses showed that estimated microstructural parameters reached higher specificity than ADC for subtyping (0.93 for D and vf vs 0.80 for ADC) and grading (0.75 for R vs 0.67 for ADC). High- and low-risk patients showed significant differences in ADC and microstructural parameters. The skewness of ρ_app was the parameter with highest AUC (0.90) and sensitivity (0.75).

CONCLUSIONS

Matching measured with simulated ADC yielded a set of potential imaging markers for meningiomas grading and response monitoring in proton therapy, showing higher specificity than conventional ADC. These markers can provide discriminative information about spatial patterns of tumor microstructure implying important advantages for patient-specific proton therapy workflows.

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

The effect of gradient nonlinearities on fiber orientation estimates from spherical deconvolution of diffusion magnetic resonance imaging data

Gradient nonlinearities in magnetic resonance imaging (MRI) cause spatially varying mismatches between the imposed and the effective gradients and can cause significant biases in rotationally invariant diffusion MRI measures derived from, for example, diffusion tensor imaging. The estimation of the orientational organization of fibrous tissue, which is nowadays frequently performed with spherical deconvolution techniques ideally using higher diffusion weightings, can likewise be biased by gradient nonlinearities. We explore the sensitivity of two established spherical deconvolution approaches to gradient nonlinearities, namely constrained spherical deconvolution (CSD) and damped Richardson-Lucy (dRL). Additionally, we propose an extension of dRL to take into account gradient imperfections, without the need of data interpolation. Simulations show that using the effective b-matrix can improve dRL fiber orientation estimation and reduces angular deviations, while CSD can be more robust to gradient nonlinearity depending on the implementation. Angular errors depend on a complex interplay of many factors, including the direction and magnitude of gradient deviations, underlying microstructure, SNR, anisotropy of the effective response function, and diffusion weighting. Notably, angular deviations can also be observed at lower b-values in contrast to the perhaps common assumption that only high b-value data are affected. In in vivo Human Connectome Project data and acquisitions from an ultrastrong gradient (300 mT/m) scanner, angular differences are observed between applying and not applying the effective gradients in dRL estimation. As even small angular differences can lead to error propagation during tractography and as such impact connectivity analyses, incorporating gradient deviations into the estimation of fiber orientations should make such analyses more reliable.

Gradient waveform design for tensor-valued encoding in diffusion MRI

Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is that it unlocks the 'shape of the b-tensor' as a new encoding dimension. By modulating the b-tensor shape, we can control the sensitivity to microscopic diffusion anisotropy which can be used as a contrast mechanism; a feature that is inaccessible by conventional diffusion encoding. Since imaging methods based on tensor-valued diffusion encoding are finding an increasing number of applications we are prompted to highlight the challenge of designing the optimal gradient waveforms for any given application. In this review, we first establish the basic design objectives in creating field gradient waveforms for tensor-valued diffusion MRI. We also survey additional design considerations related to limitations imposed by hardware and physiology, potential confounding effects that cannot be captured by the b-tensor, and artifacts related to the diffusion encoding waveform. Throughout, we discuss the expected compromises and tradeoffs with an aim to establish a more complete understanding of gradient waveform design and its impact on accurate measurements and interpretations of data.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Accuracy and precision of statistical descriptors obtained from multidimensional diffusion signal inversion algorithms

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor-valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one-dimensional Gamma fit, a generalized two-term cumulant approach, and two-dimensional and four-dimensional Monte-Carlo-based inversion techniques, using a clinically feasible tensor-valued acquisition scheme. In particular, we compare their performance at different signal-to-noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two-dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite-SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite-SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two-dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four-dimensional Monte Carlo inversion presents no infinite-SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.

Diffusion tensor distribution imaging of an in vivo mouse brain at ultrahigh magnetic field by spatiotemporal encoding

Diffusion tensor distribution (DTD) imaging builds on principles from diffusion, solid-state and low-field NMR spectroscopies, to quantify the contents of heterogeneous voxels as nonparametric distributions, with tensor "size", "shape" and orientation having direct relations to corresponding microstructural properties of biological tissues. The approach requires the acquisition of multiple images as a function of the magnitude, shape and direction of the diffusion-encoding gradients, leading to long acquisition times unless fast image read-out techniques like EPI are employed. While in previous in vivo human brain studies performed at 3 T this proved a viable option, porting these measurements to very high magnetic fields and/or to heterogeneous organs induces B0 - and B1 -inhomogeneity artifacts that challenge the limits of EPI. To overcome such challenges, we demonstrate here that high spatial resolution DTD of mouse brain can be carried out at 15.2 T with a surface-cryoprobe, by relying on SPatiotemporal ENcoding (SPEN) imaging sequences. These new acquisition and data-processing protocols are demonstrated with measurements on in vivo mouse brain, and validated with synthetic phantoms designed to mimic the diffusion properties of white matter, gray matter and cerebrospinal fluid. While still in need of full extensions to 3D mappings and of scanning additional animals to extract more general physiological conclusions, this work represents another step towards the model-free, noninvasive in vivo characterization of tissue microstructure and heterogeneity in animal models, at ≈0.1 mm resolutions.

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.

Evaluating High Spatial Resolution Diffusion Kurtosis Imaging at 3T: Reproducibility and Quality of Fit

BACKGROUND

Diffusion kurtosis imaging (DKI) quantifies the non-Gaussian diffusion of water within tissue microstructure. However, it has increased fitting parameters and requires higher b-values. Evaluation of DKI reproducibility is important for clinical purposes.

PURPOSE

To assess the reproducibility in whole-brain high-resolution DKI at varying b-values.

STUDY TYPE

Retrospective.

SUBJECTS AND PHANTOMS

In all, 44 individuals from the test-retest Human Connectome Project (HCP) database and 12 3D-printed phantoms.

FIELD STRENGTH/SEQUENCE

Diffusion-weighted multiband echo-planar imaging sequence at 3T and 9.4T. magnetization-prepared rapid acquisition gradient echo at 3T for in vivo structural data only.

ASSESSMENT

From HCP data with b-values = 1000, 2000, 3000 s/mm² (dataset A), two additional datasets with b-values = 1000, 3000 s/mm² (dataset B) and b-values = 1000, 2000 s/mm² (dataset C) were extracted. Estimated DKI metrics from each dataset were used for evaluating reproducibility and fitting quality in white matter (WM) and gray matter (GM) based on whole-brain and regions of interest (ROIs).

STATISTICAL TESTS

DKI reproducibility was assessed using the within-subject coefficient of variation (CoV), fitting residuals to evaluate DKI fitting accuracy and Pearson's correlation to investigate the presence of systematic biases. Repeated measures analysis of variance was used for statistical comparison.

RESULTS

Datasets A and B exhibited lower DKI CoVs (<20%) compared to C (<50%) in both WM and GM ROIs (all P < 0.05). This effect varies between DKI and DTI parameters (P < 0.005). Whole-brain fitting residuals were consistent across datasets (P > 0.05), but lower residuals in dataset B were detected for the WM ROIs (P < 0.001). A similar trend was observed for the phantom data CoVs (<7.5%) at varying fiber orientations for datasets A and B. Finally, dataset C was characterized by higher residuals across the different fiber crossings (P < 0.05).

DATA CONCLUSION

The study demonstrates that high reproducibility can still be achieved within a reasonable scan time, specifically dataset B, supporting the potential of DKI for aiding clinical tools in detecting microstructural changes.

Brain White-Matter Degeneration Due to Aging and Parkinson Disease as Revealed by Double Diffusion Encoding

Microstructure imaging by means of multidimensional diffusion encoding is increasingly applied in clinical research, with expectations that it yields a parameter that better correlates with clinical disability than current methods based on single diffusion encoding. Under the assumption that diffusion within a voxel can be well described by a collection of diffusion tensors, several parameters of this diffusion tensor distribution can be derived, including mean size, variance of sizes, orientational dispersion, and microscopic anisotropy. The information provided by multidimensional diffusion encoding also enables us to decompose the sources of the conventional fractional anisotropy and mean kurtosis. In this study, we explored the utility of the diffusion tensor distribution approach for characterizing white-matter degeneration in aging and in Parkinson disease by using double diffusion encoding. Data from 23 healthy older subjects and 27 patients with Parkinson disease were analyzed. Advanced age was associated with greater mean size and size variances, as well as smaller microscopic anisotropy. By analyzing the parameters underlying diffusion kurtosis, we found that the reductions of kurtosis in aging and Parkinson disease reported in the literature are likely driven by the reduction in microscopic anisotropy. Furthermore, microscopic anisotropy correlated with the severity of motor impairment in the patients with Parkinson disease. The present results support the use of multidimensional diffusion encoding in clinical studies and are encouraging for its future clinical implementation.

Motion-compensated gradient waveforms for tensor-valued diffusion encoding by constrained numerical optimization

PURPOSE

Diffusion-weighted MRI is sensitive to incoherent tissue motion, which may confound the measured signal and subsequent analysis. We propose a "motion-compensated" gradient waveform design for tensor-valued diffusion encoding that negates the effects bulk motion and incoherent motion in the ballistic regime.

METHODS

Motion compensation was achieved by constraining the magnitude of gradient waveform moment vectors. The constraint was incorporated into a numerical optimization framework, along with existing constraints that account for b-tensor shape, hardware restrictions, and concomitant field gradients. We evaluated the efficacy of encoding and motion compensation in simulations, and we demonstrated the approach by linear and planar b-tensor encoding in a healthy heart in vivo.

RESULTS

The optimization framework produced asymmetric motion-compensated waveforms that yielded b-tensors of arbitrary shape with improved efficiency compared with previous designs for tensor-valued encoding, and equivalent efficiency to previous designs for linear (conventional) encoding. Technical feasibility was demonstrated in the heart in vivo, showing vastly improved data quality when using motion compensation. The optimization framework is available online in open source.

CONCLUSION

Our gradient waveform design is both more flexible and efficient than previous methods, facilitating tensor-valued diffusion encoding in tissues in which motion would otherwise confound the signal. The proposed design exploits asymmetric encoding times, a single refocusing pulse or multiple refocusing pulses, and integrates compensation for concomitant gradient effects throughout the imaging volume.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Tensor-valued diffusion MRI differentiates cortex and white matter in malformations of cortical development associated with epilepsy

Objective:

Delineation of malformations of cortical development (MCD) is central in presurgical evaluation of drug-resistant epilepsy. Delineation using magnetic resonance imaging (MRI) can be ambiguous, however, because the conventional T₁- and T₂-weighted contrasts depend strongly on myelin for differentiation of cortical tissue and white matter. Variations in myelin content within both cortex and white matter may cause MCD findings on MRI to change size, become undetectable, or disagree with histopathology. The novel tensor-valued diffusion MRI (dMRI) technique maps microscopic diffusion anisotropy, which is sensitive to axons rather than myelin. This work investigated whether tensor-valued dMRI may improve differentiation of cortex and white matter in the delineation of MCD.

Methods:

Tensor-valued dMRI was performed on a 7 T MRI scanner in 13 MCD patients (age = 32 ± 13 years) featuring periventricular heterotopia, subcortical heterotopia, focal cortical dysplasia, and polymicrogyria. Data analysis yielded maps of microscopic anisotropy that were compared with T₁-weighted and T₂-fluid-attenuated inversion recovery images and with the fractional anisotropy from diffusion tensor imaging.

Results:

Maps of microscopic anisotropy revealed large white matter-like regions within MCD that were uniformly cortex-like in the conventional MRI contrasts. These regions were seen particularly in the deep white matter parts of subcortical heterotopias and near the gray-white boundaries of focal cortical dysplasias and polymicrogyrias.

Significance:

By being sensitive to axons rather than myelin, mapping of microscopic anisotropy may yield a more robust differentiation of cortex and white matter and improve MCD delineation in presurgical evaluation of epilepsy.

A half-century of innovation in technology-preparing MRI for the 21st century

MRI developed during the last half-century from a very basic concept to an indispensable non-ionising medical imaging technique that has found broad application in diagnostics, therapy control and far beyond. Due to its excellent soft-tissue contrast and the huge variety of accessible tissue- and physiological-parameters, MRI is often preferred to other existing modalities. In the course of its development, MRI underwent many substantial transformations. From the beginning, starting as a proof of concept, much effort was expended to develop the appropriate basic scanning technology and methodology, and to establish the many clinical contrasts (e.g., T₁, T₂, flow, diffusion, water/fat, etc.) that MRI is famous for today. Beyond that, additional prominent innovations to the field have been parallel imaging and compressed sensing, leading to significant scanning time reductions, and the move towards higher static magnetic field strengths, which led to increased sensitivity and improved image quality. Improvements in workflow and the use of artificial intelligence are among many current trends seen in this field, paving the way for a broad use of MRI. The 125th anniversary of the BJR is a good point to reflect on all these changes and developments and to offer some slightly speculative ideas as to what the future may bring.

Disentangling white-matter damage from physiological fibre orientation dispersion in multiple sclerosis

Multiple sclerosis leads to diffuse damage of the central nervous system, affecting also the normal-appearing white matter. Demyelination and axonal degeneration reduce regional fractional anisotropy in normal-appearing white matter, which can be routinely mapped with diffusion tensor imaging. However, the standard fractional anisotropy metric is also sensitive to physiological variations in orientation dispersion of white matter fibres. This complicates the detection of disease-related damage in large parts of cerebral white matter where microstructure physiologically displays a high degree of fibre dispersion. To resolve this ambiguity, we employed a novel tensor-valued encoding method for diffusion MRI, which yields a microscopic fractional anisotropy metric that is unaffected by regional variations in orientation dispersion. In 26 patients with relapsing-remitting multiple sclerosis, 14 patients with primary-progressive multiple sclerosis and 27 age-matched healthy controls, we compared standard fractional anisotropy mapping with the novel microscopic fractional anisotropy mapping method, focusing on normal-appearing white matter. Mean microscopic fractional anisotropy and standard fractional anisotropy of normal-appearing white matter were significantly reduced in both patient groups relative to healthy controls, but microscopic fractional anisotropy yielded a better reflection of disease-related white-matter alterations. The reduction in mean microscopic fractional anisotropy showed a significant positive linear relationship with physical disability, as reflected by the expanded disability status scale. Mean reduction of microscopic fractional anisotropy in normal-appearing white matter also scaled positively with individual cognitive dysfunction, as measured with the symbol digit modality test. Mean microscopic fractional anisotropy reduction in normal-appearing white matter also showed a positive relationship with total white-matter lesion load as well as lesion load in specific tract systems. None of these relationships between normal-appearing white-matter microstructure and clinical, cognitive or structural measures emerged when using mean fractional anisotropy. Together, the results provide converging evidence that microscopic fractional anisotropy mapping substantially advances the assessment of cerebral white matter in multiple sclerosis by disentangling microstructure damage from variations in physiological fibre orientation dispersion at the stage of data acquisition. Since tensor-valued encoding can be implemented in routine diffusion MRI, microscopic fractional anisotropy mapping bears considerable potential for the future assessment of disease progression in normal-appearing white matter in both relapsing-remitting and progressive forms of multiple sclerosis as well as other white-matter-related brain diseases.

Magnetic resonance imaging of mean cell size in human breast tumors

PURPOSE

Cell size is a fundamental characteristic of all tissues, and changes in cell size in cancer reflect tumor status and response to treatments, such as apoptosis and cell-cycle arrest. Unfortunately, cell size can currently be obtained only by pathological evaluation of tumor tissue samples obtained invasively. Previous imaging approaches are limited to preclinical MRI scanners or require relatively long acquisition times that are impractical for clinical imaging. There is a need to develop cell-size imaging for clinical applications.

METHODS

We propose a clinically feasible IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) approach that can characterize mean cell sizes in solid tumors. We report the use of a combination of pulse sequences, using different gradient waveforms implemented on clinical MRI scanners and analytical equations based on these waveforms to analyze diffusion-weighted MRI signals and derive specific microstructural parameters such as cell size. We also describe comprehensive validations of this approach using computer simulations, cell experiments in vitro, and animal experiments in vivo and demonstrate applications in preoperative breast cancer patients.

RESULTS

With fast acquisitions (~7 minutes), IMPULSED can provide high-resolution (1.3 mm in-plane) mapping of mean cell size of human tumors in vivo on clinical 3T MRI scanners. All validations suggest that IMPULSED provides accurate and reliable measurements of mean cell size.

CONCLUSION

The proposed IMPULSED method can assess cell-size variations in tumors of breast cancer patients, which may have the potential to assess early response to neoadjuvant therapy.

Improved fibre dispersion estimation using b-tensor encoding

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/μm², increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.

Oscillating diffusion-encoding with a high gradient-amplitude and high slew-rate head-only gradient for human brain imaging

PURPOSE

We investigate the importance of high gradient-amplitude and high slew-rate on oscillating gradient spin echo (OGSE) diffusion imaging for human brain imaging and evaluate human brain imaging with OGSE on the MAGNUS head-gradient insert (200 mT/m amplitude and 500 T/m/s slew rate).

METHODS

Simulations with cosine-modulated and trapezoidal-cosine OGSE at various gradient amplitudes and slew rates were performed. Six healthy subjects were imaged with the MAGNUS gradient at 3T with OGSE at frequencies up to 100 Hz and b = 450 s/mm² . Comparisons were made against standard pulsed gradient spin echo (PGSE) diffusion in vivo and in an isotropic diffusion phantom.

RESULTS

Simulations show that to achieve high frequency and b-value simultaneously for OGSE, high gradient amplitude, high slew rates, and high peripheral nerve stimulation limits are required. A strong linear trend for increased diffusivity (mean: 8-19%, radial: 9-27%, parallel: 8-15%) was observed in normal white matter with OGSE (20 Hz to 100 Hz) as compared to PGSE. Linear fitting to frequency provided excellent correlation, and using a short-range disorder model provided radial long-term diffusivities of D_∞,MD = 911 ± 72 µm² /s, D_∞,PD = 1519 ± 164 µm² /s, and D_∞,RD = 640 ± 111 µm² /s and correlation lengths of l_{c ,MD} = 0.802 ± 0.156 µm, l_{c ,PD} = 0.837 ± 0.172 µm, and l_{c ,RD} = 0.780 ± 0.174 µm. Diffusivity changes with OGSE frequency were negligible in the phantom, as expected.

CONCLUSION

The high gradient amplitude, high slew rate, and high peripheral nerve stimulation thresholds of the MAGNUS head-gradient enables OGSE acquisition for in vivo human brain imaging.

Motion-compensated b-tensor encoding for in vivo cardiac diffusion-weighted imaging

Motion is a major confound in diffusion-weighted imaging (DWI) in the body, and it is a common cause of image artefacts. The effects are particularly severe in cardiac applications, due to the nonrigid cyclical deformation of the myocardium. Spin echo-based DWI commonly employs gradient moment-nulling techniques to desensitise the acquisition to velocity and acceleration, ie, nulling gradient moments up to the 2nd order (M2-nulled). However, current M2-nulled DWI scans are limited to encode diffusion along a single direction at a time. We propose a method for designing b-tensors of arbitrary shapes, including planar, spherical, prolate and oblate tensors, while nulling gradient moments up to the 2nd order and beyond. The design strategy comprises initialising the diffusion encoding gradients in two encoding blocks about the refocusing pulse, followed by appropriate scaling and rotation, which further enables nulling undesired effects of concomitant gradients. Proof-of-concept assessment of in vivo mean diffusivity (MD) was performed using linear and spherical tensor encoding (LTE and STE, respectively) in the hearts of five healthy volunteers. The results of the M2-nulled STE showed that (a) the sequence was robust to cardiac motion, and (b) MD was higher than that acquired using standard M2-nulled LTE, where diffusion-weighting was applied in three orthogonal directions, which may be attributed to the presence of restricted diffusion and microscopic diffusion anisotropy. Provided adequate signal-to-noise ratio, STE could significantly shorten estimation of MD compared with the conventional LTE approach. Importantly, our theoretical analysis and the proposed gradient waveform design may be useful in microstructure imaging beyond diffusion tensor imaging where the effects of motion must be suppressed.

Higher-order diffusion MRI characterization of mesorectal lymph nodes in rectal cancer

PURPOSE

Mesorectal lymph node staging plays an important role in treatment decision making. Here, we explore the benefit of higher-order diffusion MRI models accounting for non-Gaussian diffusion effects to classify mesorectal lymph nodes both 1) ex vivo at ultrahigh field correlated with histology and 2) in vivo in a clinical scanner upon patient staging.

METHODS

The preclinical investigation included 54 mesorectal lymph nodes, which were scanned at 16.4 T with an extensive diffusion MRI acquisition. Eight diffusion models were compared in terms of goodness of fit, lymph node classification ability, and histology correlation. In the clinical part of this study, 10 rectal cancer patients were scanned with diffusion MRI at 1.5 T, and 72 lymph nodes were analyzed with Apparent Diffusion Coefficient (ADC), Intravoxel Incoherent Motion (IVIM), Kurtosis, and IVIM-Kurtosis.

RESULTS

Compartment models including restricted and anisotropic diffusion improved the preclinical data fit, as well as the lymph node classification, compared to standard ADC. The comparison with histology revealed only moderate correlations, and the highest values were observed between diffusion anisotropy metrics and cell area fraction. In the clinical study, the diffusivity from IVIM-Kurtosis was the only metric showing significant differences between benign (0.80 ± 0.30 μm² /ms) and malignant (1.02 ± 0.41 μm² /ms, P = .03) nodes. IVIM-Kurtosis also yielded the largest area under the receiver operating characteristic curve (0.73) and significantly improved the node differentiation when added to the standard visual analysis by experts based on T₂ -weighted imaging.

CONCLUSION

Higher-order diffusion MRI models perform better than standard ADC and may be of added value for mesorectal lymph node classification in rectal cancer patients.

Diffusion Kurtosis Imaging maps neural damage in the EAE model of multiple sclerosis

Diffusion kurtosis imaging (DKI) is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of microstructural model parameters has been used for assessment of tissue changes in neurodegenerative diseases and associated animal models. In this study, mouse spinal cords from the experimental autoimmune encephalomyelitis (EAE) model of multiple sclerosis (MS) were investigated for the first time using DKI in combination with biophysical modeling to study the relationship between microstructural metrics and degree of animal dysfunction. Thirteen spinal cords were extracted from animals with varied grades of disability and scanned in a high-field MRI scanner along with five control specimen. Diffusion weighted data were acquired together with high resolution T₂* images. Diffusion data were fit to estimate diffusion and kurtosis tensors and white matter modeling parameters, which were all used for subsequent statistical analysis using a linear mixed effects model. T₂* images were used to delineate focal demyelination/inflammation. Our results reveal a strong relationship between disability and measured microstructural parameters in normal appearing white matter and gray matter. Relationships between disability and mean of the kurtosis tensor, radial kurtosis, radial diffusivity were similar to what has been found in other hypomyelinating MS models, and in patients. However, the changes in biophysical modeling parameters and in particular in extra-axonal axial diffusivity were clearly different from previous studies employing other animal models of MS. In conclusion, our data suggest that DKI and microstructural modeling can provide a unique contrast capable of detecting EAE-specific changes correlating with clinical disability.

In vivo demonstration of microscopic anisotropy in the human kidney using multidimensional diffusion MRI

PURPOSE

To demonstrate the feasibility of multidimensional diffusion MRI to probe and quantify microscopic fractional anisotropy (µFA) in human kidneys in vivo.

METHODS

Linear tensor encoded (LTE) and spherical tensor encoded (STE) renal diffusion MRI scans were performed in 10 healthy volunteers. Respiratory triggering and image registration were used to minimize motion artefacts during the acquisition. Kidney cortex-medulla were semi-automatically segmented based on fractional anisotropy (FA) values. A model-free analysis of LTE and STE signal dependence on b-value in the renal cortex and medulla was performed. Subsequently, µFA was estimated using a single-shell approach. Finally, a comparison of conventional FA and µFA is shown.

RESULTS

The hallmark effect of µFA (divergence of LTE and STE signal with increasing b-value) was observed in all subjects. A statistically significant difference between LTE and STE signal was found in the cortex and medulla, starting from b = 750 s/mm2 and b = 500 s/mm2 , respectively. This difference was maximal at the highest b-value sampled (b = 1000 s/mm2 ) which suggests that relatively high b-values are required for µFA mapping in the kidney compared to conventional FA. Cortical and medullary µFA were, respectively, 0.53 ± 0.09 and 0.65 ± 0.05, both respectively higher than conventional FA (0.19 ± 0.02 and 0.40 ± 0.02).

CONCLUSION

The feasibility of combining LTE and STE diffusion MRI to probe and quantify µFA in human kidneys is demonstrated for the first time. By doing so, we show that novel microstructure information-not accessible by conventional diffusion encoding-can be probed by multidimensional diffusion MRI. We also identify relevant technical limitations that warrant further development of the technique for body MRI.

Maxwell-compensated design of asymmetric gradient waveforms for tensor-valued diffusion encoding

PURPOSE

Diffusion encoding with asymmetric gradient waveforms is appealing because the asymmetry provides superior efficiency. However, concomitant gradients may cause a residual gradient moment at the end of the waveform, which can cause significant signal error and image artifacts. The purpose of this study was to develop an asymmetric waveform designs for tensor-valued diffusion encoding that is not sensitive to concomitant gradients.

METHODS

The "Maxwell index" was proposed as a scalar invariant to capture the effect of concomitant gradients. Optimization of "Maxwell-compensated" waveforms was performed in which this index was constrained. Resulting waveforms were compared to waveforms from literature, in terms of the measured and predicted impact of concomitant gradients, by numerical analysis as well as experiments in a phantom and in a healthy human brain.

RESULTS

Maxwell-compensated waveforms with Maxwell indices below 100 (mT/m)2 ms showed negligible signal bias in both numerical analysis and experiments. By contrast, several waveforms from literature showed gross signal bias under the same conditions, leading to a signal bias that was large enough to markedly affect parameter maps. Experimental results were accurately predicted by theory.

CONCLUSION

Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient diffusion encoding that negates the effects of concomitant fields while enabling arbitrary shapes of the b-tensor. This waveform design is especially useful in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition, and large FOVs.

Tensor-valued diffusion MRI in under 3 minutes: an initial survey of microscopic anisotropy and tissue heterogeneity in intracranial tumors

PURPOSE

To evaluate the feasibility of a 3-minutes protocol for assessment of the microscopic anisotropy and tissue heterogeneity based on tensor-valued diffusion MRI in a wide range of intracranial tumors.

METHODS

B-tensor encoding was performed in 42 patients with intracranial tumors (gliomas, meningiomas, adenomas, and metastases). Microscopic anisotropy and tissue heterogeneity were evaluated by estimating the anisotropic kurtosis (MK_A ) and isotropic kurtosis (MK_I ), respectively. An extensive imaging protocol was compared with a 3-minutes protocol.

RESULTS

The fast imaging protocol yielded parameters with characteristics in terms of bias and precision similar to the full protocol. Glioblastomas had lower microscopic anisotropy than meningiomas (MK_A = 0.29 ± 0.06 vs. 0.45 ± 0.08, P = 0.003). Metastases had higher tissue heterogeneity (MK_I = 0.57 ± 0.07) than both the glioblastomas (0.44 ± 0.06, P < 0.001) and meningiomas (0.46 ± 0.06, P = 0.03).

CONCLUSION

Evaluation of the microscopic anisotropy and tissue heterogeneity in intracranial tumor patients is feasible in clinically relevant times frames.

Peripheral nerve stimulation limits of a high amplitude and slew rate magnetic field gradient coil for neuroimaging

PURPOSE

To establish peripheral nerve stimulation (PNS) thresholds for an ultra-high performance magnetic field gradient subsystem (simultaneous 200-mT/m gradient amplitude and 500-T/m/s gradient slew rate; 1 MVA per axis [MAGNUS]) designed for neuroimaging with asymmetric transverse gradients and 42-cm inner diameter, and to determine PNS threshold dependencies on gender, age, patient positioning within the gradient subsystem, and anatomical landmarks.

METHODS

The MAGNUS head gradient was installed in a whole-body 3T scanner with a custom 16-rung bird-cage transmit/receive RF coil compatible with phased-array receiver brain coils. Twenty adult subjects (10 male, mean ± SD age = 40.4 ± 11.1 years) underwent the imaging and PNS study. The tests were repeated by displacing subject positions by 2-4 cm in the superior-inferior and anterior-posterior directions.

RESULTS

The x-axis (left-right) yielded mostly facial stimulation, with mean ΔG_min = 111 ± 6 mT/m, chronaxie = 766 ± 76 µsec. The z-axis (superior-inferior) yielded mostly chest/shoulder stimulation (123 ± 7 mT/m, 620 ± 62 µsec). Y-axis (anterior-posterior) stimulation was negligible. X-axis and z-axis thresholds tended to increase with age, and there was negligible dependency with gender. Translation in the inferior and posterior directions tended to increase the x-axis and z-axis thresholds, respectively. Electric field simulations showed good agreement with the PNS results. Imaging at MAGNUS gradient performance with increased PNS threshold provided a 35% reduction in noise-to-diffusion contrast as compared with whole-body performance (80 mT/m gradient amplitude, 200 T/m/sec gradient slew rate).

CONCLUSION

The PNS threshold of MAGNUS is significantly higher than that for whole-body gradients, which allows for diffusion gradients with short rise times (under 1 msec), important for interrogating brain microstructure length scales.

Linear, planar and spherical tensor-valued diffusion MRI data by free waveform encoding in healthy brain, water, oil and liquid crystals

Recently, several biophysical models and signal representations have been proposed for microstructure imaging based on tensor-valued, or multidimensional, diffusion MRI. The acquisition of the necessary data requires non-conventional pulse sequences, and data is therefore not available to the wider diffusion MRI community. To facilitate exploration and development of analysis techniques based on tensor-valued diffusion encoding, we share a comprehensive data set acquired in a healthy human brain. The data encompasses diffusion weighted images using linear, planar and spherical diffusion tensor encoding at multiple b-values and diffusion encoding directions. We also supply data acquired in several phantoms that may support validation. The data is hosted by GitHub: https://github.com/filip-szczepankiewicz/Szczepankiewicz_DIB_2019.

Searching for the neurite density with diffusion MRI: Challenges for biophysical modeling

In vivo mapping of the neurite density with diffusion MRI (dMRI) is a high but challenging aim. First, it is unknown whether all neurites exhibit completely anisotropic ("stick-like") diffusion. Second, the "density" of tissue components may be confounded by non-diffusion properties such as T2 relaxation. Third, the domain of validity for the estimated parameters to serve as indices of neurite density is incompletely explored. We investigated these challenges by acquiring data with "b-tensor encoding" and multiple echo times in brain regions with low orientation coherence and in white matter lesions. Results showed that microscopic anisotropy from b-tensor data is associated with myelinated axons but not with dendrites. Furthermore, b-tensor data together with data acquired for multiple echo times showed that unbiased density estimates in white matter lesions require data-driven estimates of compartment-specific T2 values. Finally, the "stick" fractions of different biophysical models could generally not serve as neurite density indices across the healthy brain and white matter lesions, where outcomes of comparisons depended on the choice of constraints. In particular, constraining compartment-specific T2 values was ambiguous in the healthy brain and had a large impact on estimated values. In summary, estimating neurite density generally requires accounting for different diffusion and/or T2 properties between axons and dendrites. Constrained "index" parameters could be valid within limited domains that should be delineated by future studies.

Estimation of diffusion, perfusion and fractional volumes using a multi-compartment relaxation-compensated intravoxel incoherent motion (IVIM) signal model

Compartmental diffusion MRI models that account for intravoxel incoherent motion (IVIM) of blood perfusion allow for estimation of the fractional volume of the microvascular compartment. Conventional IVIM models are known to be biased by not accounting for partial volume effects caused by free water and cerebrospinal fluid (CSF), or for tissue-dependent relaxation effects. In this work, a three-compartment model (tissue, free water and blood) that includes relaxation terms is introduced. To estimate the model parameters, in vivo human data were collected with multiple echo times (TE), inversion times (TI) and b-values, which allowed a direct relaxation estimate alongside estimation of perfusion, diffusion and fractional volume parameters. Compared to conventional two-compartment models (with and without relaxation compensation), the three-compartment model showed less effects of CSF contamination. The proposed model yielded significantly different volume fractions of blood and tissue compared to the non-relaxation-compensated model, as well as to the conventional two-compartment model, suggesting that previously reported parameter ranges, using models that do not account for relaxation, should be reconsidered.

VERDICT MRI validation in fresh and fixed prostate specimens using patient-specific moulds for histological and MR alignment

The VERDICT framework for modelling diffusion MRI data aims to relate parameters from a biophysical model to histological features used for tumour grading in prostate cancer. Validation of the VERDICT model is necessary for clinical use. This study compared VERDICT parameters obtained ex vivo with histology in five specimens from radical prostatectomy. A patient-specific 3D-printed mould was used to investigate the effects of fixation on VERDICT parameters and to aid registration to histology. A rich diffusion data set was acquired in each ex vivo prostate before and after fixation. At both time points, data were best described by a two-compartment model: the model assumes that an anisotropic tensor compartment represents the extracellular space and a restricted sphere compartment models the intracellular space. The effect of fixation on model parameters associated with tissue microstructure was small. The patient-specific mould minimized tissue deformations and co-localized slices, so that rigid registration of MRI to histology images allowed region-based comparison with histology. The VERDICT estimate of the intracellular volume fraction corresponded to histological indicators of cellular fraction, including high values in tumour regions. The average sphere radius from VERDICT, representing the average cell size, was relatively uniform across samples. The primary diffusion direction from the extracellular compartment of the VERDICT model aligned with collagen fibre patterns in the stroma obtained by structure tensor analysis. This confirmed the biophysical relationship between ex vivo VERDICT parameters and tissue microstructure from histology.

Diffusion tensor distribution imaging

Conventional diffusion MRI yields voxel-averaged parameters that suffer from ambiguities for heterogeneous anisotropic materials such as brain tissue. Using principles from solid-state NMR spectroscopy, we have previously introduced the shape of the diffusion encoding tensor as a separate acquisition dimension that disentangles isotropic and anisotropic contributions to the observed diffusivities, thereby allowing for unconstrained data inversion into diffusion tensor distributions with "size," "shape," and orientation dimensions. Here we combine our recent non-parametric data inversion algorithm and data acquisition protocol with an imaging pulse sequence to demonstrate spatial mapping of diffusion tensor distributions using a previously developed composite phantom with multiple isotropic and anisotropic components. We propose a compact format for visualizing two-dimensional arrays of the distributions, new scalar parameters quantifying intra-voxel heterogeneity, and a binning procedure giving maps of all relevant parameters for each of the components resolved in the multidimensional distribution space.

Imaging brain microstructure with diffusion MRI: practicality and applications

This article gives an overview of microstructure imaging of the brain with diffusion MRI and reviews the state of the art. The microstructure-imaging paradigm aims to estimate and map microscopic properties of tissue using a model that links these properties to the voxel scale MR signal. Imaging techniques of this type are just starting to make the transition from the technical research domain to wide application in biomedical studies. We focus here on the practicalities of both implementing such techniques and using them in applications. Specifically, the article summarizes the relevant aspects of brain microanatomy and the range of diffusion-weighted MR measurements that provide sensitivity to them. It then reviews the evolution of mathematical and computational models that relate the diffusion MR signal to brain tissue microstructure, as well as the expanding areas of application. Next we focus on practicalities of designing a working microstructure imaging technique: model selection, experiment design, parameter estimation, validation, and the pipeline of development of this class of technique. The article concludes with some future perspectives on opportunities in this topic and expectations on how the field will evolve in the short-to-medium term.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

Tensor-valued diffusion encoding for diffusional variance decomposition (DIVIDE): Technical feasibility in clinical MRI systems

Microstructure imaging techniques based on tensor-valued diffusion encoding have gained popularity within the MRI research community. Unlike conventional diffusion encoding-applied along a single direction in each shot-tensor-valued encoding employs diffusion encoding along multiple directions within a single preparation of the signal. The benefit is that such encoding may probe tissue features that are not accessible by conventional encoding. For example, diffusional variance decomposition (DIVIDE) takes advantage of tensor-valued encoding to probe microscopic diffusion anisotropy independent of orientation coherence. The drawback is that tensor-valued encoding generally requires gradient waveforms that are more demanding on hardware; it has therefore been used primarily in MRI systems with relatively high performance. The purpose of this work was to explore tensor-valued diffusion encoding on clinical MRI systems with varying performance to test its technical feasibility within the context of DIVIDE. We performed whole-brain imaging with linear and spherical b-tensor encoding at field strengths between 1.5 and 7 T, and at maximal gradient amplitudes between 45 and 80 mT/m. Asymmetric gradient waveforms were optimized numerically to yield b-values up to 2 ms/μm2. Technical feasibility was assessed in terms of the repeatability, SNR, and quality of DIVIDE parameter maps. Variable system performance resulted in echo times between 83 to 115 ms and total acquisition times of 6 to 9 minutes when using 80 signal samples and resolution 2×2×4 mm3. As expected, the repeatability, signal-to-noise ratio and parameter map quality depended on hardware performance. We conclude that tensor-valued encoding is feasible for a wide range of MRI systems-even at 1.5 T with maximal gradient waveform amplitudes of 33 mT/m-and baseline experimental design and quality parameters for all included configurations. This demonstrates that tissue features, beyond those accessible by conventional diffusion encoding, can be explored on a wide range of MRI systems.

Eddy current nulled constrained optimization of isotropic diffusion encoding gradient waveforms

PURPOSE

Isotropic diffusion encoding efficiently encodes additional microstructural information in combination with conventional linear diffusion encoding. However, the gradient-intensive isotropic diffusion waveforms generate significant eddy currents, which cause image distortions. The purpose of this study is to present a method for designing isotropic diffusion encoding waveforms with intrinsic eddy current nulling.

METHODS

Eddy current nulled gradient waveforms were designed using a constrained optimization waveform for a 3T GE Premier MRI system. Encoding waveforms were designed for a variety of eddy current null times and sequence timings to evaluate the achievable b-value. Waveforms were also tested with both eddy current nulling and concomitant field compensation. Distortion reduction was tested in both phantoms and the in vivo human brain.

RESULTS

The feasibility of isotropic diffusion encoding with intrinsic correction of eddy current distortion and signal bias from concomitant fields was demonstrated. The constrained optimization algorithm produced gradient waveforms with the specified eddy current null times. The reduction in the achievable diffusion weighting was dependent on the number of eddy current null times. A reduction in the eddy current-induced image distortions was observed in both phantoms and in vivo human subjects.

CONCLUSION

The proposed framework allows the design of isotropic diffusion-encoding sequences with reduced image distortion.

Effects of nongaussian diffusion on "isotropic diffusion" measurements: An ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.