Detecting compartmental non-Gaussian diffusion with symmetrized double-PFG MRI

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.

Correlation Tensor MRI deciphers underlying kurtosis sources in stroke

Noninvasively detecting and characterizing modulations in cellular scale micro-architecture remains a desideratum for contemporary neuroimaging. Diffusion MRI (dMRI) has become the mainstay methodology for probing microstructure, and, in ischemia, its contrasts have revolutionized stroke management. Diffusion kurtosis imaging (DKI) has been shown to significantly enhance the sensitivity of stroke detection compared to its diffusion tensor imaging (DTI) counterparts. However, the interpretation of DKI remains ambiguous as its contrast may arise from competing kurtosis sources related to the anisotropy of tissue components, diffusivity variance across components, and microscopic kurtosis (e.g., arising from cross-sectional variance, structural disorder, and restriction). Resolving these sources may be fundamental for developing more specific imaging techniques for stroke management, prognosis, and understanding its pathophysiology. In this study, we apply Correlation Tensor MRI (CTI) - a double diffusion encoding (DDE) methodology recently introduced for deciphering kurtosis sources based on the unique information captured in DDE's diffusion correlation tensors - to investigate the underpinnings of kurtosis measurements in acute ischemic lesions. Simulations for the different kurtosis sources revealed specific signatures for cross-sectional variance (representing neurite beading), edema, and cell swelling. Ex vivo CTI experiments at 16.4 T were then performed in an experimental photothrombotic stroke model 3 h post-stroke (N = 10), and successfully separated anisotropic, isotropic, and microscopic non-Gaussian diffusion sources in the ischemic lesions. Each of these kurtosis sources provided unique contrasts in the stroked area. Particularly, microscopic kurtosis was shown to be a primary "driver" of total kurtosis upon ischemia; its large increases, coupled with decreases in anisotropic kurtosis, are consistent with the expected elevation in cross-sectional variance, likely linked to beading effects in small objects such as neurites. In vivo experiments at 9.4 T at the same time point (3 h post ischemia, N = 5) demonstrated the stability and relevance of the findings and showed that fixation is not a dominant confounder in our findings. In future studies, the different CTI contrasts may be useful to address current limitations of stroke imaging, e.g., penumbra characterization, distinguishing lesion progression form tissue recovery, and elucidating pathophysiological correlates.

Evidence for microscopic kurtosis in neural tissue revealed by correlation tensor MRI

PURPOSE

The impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, correlation tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori multi-gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state-of-the-art methods ignoring µK.

THEORY AND METHODS

CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis.

RESULTS

The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside K_aniso and K_iso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non-negligible µK substantially were found to bias prior MGC analyses of K_iso and K_aniso .

CONCLUSIONS

Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non-negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.

Diffusional Kurtosis Imaging in the Diffusion Imaging in Python Project

Diffusion-weighted magnetic resonance imaging (dMRI) measurements and models provide information about brain connectivity and are sensitive to the physical properties of tissue microstructure. Diffusional Kurtosis Imaging (DKI) quantifies the degree of non-Gaussian diffusion in biological tissue from dMRI. These estimates are of interest because they were shown to be more sensitive to microstructural alterations in health and diseases than measures based on the total anisotropy of diffusion which are highly confounded by tissue dispersion and fiber crossings. In this work, we implemented DKI in the Diffusion in Python (DIPY) project-a large collaborative open-source project which aims to provide well-tested, well-documented and comprehensive implementation of different dMRI techniques. We demonstrate the functionality of our methods in numerical simulations with known ground truth parameters and in openly available datasets. A particular strength of our DKI implementations is that it pursues several extensions of the model that connect it explicitly with microstructural models and the reconstruction of 3D white matter fiber bundles (tractography). For instance, our implementations include DKI-based microstructural models that allow the estimation of biophysical parameters, such as axonal water fraction. Moreover, we illustrate how DKI provides more general characterization of non-Gaussian diffusion compatible with complex white matter fiber architectures and gray matter, and we include a novel mean kurtosis index that is invariant to the confounding effects due to tissue dispersion. In summary, DKI in DIPY provides a well-tested, well-documented and comprehensive reference implementation for DKI. It provides a platform for wider use of DKI in research on brain disorders and in cognitive neuroscience.

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.

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.

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.

The haemodynamics of the human placenta in utero

We have used magnetic resonance imaging (MRI) to provide important new insights into the function of the human placenta in utero. We have measured slow net flow and high net oxygenation in the placenta in vivo, which are consistent with efficient delivery of oxygen from mother to fetus. Our experimental evidence substantiates previous hypotheses on the effects of spiral artery remodelling in utero and also indicates rapid venous drainage from the placenta, which is important because this outflow has been largely neglected in the past. Furthermore, beyond Braxton Hicks contractions, which involve the entire uterus, we have identified a new physiological phenomenon, the ‘utero-placental pump’, by which the placenta and underlying uterine wall contract independently of the rest of the uterus, expelling maternal blood from the intervillous space.

MRI provides important new insights into the function of the human placenta, revealing slow net flow and high, uniform oxygenation in healthy pregnancies, detecting changes that will lead to compromised oxygen delivery to the fetus in preeclampsia, and identifying a new physiological phenomenon, the ‘utero-placental pump’.

Joint RElaxation-Diffusion Imaging Moments to Probe Neurite Microstructure

Joint relaxation-diffusion measurements can provide new insight about the tissue microstructural properties. Most recent methods have focused on inverting the Laplace transform to recover the joint distribution of relaxation-diffusion. However, as is well-known, this problem is notoriously ill-posed and numerically unstable. In this work, we address this issue by directly computing the joint moments of transverse relaxation rate and diffusivity, which can be robustly estimated. To zoom into different parts of the joint distribution, we further enhance our method by applying multiplicative filters to the joint probability density function of relaxation and diffusion and compute the corresponding moments. We propose an approach to use these moments to compute several novel scalar indices to characterize specific properties of the underlying tissue microstructure. Furthermore, for the first time, we propose an algorithm to estimate diffusion signals that are independent of echo time based on the moments of the marginal probability density function of diffusion. We demonstrate its utility in extracting tissue information not contaminated with multiple intra-voxel relaxation rates. We compare the performance of four types of filters that zoom into tissue components with different relaxation and diffusion properties and demonstrate it on an in-vivo human dataset. Experimental results show that these filters are able to characterize heterogeneous tissue microstructure. Moreover, the filtered diffusion signals are also able to distinguish fiber bundles with similar orientations but different relaxation rates. The proposed method thus allows to characterize the neural microstructure information in a robust and unique manner not possible using existing techniques.

JEDI: Joint Estimation Diffusion Imaging of macroscopic and microscopic tissue properties

PURPOSE

A new method for enhancing the sensitivity of diffusion MRI (dMRI) by combining the data from single (sPFG) and double (dPFG) pulsed field gradient experiments is presented.

METHODS

This method uses our JESTER framework to combine microscopic anisotropy information from dFPG experiments using a new method called diffusion tensor subspace imaging (DiTSI) to augment the macroscopic anisotropy information from sPFG data analyzed using our guided by entropy spectrum pathways method. This new method, called joint estimation diffusion imaging (JEDI), combines the sensitivity to macroscopic diffusion anisotropy of sPFG with the sensitivity to microscopic diffusion anisotropy of dPFG methods.

RESULTS

Its ability to produce significantly more detailed anisotropy maps and more complete fiber tracts than existing methods within both brain white matter (WM) and gray matter (GM) is demonstrated on normal human subjects on data collected using a novel fast, robust, and clinically feasible sPFG/dPFG acquisition.

CONCLUSIONS

The potential utility of this method is suggested by an initial demonstration of its ability to mitigate the problem of gyral bias. The capability of more completely characterizing the tissue structure and connectivity throughout the entire brain has broad implications for the utility and scope of dMRI in a wide range of research and clinical applications.

Multidimensional diffusion MRI with spectrally modulated gradients reveals unprecedented microstructural detail

Characterization of porous media is essential in a wide range of biomedical and industrial applications. Microstructural features can be probed non-invasively by diffusion magnetic resonance imaging (dMRI). However, diffusion encoding in conventional dMRI may yield similar signatures for very different microstructures, which represents a significant limitation for disentangling individual microstructural features in heterogeneous materials. To solve this problem, we propose an augmented multidimensional diffusion encoding (MDE) framework, which unlocks a novel encoding dimension to assess time-dependent diffusion specific to structures with different microscopic anisotropies. Our approach relies on spectral analysis of complex but experimentally efficient MDE waveforms. Two independent contrasts to differentiate features such as cell shape and size can be generated directly by signal subtraction from only three types of measurements. Analytical calculations and simulations support our experimental observations. Proof-of-concept experiments were applied on samples with known and distinctly different microstructures. We further demonstrate substantially different contrasts in different tissue types of a post mortem brain. Our simultaneous assessment of restriction size and shape may be instrumental in studies of a wide range of porous materials, enable new insights into the microstructure of biological tissues or be of great value in diagnostics.

In vivo microscopic diffusional kurtosis imaging with symmetrized double diffusion encoding EPI

PURPOSE

Diffusional kurtosis imaging (DKI) measures the deviation of the displacement probability from a normal distribution, complementing the data commonly acquired by diffusion MRI. It is important to elucidate the sources of kurtosis contrast, particularly in biological tissues where microscopic kurtosis (intrinsic kurtosis) and diffusional heterogeneity may co-exist.

METHODS

We have developed a technique for microscopic kurtosis MRI, dubbed microscopic diffusional kurtosis imaging (µDKI), using a symmetrized double diffusion encoding (s-DDE) EPI sequence. We compared this newly developed µDKI to conventional DKI methods in both a triple compartment phantom and in vivo.

RESULTS

Our results showed that whereas conventional DKI and µDKI provided similar measurements in a compartment of monosphere beads, kurtosis measured by µDKI was significantly less than that measured by conventional DKI in a compartment of mixed Gaussian pools. For in vivo brain imaging, µDKI showed small yet significantly lower kurtosis measurement in regions of the cortex, CSF, and internal capsule compared to the conventional DKI approach.

CONCLUSIONS

Our study showed that µDKI is less susceptible than conventional DKI to sub-voxel diffusional heterogeneity. Our study also provided important preliminary demonstration of our technique in vivo, warranting future studies to investigate its diagnostic use in examining neurological disorders.

Preliminary evaluation of accelerated microscopic diffusional kurtosis imaging (μDKI) in a rodent model of epilepsy

PURPOSE

Our study aimed to develop accelerated microscopic diffusional kurtosis imaging (μDKI) and preliminarily evaluated it in a rodent model of chronic epilepsy.

METHODS

We investigated two μDKI acceleration schemes of reduced sampling density and angular range in a phantom and wild-type rats, and further tested μDKI method in pilocarpine-induced epilepsy rats using a 4.7 Tesla MRI. Single slice average μD_app and μK_app maps were derived, and Nissl staining was obtained.

RESULTS

The kurtosis maps from two accelerated μDKI sampling schemes (sampling density and range) are very similar to that using fully sampled data (SSIM > 0.95). For the epileptic models, μDKI showed noticeably different contrast from those obtained with conventional DKI. Specifically, the average μK_app was significantly less than that of the average of K_app (0.15 ± 0.01 vs. 0.47 ± 0.02) in the ventricle.

CONCLUSIONS

Our study demonstrated the feasibility of accelerated in vivo μDKI. Our work revealed that μDKI provides complementary information to conventional DKI method, suggesting that advanced DKI sequences are promising to elucidate tissue microstructure in neurological diseases.

JOURNAL CLUB: Evaluation of Diffusion Kurtosis Imaging of Stroke Lesion With Hemodynamic and Metabolic MRI in a Rodent Model of Acute Stroke

OBJECTIVE

Diffusion kurtosis imaging (DKI) has emerged as a new acute stroke imaging approach, augmenting routine DWI. Although it has been shown that a diffusion lesion without kurtosis abnormality is more likely to recover after reperfusion, whereas a kurtosis lesion shows poor response, little is known about the underlying pathophysiologic profile of the kurtosis lesion versus the kurtosis lesion-diffusion lesion mismatch.

MATERIALS AND METHODS

We performed multiparametric MRI, including arterial spin labeling, pH-sensitive amide proton transfer, and DKI, in a rodent model of acute stroke caused by embolic middle cerebral artery occlusion. Diffusion and kurtosis lesions were semiautomatically segmented, and multiparametric MRI indexes were compared among the kurtosis lesion, diffusion lesion, kurtosis lesion-diffusion lesion mismatch, and the contralateral normal tissue area.

RESULTS

We confirmed a significant difference between diffusion lesion and kurtosis lesion volumes (mean [± SD] volume, 151 ± 65 vs 125 ± 47 mm³; p < 0.05). Although ischemic lesions have significantly reduced cerebral blood flow compared with contralateral normal tissue, we did not find a significant difference in cerebral blood flow between the kurtosis lesion and the kurtosis lesion-diffusion lesion mismatch (mean cerebral blood flow, 0.53 ± 0.10 vs 0.47 ± 0.14 mL/g of tissue per minute; p > 0.05). Of importance, the pH of the kurtosis lesion was significantly lower than that of the lesion mismatch (mean pH, 6.81 ± 0.08 vs 6.89 ± 0.09; p < 0.01).

CONCLUSION

The present study confirms that DKI provides an expedient approach for refining the heterogeneous DWI lesion that is associated with graded metabolic derangement, which is promising for improving the infarction core definition and ultimately helping to guide stroke treatment.

Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue

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

Tensor estimation for double-pulsed diffusional kurtosis imaging

Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented.

NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy

We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.