This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and ...modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.
•We have described a new diffusion MR framework for imaging of microstructure that we call q-space trajectory imaging.•Performing diffusion encoding with a wide range of q-space trajectories is feasible on a clinical system.•The cumulant expansion of the MR signal yields the mean diffusion tensor and a fourth-order covariance tensor.•QTI can disentangle variation in size from variation in shape and direction.•QTI does not require macroscopic anisotropy and could be useful not only in white matter but also in gray matter.
In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We ...formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.
Abstract
Numerous applications in diffusion MRI involve computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient ...sampling vectors are uniformly distributed on a sphere (or ‘shell’), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres. To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its ‘isotropic part’. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.
The multiple scattering extensions of the pulsed field gradient (PFG) experiments can be used to characterize restriction-induced anisotropy at different length scales. In double-PFG acquisitions ...that involve two pairs of diffusion gradient pulses, the dependence of the MR signal attenuation on the angle between the two gradients is a signature of restriction that can be observed even at low gradient strengths. In this article, a comprehensive theoretical treatment of the double-PFG observation of restricted diffusion is presented. In the first part of the article, the problem is treated for arbitrarily shaped pores under idealized experimental conditions, comprising infinitesimally narrow gradient pulses with long separation times and long or vanishing mixing times. New insights are obtained when the treatment is applied to simple pore shapes of spheres, ellipsoids, and capped cylinders. The capped cylinder geometry is considered in the second part of the article where the solution for a double-PFG experiment with arbitrary experimental parameters is introduced. Although compartment shape anisotropy (CSA) is emphasized here, the findings of this article can be used in gleaning the volume, eccentricity, and orientation distribution function associated with ensembles of anisotropic compartments using double-PFG acquisitions with arbitrary experimental parameters.
Diffusion tensor imaging (DTI) is the most widely used method for characterizing noninvasively structural and architectural features of brain tissues. However, the assumption of a Gaussian spin ...displacement distribution intrinsic to DTI weakens its ability to describe intricate tissue microanatomy. Consequently, the biological interpretation of microstructural parameters, such as fractional anisotropy or mean diffusivity, is often equivocal. We evaluate the clinical feasibility of assessing brain tissue microstructure with mean apparent propagator (MAP) MRI, a powerful analytical framework that efficiently measures the probability density function (PDF) of spin displacements and quantifies useful metrics of this PDF indicative of diffusion in complex microstructure (e.g., restrictions, multiple compartments). Rotation invariant and scalar parameters computed from the MAP show consistent variation across neuroanatomical brain regions and increased ability to differentiate tissues with distinct structural and architectural features compared with DTI-derived parameters. The return-to-origin probability (RTOP) appears to reflect cellularity and restrictions better than MD, while the non-Gaussianity (NG) measures diffusion heterogeneity by comprehensively quantifying the deviation between the spin displacement PDF and its Gaussian approximation. Both RTOP and NG can be decomposed in the local anatomical frame for reference determined by the orientation of the diffusion tensor and reveal additional information complementary to DTI. The propagator anisotropy (PA) shows high tissue contrast even in deep brain nuclei and cortical gray matter and is more uniform in white matter than the FA, which drops significantly in regions containing crossing fibers. Orientational profiles of the propagator computed analytically from the MAP MRI series coefficients allow separation of different fiber populations in regions of crossing white matter pathways, which in turn improves our ability to perform whole-brain fiber tractography. Reconstructions from subsampled data sets suggest that MAP MRI parameters can be computed from a relatively small number of DWIs acquired with high b-value and good signal-to-noise ratio in clinically achievable scan durations of less than 10min. The neuroanatomical consistency across healthy subjects and reproducibility in test–retest experiments of MAP MRI microstructural parameters further substantiate the robustness and clinical feasibility of this technique. The MAP MRI metrics could potentially provide more sensitive clinical biomarkers with increased pathophysiological specificity compared to microstructural measures derived using conventional diffusion MRI techniques.
Display omitted
•In vivo MAP metrics show consistent neuroanatomical contrast in healthy subjects.•These microstructural scalar measures provide novel information compared with DTI.•MAP parameters can be reconstructed from diffusion datasets acquired in 10min.•These metrics derived from clinical data sets show good test–retest repeatability.
Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and ...physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in “q-space,” and the corresponding “mean apparent propagator (MAP)” describing molecular displacements in “r-space.” We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework.
We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit “displacement” sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions—the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape.
MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.
•MAP-MRI is a comprehensive method for modeling 3D (multi-shell) q-space signal.•MAP-MRI subsumes and generalizes diffusion tensor imaging (DTI).•Several novel parameters capture previously obscured microstructural features.•MAP reconstruction is performed on an excised marmoset brain dataset.•MAP-MRI is robust, efficient, and may be adapted to in vivo and clinical imaging.
•Q-space trajectory imaging (QTI) is a powerful tool for tissue characterization.•The tissue can be characterized by moments of a diffusion tensor distribution (DTD).•The first such moments have to ...obey certain positivity conditions, which we impose.•The extended framework, referred to as QTI+, utilizes semidefinite programming.•QTI+ is more robust to noise and allows for shorter acquisition protocols.
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 apparent water exchange rate (AXR) in FEXI shows anisotropy in human white matter.•The AXR perpendicular and parallel to fiber orientation are significantly different.•The perpendicular AXR is ...more sensitive to axonal water transmembrane exchange.
Transmembrane water exchange is a potential biomarker in the diagnosis and understanding of cancers, brain disorders, and other diseases. Filter-exchange imaging (FEXI), a special case of diffusion exchange spectroscopy adapted for clinical applications, has the potential to reveal different physiological water exchange processes. However, it is still controversial whether modulating the diffusion encoding gradient direction can affect the apparent exchange rate (AXR) measurements of FEXI in white matter (WM) where water diffusion shows strong anisotropy. In this study, we explored the diffusion-encoding direction dependence of FEXI in human brain white matter by performing FEXI with 20 diffusion-encoding directions on a clinical 3T scanner in-vivo. The results show that the AXR values measured when the gradients are perpendicular to the fiber orientation (0.77 ± 0.13 s − 1, mean ± standard deviation of all the subjects) are significantly larger than the AXR estimates when the gradients are parallel to the fiber orientation (0.33 ± 0.14 s − 1, p < 0.001) in WM voxels with coherently-orientated fibers. In addition, no significant correlation is found between AXRs measured along these two directions, indicating that they are measuring different water exchange processes. What's more, only the perpendicular AXR rather than the parallel AXR shows dependence on axonal diameter, indicating that the perpendicular AXR might reflect transmembrane water exchange between intra-axonal and extra-cellular spaces. Further finite difference (FD) simulations having three water compartments (intra-axonal, intra-glial, and extra-cellular spaces) to mimic WM micro-environments also suggest that the perpendicular AXR is more sensitive to the axonal water transmembrane exchange than parallel AXR. Taken together, our results show that AXR measured along different directions could be utilized to probe different water exchange processes in WM.
PDF
