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.

Diffusion tensor imaging (DTI) is the method of choice for non-invasive investigations of the structure of human brain white matter (WM). The results are conventionally reported as maps of the fractional anisotropy (FA), which is a parameter related to microstructural features such as axon density, diameter, and myelination. The interpretation of FA in terms of microstructure becomes ambiguous when there is a distribution of axon orientations within the image voxel. In this paper, we propose a procedure for resolving this ambiguity by determining a new parameter, the microscopic fractional anisotropy (μFA), which corresponds to the FA without the confounding influence of orientation dispersion. In addition, we suggest a method for measuring the orientational order parameter (OP) for the anisotropic objects. The experimental protocol is capitalizing on a recently developed diffusion nuclear magnetic resonance (NMR) pulse sequence based on magic-angle spinning of the q-vector. Proof-of-principle experiments are carried out on microimaging and clinical MRI equipment using lyotropic liquid crystals and plant tissues as model materials with high μFA and low FA on account of orientation dispersion. We expect the presented method to be especially fruitful in combination with DTI and high angular resolution acquisition protocols for neuroimaging studies of gray and white matter.

The anisotropy of water diffusion in brain tissue is affected by both disease and development. This change can be detected using diffusion MRI and is often quantified by the fractional anisotropy (FA) derived from diffusion tensor imaging (DTI). Although FA is sensitive to anisotropic cell structures, such as axons, it is also sensitive to their orientation dispersion. This is a major limitation to the use of FA as a biomarker for “tissue integrity”, especially in regions of complex microarchitecture. In this work, we seek to circumvent this limitation by disentangling the effects of microscopic diffusion anisotropy from the orientation dispersion. The microscopic fractional anisotropy (μFA) and the order parameter (OP) were calculated from the contrast between signal prepared with directional and isotropic diffusion encoding, where the latter was achieved by magic angle spinning of the q-vector (qMAS). These parameters were quantified in healthy volunteers and in two patients; one patient with meningioma and one with glioblastoma. Finally, we used simulations to elucidate the relation between FA and μFA in various micro-architectures. Generally, μFA was high in the white matter and low in the gray matter. In the white matter, the largest differences between μFA and FA were found in crossing white matter and in interfaces between large white matter tracts, where μFA was high while FA was low. Both tumor types exhibited a low FA, in contrast to the μFA which was high in the meningioma and low in the glioblastoma, indicating that the meningioma contained disordered anisotropic structures, while the glioblastoma did not. This interpretation was confirmed by histological examination. We conclude that FA from DTI reflects both the amount of diffusion anisotropy and orientation dispersion. We suggest that the μFA and OP may complement FA by independently quantifying the microscopic anisotropy and the level of orientation coherence.

The concentration of cholesterol in cell membranes affects membrane fluidity and thickness, and might regulate different processes such as the formation of lipid rafts. Since interpreting experimental data from biological membranes is rather intricate, investigations on simple models with biological relevance are necessary to understand the natural systems. We study the effect of cholesterol on the molecular structure of multi-lamellar vesicles (MLVs) composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), a phospholipid ubiquitous in cell membranes, with compositions in the range 0-60 mol% cholesterol. Order parameters, |S(CH)|, are experimentally determined by using (1)H-(13)C solid-state nuclear magnetic resonance (NMR) spectroscopy with segmental detail for all parts of both the cholesterol and POPC molecules, namely the ring system and alkyl chain of the sterol, as well as the glycerol backbone, choline headgroup and the sn-1 and sn-2 acyl chains of POPC. With increasing cholesterol concentration the acyl chains gradually adopt a more extended conformation while the orientation and dynamics of the polar groups are rather unaffected. Additionally, we perform classical molecular dynamics simulations on virtual bilayers mimicking the POPC-cholesterol MLVs investigated by NMR. Good agreement between experiments and simulations is found for the cholesterol alignment in the bilayer and for the |S(CH)| profiles of acyl chains below 15 mol% cholesterol. Deviations occur for the choline headgroup and glycerol backbone parts of POPC, as well as for the phospholipid and cholesterol alkyl chains at higher cholesterol concentrations. The unprecedented detail of the NMR data enables a more complete comparison between simulations and experiments on POPC-cholesterol bilayers and may aid in developing more realistic model descriptions of biological membranes.

Principles from multidimensional NMR spectroscopy, and in particular solid-state NMR, have recently been transferred to the field of diffusion MRI, offering non-invasive characterization of heterogeneous anisotropic materials, such as the human brain, at an unprecedented level of detail. Here we revisit the basic physics of solid-state NMR and diffusion MRI to pinpoint the origin of the somewhat unexpected analogy between the two fields, and provide an overview of current diffusion MRI acquisition protocols and data analysis methods to quantify the composition of heterogeneous materials in terms of diffusion tensor distributions with size, shape, and orientation dimensions. While the most advanced methods allow estimation of the complete multidimensional distributions, simpler methods focus on various projections onto lower-dimensional spaces as well as determination of means and variances rather than actual distributions. Even the less advanced methods provide simple and intuitive scalar parameters that are directly related to microstructural features that can be observed in optical microscopy images, e.g. average cell eccentricity, variance of cell density, and orientational order - properties that are inextricably entangled in conventional diffusion MRI. Key to disentangling all these microstructural features is MRI signal acquisition combining isotropic and directional dimensions, just as in the field of multidimensional solid-state NMR from which most of the ideas for the new methods are derived.