Homogeneous length scale of shear-induced multilamellar vesicles studied by diffusion NMR

Time-dependent diffusion in undulating thin fibers: Impact on axon diameter estimation

Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modeling axons as straight cylinders. Axons do not, however, propagate in straight trajectories, and so far the impact of the axonal trajectory on diameter estimation has been insufficiently investigated. Here, we employ a toy model of axons, which we refer to as the undulating thin fiber model, to analyze the impact of undulating trajectories on the time dependence of diffusion. We study time-dependent diffusion in the frequency domain and characterize the diffusion spectrum by its height, width, and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin fibers is the main parameter that determines the characteristics of the diffusion spectra. At lower frequencies (longer diffusion times), straight cylinders and undulating thin fibers can have virtually identical spectra. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and microscopic orientation dispersion of the fibers. At higher frequencies (shorter diffusion times), spectra from cylinders and undulating thin fibers differ. The low-frequency behavior of the spectra from the undulating thin fibers may also differ from that of cylinders, because the power law exponent of undulating fibers can reach values below 2 for experimentally relevant frequency ranges. In conclusion, we argue that the non-straight nature of axonal trajectories should not be overlooked when analyzing and interpreting diffusion MRI data.

The Kärger vs bi-exponential model: Theoretical insights and experimental validations

We revise three common models accounting for water exchange in pulsed-gradient spin-echo measurements: a bi-exponential model with time-dependent water fractions, the Kärger model, and a modified Kärger model designed for restricted diffusion, e.g. inside cells. The three models are compared and applied to experimental data from yeast cell suspensions. The Kärger model and the modified Kärger model yield very close results and accurately fit the data. The bi-exponential model, although less rigorous, has a natural physical interpretation and suggests a new experimental modality to estimate the water exchange time.

Liquid crystal phantom for validation of microscopic diffusion anisotropy measurements on clinical MRI systems

PURPOSE

To develop a phantom for validating MRI pulse sequences and data processing methods to quantify microscopic diffusion anisotropy in the human brain.

METHODS

Using a liquid crystal consisting of water, detergent, and hydrocarbon, we designed a 0.5-L spherical phantom showing the theoretically highest possible degree of microscopic anisotropy. Data were acquired on the Connectome scanner using echo-planar imaging signal readout and diffusion encoding with axisymmetric b-tensors of varying magnitude, anisotropy, and orientation. The mean diffusivity, fractional anisotropy (FA), and microscopic FA (µFA) parameters were estimated.

RESULTS

The phantom was observed to have values of mean diffusivity similar to brain tissue, and relaxation times compatible with echo-planar imaging echo times on the order of 100 ms. The estimated values of µFA were at the theoretical maximum of 1.0, whereas the values of FA spanned the interval from 0.0 to 0.8 as a result of varying orientational order of the anisotropic domains within each voxel.

CONCLUSIONS

The proposed phantom can be manufactured by mixing three widely available chemicals in volumes comparable to a human head. The acquired data are in excellent agreement with theoretical predictions, showing that the phantom is ideal for validating methods for measuring microscopic diffusion anisotropy on clinical MRI systems. Magn Reson Med 79:1817-1828, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Multilamellar vesicle formation from a planar lamellar phase under shear flow

The formation of multilamellar vesicles (MLVs) from the lamellar phase of nonionic surfactant system C12E5/D2O under shear flow is studied by time-resolved small angle neutron and light scattering during shear flow. A novel small angle neutron scattering sample environment enables the tracking of the lamellae alignment in the velocity-velocity gradient (1-2) plane during MLV formation, which was tracked independently using flow small angle light scattering commensurate with rheology. During the lamellar-to-multilamellar vesicle transition, the primary Bragg peak from the lamellar ordering was observed to tilt, and this gradually increased with time, leading to an anisotropic pattern with a primary axis oriented at ∼25° relative to the flow direction. This distorted pattern persists under flow after MLV formation. A critical strain and critical capillary number based on the MLV viscosity are demonstrated for MLV formation, which is shown to be robust for other systems as well. These novel measurements provide fundamentally new information about the flow orientation of lamellae in the plane of flow that cannot be anticipated from the large body of previous literature showing nearly isotropic orientation in the 2,3 and 1,3 planes of flow. These observations are consistent with models for buckling-induced MLV formation but suggest that the instability is three-dimensional, thereby identifying the mechanism of MLV formation in simple shear flow.

Multi-scale characterization of lyotropic liquid crystals using 2H and diffusion MRI with spatial resolution in three dimensions

The ability of lyotropic liquid crystals to form intricate structures on a range of length scales can be utilized for the synthesis of structurally complex inorganic materials, as well as in devices for controlled drug delivery. Here we employ magnetic resonance imaging (MRI) for non-invasive characterization of nano-, micro-, and millimeter scale structures in liquid crystals. The structure is mirrored in the translational and rotational motion of the water, which we assess by measuring spatially resolved self-diffusion tensors and spectra. Our approach differs from previous works in that the MRI parameters are mapped with spatial resolution in all three dimensions, thus allowing for detailed studies of liquid crystals with complex millimeter-scale morphologies that are stable on the measurement time-scale of 10 hours. The data conveys information on the nanometer-scale structure of the liquid crystalline phase, while the combination of diffusion and data permits an estimate of the orientational distribution of micrometer-scale anisotropic domains. We study lamellar phases consisting of the nonionic surfactant C₁₀E₃ in O, and follow their structural equilibration after a temperature jump and the cessation of shear. Our experimental approach may be useful for detailed characterization of liquid crystalline materials with structures on multiple length scales, as well as for studying the mechanisms of phase transitions.

From self-assembly fundamental knowledge to nanomedicine developments

This review highlights the key role of NMR techniques in demonstrating the molecular aspects of the self-assembly of surfactant molecules that nowadays constitute the basic knowledge which modern nanoscience relies on. The aim is to provide a tutorial overview. The story of a rigorous scientific approach to understand self-assembly in surfactant systems and biological membranes starts in the early seventies when the progresses of SAXRD and NMR technological facilities allowed to demonstrate the existence of ordered soft matter, and the validity of Tanford approach concerning self-assembly at a molecular level. Particularly, NMR quadrupolar splittings, NMR chemical shift anisotropy, and NMR relaxation of dipolar and quadrupolar nuclei in micellar solutions, microemulsions, and liquid crystals proved the existence of an ordered polar-apolar interface, on the NMR time scale. NMR data, rationalized in terms of the two-step model of relaxation, allowed to quantify the dynamic aspects of the supramolecular aggregates in different soft matter systems. In addition, NMR techniques allowed to obtain important information on counterion binding as well as on size of the aggregate through molecular self-diffusion. Indeed NMR self-diffusion proved without any doubt the existence of bicontinuous microemulsions and bicontinuous cubic liquid crystals, suggested by pioneering and brilliant interpretation of SAXRD investigations. Moreover, NMR self-diffusion played a fundamental role in the understanding of microemulsion and emulsion nanostructures, phase transitions in phase diagrams, and particularly percolation phenomena in microemulsions. Since the nineties, globalization of the knowledge along with many other technical facilities such as electron microscopy, particularly cryo-EM, produced huge progresses in surfactant and colloid science. Actually we refer to nanoscience: bottom up/top down strategies allow to build nanodevices with applications spanning from ICT to food technology. Developments in the applied fields have also been addressed by important progresses in theoretical skills aimed to understand intermolecular forces, and specific ion interactions. Nevertheless, this is still an open question. Our predictive ability has however increased, hence more ambitious targets can be planned. Nanomedicine represents a major challenging field with its main aims: targeted drug delivery, diagnostic, theranostics, tissue engineering, and personalized medicine. Few recent examples will be mentioned. Although the real applications of these systems still need major work, nevertheless new challenges are open, and perspectives based on integrated multidisciplinary approaches would enable both a deeper basic knowledge and the expected advances in biomedical field.

Isotropic diffusion weighting in PGSE NMR by magic-angle spinning of the q-vector

When PGSE NMR is applied to water in microheterogeneous materials such as liquid crystals, foodstuffs, porous rocks, and biological tissues, the signal attenuation is often multi-exponential, indicating the presence of pores having a range of sizes or anisotropic domains having a spread of orientations. Here we modify the standard PGSE experiment by introducing low-amplitude harmonically modulated gradients, which effectively make the q-vector perform magic-angle spinning (MAS) about an axis fixed in the laboratory frame. With this new technique, denoted q-MAS PGSE, the signal attenuation depends on the isotropic average of the local diffusion tensor. The capability of q-MAS PGSE to distinguish between pore size and domain orientation dispersion is demonstrated by experiments on a yeast cell suspension and a polydomain anisotropic liquid crystal. In the latter case, the broad distribution of apparent diffusivities observed with PGSE is narrowed to its isotropic average with q-MAS PGSE in a manner that is analogous to the narrowing of chemical shift anisotropy powder patterns using magic-angle sample spinning in solid-state NMR. The new q-MAS PGSE technique could be useful for resolving size/orientation ambiguities in the interpretation of PGSE data from, e.g., water confined within the axons of human brain tissue.

Transient and Steady-State Shear Banding in a Lamellar Phase as Studied by Rheo-NMR

Flow fields and shear-induced structures in the lamellar (L α ) phase of the system triethylene glycol mono n-decyl ether (C10E3)/water were investigated by NMR velocimetry, diffusometry, and 2 H NMR spectroscopy. The transformation from multilamellar vesicles (MLVs) to aligned planar lamellae is accompanied by a transient gradient shear banding. A high-shear-rate band of aligned lamellae forms next to the moving inner wall of the cylindrical Couette shear cell while a low-shear-rate band of the initial MLV structure remains close to the outer stationary wall. The band of layers grows at the expense of the band of MLVs until the transformation is completed. This process scales with the applied strain. Wall slip is a characteristic of the MLV state, while aligned layers show no deviation from Newtonian flow. The homogeneous nature of the opposite transformation from well aligned layers to MLVs via an intermediate structure resembling undulated multilamellar cylinders is confirmed. The strain dependence of this transformation appears to be independent of temperature. The shear diagram, which represents the shear-induced structures as a function of temperature and shear rate, contains a transition region between stable layers and stable MLVs. The steady-state structures in the transition region show a continuous change from layer-like at high temperature to MLV-like at lower temperature. These structures are homogeneous on a length scale above a few micrometers.