Introduction

The popularity of DTI¹ derives from its ability to convey information about the geometry of microscopic compartments, such as axonal fibers, from their imprint on the water diffusion propagators and tensors.^2,3 Ambiguities may arise in cases where the microscopic compartments have some unusual configuration of orientations. As an example, planar diffusion tensors would normally be interpreted as stacks of planar cells, for instance in epidermoid cysts,⁴ but may also arise from cylindrical structures with multiple orientations in a single plane – a prominent example being the “sheet” structure of fiber bundles crossing at nearly right angles.^5-7

Diffusion MRI methods with signal acquisition as a function of not only the conventional b-value and vector, but also the “shape”^8-11 of the b-matrix,^12,13 have potential for disambiguating oblate and prolate compartments even when orientational disorder disrupts the simple relations between the shapes of the microscopic tensors and the voxel-averaged ones observed in conventional DTI.¹⁴

For microimaging hardware, these new MRI methods have been validated using liquid crystals with microgeometry tunable by the chemical composition.^8,15,16 Liquid crystals with the relevant slab or cylinder compartments typically have too low water content and short T₂ for detection at the >50 ms echo times used for single-shot EPI on whole-body equipment. Using methods from the field of surface- and colloid science,^17,18 we have developed a reverse hexagonal liquid crystal yielding essentially one-dimensional diffusion on the microscopic level and having >40 wt% water, which is sufficient for use on clinical scanners.¹⁹ Expanding on these results, we here develop a lamellar liquid crystal with >85 wt% water and two-dimensional diffusion.

Methods

Liquid crystals were made from water, 1-decanol, and sodium octanoate^20,21 at a range of chemical compositions as shown in Figure 1. The phase structure was determined by polarized light microscopy,^{22 2}H NMR spectroscopy,²³ and small-angle X-ray scattering (SAXS).²⁴ A lamellar phase (“Lam”) with composition 85.79 wt% water, 9.17 wt% 1-decanol and 5.04 wt% sodium octanoate was selected for further investigations with MRI. Samples in 5 mm NMR tubes and a 0.5 L round flask were prepared for microimaging and the whole-body scanner, respectively. For reference, a micellar solution (“Mic”) and a reverse hexagonal liquid crystal (“Hex”) was prepared as described previously.¹⁹

Microimaging was performed on a Bruker 500 MHz spectrometer with a 11.7 T magnet and a MIC-5 probe generating 3 T/m gradients. Images were acquired with a spin-echo sequence and RARE image readout²⁵ at 0.3×0.3 mm² in-plane resolution, 0.6 mm slice thickness, 16×16×1 matrix size, and 50.3 ms echo time, using diffusion encoding with analytically calculated gradient waveforms¹⁵ giving 6 b-values up to 11.1·10⁹ sm^–2, b_Δ = [–0.5, 0, 0.5, 1], and 17 orientations. The 0.5 L sample was studied on a 3 T Connectome system (Siemens Healthcare) with 0.3 T/m gradients. Images were acquired with a spin echo-prepared EPI sequence^26,27 at 2×2 mm² in-plane resolution, 4 mm slice thickness, 96×96×24 matrix size, and 83 ms echo time, using numerically optimized gradients²⁸ giving 6 b-values up to 6·10⁹ sm^–2, b_Δ = [–0.5, 0, 0.5, 1], and 15 orientations.

For every voxel, Monte Carlo inversion^29,30 was employed to convert the acquired signal to nonparametric D-distributions in a primary analysis space of the axial and radial eigenvalues, D_A and D_R, and the polar and azimuthal angles, θ and φ, which were converted to the isotropic diffusivity D_iso = (D_A + 2D_R)/3, squared normalized anisotropy D_Δ² = (D_A – D_R)²/(D_A + 2D_R)²,³¹ and lab-frame diagonal elements D_xx, D_yy, and D_zz. Parameter maps were generated by calculating means E[x], variances Var[x], and covariances Cov[x,y] over the entirety or sub-divisions (“bins”) of the distribution space.³²

Results & Discussion

Figure 1 shows a ternary phase diagram of water, 1-decanol, and sodium octanoate system as well as ²H NMR and SAXS data for a sample with the composition selected for MRI measurements. This sample exhibits a lamellar microstructure with lattice spacing a = 15 nm which is retained up to 29 °C.

The quantitative parameter maps in Figure 2 show that all 5 mm samples for microimaging have the expected microstructure: Hex D_A/D_R > 4 (prolate) and D_Δ² ≈ 1, Mic D_A/D_R ≈ 1 (spherical) and D_Δ² ≈ 0, and Lam D_A/D_R < 1/4 (oblate) and D_Δ² ≈ 0.25. The direction-coded maps illustrate the lack of orientational order for in particular the Hex sample. The 0.5 L Lam sample investigated on the whole-body scanner features mainly oblate tensors similar to the 5 mm Lam, but also a central region with prolates indicating that the homogeneity of the sample could be improved, for instance by annealing of the liquid crystal structure via temperature cycling.¹⁹

Conclusions

The lamellar liquid crystal gives ample signal in single-shot EPI and features exclusively oblate components in the diffusion tensor distributions obtained on microimaging hardware. Also the 0.5 L phantom for whole-body equipment gives mainly oblates, however having a core with prolates that indicate room for improvement - for instance by annealing to give a perfectly homogeneous lamellar structure suitable for validation of novel diffusion MRI methods on clinical scanners.

Acknowledgements

This work was financially supported the Swedish Foundation for Strategic Research (ITM17-0267), Swedish Research Council (2018-03697), and Chinese Scholarship Council. DT owns shares in Random Walk Imaging AB (Lund, Sweden, http://www.rwi.se/), holding patents related to the described methods.