Introduction

Phantoms with known MR parameters are needed to validate quantitative measurements in multisite MRI studies (1). Our previous work shows that changing the concentration of lamellar lipid vesicles creates diffusion phantoms with tunable apparent diffusion and kurtosis values, D_app and K_app (2). In this work, we vary the molar ratio of lipid to surfactant to change vesicle diameter and restricted diffusion fraction; consequently changing D_app and K_app values. It is easily shown that given a constant surface area, i.e. a constant weight fraction of molecules, that the volume enclosed by vesicles will increase linearly with vesicle diameter. Figure 1 provides the 2D analogy to the 3D case and helps to visualize how increasing diameter will increase restricted fractions of water molecules.

Methods

Vesicles were made at constant 1% (w/w) solids-to-water of cetearyl alcohol (CA) and cetyl trimethyl ammonium bromide (CTAB), with CA:CTAB molar ratio varying from 1:1 to 6:1. CTAB was dissolved in hot water (80 °C) and melted CA was added to form vesicles by stirring and cooling below the lipid transition temperature. All samples were filtered with through a 5 micron polycarbonate filter. Dynamic light scattering was performed at 1 mg/ml concentration and cumulant particle diameter, <d>, and poydispersity index, pi, were determined. Transmission electron microscopy (TEM) was performed on representative samples to visualize vesicle shape and dimensions. NMR water signals were recorded on an Agilent 700 MHz system using a dual stimulated echo experiment to suppress convective flow with b values up to 10,000 s/mm². Diffusion time Δ was 100 ms and gradient duration δ was 2 ms. The diffusion NMR signal was fitted in Matlab to a biexepnential model with free and restricted diffusion, and to a kurtosis model with apparent diffusion and kurtosis values at appropriate b values (1,2). The biexponential model is given as $$$S(b)=p_{free} exp(-b D_{free}) +p_{rest.} exp(-b D_{rest.})$$$ and the kurtosis model is given as $$$ln(\frac{S(b)}{S(0)})=-b D_{app}+1/6 K_{app}(b D_{app})^2$$$ (1,2). Fitted results are shown in Fig. 3(C,D) for the biexponential model and Fig. 3(E,F) for the kurtosis model with error bars representing 95% CI.

Results

The ratio of the lipid to surfactant determines vesicle diameter in a controlled fashion. The diameter of vesicles as measured by DLS varies from 210 nm up to 1,380 nm (Fig. 2A). Representative vesicles are seen as spherical by TEM (Fig. 2B). Vesicle diameter is proportional to CA:CTAB ratio (Fig. 3A) and a biexponential model of diffusion with free and restricted components fits all data well (Fig. 3B). Free diffusion, D_free, decreases from about 0.002 to 0.0015 mm²/s in the biexponential model (Fig. 3C) whereas apparent diffusion D_app changes from 0.0021 to about 0.0009 mm²/s, highlighting model differences. More importantly, the restricted fraction in the biexponental model is proportional to the vesicle diameter, as predicted by conservation of mass and geometry (Fig. 3D). Kurtosis value (K_app) changes from 0 for the 210 nm vesicles to 1.17 for the 1,640 nm vesicles (Fig. 3F).

Discussion

The ability to choose vesicle diameter imparts increased control of phantom diffusion properties and allows specific values of D_app and K_app in a quantitative diffusion phantom. In addition, samples with vesicles of known diameter provide opportunities to study novel diffusion MRI experiments tuned to a particular vesicle size or microenvironment (3). These vesicles have polydispersity indices between 0.2 and 0.3, with the larger vesicles becoming more disperse. Though not done here, polydispersity could be reduced further by passing vesicles through appropriate sized filters.
These findings are useful because the 1% (w/w) samples have low viscosity, flow easily, and do not trap air or bubble as may happen in gels or samples of higher viscosity. In addition, starting from low viscosity and relatively large value of D_app, it would be easy to reduce D_app with a polymer such as PVP, yet leave the K_app unaffected (4).

Conclusion

Lamellar vesicles provide an ideal molecular platform for quantitative diffusion phantoms. They are stable (1), easily generated, and can be made at large volumes with tunable diffusion parameters. Additional refinement of fabrication of these systems will provide increased utility to benchmark MRI systems in muticenter clinical trials and provide well characterized nanoscopic platforms for future development of novel MRI pulse sequences.

Acknowledgements

National Institutes of Health Grants: U01CA166104, U24CA237683, P01CA085878 and P30 CA008748.