Magnetization transfer in lamellar liquid crystals

Abstract

Purpose: This study examines the relationship between quantitative magnetization transfer (qMT) parameters and the molecular composition of a model lamellar liquid crystal (LLC) system composed of 1-decyl alcohol (decanol), sodium dodecyl sulfate (SDS), and water.

Methods: Samples were made within a stable lamellar mesophase to provide different ratios of total semisolid protons (SDS + decanol) to water protons. Data were collected as a function of radiofrequency power, frequency offset, and temperature. qMT parameters were estimated by fitting a standard model to the data. Fitting results of four different semisolid line shapes were compared.

Results: A super-Lorentzian line shape for the semisolid component provided the best fit. The estimated amount of semisolids was proportional to the ratio of decanol-to-water protons. Other qMT parameters exhibited nonlinear dependence on sample composition. Magnetization transfer ratio (MTR) was a linear function of the semisolid fraction over a limited range of decanol concentration.

Conclusion: In LLC samples, MT between semisolid and water originates from intramolecular nOe among decanol aliphatic chain protons followed by proton exchange between decanol hydroxyl and water. Exchange kinetics is influenced by SDS, although SDS protons do not participate in MT. These studies provide clinically relevant range of semisolid fraction proportional to detected MTR.

Keywords: MRI; MT phantom; magnetization transfer; super-Lorentzian.

Copyright © 2013 Wiley Periodicals, Inc.

Figures

Figure 1

Conceptual diagram of the LLC phase formed by hydrophobic bilayers of SDS (black) and decanol (blue) chains that encapsulate polar water layer (blue) and sodium ions (red). The distances are given for water content of CW = 45% as measured by small angle X-ray scattering (SAXS) experiments Ref. (34). Blue color indicates LLC components (decanol and water) participating in MT. The insert on the right focuses on a sub-set of the polar / non-polar interface to reflect the MT mechanism between decanol and water protons consistent with our experimental findings, i.e., proceeding via hydroxyl proton exchange (blue arrows) and aliphatic proton nOe (green arrows). Terminal chain segments of decanol are excluded from MT due to probable large amplitude motions.

Figure 2

Experimentally observed parameters are plotted as a function of the ratio of mole fraction of SDS protons, XSDS, to mole fraction of water protons, XW, for T1obs (a), T1obs (b), and 23Na quadrupole splitting 2vQ (c). The symbol diameter is proportional to mole fraction of decanol protons, XD. The exponential fit errors for relaxation times (omitted in (a) and (b)) were within the symbol boundaries. The measurement error for 2vQ was ±300 Hz. The samples with high versus low water content (CW = 65% vs. CW = 45%) are indicated by different colors, as shown in Fig. 2 (a).

Figure 3

(a) 1H-NMR spectrum of LLC made with D2O (black line) is plotted on a log-intensity scale along with the best fit super-Lorentzian line shape (blue line) for the semisolid component participating in MT. The semisolid component fit is offset by 320Hz to account for the chemical shift of the decanol aliphatic protons at 2T. (b) An example of fitting qMT model (lines) based on offset super-Lorentzian to collected data (dots) at different power levels of applied MT pulse (see legend for color-codes). These data are for the LLC sample with CW = 65% and XD/XSDS = 0.22/0.13.

Figure 4

M0b plotted as a function of molar ratio of the total semisolid protons, XD/XSDS, to water protons, XW, in (a); molar ratio of SDS to water protons in (b); and of the molar ratio of decanol protons to water protons in (c). The data symbol diameter in (a) – (c) is proportional to mole fraction of the decanol protons, XD. The samples with high versus low water content (CW = 65% vs. CW = 45%) are indicated by different color, as shown in Fig. 4 (a). The linear fit parameters for (c) are listed in the line-fit equation. The error bars represent one standard deviation of non-linear least squares fit for qMT-model.

Figure 5

qMT-fit parameters plotted as a function of the molar ratio of SDS-to-water protons, XSDS/XW: (a) Ra; (b) Rt; (c) T2b and (d) T2a. The data symbol diameter in (a) – (d) is proportional to mole fraction of the decanol protons, XD. The samples with high versus low water content (CW = 65% vs. CW = 45%) are indicated by different color, as shown in Fig. 5 (a). The error bars represent one standard deviation of non-linear least squares fit for qMT-model.

Figure 6

Percent MTR at 5 μT RF MT-pulse for three frequency offsets (see legend for symbol assignment) as a function of the molar ratio of decanol-to-water protons (directly proportional to M0b in Fig. 4). The vertical dashed line indicates the range of semisolid fractions (participating in MT) that can be quantitatively inferred from direct MTR measurements. The horizontal dashed line illustrates the lack of detectible variation in MTR for decanol-to-water fractions above 0.3.