Figure 1.

Shifting mechanism of the ²³Na resonance in vitro. (a) Chemical structure of sodium thulium(III) 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis(methylenephosphonate) (Na₅TmDOTP). The TmDOTP⁵⁻ complex consists of the Tm³⁺ ion chelated with DOTP⁸⁻. Each phosphonate-containing pendant arm on TmDOTP^5- has electron-donating groups on the oxygen atoms (red) to stabilize the Tm³⁺ conjugation with DOTP⁸⁻. The -5 charge simultaneously attracts five Na⁺ ions (purple), which experience a shift in the observed ²³Na resonance that is dependent on [TmDOTP⁵⁻]. (b) In vivo, prior to TmDOTP⁵⁻ administration (left), the ²³Na spectrum yields only a single peak representing the total sodium (Na⁺_T) comprising blood (Na⁺_b), extracellular (Na⁺_e), and intracellular (Na⁺_i ) compartments. Following TmDOTP⁵⁻ administration (right), the peaks become spectroscopically separable based on [TmDOTP⁵⁻] in each compartment. Integrals of these peaks will be representative of aqueous [Na⁺] in each compartment. (c) A two-compartment coaxial cylinder tube setup was employed for in vitro observation of the chemical shift separation scheme (Figure S1). The inner tube (smaller volume) was filled with 150 mM NaCl, while the outer tube (larger volume) was filled with the same solution in addition to various amounts of TmDOTP⁵⁻, each subject to different pH conditions. Thus, all ²³Na spectra from this phantom setup displayed a small unshifted peak from the inner compartment and a larger shifted peak. The outer-to-inner volume ratio was 8.6, explaining the difference in sizes of the peaks. Exemplary traces of ²³Na spectra show that the shift is much more sensitive to [TmDOTP⁵⁻] (2.77 ppm/mM) than to variations in pH (0.25 ppm/pH unit) or temperature (0.03 ppm/°C). The downfield peaks in the red, blue, and/or black spectra are shifted differently due to varying TmDOTP⁵⁻ concentrations, and these shifts exceed those caused by pH, but all of these shifts are detectable independent of broadening caused by TmDOTP⁵⁻ (see also Figure S1). Plots (d,e) show that temperature, pH, and [TmDOTP⁵⁻] all contribute to variations of the ²³Na chemical shift. However, these plots depict ranges of pH and temperature that are unlikely for in vivo settings (i.e., changes over 2 full pH units and temperature changes over 15 °C). Moreover, [Na⁺] in vivo (~ 150 mM in blood and extracellular space) is extremely high compared to [TmDOTP⁵⁻]. Therefore, variations in ²³Na chemical shift are primarily dependent on [TmDOTP⁵⁻]/[Na⁺] thereby rendering (f) pH and (g) temperature dependencies negligible. Data points were fit to Chebyshev rational polynomials using TableCurve 3D v4.0.05 (Systat Software, San Jose, CA, USA; https://systatsoftware.com/products/tablecurve-3d/).