A versatile look-up algorithm for mapping pH values and magnesium ion content using ³¹P MRSI

³¹P MRSI allows for the non-invasive mapping of pH and magnesium ion content (Mg) in vivo, by translating the chemical shifts of inorganic phosphate and adenosine-5'-triphosphate (ATP) to pH and Mg via suitable calibration equations, such as the modified Henderson-Hasselbalch equation. However, the required constants in these calibration equations are typically only determined for physiological conditions, posing a particular challenge for their application to diseased tissue, where the biochemical conditions might change manyfold. In this article, we propose a multi-parametric look-up algorithm aiming at the condition-independent determination of pH and Mg by employing multiple quantifiable ³¹P spectral properties simultaneously. To generate entries for an initial look-up table, measurements from 114 model solutions prepared with varying chemical properties were made at 9.4 T. The number of look-up table entries was increased by inter- and extrapolation using a multi-dimensional function developed based on the Hill equation. The assignment of biochemical parameters, that is, pH and Mg, is realized using probability distributions incorporating specific measurement uncertainties on the quantified spectral parameters, allowing for an estimation of most plausible output values. As proof of concept, we applied a version of the look-up algorithm employing only the chemical shifts of γ- and β-ATP for the determination of pH and Mg to in vivo 3D ³¹P MRSI data acquired at 7 T from (i) the lower leg muscles of healthy volunteers and (ii) the brains of patients with glioblastoma. The resulting volumetric maps showed plausible values for pH and Mg, partly revealing differences from maps generated using the conventional calibration equations.