NMR shutter-speed elucidates apparent population inversion of ¹H₂O signals due to active transmembrane water cycling

Purpose: The desire to quantitatively discriminate the extra- and intracellular tissue ¹H₂O MR signals has gone hand-in-hand with the continual, historic increase in MRI instrument magnetic field strength [B₀]. However, recent studies have indicated extremely valuable, novel metabolic information can be readily accessible at ultra–low B₀. The two signals can be distinguished, and the homeostatic activity of the cell membrane sodium/potassium pump (Na⁺,K⁺,ATPase) detected. The mechanism allowing ¹H₂O MRI to do this is the newly discovered active transmembrane water cycling (AWC) phenomenon, which we found using paramagnetic extracellular contrast agents at clinical B₀ values. AWC is important because Na⁺,K⁺,ATPase can be considered biology’s most vital enzyme, and its in vivo steady-state activity has not before been measurable, let alone amenable to mapping with high spatial resolution. Recent reports indicate AWC correlates with neuronal firing rate, with malignant tumor metastatic potential, and inversely with cellular reducing equivalent fraction. We wish to systematize the ways AWC can be precisely measured. Methods: We present a theoretical longitudinal relaxation analysis of considerable scope: it spans the low- and high–field situations. Results: We show the NMR shutter-speed organizing principle is pivotal in understanding how trans–membrane steady–state water exchange kinetics are manifest throughout the range. Our findings illuminate an aspect, apparent population inversion, which is crucial in understanding ultra-low field results. Conclusions: Without an appreciation of apparent population inversion, significant misinterpretations of future data are likely. These could have unfortunate diagnostic consequences.