Molecular theory of field‐dependent proton spin‐lattice relaxation in tissue

Abstract

A molecular theory is presented for the field-dependent spin-lattice relaxation time of water in tissue. The theory attributes the large relaxation enhancement observed at low frequencies to intermediary protons in labile groups or internal water molecules that act as relaxation sinks for the bulk water protons. Exchange of intermediary protons not only transfers magnetization to bulk water protons, it also drives relaxation by a mechanism of exchange-mediated orientational randomization (EMOR). An analytical expression for T1 is derived that remains valid outside the motional-narrowing regime. Cross-relaxation between intermediary protons and polymer protons plays an important role, whereas spin diffusion among polymer protons can be neglected. For sufficiently slow exchange, the dispersion midpoint is determined by the local dipolar field rather than by molecular motions, which makes the dispersion frequency insensitive to temperature and system composition. The EMOR model differs fundamentally from previous models that identify collective polymer vibrations or hydration water dynamics as the molecular motion responsible for spin relaxation. Unlike previous models, the EMOR model accounts quantitatively for 1H magnetic relaxation dispersion (MRD) profiles from tissue model systems without invoking unrealistic parameter values.