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

Abstract

A molecular theory is presented for the field-dependent spinlattice 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 T 1 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 The spin-lattice relaxation time, T 1 , of tissue water is one of the principal contrast modalities in clinical MRI. Although the phenomenology of water-1 H relaxation in soft tissue is well documented (1-3), the molecular determinants of natural and pathological T 1 variations have not been established. Because of the molecular-level complexity of biological tissue, studies aimed at unraveling the relaxation mechanism have often employed aqueous gels as tissue models. The magnetic relaxation dispersion (MRD), that is, the variation of R 1 ϭ 1/T 1 with magnetic field strength (or Larmor frequency) is particularly informative about the molecular motions that induce spin relaxation. However, even though numerous MRD studies of tissue models have been conducted, we still cannot predict the MRD profile from known system properties. There is even disagreement about the nature of the molecular motions that are responsible for the observed relaxation dispersion. For example, some authors invoke slow water dynamics in the hydration layer at the biopolymer surface (4 -6), while others focus on collective biopolymer vibrations (7-10).We recently reported an extensive set of water-2 H MRD data from polysaccharide and polypeptide gels (11) (Vaca Chávez et al., submitted). Since cross-relaxation and spin diffusion can be neglected for the quadrupolar 2 H nuclide, the analysis of 2 H MRD data is relatively straightforward. The 2 H MRD profiles can be accounted for quantitatively by a model that attributes the relaxation dispersion to a small deuteron population in intimate and long-lived association with the biopolymer. These intermediary deuterons either reside in labile groups (such as hydroxyl or amino groups) or belong to water molecules that are temporarily trapped within the biopolymer. According to this model, spin re...

Nuclear magnetic relaxation induced by exchange-mediated orientational randomization: Longitudinal relaxation dispersion for a dipole-coupled spin-1/2 pair

“…A plausible but nonrigorous extension of the fastexchange result has been suggested, 18 where 25) and with the intrinsic integral relaxation rate R 1,A in state A given by expressions like Eqs. (4.12) and (4.13), but with intrinsic auto-relaxation and cross-relaxation rates obtained from Eqs.…”

“…Equation (4.25) is the two-spin version of an approximate result previously derived for a homonuclear multispin system. 18 In Fig. 5, we compare Eq.…”

“…In the past, such data have been interpreted [15][16][17] with semi-phenomenological models involving dubious assumptions about the relaxation-inducing motions. 18,19 Previous water 1 H MRD studies of biopolymer gels from this laboratory 19,20 made use of a nonrigorous extension of the multi-spin Solomon equations to conditions outside the motional-narrowing regime. For a two-spin system, this approach 18 is closely related to a well-known result 21 for twophase relaxation in the dilute regime.…”

“…18,19 Previous water 1 H MRD studies of biopolymer gels from this laboratory 19,20 made use of a nonrigorous extension of the multi-spin Solomon equations to conditions outside the motional-narrowing regime. For a two-spin system, this approach 18 is closely related to a well-known result 21 for twophase relaxation in the dilute regime. With the rigorous results presented here, the accuracy of this approximation can be assessed.…”

“…We also consider various limiting cases of the general theory and we delineate the quantitative breakdown of the previously used nonrigorous extension of the Solomon equations. [18][19][20] In Sec. V, we calculate the MRD for like (homonuclear) spin pairs, e.g., two protons, along the same lines as in Sec.…”