Internal Water Molecules and Magnetic Relaxation in Agarose Gels

Abstract

Agarose gels have long been known to produce exceptionally large enhancements of the water 1H and 2H magnetic relaxation rates. The molecular basis for this effect has not been clearly established, despite its potential importance for a wide range of applications of agarose gels, including their use as biological tissue models in magnetic resonance imaging. To resolve this issue, we have measured the 2H magnetic relaxation dispersion profile from agarose gels over more than 4 frequency decades. We find a very large dispersion, which, at neutral pH, is produced entirely by internal water molecules, exchanging with bulk water on the time scale 10(-8)-10(-6) s. The most long-lived of these dominate the dispersion and give rise to a temperature maximum in the low-frequency relaxation rate. At acidic pH, there is also a low-frequency contribution from hydroxyl deuterons exchanging on a time scale of 10(-4) s. Our analysis of the dispersion profiles is based on a nonperturbative relaxation theory that remains valid outside the conventional motional-narrowing regime. The results of this analysis suggest that the internal water molecules responsible for the dispersion are located in the central cavity of the agarose double helix, as previously proposed on the basis of fiber diffraction data. The magnetic relaxation mechanism invoked here, where spin relaxation is induced directly by molecular exchange, also provides a molecular basis for understanding the water 1H relaxation behavior that governs the intrinsic magnetic resonance image contrast in biological tissue.

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

“…This rigorous result, which is also valid outside the dilute regime, follows from Eqs. [3], [5], [6], [8]- [11], [15], and [38]. Seen in the light of our theoretical analysis, the absence of a pronounced high-frequency step in water-1 H dispersion profiles from tissue (1,2) and biopolymer gels (Vaca Chávez and Halle, this issue) indicates that the effects of internal motions and spin diffusion are unimportant.…”

“…In the EMOR model this observation is readily explained by the acid-and base-catalyzed labile-proton exchange (Vaca Chávez and Halle, this issue). The fracton/ two-pool theory also cannot explain the R 1 maximum observed as a function of temperature for agarose gels (11,35). At frequencies above ϳ100 kHz, this theory predicts that R 1 ϳ r P ϳ T. On the low-frequency plateau, where R 1 ϭ r W3 P , the identification (10) r W3 P ϭ f I /(T 2,solid ϩ I ) with T 2,solid Ϸ 10 s taken to be governed by temperatureindependent spin diffusion (10), it is clear that R 1 cannot decrease with temperature.…”

“…[12] in place of Eq. [11], and the final result for the effective intrinsic relaxation rate, ᑬ I , of the two water protons comprising class I differs from Eq. [23] only through the substitution: [26] where D W and S W are the dipole coupling constant and order parameter for the intramolecular water H-H vector, respectively, and…”

“…In the absence of spin diffusion, cross-relaxation largely cancels the adiabatic J (Ik) (0) contribution to I (see Eq. [11]), thereby making ᑬ I Ͻ Ͻ I in the high-frequency range (Fig. 9, inset).…”

“…At frequencies above ϳ100 kHz, this theory predicts that R 1 ϳ r P ϳ T. On the low-frequency plateau, where R 1 ϭ r W3 P , the identification (10) r W3 P ϭ f I /(T 2,solid ϩ I ) with T 2,solid Ϸ 10 s taken to be governed by temperatureindependent spin diffusion (10), it is clear that R 1 cannot decrease with temperature. In contrast, the EMOR model accounts quantitatively for the R 1 maximum in terms of the temperature-dependent residence time of internal water molecules (11).…”