Magnetic field dependence of proton spin‐lattice relaxation times

Abstract

The magnetic field dependence of the water-proton spin-lattice relaxation rate (1/T 1 ) in tissues results from magnetic coupling to the protons of the rotationally immobilized components of the tissue. As a consequence, the magnetic field dependence of the water-proton (1/T 1 ) is a scaled report of the field dependence of the (1/T 1 ) rate of the solid components of the tissue. The proton spin-lattice relaxation rate may be represented generally as a power law: 1/T 1 ‫؍‬ A -b , where b is usually found to be in the range of 0.5-0.8. We have shown that this power law may arise naturally from localized structural fluctuations along the backbone in biopolymers that modulate the proton dipoledipole couplings. The protons in a protein form a spin communication network described by a fractal dimension that is less than the Euclidean dimension. The model proposed accounts quantitatively for the proton spin-lattice relaxation rates measured in immobilized protein systems at different water contents, and provides a fundamental basis for understanding the parametric dependence of proton spin-lattice relaxation rates in dynamically heterogeneous systems, such as tissues. The value of the water-proton spin-lattice relaxation time, T 1 , is often an important determinant of magnetic image contrast. Therefore, understanding the magnetic field dependence of T 1 is central to a fundamental understanding of the factors that control the magnetic resonance (MR) image appearance as well as the information content. It is well known that the magnetic field dependence of the water-proton T 1 is dominated by magnetic coupling to the protons of the solid components of the tissue. As summarized in Fig. 1, the observed magnetic field dependence of 1/T 1 was shown to be a scaled representation of the magnetic relaxation dispersion of the protons in the rotationally immobilized spin components of the tissue (1,2). The magnetic coupling is carried by chemical-exchange events that include a whole water molecule exchange between specific binding sites, and proton exchange with protein functions such as amines, amides, and alcohols. Because proton-exchange is generally much slower than H 2 O exchange, the coupling is usually dominated by water molecule exchange events. In the bound environment of these unique water molecules, the magnetization transfer rate is limited, essentially by the value of T 2 , which is of the order of 10 s in the bound and immobilized environment (2-4). However, the origin of the magnetic field dependence of 1/T 1 in the rotationally immobilized proton spin system of a protein, for example, is not quantitatively understood. Kimmich and coworkers (13) have suggested that the field dependence derives from the backbone fluctuations. Our recent theoretical work (5) provides a quantitative explanation for the magnetic field dependence of 1/T 1 for the solid component spins, which, in turn, provides an explanation for the magnetic field dependence of the waterproton 1/T 1 in tissues. Although a variety of macromolecular as...

Relaxation of protons by radicals in rotationally immobilized proteins

“…Labile exchange of the protein-bound water molecules with the bulk carries the relaxation effects, including the field dependence of the paramagnetic protein protons, to the water population as a whole with the usual dilution caused by the large difference in the proton population in the water compared with the protein. We note that a limitation in the magnetization transfer rate between the paramagnetic solid and the water pool may also cause a plateau in the relaxation profile, which is observed at very low frequencies in hydrated protein systems [18][19][20]. However, the limitation observed in the present experiments is at much higher frequency and lower rates, which supports the conclusion that the plateau is correctly described as the limitation by the electron relaxation rate.…”

“…Recent work on metalloprotein conjugates has shown, however, that in the case that the paramagnetic protein centers are strongly immobilized, the electron-spin-relaxation rate constants may increase dramatically, with a consequent increase in the spin-lattice relaxation rate constant of the coupled protons [14]. Further, in the case of a rotationally immobilized protein, which is magnetically a solid in the sense that the proton-proton dipolar couplings are not averaged, the efficient spin diffusion in the macromolecule matrix provides a fundamentally different mechanism for efficient distribution of the effects of the paramagnetic center to other nuclear spins, water protons in particular [18][19][20][21].…”

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

“…In the limits of very fast ( int ϭ 0) or very slow (S ϭ 1) internal motion, where k ϭ Ik and kl ϭ 0 according to Eqs. [6] and [10], the matrix P is rigorously diagonal so that Eq. [19] becomes identical to Eq.…”

“…Several authors have argued that water-1 H dispersions in tissue and biopolymer gels are produced by collective polymer vibration modes (7)(8)(9)(10). The frequency dependence is thus taken to enter via the intrinsic relaxation rate, r P , of the P-proton pool.…”

“…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)(8)(9)(10).…”