Magnetic field dependence of proton spin-lattice relaxation times

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)omega = A omega(-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 dipole-dipole 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.