The magnetic field dependence of H-1 spin-lattice relaxation rates in noncrystalline macromolecular solids is described by a power law, 1/T-1 = A omega (-b)(0), where omega (0) is the Larmor frequency, A and b are constants. We show that the magnetic field dependence of the proton 1/T-1 may be quantitatively related to structural fluctuations along the backbone that modulate proton-proton dipolar couplings. A and b are related to the dipolar coupling strength, the energy for the highest vibrational frequency in the polymer backbone, the fractal dimensionality of the proton spatial distribution, and the spectral dimensionality that characterizes the random walk on a fractal network.