Extension of the Rorschach–Hazlewood Theoretical Model for Spin–Lattice Relaxation in Biological Systems to Low Frequencies

The water–biopolymer cross-relaxation model, proposed by H. E. Rorschach and C. F. Hazlewood (RH) [J. Magn. Reson.70,79 (1986)], explains the Larmor frequency dependence ofT1in many biological systems. However, the RH theory fails at low Larmor frequencies. In this paper, a more general version of the RH theory has been developed. This theory is valid at all frequencies. Use of the new expression for the spin–lattice relaxation rate (1/T1), earlier published experimental data in H2O/D2O bovine serum albumin, which had been measured over a wide frequency range (10 kHz to 100 MHz), were fitted over the entire frequency range. The agreement between theory and the experimental data is excellent. Theoretical expressions for the rotating-frame spin–lattice relaxation rate (1/T1ρ) were also obtained.