R_1ρ relaxation functions for weak, intermediate and strong collision models, revisited for frequency swept RF pulses

In this work, we evaluated the expressions derived for describing rotating frame longitudinal T_1ρ relaxations in the case of homonuclear dipole-dipole interactions spanning the entire range of strong, intermediate and weak collision regimes (SCR, ICR and WCR, respectively). First, the integral-based expressions for R_1ρ ≡ 1/T_1ρ in the complete range of correlation times were represented through the summation of effective spectral density function terms. Then, the formalism for continuous wave spin-lock T_1ρ was expanded to the time-dependent T_1ρ(t) during radiofrequency (RF) irradiation delivered with amplitude and frequency modulated hyperbolic secant (HS) pulses, and the effective spectral density function terms were propagated through the HS pulses. The derived expressions are in good agreement with the formalism obtained previously for dipole-dipole relaxations in the weak collision case during HS pulses. The derived theory describes well the spin-lock T_1ρ relaxation data of polyacetal (Delrin) in the SCR. In addition, we provided an application of the derived theory to spin-lock off-resonance T_1ρ relaxation data of glycogen. Because the developed formalism is valid for the entire motional regime, from ultra-slow to fast motions, its applicability in vivo is plausible.