Deciphering adiabatic rotating frame relaxometry in biological tissues.

ABSTRACT

PURPOSE: This work aims to unravel the intricacies of adiabatic rotating frame relaxometry in biological tissues. THEORY AND METHODS: The classical formalisms of dipolar relaxation R 1 ρ $$ {R}_{1\rho } $$ and R 2 ρ $$ {R}_{2\rho } $$ were systematically analyzed for water molecules reorienting on "fast" and "slow" timescales. These two timescales are, respectively, responsible for the absence and presence of R 1 ρ $$ {R}_{1\rho } $$ dispersion. A time-averaged R 1 ρ $$ {R}_{1\rho } $$ or R 2 ρ $$ {R}_{2\rho } $$ over an adiabatic pulse duration was recast into a sum of R 1 $$ {R}_1 $$ and R 2 $$ {R}_2 $$ , but with different weightings. These weightings depend on the specific modulations of adiabatic pulse waveforms. In this context, stretched hyperbolic secant ( HSn $$ HSn $$ ) pulses were characterized. Previously published H S 1 $$ HS1 $$ R 1 ρ $$ {R}_{1\rho } $$ , continuous-wave (CW) R 1 ρ $$ {R}_{1\rho } $$ , and R 1 $$ {R}_1 $$ measures from 12 agarose phantoms were used to validate the theoretical predictions. A similar validation was also performed on previously published HSn $$ HSn $$ R 1 ρ $$ {R}_{1\rho } $$ ( n $$ n $$ =1, 4, 8) and HS 1 $$ HS1 $$ R 2 ρ $$ {R}_{2\rho } $$ from bovine cartilage specimens. RESULTS: Longitudinal relaxation weighting decreases for HSn $$ HSn $$ pulses as n $$ n $$ increases. Predicted CW R 1 ρ cal $$ {R}_{1\rho}^{cal} $$ values from agarose phantoms align well with the measured CW R 1 ρ exp $$ {R}_{1\rho}^{exp} $$ values, as indicated by a linear regression function R 1 ρ cal = 1.04 * R 1 ρ exp - 1.96 $$ {R}_{1\rho}^{cal}={1.04}^{\ast }{R}_{1\rho}^{exp}-1.96 $$ . The predicted adiabatic R 1 ρ $$ {R}_{1\rho } $$ and R 2 ρ $$ {R}_{2\rho } $$ from cartilage specimens are consistent with those previously measured, as quantified by R 1 ρ , 2 ρ cal = 1.10 * R 1 ρ , 2 ρ exp - 0.41 $$ {R}_{1\rho, 2\rho}^{cal}={1.10}^{\ast }{R}_{1\rho, 2\rho}^{exp}-0.41 $$ . CONCLUSION: This work has theoretically and experimentally demonstrated that adiabatic R 1 ρ $$ {R}_{1\rho } $$ and R 2 ρ $$ {R}_{2\rho } $$ can be recast into a sum of R 1 $$ {R}_1 $$ and R 2 $$ {R}_2 $$ , with varying weightings. Therefore, any suggestions that adiabatic rotating frame relaxometry in biological tissues could provide more information than the standard R 1 $$ {R}_1 $$ and R 2 $$ {R}_2 $$ warrant closer scrutiny.