Pang Y. Deciphering adiabatic rotating frame relaxometry in biological tissues.
Magn Reson Med 2024. [PMID:
39099141 DOI:
10.1002/mrm.30240]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2024] [Revised: 06/26/2024] [Accepted: 07/12/2024] [Indexed: 08/06/2024]
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 relaxationR 1 ρ $$ {R}_{1\rho } $$ andR 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 ofR 1 ρ $$ {R}_{1\rho } $$ dispersion. A time-averagedR 1 ρ $$ {R}_{1\rho } $$ orR 2 ρ $$ {R}_{2\rho } $$ over an adiabatic pulse duration was recast into a sum ofR 1 $$ {R}_1 $$ andR 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 publishedH S 1 $$ HS1 $$ R 1 ρ $$ {R}_{1\rho } $$ , continuous-wave (CW)R 1 ρ $$ {R}_{1\rho } $$ , andR 1 $$ {R}_1 $$ measures from 12 agarose phantoms were used to validate the theoretical predictions. A similar validation was also performed on previously publishedHSn $$ HSn $$ R 1 ρ $$ {R}_{1\rho } $$ (n $$ n $$ =1, 4, 8) andHS 1 $$ HS1 $$ R 2 ρ $$ {R}_{2\rho } $$ from bovine cartilage specimens.
RESULTS
Longitudinal relaxation weighting decreases forHSn $$ HSn $$ pulses asn $$ n $$ increases. Predicted CWR 1 ρ cal $$ {R}_{1\rho}^{cal} $$ values from agarose phantoms align well with the measured CWR 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 adiabaticR 1 ρ $$ {R}_{1\rho } $$ andR 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 adiabaticR 1 ρ $$ {R}_{1\rho } $$ andR 2 ρ $$ {R}_{2\rho } $$ can be recast into a sum ofR 1 $$ {R}_1 $$ andR 2 $$ {R}_2 $$ , with varying weightings. Therefore, any suggestions that adiabatic rotating frame relaxometry in biological tissues could provide more information than the standardR 1 $$ {R}_1 $$ andR 2 $$ {R}_2 $$ warrant closer scrutiny.
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