Deciphering adiabatic rotating frame relaxometry in biological tissues

This work aims to unravel the intricacies of adiabatic rotating frame relaxometry in biological tissues.

The classical formalisms of dipolar relaxation $R_{1\rho }$ and $R_{2\rho }$ were systematically analyzed for water molecules reorienting on "fast" and "slow" timescales. These two timescales are, respectively, responsible for the absence and presence of $R_{1\rho }$ dispersion. A time-averaged $R_{1\rho }$ or $R_{2\rho }$ over an adiabatic pulse duration was recast into a sum of $R_1$ and $R_2$ , but with different weightings. These weightings depend on the specific modulations of adiabatic pulse waveforms. In this context, stretched hyperbolic secant ( $\mathrm{HSn}$ ) pulses were characterized. Previously published $HS1$ $R_{1\rho }$ , continuous-wave (CW) $R_{1\rho }$ , and $R_1$ measures from 12 agarose phantoms were used to validate the theoretical predictions. A similar validation was also performed on previously published $\mathrm{HSn}$ $R_{1\rho }$ ( $n$ =1, 4, 8) and $\mathrm{HS}1$ $R_{2\rho }$ from bovine cartilage specimens.

Longitudinal relaxation weighting decreases for $\mathrm{HSn}$ pulses as $n$ increases. Predicted CW $R_{1\rho }^{\mathrm{cal}}$ values from agarose phantoms align well with the measured CW $R_{1\rho }^{\exp }$ values, as indicated by a linear regression function: $R_{1\rho }^{\mathrm{cal}}=1.04*R_{1\rho }^{\exp }-1.96$ . The predicted adiabatic $R_{1\rho }$ and $R_{2\rho }$ from cartilage specimens are consistent with those previously measured, as quantified by: $R_{1\rho ,2\rho }^{\mathrm{cal}}=1.10*R_{1\rho ,2\rho }^{\exp }-0.41$ .

This work has theoretically and experimentally demonstrated that adiabatic $R_{1\rho }$ and $R_{2\rho }$ can be recast into a sum of $R_1$ and $R_2$ , with varying weightings. Therefore, any suggestions that adiabatic rotating frame relaxometry in biological tissues could provide more information than the standard $R_1$ and $R_2$ warrant closer scrutiny.