Advancing oxygen-enhanced MRI acquisition and modelling through dynamic $ΔR_{1}$ and $ΔR_2^*$ sensing
Purpose: To develop a multiparametric mapping framework for quantifying fat- and water-specific longitudinal and effective transverse relaxation rates, as well as changes in these parameters induced by a gas challenge. Theory and Methods: The proposed framework, termed SR-Fat DESPOT (single-reference fat-water separated driven equilibrium single-pulse observation of $T_1$), combines a two-component signal model with a single-reference variable flip angle (SR-VFA) approach. The signal model explicitly incorporates gas challenge-induced changes in relaxation rates. The single-reference acquisition strategy reduces data acquisition requirements while preserving sensitivity to both baseline parameters and dynamic changes. Sequence parameters were optimized using Cramer-Rao lower bound theory. SR-Fat DESPOT was evaluated using a modified open-surce abdominal numerical phantom and in two in vivo experiments: a single participant test-retest experiment and a pilot study with six participants. Results: In the abdominal numerical phantom, SR-Fat DESPOT was accurate for quantification of baseline relaxation rates with a normalized median absolute error (nMedAE) <3% for signal-to-noise ratio (SNR) >30 when comparing ground truth and estimates. SR-Fat DESPOT was also able to accurately recover median changes in relaxation rates, with differences within 0.001 $s^-1$ when compared to ground truth. In vivo, SR-Fat DESPOT measured changes in relaxation rates for spleen, kidneys, liver, and muscle under 100% O2 breathing, consistent with reports in literature. Changes detected in the spleen and kidneys were statistically significant across participants. Conclusion: SR-Fat DESPOT can quantify changes in relaxation rates induced by a gas challenge while reducing data requirements compared to more conventional approaches used in MR-oximetry literature.