Physics-embedded CycleGAN for robust metabolite mapping in short-readout deuterium metabolic imaging

Deuterium metabolic imaging (DMI) enables noninvasive, spatially resolved mapping of in vivo metabolism by tracking deuterium-labeled substrates and downstream products, yet it is frequently signal-to-noise-ratio (SNR) limiteddue to the low gyromagnetic ratio of 2 H and low metabolite concentration. Balanced steady-state free precession (bSSFP) can improve scan-time SNR efficiency for DMI, but operation in the short repetition time (TR)regime restricts readout duration and the number of acquired free induction decay (FID) points. The resulting loss of spectral resolvability increases metabolite overlap, renders separation ill-conditioned, and destabilizes fast Fourier transform (FFT)-basedprocessing and IDEAL-type model-based least-squares decomposition via strong cross-talk. We propose a physics-embedded CycleGAN for robust metabolite mapping in short-readout DMI using unpaired training. The key innovation is to embed an analytical bSSFP-DMI forward model directly into the cycle-consistency pathway by replacing one generator with a deterministic physics operator, thereby enforcing measurement consistency without requiring paired ground truth. A U-Net generator estimates metabolite maps and an off-resonance field map, with an off-resonance field map (B0) constrained to be spatially smooth via spline-basis parameterization. The physics operator synthesizes voxel wise time-domain signals, enabling a signal-domain cycle loss. Across simulation stress tests and in vivo mouse experiments, our method consistently suppresses inter-metabolite leakage and preserves spatial structure as readout length decreases, outperforming FFT peak integration and IDEAL-type fitting in the short-readout regime.