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Purpose: Phosphorus saturation-transfer experiments can quantify metabolic fluxes non-invasively. Typically, the forward flux through the creatine-kinase reaction is investigated by observing the decrease in phosphocreatine (PCr) after saturation of $γ$-ATP. The quantification of total ATP utilisation is currently under-explored, as it requires simultaneous saturation of inorganic phosphate (Pi) and PCr. This is challenging, as currently available saturation pulses reduce the already-low $γ$-ATP signal present. Methods: Using a hybrid optimal-control and Shinnar-Le-Roux method, a quasi-adiabatic RF pulse was designed for the dual-saturation of PCr and Pi to enable determination of total ATP utilisation. The pulses were evaluated in Bloch equation simulations, compared with a conventional hard-cosine DANTE saturation sequence, before application to perfused rat hearts at 11.7 Tesla. Results: The quasi-adiabatic pulse was insensitive to a $>2.5$-fold variation in $B_1$, producing equivalent saturation with a 53% reduction in delivered pulse power and a 33-fold reduction in spillover at the minimum effective $B_1$. This enabled the complete quantification of the synthesis and degradation fluxes for ATP in 30-45 minutes in the perfused rat heart. While the net synthesis flux ($4.24\pm0.8$ mM/s, SEM) was not significantly different from degradation flux ($6.88\pm2$ mM/s, $p=0.06$) and both measures are consistent with prior work, nonlinear error analysis highlights uncertainties in the Pi-to-ATP measurement that may explain a trend suggesting a possible imbalance. Conclusion: This work demonstrates a novel quasi-adiabatic dual-saturation RF pulse with significantly improved performance that can be used to measure ATP turnover in the heart in vivo.