Optimizing Proton Stopping Power Ratio Prediction with Dual-Energy Cone-Beam CT Using the Cramér-Rao Lower Bound

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Cone-beam computed tomography (CBCT) and X-ray projection radiography are commonly used in the proton therapy workflow for the verification of patient positioning. The prospect of using the CBCT images for dose calculation purposes is attractive but currently hampered by the poorer image quality compared to the planning (fan-beam) CT. Ideally, the CBCT scan with the patient's anatomy of the day would provide sufficiently accurate proton stopping power ratios (SPR) to directly replan the treatment if needed. Dual-energy fan-beam CT has been proven to increase the accuracy of calculated SPR values compared to single-energy CT. A similar outcome may therefore be expected for dual-energy/spectral CBCT. This work aims to compare two possible realizations of dual-energy CBCT, namely a rapid kVp-switching source CBCT and a photon-counting detector (PCD) CBCT with two energy bins, with respect to their suitability for extracting SPR values. To perform this comparison, we determine the Cramér-Rao Lower Bound on the variance of the estimated electron density and effective atomic number. In our simulation study, we find that for the rapid kVp-switching setup the optimum voltage pair is 80/140 kVp, and the optimum ratio of the source current at 80 kVp to the source current at 140 kVp is 2:1 (4:1) for extracting the electron density (effective atomic number). In case of the PCD-based setup, a 140 kVp (100 kVp) spectrum and energy bins of [20; 50), [50; 150) keV appear best suited for extracting electron density (effective atomic number), outperforming the kVp-switching setup by a factor of 3.8 (4.9).