Patient-Specific Stopping Power Calibration of Treatment Planning X-Ray CT Using Integrated Depth-Dose Profiles Acquired by Proton Transmission Imaging - A Feasibility Study

OBJECTIVE: Range uncertainties in proton therapy largely arise from the semi-empirical conversion of X-ray computed tomography (CT) Hounsfield Units to stopping power relative to water (RSP), requiring generous safety margins or robust optimization. Pencil beam-wise integrated depth-dose profiles (IDDs), obtained via proton transmission imaging using a particle integrating detector, can be combined with the treatment planning CT to obtain patient-specific conversion curves. Existing calibration approaches rely on projection images or water-equivalent path length (WEPL) histograms derived from IDDs via signal decomposition or deconvolution. A direct optimization approach based on the acquired IDD signal is proposed, avoiding the need for decomposition or deconvolution and their associated WEPL accuracy and resolution limitations. Approach: The RSP conversion curve is iteratively optimized using Monte Carlo-simulated IDDs acquired from two orthogonal projection angles in a line-scan proton imaging setup. The differentiable implementation of the forward projection operator is embedded in a gradient-based optimization scheme. Main results: The proposed IDD-based optimization approach significantly reduces the calibration error compared to the initial guess. The median mean absolute percentage error on a set of axial CT slices decreases from 1.88% to 0.58%, with a median computation time of 5.47 hours per slice. The optimized calibration improves dose accuracy for an exemplary treatment pencil beam. Increasing the spot spacing by a factor of ten decreases the computation time to 0.60 hours with minimal loss of accuracy. Using a single projection angle yields comparable results to using both projections (0.64% vs. 0.57%). With current detector depth resolutions of ~2 mm, calibration accuracy of ~0.7% is achievable, with potential improvements using finer-resolution detectors. Significance: Particle integrating detectors offer potential for clinical translation due to lower cost and complexity. Direct optimization on IDDs using a differentiable forward operator enables accurate, fully automated calibration, improving upon earlier manual IDD-based or automated WEPL-based approaches.