Optimal dimensionality and fundamental limits of proton stopping power estimation with photon-counting CT material decomposition

Objective. Proton therapy can achieve high radiation dose to the tumor while sparing normal tissue beyond the dose fall-off. Accurate estimation of proton stopping power ratio (SPR) and range from computed tomography (CT) data is a prerequisite for minimizing range uncertainty and treatment margins. Photon-counting CT (PCCT) could potentially improve the accuracy of SPR estimation with the increased number of energy measurements. This work aims to assess the fundamental limits of SPR and range estimation via material decomposition (MD) with PCCT, while evaluating the feasibility for higher MD dimensionalities for proton treatment planning. Approach. Eigentissue decomposition is used for computing optimal basis materials for elemental composition estimation. We model a water phantom with a centered test tissue insert, and use Cramér-Rao Lower Bound to estimate the covariance of basis material sinogram noise for MD dimensionalities 1, 2, 3, and 4. We model an ideal photon-counting detector with 1 mm 2 detector pixels, and fluence corresponding to 260 mAs at 120 kV. For each dimensionality, the noise is propagated to SPR level and corresponding SPR bias error is calculated. Range uncertainties are estimated through simulations in RayStation, with SPR volumes corresponding to calculated bias and noise for each dimensionality. Main results. The three-material decomposition was optimal for soft tissues, while two-material decomposition was optimal for bone when estimating proton range. The noise increase for the three-material decomposition did not generally translate to greater deviations at range level. The lowest range RMSEs with an ideal photon-counting detector were <0.1-0.7 %, depending on tissue type and depth. Significance. This work indicates the limits for SPR and range estimation accuracy using PCCT with an MD-based approach, and shows that multimaterial decomposition through quantiative imaging with PCCT could improve tissue characterization and range estimation in proton therapy.