Pre-treatment patient-specific stopping power by combining list-mode proton radiography and x-ray CT

The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining (1) pre-treatment x-ray CT and (2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin(parallel to Ax - b parallel to(2)(2))). The parameter A represents the cumulative path-length crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness/physical thickness) are denoted by x. The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linear-solver with x >= 0. A was computed by superposing proton trajectories calculated with a cubic or linear spline approach to the CT. The material's RSP assigned in Geant4 were used for reference while the clinical HU-RSP calibration curve was used for comparison. The Gammex RMI-467 phantom was first investigated. The standard deviation between the estimated material RSP and the calculated RSP is 0.45%. The robustness of the techniques was then assessed as a function of the number of projections and initial proton energy. Optimization with two initial projections yields precise RSP (<= 1.0%) for 330 MeV protons. 250 MeV protons have shown higher uncertainty (<= 2.0%) due to the loss of precision in the path estimate. Anthropomorphic phantoms of the head, pelvis, and lung were subsequently evaluated. Accurate RSP has been obtained for the head (mu = 0.21 +/- 1.63%), the lung (mu = 0.06 +/- 0.99%) and the pelvis (mu = 0.90 +/- 3.87%). The range precision has been optimized using the calibration curves obtained with the algorithm, yielding a mean R-80 difference to the reference of 0.11 +/- 0.09%, 0.28 +/- 0.34% and 0.05 +/- 0.06% in the same order. The solution's accuracy is limited by the assumed HU/RSP bijection, neglecting inherent degeneracy. The proposed formulation of the problem with prior knowledge x-ray CT demonstrates potential to increase the accuracy of present RSP estimates.