Analytical investigation on the role of ion radiography for Hounsfield Unit conversion into relative stopping power in ion beam therapy

In ion beam therapy the empirical calibration from Hounsfield Unit (HU) to Relative Stopping Power (RSP) can lead to range inaccuracies up to several millimeters. The purpose of this work is to investigate the role of ion radiography in improving the HU to RSP conversion (HU-RSP calibration curve refinement) using analytically simulated scanned proton and carbon ion pencil beams and different detector configurations. Proton and carbon ion radiographies of an anthropomorphic phantom were simulated using both list-and integration-mode detector configurations. Controlled inaccuracies Δtrue were randomly applied to the clinical-like true calibration so that RSPempirical=Δtrue RSPtrue. The root-mean-square error (RMSE) between the (empirically calibrated) digitally reconstructed radiography (DRR) and the (truly calibrated) ion radiography was minimized as argminΔ{RMSE[ΣL(RSPtrue-RSPempirical(Δ))]}, where L was the ion trajectory. The latter was estimated as straight for carbon ions whereas curved for protons due to multiple Coulomb scattering. Accuracy and robustness were investigated as a function of increasing: I) number of radiographies (≤128) II) deviation Δ (≤30% RSPtrue) III) noise variance σ2 (≤10-1 RSPtrue 2). In case of carbon ions, the RMSE was negligible (≈10-11) within all settings in I) and II) while in III) the RMSE followed a power law trend a (σ2)b (a≈90.1, b≈4.8 10-1) up to 29.8 for extremely high noise variance σ2=10-1. With protons, list-mode detector configuration performed better than integration-mode, showing a RMSE median (interquartile-range) equal to 1.5 (0.8), whereas 4.7 (1.3) for integration-mode. The HU-RSP calibration curve refinement resulted sensitive to the ion radiography noise and, as highlighted by protons, to the ion trajectory estimation enabled by the detector configuration. An enhanced sensitivity to interfractional anatomical changes is expected, as suggested by a twelve orders of magnitude larger RMSE for the carbon ion radiographies of a breathing anthropomorphic phantom. Hence, deformable image registration is foreseen to be incorporated in the HU-RSP calibration curve refinement.