Optimum size of a calibration phantom for x-ray CT to convert the Hounsfield units to stopping power ratios in charged particle therapy treatment planning

In charged-particle therapy treatment planning, the volumetric distribution of stopping power ratios (SPRs) of body tissues relative to water is used for patient dose calculation. The distribution is conventionally obtained from computed tomography (CT) images of a patient using predetermined conversion functions from the CT numbers to the SPRs. One of the biggest uncertainty sources of patient SPR estimation is insufficient correction of beam hardening arising from the mismatch between the size of the patient cross section and the calibration phantom for producing the conversion functions. The uncertainty would be minimized by selecting a suitable size for the cylindrical water calibration phantom, referred to as an 'effective size' of the patient cross section, L-effective. We investigated the Leffective for pelvis, abdomen, thorax, and head and neck regions by simulating an ideal CT system using volumetric models of the reference male and female phantoms. The Leffective values were 23.3, 20.3, 22.7 and 18.8 cm for the pelvis, abdomen, thorax, and head and neck regions, respectively, and the L-effective for whole body was 21.0 cm. Using the conversion function for a 21.0-cm-diameter cylindrical water phantom, we could reduce the root mean square deviation of the SPRs and their mean deviation to <= 0.011 and <= 0.001, respectively, in the whole body. Accordingly, for simplicity, the effective size of 21.0 cm can be used for the whole body, irrespective of body-part regions for treatment planning in clinical practice.