An evaluation method of clinical impact with setup, range, and radiosensitivity uncertainties in fractionated carbon-ion therapy.

In light ion therapy, the dose concentration is highly sensitive to setup and range errors. Here we propose a method for evaluating the effects of these errors by using the correlation between fractions on tumour control probability (TCP) in carbon-ion therapy. This method incorporates the concept of equivalent stochastic dose (Cranmer-Sargison and Zavgorodni 2005 Phys. Med. Biol. 50 4097-109), which was defined as a dose that gives the mean expected survival fraction (SF) for the stochastically variable dose. The mean expected SFs were calculated while considering the correlation between fractions for setup and range errors. By using this SF, equivalent stochastic clinical doses (ESCD), which are weighted by relative biological effectiveness, of lung and prostate cases with varying errors were derived. To account for spatial dose heterogeneity, equivalent uniform stochastic clinical doses (EUSCD) were obtained by using the mean expected SF in the volume of interest. TCP curves were calculated for each assumed error considering inter-patient sensitivity variation with a fractionation effect. ESCD distributions, EUSCD, and TCP curves were affected by the inter-fraction correlation and the contribution of setup and range errors. Irradiated areas that could be affected by these errors can be visualized quantitatively by using the ESCD distribution. TCP curves for the errors of various conditions converged around the TCP curve in nominal conditions by using the EUSCD. EUSCD correlated well with TCP in setup and range errors when the errors were not large and was comparatively stably insensitive to uncertain biological parameters. The proposed evaluation method with EUSCD and TCP calculations will be useful to indicate tumour doses to improve realistic dose distributions in carbon-ion therapy.