A novel pencil beam model for carbon-ion dose calculation derived from Monte Carlo simulations

An accurate kernel model is of vital importance for pencil-beam dose algorithm in charged particle therapy using precise spot-scanning beam delivery, in which an accurate depiction of the low dose envelope is especially crucial. Based on the Monte Carlo method, we investigated the dose contribution of secondary particles to the total dose and proposed a novel beam model to depict the lateral dose distribution of carbon-ion pencil beam in water. We demonstrated that the low dose envelope in single-spot profiles in water could be adequately modelled with the addition of a logistic distribution to a double Gaussian one, which was verified in both single carbon-ion pencil beam and superposed fields of different sizes with multiple pencil beams. Its superiority was mainly manifested at medium depths especially for high-energy beams with small fields compared with single, double and triple Gaussian models, where the secondary particles influenced the total dose considerably. The double Gaussian-logistic model could reduce the deviations from 4.1%, 1.7% to 0.3% in the plateau and peak regions, and from 19.2%, 4.9% to 1.2% in the tail region compared for the field size factor (FSF) calculations of 344 MeV/u carbon-ion pencil beam with the single and double Gaussian models. Compared with the triple Gaussian one, our newly-proposed model was on a par with it, even better than it in the plateau and peak regions. Thus our work will be helpful for improving the dose calculation accuracy for carbon-ion therapy.