Evaluation of a pencil beam algorithm for therapeutic carbon ion beam in presence of bolus

Hot- and cold-dose spots at a shallow depth in a target are formed by carbon ions passing through the bolus with sharp gradients. These spots are caused by sidescatter disequilibrium due to various multiple scattering effects in the different bolus thicknesses. When the dose calculation method by the broad beam algorithm (BBA) is used for treatment planning, these spots cannot be predicted, because the BBA neglects the multiple scattering effects in materials (rms error of 3.9%). On the other hand, since the dose calculation method by the pencil beam algorithm (PBA) takes into account the scattering effects, the results calculated by the PBA agreed better than the BBA with the measured hot- and cold-dose spots, having a rms error of 1.9%. Thus, dose calculation by the PBA improves the accuracy of dose prediction at the shallow depth. However, since dose distributions at deeper positions are affected by many light fragment particles generated by fragment reactions, the results calculated by the PBA disagree with the experimental ones. It is necessary that even the PBA accurately models behavior of fragment particles.