Practical Implementation of a Collapsed Cone Convolution Algorithm for a Radiation Treatment Planning System

A collapsed cone convolution algorithm was applied to a treatment planning system for the calculation of dose distributions. The distribution of beam fluences was determined using a three-source model by considering the source strengths of the primary beam, the beam scattered from the primary collimators, and an extra beam scattered from extra structures in the gantry head of the radiotherapy treatment machine. The distribution of the total energy released per unit mass (TERMA) was calculated from the distribution of the fluence by considering several physical effects such as the emission of poly-energetic photon spectra, the attenuation of the beam fluence in a medium, the horn effect, the beam-softening effect, and beam transmission through collimators or multi-leaf collimators. The distribution of the doses was calculated by using the convolution of the distribution of the TERMA and the poly-energetic kernel. The distribution of the kernel was approximated to several tens of collapsed cone lines to express the energies transferred by the electrons that originated from the interactions between the photons and the medium. The implemented algorithm was validated by comparing the calculated percentage depth doses (PDDs) and dose profiles with the measured PDDs and relevant profiles. In addition, the dose distribution for an irregular-shaped radiation field was verified by comparing the calculated doses with the measured doses obtained via EDR2 film dosimetry and with the calculated doses obtained using a different treatment planning system based on the pencil beam algorithm (Eclipse, Varian, Palo Alto, USA). The majority of the calculated doses for the PDDs, the profiles, and the irregular-shaped field showed good agreement with the measured doses to within a 2% dose difference, except in the build-up regions. The implemented algorithm was proven to be efficient and accurate for clinical purposes in radiation therapy, and it was found to be easily implementable in treatment planning systems.