Modified sector-integration method for predicting the output factors of electron beams including extended source to surface distance

A modified sector-integration method is presented that can predict the output factors of irregular shaped electron fields even in the case of extended source to surface distance (SSD). The model takes as input measured output factors for circular inserts of various radii. These circular fields were measured at SSDs of 100, 105 and 110 cm to determine the effective source distance as a function of radius (ESD(r)). For an arbitrary electron field at any SSD, the shape is divided into small sectors, and the contribution calculated from the radius and ESD(r). The calculated output factors were verified by direct measurements of various types of electron fields mainly based on clinical use. The energies modelled were 8, 10 and 12 MeV for applicator sizes of 10 cm x 10 cm and 14 cm x 14 cm (defined at 95 cm). The calculated values agreed with the measured data within 1% for the various rectangular cutouts including extended source to surface distance. We retrospectively modelled 97 patient inserts of irregular shape, and found agreement within 2% of measured values.