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

Abstract

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.

An enhanced sector integration model for output and dose distribution calculation of irregular concave shaped electron beams

“…Since the enhanced sector integration model is, in some way, related to the sector integration model by Jursinic and Mueller 14 ͑later modified by Choi and co-workers 15,16 ͒, it would be beneficial to compare them to highlight differences and improvements in the accuracy of the calculations.…”

“…Apart from the empirical and theoretical models, there was a few published semiempirical models based on the sector integration concept. [13][14][15][16] The sector integration concept was similar to the one introduced by Clarkson 17 for the calculation of the output factor for photon beams. The original method by Jursinic and Mueller 14 has been further modified by Choi and co-workers 15,16 to allow for the calculation of ROF of irregular shaped electron fields in the case of extended source to surface distance.…”

“…[13][14][15][16] The sector integration concept was similar to the one introduced by Clarkson 17 for the calculation of the output factor for photon beams. The original method by Jursinic and Mueller 14 has been further modified by Choi and co-workers 15,16 to allow for the calculation of ROF of irregular shaped electron fields in the case of extended source to surface distance. Nevertheless, one of the limitations of their methods was the inability to calculate the depth of maximum dose d max shift to shallower depths for very small electron fields and the accuracy of ROF for the concaved shaped cutouts was rather poor ͑errorsϾ 3%͒.…”

Parameterization of electron beam output factor

“…Khan et al [9] reported a method for predicting ROF with irregular field using lateral build-up ratio concept. The sector integration concept [4,5,21], which is similar to Clarkson's model for calculation of the output factor for photon beams [22], has also been reported with accurate prediction of ROF. Even though we have not verified, sector integration similar to Khan et al [9] could be used with our equation and will be reported in a separate study.…”

“…As a result, the ROF of a specific treatment is usually measured individually in order to achieve an acceptable accuracy. These patient-specific electron measurements are time consuming and prone for significant error due to selection of detector and respective d max .There are many publications on analytical methods to calculate the percent depth dose (PDD) [3] and/or ROF for electron beams, including the sector-integration method [4,5], Gaussian pencil model plus collimator scattering [6,7], two-source model [8], and a method based on the lateral build-up ratio [9e11]. The current generation of treatment planning systems for clinical use depend on pencil-beam algorithms [12,13].…”