Analytical description of dose profile behaviour in Gamma Knife radiosurgery

Stereotactic Gamma Knife radiosurgery utilizes ionizing beams from (60)Co sources and relies on a combination of collimator sizes, weighting, etc to generate a high-dose region that is conformal with a designated target volume. Dose computation is typically performed by computer, but in this paper, single collimator dose profile behaviour is modelled analytically and then extended to accommodate multiple collimators of different weights with co-located isocentres. The dose profile from a single helmet is derived from a top-hat beam profile approximation and an idealized symmetric distribution of sources is used to represent the 201 sources within a collimating helmet. The results from the analysis are validated by an independent numerical model and also compared with those obtained by other groups using numerical and experimental methods. With respect to multiple collimators, the relationship between the size (full width half maximum) of the irradiated volume and relative collimator weighting is also examined using the simple analytical model. The simplicity of the mathematics clarifies the relationship between beam profile, dose profile and multiple collimator behaviour, and provides data that compare favourably with published literature.