Effects of bone- and air-tissue inhomogeneities on the dose distributions of the Leksell Gamma Knife® calculated with PENELOPE

Monte Carlo simulation with PENELOPE (version 2003) is applied to calculate Leksell Gamma Knife dose distributions for heterogeneous phantoms. The usual spherical water phantom is modified with a spherical bone shell simulating the skull and an air-filled cube simulating the frontal or maxillary sinuses. Different simulations of the 201 source configuration of the Gamma Knife have been carried out with a simplified model of the geometry of the source channel of the Gamma Knife recently tested for both single source and multisource configurations. The dose distributions determined for heterogeneous phantoms including the bone- and/or air-tissue interfaces show non-negligible differences with respect to those calculated for a homogeneous one, mainly when the Gamma Knife isocentre approaches the separation surfaces. Our findings confirm an important underdosage (approximately 10%) nearby the air-tissue interface, in accordance with previous results obtained with the PENELOPE code with a procedure different from ours. On the other hand, the presence of the spherical shell simulating the skull produces a few per cent underdosage at the isocentre wherever it is situated.

A simplified model of the source channel of the Leksell Gamma Knife®: testing multisource configurations with PENELOPE

A simplification of the source channel geometry of the Leksell Gamma Knife (GK), recently proposed by the authors and checked for a single source configuration (Al-Dweri F M O, Lallena A M and Vilches M 2004 Phys. Med. Biol. 49 2687-703), has been used to calculate the dose distributions along the x, y and z axes in a water phantom with a diameter of 160 mm, for different configurations of the Gamma Knife, including 201, 150 and 102 unplugged sources. The code PENELOPE (v. 2001) has been used to perform the Monte Carlo simulations. In addition, the output factors for the 14, 8 and 4 mm helmets have been calculated. The results found for the dose profiles show a qualitatively good agreement with previous ones obtained with EGS4 and PENELOPE (v. 2000) codes and with the predictions of GammaPlan. The output factors obtained with our model agree within the statistical uncertainties with those calculated with the same Monte Carlo codes and with those measured with different techniques. Owing to the accuracy of the results obtained and to the reduction in the computational time with respect to full geometry simulations (larger than a factor 15), this simplified model opens the possibility of using Monte Carlo tools for planning purposes in the Gamma Knife.

Effect on tumour control of time interval between surgery and postoperative radiotherapy: an empirical approach using Monte Carlo simulation

In this work, a procedure, based on Monte Carlo techniques, to analyse the effect on the tumour control probability of the time interval between surgery and postoperative radiotherapy is presented. The approach includes the tumour growth as well as the survival of tumour cells undergoing fractionated radiotherapy. Both processes are described in terms of the binomial distribution. We have considered two different growth models, exponential and Gompertz, the parameters of which have been fixed to reproduce the clinical outcome corresponding to a retrospective study for patients with head and neck squamous cell carcinomas. In the cases analysed, we have not found significant differences between the results obtained for both growth models. The mean doubling times found for residual clonogens after surgery are less than 40 days. The rate of decrease in local control is around 0.09% per day of delay between surgery and radiotherapy and the corresponding time factor is about 0.11 Gy per day.

A simplified model of the source channel of the Leksell GammaKnife® tested with PENELOPE

Monte Carlo simulations using the code PENELOPE have been performed to test a simplified model of the source channel geometry of the Leksell GammaKnife. The characteristics of the radiation passing through the treatment helmets are analysed in detail. We have found that only primary particles emitted from the source with polar angles smaller than 3 degrees with respect to the beam axis are relevant for the dosimetry of the Gamma Knife. The photon trajectories reaching the output helmet collimators at (x, v, z = 236 mm) show strong correlations between rho = (x2 + y2)(1/2) and their polar angle theta, on one side, and between tan(-1)(y/x) and their azimuthal angle phi, on the other. This enables us to propose a simplified model which treats the full source channel as a mathematical collimator. This simplified model produces doses in good agreement with those found for the full geometry. In the region of maximal dose, the relative differences between both calculations are within 3%, for the 18 and 14 mm helmets, and 10%, for the 8 and 4 mm ones. Besides, the simplified model permits a strong reduction (larger than a factor 15) in the computational time.

Dosimetry for radiocolloid therapy of cystic craniopharyngiomas

The dosimetry for radiocolloid therapy of cystic craniopharyngiomas is investigated. Analytical calculations based on the Loevinger and the Berger formulas for electrons and photons, respectively, are compared with Monte Carlo simulations. The role of the material of which the colloid introduced inside the craniopharyngioma is made of as well as that forming the cyst wall is analyzed. It is found that the analytical approaches provide a very good description of the simulated data in the conditions where they can be applied (i.e., in the case of a uniform and infinite homogeneous medium). However, the consideration of the different materials and interfaces produces a strong reduction of the dose delivered to the cyst wall in relation to that predicted by the Loevinger and the Berger formulas.