An empirical model for independent dose verification of the Gamma Knife treatment planning

A formalism for an independent dose verification of the Gamma Knife treatment planning is developed. It is based on the approximation that isodose distribution for a single shot is in the shape of an ellipsoid in three-dimensional space. The dose profiles for a phantom along each of the three major axes are fitted to a function which contains the terms that represent the contributions from a point source, an extrafocal scattering, and a flat background. The fitting parameters are extracted for all four helmet collimators, at various shot locations, and with different skull shapes. The 33 parameters of a patient's skull shape obtained from the Skull Scaling Instrument measurements are modeled for individual patients. The relative doses for a treatment volume in the form of 31 x 31 x 31 matrix of points are extracted from the treatment planning system, the Leksell Gamma-Plan (LGP). Our model evaluates the relative doses using the same input parameters as in the LGP, which are skull measurement data, shot location, weight, gamma-angle of the head frame, and helmet collimator size. For 29 single-shot cases, the discrepancy of dose at the focus point between the calculation and the LGP is found to be within -1% to 2%. For multi-shot cases, the value and the coordinate of the maximum dose point from the calculation agree within +/-7% and +/-3 mm with the LGP results. In general, the calculated doses agree with the LGP calculations within +/-10% for the off-center locations. Results of calculation with this method for the dimension and location of the 50% isodose line are in good agreement with results from Leksell GammaPlan. Therefore, this method can be served as a useful tool for secondary quality assurance of Gamma Knife treatment plans.