The Variable Ellipsoid Modeling Technique as a Verification Method for the Treatment Planning System of Gamma Knife Radiosurgery

Objective : The secondary verification of Leksell Gamma Knife treatment planning system (LGP) (which is the primary verification system) is extremely important in order to minimize the risk of treatment errors. Although prior methods have been developed to verify maximum dose and treatment time, none have studied maximum dose coordinates and treatment volume. Methods : We simulated the skull shape as an ellipsoid with its center at the junction between the mammillary bodies and the brain stem. The radiation depths of the beamlets emitted from 201 collimators were calculated based on the relationship between this ellipsoid and a single beamlet expressed as a straight line. A computer program was coded to execute the algorithm. A database system was adopted to log the doses for $31{\times}31{\times}31$ or 29,791 matrix points allowing for future queries to be made of the matrix of interest. Results : When we compared the parameters in seven patients, all parameters showed good correlation. The number of matrix points with a dose higher than 30% of the maximal dose was within ${\pm}\;2%$ of LGP. The 50% dose volume, which is generally the target volume, differs maximally by 4.2%. The difference of the maximal dose ranges from 0.7% to 7%. Conclusion : Based on the results, the variable ellipsoid modeling technique or variable ellipsoid modeling technique (VEMT) can be a useful and independent tool to verify the important parameters of LGP and make up for LGP.