A comparison of four skull models for independent dose calculations for Gamma Knife® PERFEXION™

Abstract

It is recommended to have a method for independently verifying planned doses in stereotactic radiosurgery. The problem is one of how to model the geometry of a skull sampled by a limited number of points and how to subsequently calculate numerous attenuation pathlengths through the modeled skull. While methods of verification have been previously published for model B and C Gamma Knife units, the aims of the current work were to apply the principles of these previously published techniques for the verification of plans for Gamma Knife PERFEXIONTM, to present a new method of verification, and to compare all methods in terms of their agreement with GammaPlan. Four algorithms were implemented: the previously published spherical approximation method (SAM) and bubble helmet skull (BHS), plus a modified BHS named interpolated BHS (IBHS) and a newly developed variable radius SAM (VRSAM). Reference point doses calculated by the four algorithms were compared to those reported by GammaPlan for 54 simple test plans and for 35 targets in 20 recent patient plans. For test plans, the mean (standard deviation) discrepancies against GammaPlan-reported doses were 0.3 (1.3)%, 0.3 (1.3)%, -1.6 (3.4)%, and -0.4 (1.0)% for SAM, VRSAM, BHS, and IBHS, respectively. For patient plans both the VRSAM and IBHS showed insignificant (p=0.22 and p = 0.50) discrepancies against GammaPlan of 0.38 (1.86)% and -0.11 (1.86)%, respectively. More significant discrepancies against GammaPlan (p < 0.0001) of 2.64 (2.98)% and -4.43 (3.39)% were observed for the SAM and BHS. The SAM can lead to large discrepancies against GammaPlan when a sphere is a poor approximation of the true skull surface, and in peripheral locations can lead to nonreal solutions to the attenuation pathlength calculations. While the BHS does not suffer the same geometric assumptions of the SAM, it can underestimate dose for peripherally located shots. The IBHS exhibits better agreement with GammaPlan than does the BHS, but requires two-dimensional interpolation that was found to be impractical to implement in the Excel-based software used in the current work. Combining aspects of both the previously published SAM and BHS algorithms, the newly presented VRSAM exhibits comparable results to the IBHS but without the need for interpolation and is therefore considered the preferred technique of the four implemented.