GammaPlan-Leksell Gamma Knife radiosurgery treatment planning verification method.

This work provides a method for an independent check of Gamma Knife GammaPlan radiosurgery calculations, named the spherical approximation method or SAM. Based on skull dimension measurements, the treated volume of the head is modeled as a sphere of radius R. With this approximation, an analytical solution for fast ray tracing of the path length, for each of the 201 beamlets, of the Gamma Knife helmet collimator was possible. The dose rate at the focus of a single shot is the sum of the contributions of all active beamlets adjusted for both the collimator factor and attenuation. For an arbitrary point, the dose rate is derived at the beamlet level from the focus values adjusted for the new path length attenuation and the appropriate collimators' off-axis profiles. The sum over all beamlets' contributions gives the dose rate at that particular point. At the single shot level, SAM independent check results agree with the GammaPlan for patient calculations to better than +/-6% and, as expected, in spherical phantoms the agreements improve to better than +/-1.0%. For an arbitrary point, multi-shot procedure, the agreement is better than +/-3% and +/-1.5, respectively.