Determination and verification of a 2D pencil-beam kernel for a radiosurgery system with cones

The quality and correctness of dosimetric data of small fields in stereotactic radiosurgery (SRS) depends significantly on the election of the detector employed in the measurements. This work provides an independent method of verification of these data through the determination of a polyenergetic 2-dimensional pencil-beam kernel for a BrainLAB SRS system with cones, employing the deconvolution/convolution of a reference experimental off-axis ratio (OAR) profile (cone diameter c0 = 35 mm). The kernel in real space k(c(0))(r,z(0)) is convolved with the ideal fluence Φ for the cones 7.5 to 35 mm in diameter to obtain the OAR profiles, and the total scatter factors, St, which are compared with experimental values of the same quantities. The experimental OARs and St factors are measured in water with a PTW 60003 diamond detector. Additionally, the reference OAR is corrected for beam divergence and spectral fluence fluctuations defining a function of boundary correction factors (BF). The BF and Φ functions are transformed to the conjugate space with the zeroth-order Hankel transform, appropriated to the radial symmetry of the cones. Therefore, the kernel in real space k(c(0))(r,z(0)) is the inverse Hankel transform of the ratio of the Hankel transforms of BF and Φ. Finally, an uncertainty analysis according to the Guide to the Expression of Uncertainty in Measurement is carried out for 3 different values of k(c(0))(r,z(0)). Calculated and measured OARs agree within the dose/distance-to-agreement criteria of 2%/0.12 mm; while, St factors agree within 2%. This procedure supplies an independent method to validate the dosimetric data necessary to feed treatment planning systems for SRS with cones.