Model-based calculations of off-axis ratio of conic beams for a dedicated 6 MV radiosurgery unit

Purpose: Because the small-radius photon beams shaped by cones in stereotactic radiosurgery (SRS) lack lateral electronic equilibrium and a detector's finite cross section, direct experimental measurement of dosimetric data for these beams can be subject to large uncertainties. As the dose calculation accuracy of a treatment planning system largely depends on how well the dosimetric data are measured during the machine's commissioning, there is a critical need for an independent method to validate measured results. Therefore, the authors studied the model-based calculation as an approach to validate measured off-axis ratios (OARs). Methods: The authors previously used a two-component analytical model to calculate central axis dose and associated dosimetric data (e.g., scatter factors and tissue-maximum ratio) in a water phantom and found excellent agreement between the calculated and the measured central axis doses for small 6 MV SRS conic beams. The model was based on that of Nizin and Mooij ["An approximation of central-axis absorbed dose in narrow photon beams," Med. Phys. 24, 1775-1780 (1997)] but was extended to account for apparent attenuation, spectral differences between broad and narrow beams, and the need for stricter scatter dose calculations for clinical beams. In this study, the authors applied Clarkson integration to this model to calculate OARs for conic beams. OARs were calculated for selected cones with radii from 0.2 to 1.0 cm. To allow comparisons, the authors also directly measured OARs using stereotactic diode (SFD), microchamber, and film dosimetry techniques. The calculated results were machine-specific and independent of direct measurement data for these beams. Results: For these conic beams, the calculated OARs were in excellent agreement with the data measured using an SFD. The discrepancies in radii and in 80%-20% penumbra were within 0.01 cm, respectively. Using SFD-measured OARs as the reference data, the authors found that the calculated OARs were more accurate than those measured with a microchamber or film dosimetry. Conclusions: The model produces sufficiently accurate conic beam dosimetric data that can be used to validate direct measurement results for such beams.