Analytical calculation of central-axis dosimetric data for a dedicated 6-MV radiosurgery linear accelerator

Narrow beams are extensively used in stereotactic radiosurgery. The accuracy of treatment planning dose calculation depends largely on how well the dosimetric data are measured during the machine commissioning. Narrow beams are characterized by the lack of lateral electronic equilibrium. The lateral electronic disequilibrium in the radiation field and detector's finite size are likely to compromise the accuracy in dose measurements in these beams. This may have a profound impact on outcome in patients who undergo stereotactic radiosurgery. To confirm the measured commissioning data for a dedicated 6-MV linear accelerator-based radiosurgery system, we developed an analytical model to calculate the narrow photon beam central-axis dose. This model is an extension of a previously reported method of Nizin and Mooij for the calculation of the absorbed dose under lateral electronic disequilibrium conditions at depth of dmax or greater. The scatter factor and tissue-maximum ratio were calculated for narrow beams using the parametrized model and compared to carefully measured results for the same beams. For narrow beam radii ranging from 0.2 to 1.5 cm, the differences between the analytical and measured scatter factors were no greater than 1.4%. In addition, the differences between the analytical and measured tissue-maximum ratios were within 3.3% for regions greater than the maximum dose depth. The estimated error of this analytical calculation was less than 2%, which is sufficient to validate measurement results.