Analytical representation of head scatter factors for shaped photon beams using a two-component x-ray source model.

An analytic representation proposed for the relative intensity distribution of the extra-focal source in a two-component x-ray source model serves as the basis for calculation. From this representation, a closed-form expression for head scatter factors defined on the central beam axis is derived by integrating over the area of the extra-focal source plane visible from the measurement point. The resulting expression is applicable to photon beams from different Varian accelerators and different photon energies, and includes effects arising from beam shaping with cerrobend blocks or multileaf collimators (MLCs). For 6- and 15-MV photon beams from Varian 600 C and 2300 CD accelerators (Varian Oncology Systems, Palo Alto, CA), 361 measured head scatter factors for square, rectangular, asymmetric, and arbitrarily shaped fields, formed by either the X and Y jaws, the MLC and Y jaws, or by the MLC alone, were compared with model calculations. Results show that 93.4% of calculated values match corresponding experimental points to within 0.5%, the average deviation being 0.23% and the maximum deviation 0.9%. Thus, as a consequence of this work, the different influence of the X jaws, the Y jaws, and the MLC on head scatter factors is quantitatively described. In particular, it is demonstrated that in the case of radially symmetric scattering, the collimator exchange effect arises as a result of the different distances of the X and Y jaws from the focal spot.