Beam hardening of 10 MV radiotherapy x-rays: analysis using a convolution/superposition method

Total and primary polyenergetic dose spread arrays (PDSA) have been generated for a high energy 10 MV radiotherapy photon beam using the electron gamma shower (EGS) Monte Carlo code. By considering the attenuation of fluence per energy interval, PDSA have been produced at radiological depths of 0 cm (the surface PDSA) and 40 cm (the beam hardened PDSA). By comparing primary PDSA produced at these different depths, the effect of beam hardening on the PDSA has been quantified. Calculations show that the mean electron range due to the surface primary PDSA is 6.67 mm and the mean electron range of the beam hardened primary PDSA is 8.24 mm. In comparison, a 3 MeV primary monoenergetic dose spread array (MDSA) has a much smaller mean electron range of 4.81 mm. A radiotherapy x-ray beam computation method is introduced which involves a single superposition of the surface generated PDSA or beam hardened PDSA with a polyenergetic TERMA. The mean percentage difference between depth-dose curves obtained using super-position of surface and beam hardened PDSA is only 0.1%. The mean percentage difference from experimental data for these superposition curves is 2.8% down to 40 cm in a homogeneous phantom. The superposition process is shown to be forgiving to spectral differences when calculating the PDSA, but sensitive to the incident photon energy spectrum used to calculate the TERMA.