Convolution-based modified Clarkson integration (CMCI) for electron cutout factor calculation

Electron therapy is widely used to treat shallow tumors because of its characteristic sharp dose fall-off beyond a certain range. A customized cutout is typically applied to block radiation to normal tissues. Determining the final monitor unit (MU) for electron treatment requires an output factor for the cutout, which is usually generated by measurement, especially for highly irregular cutouts. However, manual measurement requires a lengthy quality assurance process with possible errors. This work presents an accurate and efficient cutout output factor prediction model, convolution-based modified Clarkson integration (CMCI), to replace patient-specific output factor measurement. Like the Clarkson method, we decompose the field into basic sectors. Unlike the Clarkson integration method, we use annular sectors for output factor estimation. This decomposition method allows calculation via convolution. A 2D distribution of fluence is generated, and the output factor at any given point can be obtained. We applied our method to 10 irregularly shaped cutouts for breast patients for 6E, 9E, and 15E beams and compared the results with measurements and the electron Monte Carlo (eMC) calculation using the Eclipse planning system. While both the CMCI and eMC methods showed good agreement with chamber measurements and film measurements in relative distributions at the nominal source to surface distance (SSD) of 100 cm, eMC generated larger errors than the CMCI method at extended SSDs, with up to -9.28% deviations from the measurement for 6E beam. At extended SSD, the mean absolute errors of our method relative to measurements were 0.92 and 1.14, while the errors of eMC were 1.42 and 1.79 for SSD 105 cm and 110 cm, respectively. These results indicate that our method is more accurate than eMC, especially for low-energy beams, and can be used for MU calculation and as a QA tool for electron therapy.