A multi-institutional study of independent calculation verification in inhomogeneous media using a simple and effective method of heterogeneity correction integrated with the Clarkson method

In inhomogeneous media, there is often a large systematic difference in the dose between the conventional Clarkson algorithm (C-Clarkson) for independent calculation verification and the superposition-based algorithms of treatment planning systems (TPSs). These treatment site–dependent differences increase the complexity of the radiotherapy planning secondary check. We developed a simple and effective method of heterogeneity correction integrated with the Clarkson algorithm (L-Clarkson) to account for the effects of heterogeneity in the lateral dimension, and performed a multi-institutional study to evaluate the effectiveness of the method. In the method, a 2D image reconstructed from computed tomography (CT) images is divided according to lines extending from the reference point to the edge of the multileaf collimator (MLC) or jaw collimator for each pie sector, and the radiological path length (RPL) of each line is calculated on the 2D image to obtain a tissue maximum ratio and phantom scatter factor, allowing the dose to be calculated. A total of 261 plans (1237 beams) for conventional breast and lung treatments and lung stereotactic body radiotherapy were collected from four institutions. Disagreements in dose between the on-site TPSs and a verification program using the C-Clarkson and L-Clarkson algorithms were compared. Systematic differences with the L-Clarkson method were within 1% for all sites, while the C-Clarkson method resulted in systematic differences of 1–5%. The L-Clarkson method showed smaller variations. This heterogeneity correction integrated with the Clarkson algorithm would provide a simple evaluation within the range of −5% to +5% for a radiotherapy plan secondary check.