A multivariate approach to determine electron beam parameters for a Monte Carlo 6 MV Linac model: Statistical and machine learning methods

Abstract

Purpose: This study aimed to determine the optimal initial electron beam parameters of a Linac for radiotherapy with a multivariate approach using statistical and machine-learning tools.

Methods: For MC beam commissioning, a 6 MV Varian Clinac was simulated using the Geant4 toolkit. The authors investigated the relations between simulated dose distribution and initial electron beam parameters, namely, mean energy (E), energy spread (ES), and radial beam size (RS). The goodness of simulation was evaluated by the slope of differences between the simulated and the golden beam data. The best-fit combination of the electron beam parameters that minimized the slope of dose difference was searched through multivariate methods using conventional statistical methods and machine-learning tools of the scikit-learn library.

Results: Simulation results with 87 combinations of the electron beam parameters were analyzed. Regardless of being univariate or multivariate, traditional statistical models did not recommend a single parameter set simultaneously minimizing slope of dose differences for percent depth dose (PDD) and lateral dose profile (LDP). Two machine learning classification modules, RandomForestClassifier and BaggingClassifier, agreed in recommending (E = 6.3 MeV, ES = ±5.0%, RS = 1.0 mm) for predicting simultaneous acceptance of PDD and LDP.

Conclusions: The machine learning with random-forest and bagging classifier modules recommended a consistent result. It was possible to draw an optimal electron beam parameter set using multivariate methods for MC simulation of a radiotherapy 6 MV Linac.

Keywords: Electron beam parameters; Linac; Machine learning; Monte Carlo simulation; Multivariate analysis; Statistical method.