Purpose: The three‐dimensional (3D) dose distribution covering a tumor region tends to be more breakable if the beam's eye view (BEV) of the 3D electron density (ED) map in a beam direction changes more abruptly with large fluctuations. Our aim of this study was to develop an automated determination method of robust beam directions against the patient setup error based on the ED‐based BEV in the beam direction in the particle therapy. Methods: The basic idea of our proposed method was to find the robust beam directions, whose the ED‐based BEV has the spatial fluctuations with low special frequency and small amplitude. For evaluation of the spatial fluctuation in the ED‐based BEV in a beam direction, we obtained power spectra of the ED‐based BEVs in all directions, i.e., 0 to 355 degree, with an interval of 5 degree. It was assumed that as the average spatial frequency and amplitude of the fluctuation in the ED‐based BEV in a beam direction is lower and smaller, respectively, the absolute value of a gradient of the power spectrum becomes larger. Therefore the gradient of the power spectrum was calculated for determination of the robust beam direction. The ED‐based BEV was produced by projecting a 3D electron density map derived from the computed tomography (CT) image from a beam source to the distal end of a planning target volume (PTV). Four cases of head and neck cancer patients were selected for evaluation of the proposed method. Results: As a preliminary result, radiation oncologists agreed with most beam directions, which seem to be robust against patient setup errors, suggested by the proposed method. Conclusions: Our proposed method could be feasible to suggest the robust beam directions against patient setup errors in hadron particle therapy.
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