Gaussian fitting algorithm with multi‐geometric parameters for rotated elliptical beam profiling using pixel ion chamber

Abstract

A high-precision rotated elliptical beam profiling method based on pixel ion chamber is proposed in this paper. This method aims to improve the accuracy by modeling the transverse profile of rotated beam as an ellipse with additional correlation coefficient and eliminating the fitting error due to the volume averaging effect of pixel ion chamber. In pencil beam scanning (PBS) proton therapy systems, the transverse beam profile model is generally represented as a standard Gaussian distribution. Considering the elliptical spots, two-dimensional (2D) joint Gaussian distribution characterized with the correlation coefficient ρ is adopted in this study. Gaussian-type particle distribution with white noise was generated and processed in MATLAB to simulate the secondary particle collection in the pixel ion chamber. The simulated pixel ion chamber is a commercially available ion chamber which consists of 12×12small square pixels (3.75×3.75mm2 ) with a 0.05mm interval. The simulated signals were preprocessed by filtering with the noise threshold and extracting the maximum simply connected domain (MSCD) of the signal. Then, five geometric parameters that identify the transverse beam profiles were fitted under different signal-to-noise ratio (SNR) conditions: the center of the beam (x0 , y0 ), the spot size (σmajor , σminor ), and the rotation angle θ formed between the major axes of elliptical spot and the x axes of the ion chamber. First, the simulated signals were preprocessed by filtering with the noise threshold and extracting the MSCD of the signal. Second, a rectification curve of systematic error in fitted spot size versus the prescribed spot size was used to predict the systematic error due to the volume averaging effect. Finally, the effects of fitting errors on therapeutic dose were evaluated in terms of gamma index and relative dose difference. When the SNR is not less than 20dB, the relative fitting error of spot size and the absolute fitting error of angle θ are less than 1% and 6.1°, respectively. The fitting error of beam center increases with spot size and will not exceed 0.22mm when spot size reaches up to 12mm. At a SNR equal to 20dB, neither cold nor hot spots were presented in dose distribution calculated with the fitted spot parameters. The improved Gaussian fitting algorithm performs well when SNR is not less than 20dB. This method can effectively distinguish the nominal beam and rotated elliptical beam. An ideal systematic error curve can be predicted and used to correct the fitted spot size, thus eliminating the systematic error due to the volume averaging effect of the pixel ion chamber. The fitting error of spot size cannot be fully corrected, but it is negligible and shows little effect on the overall therapeutic dose.