A mathematical expression for depth-light curves of therapeutic proton beams in a quenching scintillator.

ABSTRACT

PURPOSE: Recently, there has been increasing interest in the development of scintillator-based detectors for the measurement of depth-dose curves of therapeutic proton beams (Beaulieu and Beddar [2016], Phys Med Biol., 61R305-R343). These detectors allow the measurement of single beam parameters such as the proton range or the reconstruction of the full three-dimensional dose distribution. Thus, scintillation detectors could play an important role in beam quality assurance, online beam monitoring, and proton imaging. However, the light output of the scintillator as a function of dose deposition is subject to quenching effects due to the high-specific energy loss of incident protons, particularly in the Bragg peak. The aim of this work is to develop a model that describes the percent depth-light curve in a quenching scintillator and allow the extraction of information about the beam range and the strength of the quenching. METHODS: A mathematical expression of a depth-light curve, derived from a combination of Birks' law (Birks [1951], Proc Phys Soc A., 64874) and Bortfeld's Bragg curve (Bortfeld [1997], Med Phys., 242024-2033) that is termed a "quenched Bragg" curve, is presented. The model is validated against simulation and measurement. RESULTS: A fit of the quenched Bragg model to simulated depth-light curves in a polystyrene-based scintillator shows good agreement between the two, with a maximum deviation of 2.5% at the Bragg peak. The differences are larger behind the Bragg peak and in the dose build-up region. In the same simulation, the difference between the reconstructed range and the reference proton range is found to be always smaller than 0.16 mm. The comparison with measured data shows that the fitted beam range agrees with the reference range within their respective uncertainties. CONCLUSIONS: The quenched Bragg model is, therefore, an accurate tool for the range measurement from quenched depth-dose curves. Moreover, it allows the reconstruction of the beam energy spread, the particle fluence, and the magnitude of the quenching effect from a measured depth-light curve.