Investigating the lateral dose response functions of point detectors in proton beams

Abstract

Objective Point detector measurements in proton fields are perturbed by the volume effect originating from geometrical volume-averaging within the extended detector’s sensitive volume and density perturbations by non-water equivalent detector components. Detector specific lateral dose response functions K(x) can be used to characterize the volume effect within the framework of a mathematical convolution model, where K(x) is the convolution kernel transforming the true dose profile D(x) into the measured signal profile of a detector M(x). The aim of this work is to investigate K(x) for detectors in proton beams. Approach The K(x) for five detectors were determined by iterative deconvolution of measurements of D(x) and M(x) profiles at 2 cm water equivalent depth of a narrow 150 MeV proton beam. Monte Carlo simulations were carried out for two selected detectors to investigate a potential energy dependence, and to study the contribution of volume-averaging and density perturbation to the volume effect. Main results The Monte Carlo simulated and experimentally determined K(x) agree within 2.1% of the maximum value. Further simulations demonstrate that the main contribution to the volume effect is volume-averaging. The results indicate that an energy or depth dependence of K(x) is almost negligible in proton beams. While the signal reduction from a Semiflex 3D ionization chamber in the center of a gaussian shaped field with 2 mm sigma is 32% for photons, it is 15% for protons. When measuring the field with a microDiamond the trend is less pronounced and reversed with a signal reduction for protons of 3.9% and photons of 1.9%. Significance The determined K(x) can be applied to characterize the influence of the volume effect on detectors measured signal profiles at all clinical proton energies and measurement depths. The functions can be used to derive the actual dose distribution from point detector measurements.

Comprehensive investigation of lateral dose profile and output factor measurements in small proton fields from different delivery techniques

“…The one-dimensional K(x) for three ionization chambers: a Semiflex 3D 31021 and a PinPoint 3D 31022 (PTW Freiburg, Germany), and a CC01G Razor chamber (IBA Dosimetry, Schwarzenbruck, Germany), a microSilicon diode 60023 and a microDiamond detector 60019 (PTW Freiburg, Germany) have been previously reported in Kretschmer et al 14 for the axial orientation, that is, the detector's axis is parallel to the beam's axis. Additionally, Monte Carlo simulations in GATE9.0/Geant4.10.06.p03 38,39 were performed in this work according to the methods reported in Kretschmer et al 14 to determine K(x) for an Advanced Markus 34045 ionization chamber (PTW Freiburg, Germany) not included in the previous work. These functions derived using a narrow slit beam geometry are also referred to as the line spread function.…”

“…Figure 1 shows the rotational symmetrical K(r) for the six point detectors derived from the corresponding K(x) determined experimentally in Kretschmer et al 14 or simulated in this work (Advanced Markus chamber). The width of K(r) increases with increasing diameter of the sensitive volume such that the Advanced Markus chamber has the broadest function, while the K(r) of the smallest microSilicon diode is the narrowest among the investigated detectors.…”

“…[7][8][9] Such measurements are usually acquired using point detectors with extended sensitive volume that may be subject to perturbations 1,2,[10][11][12] related to the so-called volume effect. 13,14 Although several studies found that the detector's volume effect does not noteworthy perturb measurements of proton fields with Gaussian shaped profiles or large fields with broad lateral penumbra as, for example, occurring in pencil beam scanning (PBS) fields, 13,[15][16][17] volume effect perturbations have been identified in some studies and especially for proton beam delivery techniques leading to reduced penumbras. 1,2,10,12 While small proton fields are used in ocular treatments, treatments of pediatric patients, minibeam irradiations or stereotactic treatments, 4,10,[18][19][20] the smallest possible lateral penumbra is generally desired as this allows for better sparing of adjacent organs at risk.…”

“…The function K(x,y) encompasses the detector perturbation due to geometrical volume averaging and disturbances of the local particle fluence by non-water equivalent detector components,where the latter is often called the density perturbation in the literature. 14,30,32,33 In the following, the combined effect is referred to as the volume effect.…”

“…Recently, Kretschmer et al 14 investigated the volume effect of point detectors in proton fields and presented one-dimensional K(x) measured in a 150 MeV proton slit beam for various detectors, including ionization chambers and diode-type detectors. The results indicated that K(x) in proton fields can be generally considered as energy and depth independent.…”