Energy-Related Scatter Analysis for Determining the Effective Point of Measurement of Cylindrical Ion Chamber in Heavy Charged Particle Carbon Ion Beam

Abstract

Purpose. An experimental and mathematical study for determining the effective point of measurement ( $P_{\text{eff}}$ ) for a Farmer-type cylindrical chamber in a carbon ion passive scatter beam is presented. Methods. The ionization depth curves measured by the Bragg peak chamber were plotted according to the position of the inner surface of the entrance window, while the Farmer chamber was plotted at the tip of the cylindrical geometric center. The ionization depth curves measured by a cylindrical chamber in the 3D water phantom were then compared with a high-precision parallel-plate PTW Bragg peak chamber for inspecting the upstream shift correction of the cylindrical chamber in the carbon ion beam. A component of the vertical and horizontal integration method and the barrier model, $\cos \phi =1-\left[2\alpha R_L/\left(1+\alpha -R_L\right)\right]$ , for analyzing the shift of effective point of measurement in different carbon ion energies and various field sizes, were studied. Results. The shift between the maximum peak of the Bragg peak chamber and the Farmer chamber in a field size of $10\text{cm}\times 10\text{cm}$ with an energy of 330 MeV/u of carbon ion is 2.3 mm. This upstream shift corresponds to $\left(0.744\pm 0.07\right)r$ , where $r$ is the Farmer chamber inner radius of 3.05 mm. Carbon ion energy from 120 MeV/u to 400 MeV/u with different field sizes show different shifts of effective point of measurement in a range of $\left(0.649\pm 0.02\right)r$ to $\left(0.843\pm 0.06\right)r$ of $3\text{cm}\times 3\text{cm}$ at an energy of 400 MeV/u and $10\text{cm}\times 10\text{cm}$ at an energy of 120 MeV/u, respectively. The vertical and horizontal scatter analysis by the barrier model can precisely describe the shift of the effective point of measurement at different carbon ion energies with various field sizes. Conclusions. We conclude that the Farmer chamber can be used for a patient-specific dose verification check in carbon ion beam treatment if $P_{\text{eff}}$ is well calibrated.