The effective depth of cylindrical ionization chambers in water for clinical proton beams

Gradient corrections for reference dosimetry using Farmer-type ionization chambers in single-layer scanned proton fields

PURPOSE

The local depth dose gradient and the displacement correction factor for Farmer-type ionization chambers are quantified for reference dosimetry at shallow depth in single-layer scanned proton fields.

METHOD

Integrated radial profiles as a function of depth (IRPDs) measured at three proton therapy centers were smoothed by polynomial fits. The local relative depth dose gradient at measurement depths from 1 to 5 cm were derived from the derivatives of those fits. To calculate displacement correction factors, the best estimate of the effective point of measurement was derived from reviewing experimental and theoretical determinations reported in the literature. Displacement correction factors for the use of Farmer-type ionization chambers with their reference point (at the center of the cavity volume) positioned at the measurement depth were derived as a ratio of IRPD values at the measurement depth and at the effective point of measurement.

RESULTS

Depth dose gradients are as low as 0.1-0.4% per mm at measurement depths from 1 to 5 cm in the highest clinical proton energies (with residual ranges higher than 15 cm) and increase to 1% per mm at a residual range of 4 cm and become larger than 3% per mm for residual ranges lower than 2 cm. The literature review shows that the effective point of measurement of Farmer-type ionization chambers is, similarly as for carbon ion beams, located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. If a maximum displacement correction of 2% is deemed acceptable to be included in calculated beam quality correction factors, Farmer-type ICs can be used at measurements depths from 1 to 5 cm for which the residual range is 4 cm or larger. If one wants to use the same beam quality correction factors as applicable to the conventional measurement point for scattered beams, located at the center of the SOBP, the relative standard uncertainty on the assumption that the displacement correction factor is unity can be kept below 0.5% for measurement depths of at least 2 cm and for residual ranges of 15 cm or higher.

CONCLUSION

The literature review confirmed that for proton beams the effective point of measurement of Farmer-type ionization chambers is located 0.75 times the cavity radius closer to the beam origin as the center of the cavity. Based on the findings in this work, three options can be recommended for reference dosimetry of scanned proton beams using Farmer-type ionization chambers: (a) positioning the effective point of measurement at the measurement depth, (b) positioning the reference point at the measurement depth and applying a displacement correction factor, and (c) positioning the reference point at the measurement depth without applying a displacement correction factor. Based on limiting the acceptable uncertainty on the gradient correction factor to 0.5% and the maximum deviation of the displacement perturbation correction factor from unity to 2%, the first two options can be allowed for residual ranges of at least 4 cm while the third option only for residual ranges of at least 15 cm.

Dosimetric verification of IMPT using a commercial heterogeneous phantom

The purpose of this study was to propose a verification method and results of intensity‐modulated proton therapy (IMPT), using a commercially available heterogeneous phantom. We used a simple simulated head and neck and prostate phantom. An ionization chamber and radiochromic film were used for measurements of absolute dose and relative dose distribution. The measured doses were compared with calculated doses using a treatment planning system. We defined the uncertainty of the measurement point of the ionization chamber due to the effective point of the chamber and mechanical setup error as 2 mm and estimated the dose variation base on a 2 mm error. We prepared a HU‐relative stopping power conversion table and fluence correction factor that were specific to the heterogeneous phantom. The fluence correction factor was determined as a function of depth and was obtained from the ratio of the doses in water and in the phantom at the same effective depths. In the simulated prostate plan, composite doses of measurements and calculations agreed within ±1.3% and the maximum local dose differences of each field were 10.0%. Composite doses in the simulated head and neck plan agreed within 4.0% and the maximum local dose difference for each field was 12.0%. The dose difference for each field came within 2% when taking the measurement uncertainty into consideration. In the composite plan, the maximum dose uncertainty was estimated as 4.0% in the simulated prostate plan and 5.8% in the simulated head and neck plan. Film measurements showed good agreement, with more than 92.5% of points passing a gamma value (3%/3 mm). From these results, the heterogeneous phantom should be useful for verification of IMPT by using a phantom‐specific HU‐relative stopping power conversion, fluence correction factor, and dose error estimation due to the effective point of the chamber.