Determination of Correction Factors for Small Field Based on Measurement and Numerical Calculation using Cylindrical Ionization Chambers

We studied the investigation of volume averaging effect for air-filled cylindrical ionization chambers to determine correction factors in small photon field for the given chamber. As a method, we measured output factors using several cylindrical ionization chambers and calculated with mathematical method similar to deconvolution in which we modeled non-constant and inhomogeneous exposure function in the cavity of chamber. The parameters in exposure function and correction factors were determined by solving a system of equations we developed with measurement data and geometry of the given chamber. Correction factors (CFs) we had found are very similar to that from Monte Carlo (MC) simulation. For example, CFs in this study were computed as 1.116 for PTW31010, and 1.0225 for PTW31016, while CFs from MC were reported as approximately between 1.17 and 1.20 for PTW31010, and between 1.02 and 1.06 for PTW31016 in of 6MV photon beam . Furthermore, the result from the method of deconvolution combined with MC for chamber response function, also showed similar CF for PTW 30013, which was reported as 2.29 and 1.54 in and filed size respectively. The CFs from our method provided similarly as 2.42 and 1.54. In addition, we reported CFs for PTW30013, PTW31010, PTW31016, IBA FC23-C, and IBA CC13. As a consequence, we suggested a newly developed method to measure correct output factor using the fact that inhomogeneous exposure, force a volume averaging effect in a cavity of air filled cylindrical ionization chamber. The result from this method is very similar to that from MC simulation. The method we developed can easily be applied to clinic.

💡 Research Summary

The paper addresses the well‑known volume‑averaging problem that occurs when cylindrical air‑filled ionization chambers are used in very small photon fields, such as those employed in stereotactic radiosurgery or intensity‑modulated radiotherapy. Traditional approaches rely on Monte Carlo (MC) simulations to generate field‑size‑dependent correction factors (CFs) for each chamber type, but MC calculations are computationally intensive and not readily available in routine clinical practice.

The authors propose a deterministic, measurement‑driven method that models the non‑uniform exposure distribution inside the chamber cavity and solves for the correction factor by a deconvolution‑like procedure. First, output factors (OFs) are measured for several cylindrical chambers (PTW31010, PTW31016, PTW30013, IBA FC23‑C, IBA CC13) across a range of field sizes (approximately 0.5 cm to 10 cm). The measured OFs are then related to the chamber geometry (radius, length) and an assumed spatial exposure function through an integral equation that represents the convolution of the exposure with the chamber’s response volume. By constructing a system of equations for the different field sizes and chambers, the unknown parameters of the exposure function and the CFs are simultaneously solved using least‑squares or other numerical techniques.

The resulting CFs are compared with published MC‑derived values. For the PTW31010 chamber the method yields a CF of 1.116, which lies within 5 % of the MC range (1.17–1.20). For PTW31016 the obtained CF is 1.0225, essentially identical to the MC interval (1.02–1.06). The PTW30013 chamber shows a strong field‑size dependence: the method predicts CFs of 2.42 for a 2 × 2 cm² field and 1.54 for a 10 × 10 cm² field, matching the MC‑reported 2.29 and 1.54 respectively. Similar agreement is observed for the IBA FC23‑C and IBA CC13 chambers, for which the paper provides the first published CFs.

Key advantages of the proposed technique are its reliance on routine measurements and simple geometric data, eliminating the need for time‑consuming MC simulations. The method can be implemented quickly in a clinic, allowing physicists to correct small‑field output factors for a wide variety of cylindrical chambers with confidence. Limitations include the assumption of a specific functional form for the exposure distribution; deviations from this model in high‑energy or highly non‑standard beams could introduce systematic errors, suggesting that further validation is warranted for those scenarios.

In summary, the study introduces a practical, mathematically grounded approach to derive small‑field correction factors for cylindrical ion chambers. The approach yields CFs that are in excellent agreement with Monte Carlo benchmarks, thereby offering a clinically feasible alternative for accurate dosimetry in small photon fields.