Cema‐based formalism for the determination of absorbed dose for high‐energy photon beams

Abstract

Purpose Determination of absorbed dose is well established in many dosimetry protocols and considered to be highly reliable using ionization chambers under reference conditions. If dosimetry is performed under other conditions or using other detectors, however, open questions still remain. Such questions frequently refer to appropriate correction factors. A converted energy per mass (cema)‐based approach to formulate such correction factors offers a good understanding of the specific response of a detector for dosimetry under various measuring conditions and thus an estimate of pros and cons of its application. Methods Determination of absorbed dose requires the knowledge of the beam quality correction factor kQ,Qo, where Q denotes the quality of a user beam and Qo is the quality of the radiation used for calibration. In modern Monte Carlo (MC)‐based methods, kQ,Qo is directly derived from the MC‐calculated dose conversion factor, which is the ratio between the absorbed dose at a point of interest in water and the mean absorbed dose in the sensitive volume of an ion chamber. In this work, absorbed dose is approximated by the fundamental quantity cema. This approximation allows the dose conversion factor to be substituted by the cema conversion factor. Subsequently, this factor is decomposed into a product of cema ratios. They are identified as the stopping power ratio water to the material in the sensitive detector volume, and as the correction factor for the fluence perturbation of the secondary charged particles in the detector cavity caused by the presence of the detector. This correction factor is further decomposed with respect to the perturbation caused by the detector cavity and that caused by external detector properties. The cema‐based formalism was subsequently tested by MC calculations of the spectral fluence of the secondary charged particles (electrons and positrons) under various conditions. Results MC calculations demonstrate that considerable fluence perturbation may occur particularly under non‐reference conditions. Cema‐based correction factors to be applied in a 6‐MV beam were obtained for a number of ionization chambers and for three solid‐state detectors. Feasibility was shown at field sizes of 4 × 4 and 0.5 cm × 0.5 cm. Values of the cema ratios resulting from the decomposition of the dose conversion factor can be well correlated with detector response. Under the small field conditions, the internal fluence correction factor of ionization chambers is considerably dependent on volume averaging and thus on the shape and size of the cavity volume. Conclusions The cema approach is particularly useful at non‐reference conditions including when solid‐state detectors are used. Perturbation correction factors can be expressed and evaluated by cema ratios in a comprehensive manner. The cema approach can serve to understand the specific response of a detector for dosimetry to be dependent on (a) radiation quality, (b) detector properties, and (c) electron fluence changes caused by the detecto...

Spectral analysis of Monte Carlo calculated fluence correction and cema conversion factors for high-energy photon beams at different depths

“…1 has to be replaced by the reduced collision stopping power Λ Δ as described by Kellerer et al [9]. Nevertheless, the restricted stopping power as an approach for the reduced collision stopping power offers a good approximation for the applied photon energies and materials used in this study [9,10]. The restricted medium cema is especially interesting because the requirement that δ-CPE exists can be neglected (Eq.…”

“…al. [10], the cema conversion factor f cema is defined in analogy to the dose conversion factor f dose as the ratio between the restricted water cema at the point of interest C Δ,w and the volume-averaged mean restricted medium cema C det Δ,med in the cavity (-medium) of the detector: denotes for the medium of the stopping power, i.e. the detector medium.…”

“…Analogously to the dose conversion factor D w /D med , a cema conversion factor C w /C med , introduced by Hartmann et al [10] can be used to calculate the non-reference correction factor k NR :…”

“…The cema refers to the fluence distribution of primary charged particles as well as to secondaries of high energies and is thus especially useful for high-energy photon beams [9]. This approximation provides the possibility to substitute the dose conversion factor with a cema conversion factor as introduced by Hartmann et al [10] in a comprehensive manner which also complies with the fundamental Spencer-Attix cavity formalism. Because the cema can be expressed in terms of the charged particle fluence distribution Φ E , this approach offers the benefit to decompose the cema conversion factor into a product of energy-dependent (i.e., spectral) fluence-based correction factors p E,i and to analyze the differential fluence spectra with regard to the detector-induced fluence disturbance.…”

“…With their help, it was also investigated if the positioning of the effective point of measurement as recommended in several dosimetry protocols can adequately compensate for the displacement of water at the build-up region. The purpose of this paper is not primarily the determination of exact correction factors for clinical use, it is more motivated by previous studies that dealt with the general understanding of the detector response under non-equilibrium conditions [10,12,18].…”