A new sigmoidal function describing the small field dose profile data from a linear accelerator

Parameterization of photon beam dosimetry for a linear accelerator

PURPOSE

In radiation therapy, accurate data acquisition of photon beam dosimetric quantities is important for (1) beam modeling data input into a treatment planning system (TPS), (2) comparing measured and TPS modeled data, (3) the quality assurance process of a linear accelerator's (Linac) beam characteristics, (4) the establishment of a standard data set for comparison with other data, etcetera. Parameterization of the photon beam dosimetry creates a data set that is portable and easy to implement for different applications such as those previously mentioned. The aim of this study is to develop methods to parameterize photon beam dosimetric quantities, including percentage depth doses (PDDs), profiles, and total scatter output factors (S(cp)).

METHODS

S(cp), PDDs, and profiles for different field sizes, depths, and energies were measured for a Linac using a cylindrical 3D water scanning system. All data were smoothed for the analysis and profile data were also centered, symmetrized, and geometrically scaled. The S(cp) data were analyzed using an exponential function. The inverse square factor was removed from the PDD data before modeling and the data were subsequently analyzed using exponential functions. For profile modeling, one halfside of the profile was divided into three regions described by exponential, sigmoid, and Gaussian equations. All of the analytical functions are field size, energy, depth, and, in the case of profiles, scan direction specific. The model's parameters were determined using the minimal amount of measured data necessary. The model's accuracy was evaluated via the calculation of absolute differences between the measured (processed) and calculated data in low gradient regions and distance-to-agreement analysis in high gradient regions. Finally, the results of dosimetric quantities obtained by the fitted models for a different machine were also assessed.

RESULTS

All of the differences in the PDDs' buildup and the profiles' penumbra regions were less than 2 and 0.5 mm, respectively. The differences in the low gradient regions were 0.20% ± 0.20% (<1% for all) and 0.50% ± 0.35% (<1% for all) for PDDs and profiles, respectively. For S(cp) data, all of the absolute differences were less than 0.5%.

CONCLUSIONS

This novel analytical model with minimum measurement requirements was proved to accurately calculate PDDs, profiles, and S(cp) for different field sizes, depths, and energies.

Assessment of the setup dependence of detector response functions for mega-voltage linear accelerators

PURPOSE

Accurate modeling of beam profiles is important for precise treatment planning dosimetry. Calculated beam profiles need to precisely replicate profiles measured during machine commissioning. Finite detector size introduces perturbations into the measured profiles, which, in turn, impact the resulting modeled profiles. The authors investigate a method for extracting the unperturbed beam profiles from those measured during linear accelerator commissioning.

METHODS

In-plane and cross-plane data were collected for an Elekta Synergy linac at 6 MV using ionization chambers of volume 0.01, 0.04, 0.13, and 0.65 cm3 and a diode of surface area 0.64 mm2. The detectors were orientated with the stem perpendicular to the beam and pointing away from the gantry. Profiles were measured for a 10 x 10 cm2 field at depths ranging from 0.8 to 25.0 cm and SSDs from 90 to 110 cm. Shaping parameters of a Gaussian response function were obtained relative to the Edge detector. The Gaussian function was deconvolved from the measured ionization chamber data. The Edge detector profile was taken as an approximation to the true profile, to which deconvolved data were compared. Data were also collected with CC13 and Edge detectors for additional fields and energies on an Elekta Synergy, Varian Trilogy, and Siemens Oncor linear accelerator and response functions obtained. Response functions were compared as a function of depth, SSD, and detector scan direction. Variations in the shaping parameter were introduced and the effect on the resulting deconvolution profiles assessed.

RESULTS

Up to 10% setup dependence in the Gaussian shaping parameter occurred, for each detector for a particular plane. This translated to less than a +/- 0.7 mm variation in the 80%-20% penumbral width. For large volume ionization chambers such as the FC65 Farmer type, where the cavity length to diameter ratio is far from 1, the scan direction produced up to a 40% difference in the shaping parameter between in-plane and cross-plane measurements. This is primarily due to the directional difference in penumbral width measured by the FC65 chamber, which can more than double in profiles obtained with the detector stem parallel compared to perpendicular to the scan direction. For the more symmetric CC13 chamber the variation was only 3% between in-plane and cross-plane measurements.

CONCLUSIONS

The authors have shown that the detector response varies with detector type, depth, SSD, and detector scan direction. In-plane vs. cross-plane scanning can require calculation of a direction dependent response function. The effect of a 10% overall variation in the response function, for an ionization chamber, translates to a small deviation in the penumbra from that of the Edge detector measured profile when deconvolved. Due to the uncertainties introduced by deconvolution the Edge detector would be preferable in obtaining an approximation of the true profile, particularly for field sizes where the energy dependence of the diode can be neglected. However, an averaged response function could be utilized to provide a good approximation of the true profile for large ionization chambers and for larger fields for which diode detectors are not recommended.

Clinical impact of the detector size effect in 3D-CRT

OBJECTIVE

The detector size artificially increases the measured penumbra of radiotherapy fields. The aim of this work is to determine the influence of the detector size when planning three-dimensional conformal radiation therapy (3D-CRT) treatments.

MATERIAL AND METHODS

Two anatomical sites of interest in 3D-CRT were studied: prostate and hypophysis chordoma. Conventional 3D-CRT treatments for two cases in these locations were planned with a FOCUS 4.0.0 (Computerized Medical Systems, USA) treatment planning system (TPS) equipped with Fast Fourier Transform Convolution (FFTC) and Multigrid Superposition (MGS) algorithms, making use of beams modelled from radiation profiles measured either with a 2.0 mm diameter detector (PFD(3G) diode) or with a 5.5 mm diameter detector (PTW-31002 ionisation chamber). These detectors cover up the range of detector sizes commonly used to measure radiation profiles for 3D-CRT. Dose-volume histograms (DVHs), radiobiological indexes, tumor control probability (TCP) and normal tissue complication probability (NTCP) were analysed and compared for planning target volumes (PTVs) and organs at risk (OAR) studied.

RESULTS

Important differences in DVH were found. OAR received higher dose levels when a 5.5 mm detector was used to measure profiles compared to the case in which a 2.0 mm detector was used. A 2 Gy increment in the mean rectal dose was found when the larger detector was used. In the same way, NTCP of brain stem in hypophysis chordoma treatments was doubled when this detector was used.

CONCLUSION

The current use of ionisation chambers of about 5 mm active diameter to get the necessary data to model treatment machines in radiotherapy treatment planning systems (TPS) implies a significant overirradiation of OAR close to the PTV in 3D-CRT treatments due to errors in the measured penumbra of beam profiles. To avoid this overirradiation, the measured profiles should either being acquired with a suitable detector size (2-3 mm active diameter) or being deconvoluted.