Received 26 November 2015; accepted 1 February 2016; published 4 February 2016
The complex 3D shapes of new and sophisticated treatment methods, such as Intensity-Modulated Radiation Therapy (IMRT), Volumetric Modulated Arc Therapy (VMAT), Gamma-Knife and Tomo-Therapy treatments often demand that dissymmetry measurement techniques be reviewed. Understanding the limitations when using dosimeters is critical to administer safe implementation. For point-dose measurements of total delivered dose, small volume cylindrical ionization chambers are generally used, due to their excellent stability and linear re- sponse to absorbed dose. These cylindrical ionization chambers have high-spatial resolution and cylindrical symmetry in relevance to small fields. In measurements of treatments such as IMRT or VMAT treatment plans, that include non-coplanar beams, the angular dependence of the ion chamber is essential. Limited data is cur- rently available about oblique-incidence response of small cylindrical ionization chambers to megavoltage beams  and Gamma-Knife dosimetry   .
Several studies of ion chamber angular response dependence were recently published. A few publications re- ported correction factors for the angular dependence of several ion chambers in various energies using a radio- active source, such as 137Cs and 60Co.
In the papers of Takata et al.   and Kurosawa et al.  dose response measurements results versus angle were presented for both small and large ion chambers. In these papers, the presented measured angular depen- dence was above 3%, and was flattened toward ±0.5% using a wall correction function by linear extrapolation techniques. The correction is calculated by the elimination of the wall attenuation, the center of electron produc- tion factor and the scattering correction function. Apparently, for several ion chambers the angular dependence can be significant.
Araki et al. and Hrshak et al. showed the angular dependence when using different types of detectors (glass rod dosimeter, a diode detector and the PinPoint PTW31006 ionization chamber) to measure in the Gamma- Knife helmet output factors   . Hrshak’s study showed an angular dependence of over 10% for a 4 mm col- limated beam and up to 3% for bigger beams (18, 14 and 8 mm). The angular dependence in Hrshak’s study was limited to angles in the range of 54˚ - 84˚.
Two cylindrical chambers, commonly used for radiotherapy dosimetry, PinPoint (PTW) such as used in Hrshak’s study, and the CC01 (IBA), were examined in this study in oblique-incidence for low and high energy beams (6 MV and 15 MV). The angular dependence was first measured for the CC01 chamber for the relevant couch angular range (0˚ - 110˚). Monte Carlo calculations were carried out for each chamber, and were com- pared to the measured results for the CC01 and to Hrshak’s study for the PinPoint  .
2. Materials and Methods
2.1. Experimental Setup
A cylindrical water phantom perpendicular to the beam, dimensions: 15 cm diameter and 35 cm height, was de- signed and set up on the couch in the isocenter of a Varian, Clinac Trilogy, linear accelerator. The IBA Compact Chamber CC01 cylindrical ionization chamber was inserted into the center of the phantom in parallel to the beam plane. This phantom and chamber were positioned using room lasers and the accelerator crosser as can be seen in Figure 1. A comparison between technical data for these chambers can be seen in Table 1. For the IBA Compact Chamber CC01 we used a ruler in order to position the isocenter at the reference measuring point, 2.3 mm from the chamber end. Portal images from the On Board Imager (OBI) were used to ensure positioning of the phantom and the ion chamber―Figure 2. The ion chamber was connected to a PTW Electrometer UNIDOSE-E Universal Dosimeter 10009. A square 3 × 3 cm2 field size was set using the LINAC jaws. Measurements were performed for oblique incidence every 10 degrees between 0˚ to 110˚. Each measurement was obtained for 100 monitor units (MU), and was repeated three times. All measurements were taken both for the 6 MV and 15 MV photon beams.
2.2. Monte Carlo Simulations
The Monte Carlo simulations were written using the EGS5 code system  . The EGS5 Monte Carlo code system is a new generation of the EGS4 well validated code for photons and electrons transport. The EGS (Electron-Gamma Shower) code system is a general purpose package for the Monte Carlo simulation of the coupled transport of electrons and photons in an arbitrary geometry for particles with energies ranging from above a few keV up to several hundred GeV.
The EGS5 is a FORTRAN open source program. Since the 1990s, when the previous EGS4 code was released,
Figure 1. The setup of the CC01 ion chamber in the water phantom. Measurements were taken for every 10˚ between angles 0˚ to 110˚.
Figure 2. Kilo-voltage portal image of CC01 ion chamber positioned in the water phantom at the isocenter.
Table 1. Technical data for the two ion chambers used in this work the IBA Compact Chamber CC01 and the PTW PinPoint chamber.
it has been used in a wide variety of applications, particularly in medical physics, radiation measurement studies, and industrial development. The EGS5 code system contains, among many other subprograms, four user-called subroutines: BLOCK SET, PEGS5, HATCH, and SHOWER. These routines call other subroutines in the EGS5 code, some of which call two user-written subroutines, HOWFAR and AUSGAB, which respectively define geometry, and scoring output. The EGS5 transport code for electrons is fundamentally different and advanced from the previous EGS4 code. The electron step in EGS5 is treated by splitting each step into two segments, and a scattering hinge is applied in between the segments  .
The user communicates with EGS5 by means of the subroutines mentioned above, which enable him to access variables contained in various COMMON blocks. To use EGS5, the user must write a MAIN program and the subroutines HOWFAR and AUSGAB. The EGS5 consists of newly developed pseudo-random generator, accu- rate low-energy photon fluorescence transitions and a new algorithm for Bremsstrahlung radiation, which assure reliable results for radiation simulations studies. All used cross-sections for the interactions are described in the EGS5 user manual Appendix E  . The EGS5 includes several tools, such as the CG-VIEW used for geometry editing and as a viewer, and the PEGS5 editor for media cross sections definitions. In recent years the use of EGS5 for dosimetry calculations in the field of medical physics has been proven as successful as showed in sev- eral papers (e.g. in ref.  - ).
All kinetic energy cut-offs were set to be at 1 keV throughout this study. The detailed geometry of the same setup, as described above in the experiment, including the IBA Compact Chamber CC01 and the PTW PinPoint, were constructed in detail for the simulations using the CG-VIEW program. The CG-VIEW program is a com- plementary part of the EGS5 package setup. The media used in the CC01 simulations are: Shonka (C-552) used for outer electrode, steel used for the inner electrode, PEEK used for the chamber stem (based on the compact chamber User’s Manual  ) and air in the active volume. The PinPoint materials are: Steel used for the inner electrode, carbon coating for the inner wall of the outer electrode, Perspex as the wall material, Kapton was used for the inner isolation and air in the active volume. In both cases Perspex was used for the phantom walls, water, and air. Detector dimensions for both chambers are shown in Figure 3(a), Figure 3(b).
The spectra for the 6 MV and the 15 MV beams were taken from the Varian ECLIPSE treatment planning system (ECLIPSE™, Varian Medical Systems). The source definition is an important part of the main code. It has to be carefully mathematically described due to the source position and the rays’ direction.
In this work we chose to simplify the source description as a homogeneous, uni-directional photon beam, where the angle of the beam changes according to the “bed angle” (see Figure 1) from the experimental setup. Therefore, there is no necessity to use the BEAMnrc code  , since we took into consideration in the simul- ations, only the outgoing beam from the exit of the LINAC head.
The source position vector as depended on the “bed angle” was described as:
Figure 3. (a) The CC01 ion chamber geometry and dimensions for the Monte Carlo simulation; (b) The PinPiont ion chamber geometry and dimensions for the Monte Carlo simulation.
where 66.8 is the approximate distance from the jaw to the iso-center; 1.5 is due to the field opening of 3 × 3 cm2; β describes the “bed angle” and φ1 and φ2 are uniform random numbers that were changed for each history.
The source direction vector as depended on the “bed angle” β was described as:
The spectral data for the simulations introduced to the user code were taken from the ECLIPSE planning system and were fitted to produce cumulative density functions (CDF’s). The CDF for each beam energy was obtained using non-linear fit with a uniform random number ξ:
CDF 6 MV:
With a coefficient of determination of R2 = 0.9581.
In this spectrum, three discontinuity points were populated using discrete sampling along with the continuous CDF [E from Equation (3)―39%; E = 0.3 MeV―20%; E = 0.525 MeV―11%; E = 0.825 MeV―20%].
CDF 15 MV:
With a coefficient of determination of R2 = 0.9677.
All the simulations were run for 100 million histories (runtime = 62 hours), and the results were normalized to the results at angle 90˚.
The measured angular dependence for the CC01 ion chamber is presented as dependence on the beam energy in Figure 4 symbol with circles (in red) for 6 MV beam and for 15 MV beam. Each measurement was repeated three times, and the average is presented with an estimated error of not more than 0.5%. The IBA Compact Chamber CC01 demonstrated a significant angular dependence, up to 2.4%, the angular dependence was more pronounced for the 6 MV beam than for the 15 MV beam.
3.2. EGS5 Simulations
A comparison of the angular dependence between the experimental setup and the EGS5 simulations are presented for the CC01 chamber in both energies in Figure 4 between 0˚ to 110˚. The EGS5 demonstrated similar angular dependence along the range, up to 3.2% for the 6 MV and 3.0% for the 15 MV.
For the PinPoint chamber we performed EGS5 simulations for 6 MV and 15 MV energies, as presented in Figure 5. The PinPoint angular response from the simulations showed comparable results to those published by Hrsak et al for the 6 MV collimation of 2 × 2 cm2  . Hrsak et al. reported the angular dependence for the range of 54˚ - 84˚ only, and showed a similar trend to the Monte Carlo results in this study. The Monte Carlo results for the PinPoint showed a higher angular dependence compared to the CC01. For the PinPoint chamber in 6 MV beam, we found a difference of up to 11% and for the 15 MV beam, we found a difference between (−2)% at 110˚ to 12% at 0˚.
3.3. Simulation Statistical Uncertainties
In order to estimate the statistical uncertainties in the Monte Carlo simulations results, we set a separate simpli- fied configuration that consisted of the water phantom with a symmetric sphere positioned at the system’s iso- center. The sphere was set to be in a volume equal to the CC01 chamber volume, which is the smaller of the two detectors. The aim of this simplified simulation was to study the influence of the statistical fluctuations for each response along the angular range.
In the case of 6 MV with 100 million histories, the fluctuations indicated amplitude up to 2%, as evinced in
Figure 4. The CC01 ion chamber response vs. angular position, measured compared to the EGS5 simulations, at 6 MV and 15 MV. All results are normalized to the response at 90˚.
Figure 5. The PinPoint ion chamber calculated response vs. angular position using EGS5 simulations at 6 MV and 15 MV. All results are normalized to the response at 90˚.
Figure 6. In 15 MV the symmetrical simulation indicated no fluctuations in all directions for 100 million histories (same value for an 8 digits precision). To ensure the statistical significance when using Monte Carlo simulations, we found that it is efficient to perform simplified simulations in order to investigate simulation statistical uncertainties.
When using different ion chambers, in measurements that include non-coplanar beams, in radiotherapy, the angular dependence of the ion chamber is significant. We found relatively major differences between the two ion chambers in this study. The CC01 ion chamber showed a very small angular dependence compared to the PinPoint ion chamber. This can result from a combination of two reasons. The first is due to the differences in the ion chambers’ structures and materials. As showed in Figure 2, the PinPoint chamber consists of an outer wall made of PMMA with an inner coating of graphite used as the outer electrode, whereas in the CC01 the outer electrode is the Shonka (C-552) with no extra outer wall. Kurosawa et al. showed the influence of the wall thick- ness on the angular dependence  . This can explain the stronger angular dependence in the case of the PinPoint.
Figure 6. Fluctuations from the EGS5 simplified system simulations vs. beam angle for 6 MV with 100 million histories.
The second reason is the difference in the chambers’ length. The PinPoint’s active volume is a little longer than the CC01 active volume. Therefore, choosing the suitable ion-chamber when measuring non-coplanar beams is essential. The results in this study showed a clear difference in angular dependence between two ion chambers, although only a field of 3 × 3 cm2 was used. Extra study could be carried out on angular dependence of these chambers or others in smaller field sizes.