Peripheral dose around a mobile linac for intraoperative radiotherapy: radiation protection aspects

Measurements of the PDDs and dose profiles for the largest 10 cm diameter applicator and outputs were performed with the computerised beam model of MP3 (PTW, Freiburg, Germany) by using EFD^3G diodes (Scanditronix Wellhöfer AB, Uppsala, Sweden) of 2.5 mm active diameter. These diodes were designed for absorbed dose measurements of electron beams of energy between 1 and 50 MeV.

In the following, all distances are referred to a coordinate system shown in figure 2 and based on the Mobetron 1000 itself as proposed by Krechetov et al [21]. The origin of such coordinate system is taken at the point of intersection of the beam axis on the floor.

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Area dosimetry was carried out with the radiation monitor model 451P-DE-SI [22] (Fluke Biomedical, Cleveland, USA). This radiation monitor consists on an ionization chamber detection system of 230 cm³ of pressurised air at 6 atm. The active volume of the detector can be approximated to a cylinder 2.8 cm in radius and 9.35 cm in height. It detects β-radiation with energies greater than 1 MeV and γ-radiation above 25 keV. This detector is calibrated in terms of H*(10). At each point H*(10) is expressed as a fraction of the absorbed dose at d_max (μSv Gy⁻¹). It was measured for the 10 cm applicator using irradiations between 200 and 500 MU.

The area dosimetry was measured around the Mobetron 1000, both inside and outside the OR.

Measurements inside the OR were performed at the three different heights representative of patient-plane, second scatter plane and the union of the two acceleration sections, respectively. Five locations were chosen around the Mobetron 1000, named A, B, C, D and E and shown in figure 2. The coordinates of these points (x, y) are specified in table 1. The measurements were performed using a RW3 (PTW, Freiburg, Germany) [23] phantom made of fifteen 30 cm × 30 cm sheets of 10 mm thickness each to mimic typical clinical conditions.

Outside the OR and behind the structural barriers, area dosimetry was taken at six locations described in table 2. In this table, the location coordinates and the barrier thickness/material are given. We have labelled the locations in each barrier according to the names of the rooms they are adjacent with (see figure 1). The measurements were performed with two phantoms, the aforementioned RW3 and the one provided with the Mobetron 1000 unit for QA purposes (QAP). This phantom incorporates at the end of the 10 cm diameter aluminium applicator a cylinder of plastic 13.5 cm in diameter and 8.5 cm high. The reason to select different points in this study for MC and measurements is that in our facility during treatment the unit is located close to one of the walls (see figure 1(b)) while the MC studies in the literature usually assume that the unit is located at the centre of the OR.

H*(10) and H*(10) rate for neutrons was measured using a BERTHOLD model LB6411 (Berthold Technologies, BadWilbad, Germany). This detector has been calibrated using an Am-Be source for neutrons of energies up to 20 MeV and consists of a ³He filled proportional counter located in the centre of a moderator system made of a sphere of polyethylene of 25 cm of external diameter. The active volume of the detector is 45 cm³.

In order to compare with similar measurements performed by Loi et al [24], H*(10) was obtained at various heights, from 13 to 130 cm, and distances, from 30 to 73 cm, in two different positions, in the frontal and lateral sides of the Mobetron 1000.

PDDs in water were calculated and compared with the measured ones. New simulations were performed modifying the incident electron beam energy spectrum, both its mean energy and Gaussian width, independently for each MC code until the agreement of measured and calculated PDD was good enough.

After fully constraining the details of the MC simulation of the Mobetron 1000 head, the only remaining details to be determined were the characteristics of the most relevant shielding structures present in the accelerator head and inside the cabinet behind the stand. The shielding located below the patient was also considered. These shielding structures are shown in figure 4.

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Due to the unfeasibility of reproducing the precise geometry and composition of the electronics inside the case forming the outer part of the accelerator head, it was filled with a material equivalent to integrated electronic circuitry with an effective density of 1.4 g cm⁻³ to mimic it sparseness [27]. Nevertheless, two structures of importance in the production of leakage radiation were explicitly included inside the case: the acceleration section, made of cooper, and the lead plates covering them on three sides. A rectangular prism-like structure simulating the magnetron was also located inside the box. This structure is positioned to the right of the intersection of the acceleration sections (figure 4 left). For the sake of simplicity, we assumed that it was made entirely of iron with a density of 3 g cm⁻³. Regarding the cabinet located behind the stand, we considered it solid and also filled by the same iron-equivalent material as the magnetron. We consider that for the purpose of this work the simplifications introduced in modelling are sufficient and will not make the simulation results unrealistic, as we will see in the next sections.

Once the Mobetron accelerator head was fully established, several MC simulations were performed with the Geant4 code using the full model described. The Mobetron 1000 was placed in the treatment configuration, i.e., with the gantry and the head aligned vertically, with the 10 cm in diameter flat end applicator and delivering a maximum dose rate of 1000 MU min⁻¹. The scatter on the patient was simulated using plastic dummy RW3 (PTW, Freiburg, Germany) [23] made of fifteen 30 cm × 30 cm sheets of 10 mm thickness each. The flat end of the applicator was put in contact with the phantom. In this way, the most unfavourable treatment conditions were reproduced.

The first simulation was performed to obtain air collision kerma and absorbed dose around the Mobetron 1000 inside the OR for the energies of 6, 9 and 12 MeV (see figure 2) and was evaluated at the locations described in table 1.

Simulations were also performed by varying the shielding structures of the Mobetron 1000 (in a range from half the nominal density to doubling the density) to quantify the importance of these unknown parameters in the calculated doses. To obtain a good spatial resolution with adequate statistical uncertainty and preventing an excessively large calculation time, air cubic voxels of Δx = Δy = Δz = 10 cm were adopted.

The second simulation was carried out incorporating to the modelling the OR structural barriers. Air collision kerma for all available energies were evaluated at the locations outside the OR (see table 2). In this case air collision kerma values were converted to H*(10) values using the conversion factors taken from table A2 of ICRU 47 [20].

Finally, for the case of an electron beam with an energy of 12 MeV a simulation was performed to estimate the fluence of neutrons at points indicated in table 1 around the Mobetron 1000.

For the H*(10) measurements performed with the Fluke monitor, according to the information provided by the manufacturer the uncertainty associated with the calibration factor of the detector in H*(10) is ±3.6%, while those associated with its accuracy and precision are ±10% and ±5%, respectively.

Regarding the energy response, it has been found that this type of detectors has an optimal response except at low energies. According to IEC standard 1017-2 [28], the response of these monitors to incident radiation energy in the 50–150 keV range will not differ by more than 30% from the calibration performed using ¹³⁷Cs. Also, the manual indicates that there is a greater deviation in the range of energies of 25–80 keV [22], not describing its behaviour above 1500 keV. Since in most part of the photon energy spectrum the behaviour of the detector with the energy is similar to the one used for its calibration, an additional uncertainty of ±10% associated to the dependence of the detector with the energy of the incident particle has been estimated.

We have not considered any uncertainty associated with the dependence on the angle of incidence, since all measurements were taken with the detector aligned towards the applicator and the variation of the response with the angle of incidence of the radiation is very low between ±90°, coincident with the bibliography [28].

With respect to the uncertainty of positioning, it has been verified experimentally that a variation in the position of up to 2 cm in any of the three axes has a negligible repercussion in the measurements.

The stability of the reference dose has been extensively discussed in the literature [29]. An uncertainty of ±3% has been assigned to the accelerator monitor system independently of the energy considered.

Therefore, by taking into account all these factors (see table 3 for a summary), we have estimated an expanded uncertainty of ±20%. This is the value assigned to the H*(10) measured data.

Finally, for the measurements of H*(10) rate due to neutrons made with the neutron dosimeter BERTHOLD model LB6411, according to the information supplied by the manufacturer, the uncertainty associated to the calibration factor in H*(10) is of ±3%, the one associated with accuracy is ±5% and due to the spherical symmetry of the moderator and detector, the one corresponding to the directional dependence is less than ±10% across the entire range of energies of interest.

The characteristic of our detector that influences most negatively the accuracy of our measurements is the energy dependence between 50 keV and 10 MeV. The associated uncertainty gave a value of ±30%.

In addition, the Mobetron 1000 absorbed dose rate cannot be monitored directly in real-time. Therefore, its inherent instabilities have been minimised by using a prolonged stabilization period (more than 8 h) and with a previous warming-up period before measuring. For nominal rates of 1000 MU min⁻¹, the MU rates registered have oscillated between 960 and 1020 MU min⁻¹. Hence, the uncertainty associated with the MU rate and calibration factor cGy MU⁻¹ has been estimated to be ±4%. By considering all these issues, an expanded uncertainty of ±38% (k = 2) has been obtained for the H*(10) measured data (see table 4 for a summary).

With respect to the MC modelling of the Mobetron 1000 radiation head, for the Penelope2008 simulation the global MC uncertainty is defined as the average uncertainty of all those voxels whose value is above 50% of the maximum absorbed dose. This global Type A uncertainty is 0.2%–0.4% depending on the energy considered. In the case of specific voxels, the precision near the maximum absorbed dose in the depth dose curves may reach 1%–1.5%. In the case of the Geant4 simulation, the Type A uncertainty was less than 1% in the PDDs and less than 2% for the off-axis profiles.

In the case of the MC simulations performed using Geant4 including all shielding structures, the Type A uncertainty is less than 5% in the points of interest for the study.

In addition to of the Type A uncertainty, there is a Type B uncertainty difficult to quantify. This is due to the lack of knowledge on the head and cabinet composition, in both materials and densities. Another relevant component of Type B uncertainties to be considered is that the MC simulation performed does not take into account the leakage radiation in the radiation head. For all of the above, by combining Type A and Type B uncertainties, we estimate a global uncertainty on the MC of ±20% (k = 2).

Figure 5 presents the PDDs measured compared with those obtained with Penelope2008 and Geant4. Comparison of measured PDDs versus MC.

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We measured the ambient dose equivalent H*(10) values due to photons and electrons at the points described in figure 2 around the Mobetron 1000 expressed as a fraction of the absorbed treatment dose at d_max for each energy (μSv Gy⁻¹). The results are given in table 5.

In table 6 we present the measured the ambient dose equivalent H*(10) values at the points described in table 2 outside the OR and behind the structural barriers. The H*(10) values are expressed as a fraction of the absorbed treatment dose at d_max for each energy (in 10⁻³ μSv Gy⁻¹). Due to the fact that the barriers at floor and ceiling are thicker than 30 cm of concrete, the H*(10) measurements was background.

Measured H*(10) rate values for neutrons at points near the Mobetron 1000 are detailed in table 7. To facilitate the comparison with similar measurements performed by Loi et al [24] we have considered the locations used there instead of those chosen in this work for the photon and electron case. H*(10) values were obtained from the neutron ambient equivalent dose rate measurements for a Mobetron 1000 nominal rate of 1000 MU min⁻¹.

The parameters of the radiation beams obtained from the MC simulations are shown in table 8. Initially, the energy distributions obtained by Janssen et al 2008 [11] were adopted for both codes. However, since each code implements different physical models, it was necessary to use different values for each code.

In table 9 we present the calculated air collision kerma values at the points indicated in table 1 around the Mobetron 1000 expressed as a fraction of the absorbed treatment dose at dmax for each energy (μGy Gy⁻¹).

In order to analyse the dependence of the results on the shielding composition of the Mobetron 1000 used in the modelling, several simulations were made modifying the densities of the materials described in section 2.3.

Air collision kerma and ambient dose equivalent H*(10) values obtained from the MC simulation at the calculation points given in table 2 are given in tables 10 and 11, respectively. They are expressed in units of 10⁻³ μGy Gy⁻¹ of absorbed dose at d_max for the applicator of 10 cm. An average energy value considering equal contribution of all energy beams is also obtained.

In figure 6, we depict air collision kerma and absorbed dose for the y = 0 cm plane and for the 12 MeV case. It can be observed that in many locations around the Mobetron 1000 the dose component due to low energy electrons is 20 times larger than that of the photons.

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With respect to the MC simulations performed, the excessive computational time required makes a detailed MC simulation of this component impracticable. The reason is the very low numerical efficiency of the neutron production mechanism. For each 10⁸ primary electrons only about 100 neutrons were produced, of that only one reach the measuring points. Therefore, although one could increase the simulation time, the calculated dose values would remain small as compared to the photon and electron component and the statistical uncertainties too large.