In modeling patient and staff, close similarity has been noted between the ICRP reference man and the voxelized phantom HDRK-man, including height and weight, a matter encouraging the use of the latter. Constructed from high-resolution photographic anatomical images, HDRK-man has a height of 171 cm and weight of 68 kg. Whereas, the ICRP models human having a height of 176 cm and weight of 73 kg. The considered phantom consists of some 30 million voxels, resolution 1.981 × 1.981 × 2.0854 mm³, distributed along a 3D array of dimension 247 × 141 × 850, along the x, y and z coordinate axes, respectively. The elemental composition and density of each voxel were obtained from ICRU 46 [17] , defining some 40 tissues/organs.

The GE Infinia II 3/8” C-arm machine modeled in this study has an inner radius of 1m and is made from a sturdy, rigid foam material (density 0.7 g/cm³ and elemental composition of 50% H, 30% C, 10% N and 10% O). As shown in Figure 1, the gantry supports a CsI flat panel imager (48 × 48 × 10 cm³) positioned close to the upper surface of the patient, while the under-couch X-ray tube is contained in an iron shielding surround. The couch is a 45 × 190 × 1.5 cm³ table made of PMMA material. A typical beam-hardening Pb sheet of 0.5 mm thickness has been added to the patient table in front of the primary X-ray beam. In generating the X-ray tube outputs, as modified by the particular choice of total filtration and parameter selection (kVp and mAs), use was made of the software known as spektr [18] .

The parameters studied during this work were as follows:

・ X-ray photon spectra: 60 kVp (Half Value Layer (HVL) = 2.3 mm Al), 80 kVp (HVL = 3.2 mm Al) and 120 kVp (HVL = 4.3 mm Al)

・ C-arm orientation (fixed): vertical

・ Exposure and patient orientation: postero-anterior (PA), lying on the bed

・ Irradiated body area (denoted as FoV) (four values): 15 × 15, 20 × 20, 25 × 25, and 30 × 30 cm², centered at chest

・ Staff locations (eight values): about 40 cm around the patient table, as proposed in literature [19] and shown in Figure 1

・ Table height (fixed): 75 cm

For MC simulation, use has been made of the Geant4 version 10.3 multithreaded mode [16] [20] . In respect of the large number of voxels representing the patient, utilization has been made of the nested parameterization provided for by the G4VNested Parameterization class. For the simulated X-ray room, a particular typical example of dimension 4.8 × 6.4 × 2.89 m³ was chosen. Spectra generated through use of the spektr software have been included in the Geant4-based program, the inverse transform method being used to randomly generate the corresponding energies. Such method consisting of the sampling of random numbers from a given probability distribution function, uses the inverse cumulative distribution defined by the calculation of the cumulative integration for a given set of samples. For all cases, a pyramidal-shaped primary beam has been assumed, emanating from a point-like X-ray source towards the chest of the patient. In allowing simulation of the spatial distribution of the stray radiation, the room space was subdivided into 80 × 80 × 34 air-filled boxes, each of the dimension 5 × 5 × 5 cm³. The scenario allows for scattered radiation evaluation up to 2 m away from the centre of the irradiation field. For a given choice of set-up, simulation has been made to obtain the air kerma free-in-air within air-filled boxes of the dimensions 10 × 10 × 10 cm³, evaluated at the level of the lens of the eye, lung and prostate, at 165, 150 and 84 cm directly above the floor respectively. In order to obtain the parameter ESAK, simulation was made of the absorbed dose evaluated within 10 × 10 × 1 cm³ air-filled boxes inserted directly under the patient table; this allows X-ray backscattering to be taken into account. All simulations were carried out on a Dell Precision T7610 workstation with 40 cores, equipped with an Intel Xeon E5-2680v2 CPU at 2.80 GHz and 256 GB RAM, working on the Linux operating system (Ubuntu 14.04). The number of generated primary particles was 5 × 10⁸ (allowing statistical uncertainty of <3%) for all cases, with run times ranging from 8500 s to 17560 s (i.e. from 2.4 hours up to just below 5 hours).

To assess the influence of kVp on the simulated scattered radiation distributions, comparison has been made of three cases: 120 kVp (HVL = 4.3 mm Al), 80 kVp (HVL = 3.2 mm Al) and 60 kVp (HVL = 2.3 mm Al) for a fixed value of FoV. Figures 2-4 provide dose maps at the particular organ levels. In changing the kVp from 60 to 80 to 120, the distribution of stray radiation is seen to progressively concentrate around the irradiated area of the patient.

Such results are in accord with literature [10] and theory, the latter depicted in Figure 5 showing polar plots of the Compton scattering cross-section as a function of energy [21] , the forward direction becoming increasingly favored. Table 1 illustrates the ratios of air kerma free-in-air to entrance surface air kerma (ESAK), namely the scatter fraction, quoted in µGy/Gy∙cm² [22] , for all combinations of the eight staff locations, organ levels, FoV and spectral influence of kVp. As previously mentioned, observation is made of an inverse proportionality between ESAK and kVp. Moreover, in changing the kVp from 60 to 80 and from 80 to 120, keeping the FoV fixed, the scatter fraction is observed to approximately double, remaining almost constant for the three organ levels and the eight staff locations.

This can be rationalized to be due to the penetration and scattering abilities characterizing the spectral X-ray beam. Given the limited number of interventional scenarios studied, including the overall shape of the phantom, the choice

of C-arm machine and buildup specifications, the findings are not to be generalized. Nevertheless, while each interventional procedure will undoubtedly produce its own scattered radiation distribution, the current study can be considered to provide a good estimation of the overall situation.

In the example case of 80 kVp, stray radiation maps have been provided for particular likely FoV values of 15, 20, 25 and 30 cm. Horizontal plans corresponding to the patient table level are shown in Figure 4. No significant trend is discernible at this level, contrary to the ESAK and the scatter fraction distributions. In changing from a FoV of 15 to 30 cm, ESAK decreases continuously reaching values of a factor of three or better. Although limited to 80 kVp and to 14, 20 and 28cm circular shaped FoVs, Bethe et al. [23] found this to be an important effect on the stray radiation when changing the FoV parameter; the present work confirms their findings. Also supported is the trend towards near constancy of scatter fractions for a given value of kVp. Thus, we can generalize that the scatter fraction remains an almost constant function of the FoV for a fixed kVp parameter. This situation should be explored by extending the present study to take into account the effect of focal-to-skin and focal-to-detector distances.

The effect of changing staff location (as shown in Figure 1) on the scatter fraction at the level of the lens of the eye, lung and prostate is illustrated in Table 1. Despite buildup effects as observed in the measurements, applicability of the inverse square law has been confirmed, in terms of scattered fraction values, for the coupled staff locations of (1 and 5), (2 and 6) and (3 and 7). Moreover, we observe the typical times spent by the different members of staff (IR, IC and N) during an interventional procedure [19] to be optimal. This said, the present study has been limited to the PA projection; further simulations would help, extending findings to other irradiation conditions of AP, LAO, RAO and such like.