Interventional radiology (IR) and cardiology (IC) are of undoubted value in the diagnosis and treatment of diseases, their efficacy being reflected in the growing availability of these procedures within many larger medical centers throughout the world. The procedures are conducted by a team of medical staff who during the intervention all remain within the specialized theatre, typically being in close proximity to the patient. Given that such live-time imaging procedures are typically of protracted duration, it is of no surprise that when compared to other frequent radiological methods, IR and IC represent two of the most significant in terms of radiation exposure to medical staff. Although perhaps obvious, it is nevertheless worth noting that with the ever-increasing demand for the conduct of such procedures there comes an associated increase in radiation exposure to staff. A priori knowledge of the occupational absorbed dose to such staff can assist in keeping exposure levels as low as reasonably achievable  . Of interest is that previous success in maintaining levels below the dose limit has not always prevented cataract formation, with incidences of brain cancer among radiologists also being suggested as being implicated      . As such, computational-exposure scenarios mimicking realistic interventional procedures are important in predicting the 3D scatter (stray) radiation arising from the patient and apparatus. Over the last decade, investigations of patient and staff exposure during IR and IC have been performed via measurement      . Study of interventional radiology occupational exposures has also been made using the Monte Carlo (MC) technique    . This said, the stray radiation 3D distribution has not been previously obtained via MC simulation using the high definition reference Korean-man (HDRK-man) virtual anthropomorphic phantom  . Herein modeling has been made of staff exposure, the patient being imaged with a GE Infinia 3/8” machine, utilizing the versatile Geant4 toolkit  . The aim has been to study the effect of key parameters on occupational exposure distribution within the theatre. Specifically, the influence of kVp, field of view (FoV) and staff position has been investigated, focusing on three radiosensitive organs (lens of the eye, and lung and prostate).
2. Materials and Methods
Description is provided herein of the adopted methodology, presenting the voxelized phantom corresponding to the patient and staff, the X-ray imaging machine and X-ray tube output. Different proposed interventional imaging procedure scenarios are also outlined. We note that there are three phantom format types (stylized, voxel and hybrid) and four morphometric categories (reference, patient-dependent, patient-sculpted and patient-specific). Here we are limited to voxel type and reference category (patient matching by age only) to model phantoms.
2.1. Patient and Operator Modeling
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  , defining some 40 tissues/organs.
2.2. Gamma Camera and X-Ray Spectra
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  .
2.3. Irradiation Scenarios
The parameters studied during this work were as follows:
Figure 1. Simulated experimental set-up, including the C-arm machine (Gantry, X-ray tube holder, CsI flat panel) and the HDRK-Man phantom lying on a table shielded with 0.5 mm Pb on its left side. Also shown: the eight most likely occupied locations by staff (Interventional Radiologist (IR), Interventional Cardiologist (IC) and Nurse (N)) with their occurrence (in %) during an interventional procedure.
・ 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  and shown in Figure 1
・ Table height (fixed): 75 cm
2.4. Simulation and Data Collection
For MC simulation, use has been made of the Geant4 version 10.3 multithreaded mode   . 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).
3. Results and Discussion
Results and analysis are provided herein, concerning the three dominating parameters modifying the 3D stray radiation dose distribution, kVp, FoV and staff location, evaluated at the level of the eyes, lung and prostate.
3.1. Effect of kVp
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  and theory, the latter depicted in Figure 5 showing polar plots of the Compton scattering cross-section as a function of energy  , 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  , 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
Figure 2. Simulated stray radiation obtained at 120 kVp (4.3 mm Al) and 30 cm FoV. Shown are dose maps for three horizontal plans, corresponding to eye lens (top left), lung (top right) and prostate (bottom left) levels; a vertical plan perpendicular to the C-arm gantry is shown at the bottom right. The colour bar indicates the relative strength of scattered radiation, from lowest values at the blue end to yellow at the upper end of the scale.
Figure 3. Simulated stray radiation obtained at 60 kVp (2.3 mm Al) and 30 cm FoV. Dose maps are shown for three horizontal plans at the level of the lens of eye (top left), lung (top right) and prostate (bottom left); a vertical plan normal to the C-arm gantry is shown at the bottom right.
Figure 4. Simulated stray radiation obtained at 80 kVp (3.2 mm Al) corresponding to the horizontal patient level when varying the FoV from 15 cm (top left) to 30 cm (bottom right).
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.
Figure 5. Klein-Nishina differential cross-sections as a function of the scattering angle and incoming photon energies.
Table 1. Simulated scatter fractions (in µGy/Gy∙cm2) at the level of the lens of the eye, and lung and prostate, also the ESAK values. Data are given for all possible combinations of kVp (60, 80 and 120) and FoV (15, 20, 25 and 30 cm). The eight most likely occupied locations (Loc.) were emphasized. Cells highlighted in gray correspond to the radiological safe side.
3.2. Effect of the FoV
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.  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.
3.3. Effect of Operator Location
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  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.
There is an increasingly pressing need to quantify medical staff during interventional procedures. The present study, concerning scattered radiation from the patient and C-arm, has examined the influence of kVp, FoV and staff location on the 3D distribution and dose. Using an anthropomorphic voxelized phantom incorporated into a Geant4-based program, evaluation has been made of ESAK and scatter fraction at three organ levels of members of staff (eye lens, lung and prostate). For a given value of the FoV, ESAK is seen to increase with a decrease in kVp, supporting existing literature. Secondly, modification of kVp from 120 to 80 has a negligible effect (average deviation of 13.4%); conversely, in changing from 80 to 60 kVp an average decrease of 35.9% is found. Finally, the typically adopted locations of the various members of staff during interventions, in accordance with their roles, are found to be an optimal choice. From such findings, we urge the implementation of appropriate in-house protocols in seeking to mitigate the potential deleterious effects of radiation on members of staff.