Real‐time, ray casting‐based scatter dose estimation for c‐arm x‐ray system

Abstract Objectives Dosimetric control of staff exposure during interventional procedures under fluoroscopy is of high relevance. In this paper, a novel ray casting approximation of radiation transport is presented and the potential and limitation vs. a full Monte Carlo transport and dose measurements are discussed. Method The x‐ray source of a Siemens Axiom Artix C‐arm is modeled by a virtual source model using single Gaussian‐shaped source. A Geant4‐based Monte Carlo simulation determines the radiation transport from the source to compute scatter from the patient, the table, the ceiling and the floor. A phase space around these scatterers stores all photon information. Only those photons are traced that hit a surface of phantom that represents medical staff in the treatment room, no indirect scattering is considered; and a complete dose deposition on the surface is calculated. To evaluate the accuracy of the approximation, both experimental measurements using Thermoluminescent dosimeters (TLDs) and a Geant4‐based Monte Carlo simulation of dose depositing for different tube angulations of the C‐arm from cranial‐caudal angle 0° and from LAO (Left Anterior Oblique) 0°–90° are realized. Since the measurements were performed on both sides of the table, using the symmetry of the setup, RAO (Right Anterior Oblique) measurements were not necessary. Results The Geant4‐Monte Carlo simulation agreed within 3% with the measured data, which is within the accuracy of measurement and simulation. The ray casting approximation has been compared to TLD measurements and the achieved percentage difference was −7% for data from tube angulations 45°–90° and −29% from tube angulations 0°–45° on the side of the x‐ray source, whereas on the opposite side of the x‐ray source, the difference was −83.8% and −75%, respectively. Ray casting approximation for only LAO 90° was compared to a Monte Carlo simulation, where the percentage differences were between 0.5–3% on the side of the x‐ray source where the highest dose usually detected was mainly from primary scattering (photons), whereas percentage differences between 2.8–20% are found on the side opposite to the x‐ray source, where the lowest doses were detected. Dose calculation time of our approach was 0.85 seconds. Conclusion The proposed approach yields a fast scatter dose estimation where we could run the Monte Carlo simulation only once for each x‐ray tube angulation to get the Phase Space Files (PSF) for being used later by our ray casting approach to calculate the dose from only photons which will hit an movable elliptical cylinder shaped phantom and getting an output file for the positions of those hits to be used for visualizing the scatter dose propagation on the phantom surface. With dose calculation times of less than one second, we are saving much time compared to using a Monte Carlo simulation instead. With our approach, larger deviations occur only in regions with very low doses, whereas it provides a high precision in high‐dose regions.


Conclusion:
The proposed approach yields a fast scatter dose estimation where we could run the Monte Carlo simulation only once for each x-ray tube angulation to get the Phase Space Files (PSF) for being used later by our ray casting approach to calculate the dose from only photons which will hit an movable elliptical cylinder shaped phantom and getting an output file for the positions of those hits to be used for visualizing the scatter dose propagation on the phantom surface. With dose calculation times of less than one second, we are saving much time compared to using a Monte Carlo simulation instead. With our approach, larger deviations occur only in regions with very low doses, whereas it provides a high precision in high-dose regions. Germany. 1 These days x-rays are widely-used in several areas of medicine outside radiology, such as interventional cardiology, orthopedics, and urology and even for treatment in radiotherapy to name a few. In many of these fields, staff is required to stand near the patient during imaging, thus receiving substantial scatter radiation. The majority of scattered radiation originates from the patient, but other objects in the intervention room like the table and the roof and ceiling contribute to the dose as well. Repeating the procedure several times per day, staff receives significant dose. This may add up to 3.5 mSv additional dose per year for cardiologists as shown by Tsapaki et al. 2 compared to about 2.4 mSv/a from natural sources. [3][4][5][6] Data evaluated from radiation incidents such as the Chernobyl nuclear power plant disaster, the atomic bombing of Japan and other recorded radiation accidents indicate harmful effects of ionizing radiation, such as thyroid diseases, 5 cataract, 6 cerebral dysfunctionality, 7 and several kinds of cancer. 8 During past decades, the increasing use of x-rays in the operating room and in remote locations has revolutionized the practices of several surgical and treatment specialties. Fluoroscopy coupled with image intensifiers and video displays has significantly improved the surgical care of patients by providing immediate situs information to physicians. C-arm systems offer both a spot imaging mode and a fluoroscopic imaging mode that allows the generation of continuous real-time moving images. 9 The disadvantage of the increased use of kV x-rays is the exposure of operating room personnel to ionizing radiation. The scattered radiation from the patient comprises the main source of radiation dose to staff. 10 Factors like treatment table, x-ray source rotation and patient body mass found to be influencing the radiation dose and have been explored in several studies. [11][12][13][14] The dependency of C-arm angulation for reducing peak skin dose (PSD) has been discussed. 15 Several studies have underlined substantial dose for interventional physicians, 16 29 however, the results of the simulation has not been validated by real measurements. 31 To our knowledge, there is no method published so far that allows real-time estimation of dose distributions (which would allow for acquiring the dose while staff is moving in the room) while achieving a realistic accuracy of the estimate. In this paper, we propose a novel ray casting approximation for real-time scatter dose estimation in C-arm. The approach offers a real-time risk map of expected dose contamination allowing to improve the awareness of clinicians toward scattered dose they might receive.

| METHODS
The best approximation for radiation transport so far is the Monte Carlo simulation. However, this is also one of the most expensive techniques. Monte Carlo requires the modeling of the source and then computes the ensemble result of many randomly generated individual photons or particles that are emitted by the source. In many applications, one uses phase space files, that is, the particles ALNEWAINI ET AL.
| 145 and photons that pass through an imaginary plane are stored in both type but also the phase space information, that is, type, position, velocity, and energy. The main idea of our approach is to precompute sophisticated phase spaces around static objects that contribute to most of the scatter in the scene and approximate the remaining radiation transport by neglecting further scattering and those particles that might be absorbed before reaching the object of interest (surfaces representing staff). Thereby, we identify the patient includ- In this ray casting step (bottom row), only elements of the phase space that directly hit the object of interest are considered and their full dose is assigned at the spot where they hit this object.
Ignoring additional scatter reduces the computations to pure collision detection and is hereby a cheap operation, whereas the main sources of scattering (the patient and table) are considered in detail by the initial Monte Carlo simulation. This is the origin of the realtime capability of our strategy.
In the following, this strategy is described in more detail.

2.A | GDML modeling
The C-arm x-ray system was modeled using the (GraXML) toolkit, 32 as shown in Fig. 2. The Geometry Description Markup Language (GDML) hereby describes the geometries, including materials, as the basis for the Monte Carlo simulation. The GDML file was read in and validated of Geant4 and then further used for simulation. 33 Geometry data were based on the information from manuals for SIE-

MENS Axiom Artis C-arm system at the University Medical Center
Mannheim, Institute for Clinical Radiology and Nuclear Medicine.
Elliptical cylinders represented the patient's shape on the table and F I G . 1. Model Overview. The figure shows the scheme for a full Monte Carlo simulation for calculating the scatter radiation dose received by staff phantom (a), (b), as well as our optimization that performs a ray casting for particles that were been stored on a phase space in the first step (c), (d).
two staff phantoms in the treatment room. For each tube angulation of the C-arm, an own GDML file was generated.

2.B | Beam commissioning
One beam of the C-arm x-ray system was modeled and commissioned with Monte Carlo simulation similar to the protocol used by Alaei 34 ; the fitted beam parameter data used in the commissioning is shown in Table 1. All measurements were performed using an ion chamber with a 0.3 cm 3 detector volume (PTW 30016, Freiburg, Germany), calibrated with a Sr 90 isotope and corrected for air density before each measurement. The AAPM Task Group 61 protocol 35 was used to compute the absorbed dose from ionization.
The beam used for the measurements was 125 kV energy with (SSD) of 100 cm. No filtrations used, x-ray tube rotation was 0°(kV x-ray tube is under the patient's table). Measurements for depthdose profile and cross profiles were performed. For depth-dose profile measurements, a phantom consisting of a 12 9 30 9 30 cm 3 stack of solid water-equivalent slabs and a 7 cm backscatter was chosen. Source-to-surface distance (SSD) was 100 cm. 26 measurements for depth from 0-12 cm were performed using 120 image frames for each depth. Likewise for cross profiles, 43 measurements for each X and Y axis at 1 cm depth were performed. The viability of water-equivalent slabs for soft x-ray dosimetry was found accurate within 1% according to Hill. 36 This protocol was selected for commissioning a kV system for CBCT hence we used it for our C-arm kV system as well. The only difference was that the x-ray source position is under the table and all the geometries of the water slabs were turned upside down, so all of the 7 cm back scatter water slabs were up facing the ceiling.

2.C | Validation of modeling
GDML modeling for C-arm system with 0°degree (the xray tube is under the table). The model was visualized using the GraXML toolkit.
T A B L E 1 kV beam parameters used with measurements and simulations for C-arm.

Parameters
C-arm kV system  pre-calculating the phase space files, for every possible rotation of the C-arm, particles (only photons) that leave a phase space volume are recorded and written to a phase space file (Fig. 4). For each particle, its position, momentum, type, total energy and weight were stored. A phantom mimicking the surface of staff persons is described by a 16 9 100 9 17.48 cm elliptical cylinder in the Geant4 simulation. During the simulation, some of the particles passed through the patient phantom without any energy deposit (no energy loss), we retrieve a factor named as energy-absorption ratio and this was done for each rotation.

2.E | Ray casting-based approach
The ray casting was a separate C++ application. Previously generated phase space files were read. A staff phantom position, width, height, etc., were adjusted. For all particles from the phase space files, collision detection with the staff phantom was determined, that is, by a ray-cylinder intersection test. 39 For visualization individual hit posi- x-ray tube. The difference in the number of particles that were hitting the staff phantom is compared in Table 3

3.B | Monte Carlo simulation and validation
The average percentage of error values for all TLDs was 1.33%, whereas the dose calculation accuracy for Gean4 simulation was within 1%. The average doses of data from TLDs measurements, Monte Carlo simulation, and ray casting approach for the 7 x-ray tube angulations (0°-90°) with a summary statistics for both data comparison is presented in Fig. 6(a) and 6(b). The analysis of values shows an absolute average difference of 3.98% between Monte Carlo simulated and TLDs measured data.

3.C | Ray casting approach and validation
The results, as shown in Fig. 6(a) and 6(b), indicate a variance in the percentage error difference depending on the x-ray source rotation.
The left TLD sheet (left side of the patient) presented the best values between 45°-90°tube angulations and provides an average difference of À7.4% for data comparison between ray casting approximation and TLD measurements, whereas the average difference for tube angulations between 0°-45°was À29.29%. Data from ray casting approximation compared with Monte Carlo simulation for sheet located left side of the patient show an average difference of À4.93% for tube angulations between 45°-90°, whereas it records an average difference of À19.97% for tube angulations between 0°-45°.  the left side of the patient and scattered photons from the table & patient, the number of photons is about one order of magnitude less compared to the case of the right side of the patient. The number of photons coming from roof or ceiling are one to two orders of magnitude less than those from the table & patient therefore they can be ignored.   (Fig. 6).

3.D | Ray casting-based risk map
As tools in our geometry model. However, we could easily include them by computing which of the emitted photons are blocked by these structures. Further experimental works are needed to estimate a set of beams to be modeled and commissioned covering all C-arm investigation protocols with more x-ray source rotations.

| CONCLUSION
This paper identifies the potential and limitation of a real-time ray casting approximation for determining dose received by staff. It offers a viable strategy for further questions of radiation hygiene in other settings where due to construction only geometric parameters are to be included that can be designed by a standard Computer Aided Design tool. Hence, no programming would be necessary to use this tool for any other sort of application.