Effective dose estimation in cone-beam computed tomography for dental use by Monte-Carlo simulation optimizing calculation numbers using a step-and-shoot method

Abstract

Objective:

The objective of this study was to perform effective dose estimation in cone-beam CT for dental use (CBCT) using a Monte-Carlo simulation employing a step-and-shoot method as well as to determine the optimal number of steps.

Methods:

We simulated 3DX Accuitomo FPD8 as a CBCT model and estimated the effective doses of a large and a small field of view (FOV) examination against the virtual Rando phantom using a particle and heavy ion transport code system. We confirmed the results compared to those from a thermo-luminescence dosemeter (TLD) system in a real phantom and investigated how the reduced angle calculations could be accepted.

Results:

The effective doses of both FOVs estimated with each one degree were almost the same as those estimated from the TLD measurements. Considering the effective doses and the itemized organ doses, simulation with 5° and 10° is acceptable for the large and small FOV, respectively. We tried to compare an effective dose with a large FOV as well as with multiple small FOVs covering the corresponding area and found that the effective dose from six small FOVs was approximately 1.2 times higher than that of the large FOVs.

Conclusion:

We successfully performed a Monte-Carlo simulation using a step-and-shoot method and estimated the effective dose in CBCT. Our findings indicate that simulation with 5° or 10° is acceptable based on the FOV size, while a small multiple FOV scan is recommended from a radiation protection viewpoint.

Introduction

Radiological examinations are essential for dental practice, with cone-beam computed tomography for dental use(CBCT) being a widely used approach. Importantly, CBCT enables the diagnosis of lesions or understanding anatomical structures in a three-dimensional manner.¹ When dentists decide to employ CBCT examination, it is important to consider its justification and optimization because of its relatively higher radiation dose compared to other dental X-ray modalities.^2,3 Therefore, it is crucial to know in advance the effective dose that can be given to patients.^4,5

Estimation of the effective dose in radiological examinations is typically performed by employing thermo-luminescence dosimeters (TLDs) or radiochromic films located in a Rando phantom, as evidenced by previous studies using CBCT.^4,6–8 However, this method is not without concerns, since TLD chips or radiochromic films have a direction, that are influenced by an X-ray incidence angle, and an energy dependency. Due to the variation in its sensitivity, the operator needs to be experienced in order to obtain a stable result,⁹ and a certain number of measuring points.¹⁰ In addition, it is difficult to collect accurate measurements in a complicated situation, such as in a comparison of an effective dose with a large field of view (FOV) and multiple small FOVs covering the corresponding area.

Recently, a Monte-Carlo simulation method was introduced in the field, which can simulate photon behaviours interacting with matter in silico.^5,11–13,15 Importantly, the software packages, such as MCNP (STUK, Helsinki, Finland), GEANT4,¹⁶ EGSnrc,¹⁷ and PHITS,¹⁸ can run on a personal computer. Although some training is necessary to master the software, it enables us to estimate the effective dose in a complicated situation and provides reproducible results. That is, we can precisely adjust the X-ray source location and its angle using mathematical coordinates as well as set measuring points at any position in a virtual voxel phantom. The findings from previous CBCT examinations using this method roughly corresponded to those employing a TLD system.^11–13 However, it is difficult to simulate a constantly moving X-ray source that continuously emits X-rays using a Monte-Carlo method. This is because the simulation is typically performed assuming a motionless X-ray source, a factor previous studies have not considered.

In this study, we employed a step-and-shoot method to simulate X-ray source movement in CBCT which limited the calculating ability.¹⁹ The smaller the step intervals, the closer the dose is to reality, but it is impossible to divide it infinitely; hence, it is necessary to find an acceptable angle for rounding the calculations. Based on this, the simulation could be performed in a shorter time and allow for the assessment of more complicated situations using the extra time. Here, we set the minimum step to 1° and compared the values between different step intervals. The aim of this study was to perform effective dose estimations in CBCT using a Monte-Carlo simulation employing a step-and-shoot method and to determine the optimal number of steps. Finally, we compared the effective doses from a large FOV and from six small FOVs covering the corresponding area by the simulation.

Methods

CBCT model

In this study, we simulated 3DX Accuitomo FPD8 (Morita Corp., Kyoto, Japan) as a CBCT model. Although this CBCT machine has three types of FOVs, we investigated two FOVs with a size of 8 × 8 cm and a small of 4 × 4 cm (diameter × height), which could obtain all tooth and incisor tooth areas, respectively (Figure 1). The scanning parameters were as follows: tube voltage, 80kV; tube current, 7 mA; acquisition time, 17.5 s (360° rotation); and no dose reduction mode was selected. The dose area products were 889 and 222 mGy•cm² in 8 × 8 cm and 4 × 4 cm FOVs, respectively.

Figure 1.

The virtual phantom appearance and the field of view (FOV) settings. (a) The virtual phantom was created from the Rando phantom. It was composed of 5-mm thick images and the steps that could be seen. The small and large FOVs set in the phantom are indicated in the orange and yellow areas, respectively, in sagittal (b), coronal (c), and axial (d) views.

Monte-carlo simulation

We employed a PHITS (Particle and Heavy Ion Transport code version 2.52) as a Monte-Carlo simulation in this study.¹⁸ PHITS was run on Windows 7, 64-bit operating system (CPU: Intel Core i5 760, Clocks: 2.80 GHz, Cores: 4, RAM size: 16 GB). We did not use electron γ power computation mode. The simulation computations were repeated 10⁷ times per X-ray shoot, and the cut-off energy in photons was set to one keV. PHITS outputs the data as the total heat quantity (MeV/cm³) of each voxel.

Setting of the X-ray source: We set the focal spot of the X-ray tube as a point source with a diameter of 100-µm circle focal spot with a 20°-degree beam angle. We assessed the field shape and the size of the 3D Accuitomo by placing an imaging plate (Fujifilm Medical, Tokyo, Japan) on the surface of the flat panel detector under the maintenance mode that can stop the arm rotation. The distance between the focus and the imaging plate was 63 cm and 74 cm in the large and small FOV, respectively. The FOVs were square and the sizes of them were 12.3 × 12.3 cm and 7.4 × 7.4 cm, respectively. Therefore, we set the thickness of the lead collimator to 35 mm making the beam size 5.2 × 5.2 cm and 3.0 × 3.0 cm at the 30 cm distance from the focus to realize the shape and the size for each FOVs (Figure 2a). As a result, the X-ray bundle formed a quadrangular pyramid shape. The X-ray generation spectrum was set to that shown in Figure 2b when the 80 kV electrons collided with a tungsten target with a filter of 2-mm aluminum equivalent thickness that was cited from the textbook of Johns HE.²⁰ The X-ray source was located 500 mm from the rotation axis and was adjusted so that it could irradiate from the periphery to the axis. As the real machine scans an object with an overlap of 20° from −100 to 280° based on the midline of the face at 0° (Figure 2c). We simulated the irradiation steps within the overlap when the step interval was less than 20°.

Figure 2.

The schema of simulation settings. (a) X-ray source was set as a point focus and with a 20° beam angle. The beam was collimated with 35 mm thickness lead collimator. The size of the large field of view (FOV) was set to 5.2 × 5.2 cm (shown in this figure), and 3.0 × 3.0 cm for the small FOV (not shown). The red line circle in the centre indicates the contour of the voxel phantom. You can see the beam bundle from the focus that attenuated through the phantom and the scattered radiations around the phantom. (b) An X-ray spectrum of 80 kV with 2.0-mm aluminium filter. (c) Schema showing the movement of the X-ray source from the top view. The X-ray source was located 500 mm from the rotation axis and irradiated the phantom from the periphery to the axis. The examination started from −100 to 280° based on the midline of the face being at 0°, with a 20° overlap.

The voxel phantom: We wanted to compare the results from a PHITS simulation to a TLD measurement against the same subject; hence, we made a voxel phantom of the Rando phantom (Radiology Support Devices Inc., CA, USA). The Rando phantom consisting of slices 1–8 (Figure 3a) was scanned by a medical multi-slice CT scanner (Somatom Sensation 64, Siemens, Forchheim, Germany) at a tube voltage of 140 kV, tube current of 900 mA, collimation of 0.6 × 64, pitch of 0.6. Then, sectional images with 5-mm slice thickness and H40s soft tissue reconstruction kernel were exported as Digital Imaging and COmmunicating in Medicine (DICOM) data. They were imported to PHITS and transferred to a voxel phantom, as shown in Figure 1a. The dose measuring areas were set to 18 sites with a 1 cm cubic area at the same points as the TLD insert holes (Figure 3b).

Figure 3.

The Rando phantom and the measurements points. (a) The appearance of Rando phantom. This study employed the slices from 1 to 8, from the top of the head to the supraclavicular area. (b) Slices and the thermo-luminescence dosemeter (TLD) locations in each slice.

Setting of the simulation: The real machine performs an examination emitting X-rays continuously during the entire scanning (not employing pulse irradiation); hence, a strict simulation would be difficult because calculations with infinite division are impossible. Therefore, we had to employ a step-and-shoot method for the simulation.^{14,19, 21} Specifically, we simulated the X-ray irradiation steps divided into a minimum of one degree and calculated the effective doses by each simulation of 1°, 2°, 5°, 10°, 20°, 30°, 45° and 90°, and we compared the results to determine how the angle-reduced calculation was acceptable. The absorbed doses for the brain, saliva, thyroid, organ mucosa, skin, esophagus, bone marrow, bone surface, eye lens and pharynx were estimated. For the organs included in slice numbers eight and above of the Rando phantom, each absorbed dose was multiplied by its respective coefficient, due to a ratio of organ weight in the slice number from 1 to 8 to organ weight in the whole body. More specifically, the coefficient was set to 0.1 for skin, bone marrow and bone surface, and was set to 0.3 for the esophagus.^4,22 The absorbed dose for each organ was obtained by converting the value in MeV/cm³ units to J/kg (Gy) by multiplying it by 1.602 × 10⁻¹⁰, using X-ray conversion efficiency: KVZ is equal to 1.83 × 10⁻⁹80 ×x10³ (V) × 74, by electron number per 1 A is equal to 6.24 × 10¹⁸ (s⁻¹), by an exposure time of 17.5 (s), and by dividing by each organ density. Here, K was determined to be 1.83 × 10⁻⁹ by comparing the irradiation dose in air measured with an ionization chamber (Victoreen Model 500, AcroBio., Tokyo, Japan) and the estimated value by a PHITS simulation, and Z is a tungsten atomic number 74. Each organ density was set at 1.07 (g/cm³), which was obtained from the average height and weight of Japanese adult males. In this study, the equivalent doses were equal to the absorbed doses because the simulation was limited to X-rays or photoelectrons. Then, the effective dose was obtained as the sum of all the equivalent doses and corresponding tissue-weighting factors listed in Tables 1 and 2, based on the ICRP report 103.²²

Table 1.

Measurement from TLD and simulation results of PHITS about FOV 8 × 8 cm

Organ	Tissue weighting factor	TLD measurement	Equivalent dose (mSv)
			PHITS simulation
			each 1 degree	each 2 degrees	each 5 degrees	each 10 degrees	each 20 degrees	each 30 degrees	each 45 degrees	each 90 degrees
Brain	0.01	0.332 ± 0.004	0.236	0.239	0.231	0.230	0.225	0.226	0.230	0.229
Salivary	0.01	2.942 ± 0.120	3.263	3.246	3.178	3.029	4.267	4.338	4.525	4.316
Thyroid	0.04	0.430 ± 0.008	0.317	0.317	0.292	0.272	0.322	0.322	0.324	0.325
OralMucosa	0.12	0.287 ± 0.011	0.276	0.275	0.274	0.268	0.208	0.209	0.212	0.212
Skin	0.01	0.184 ± 0.009	0.136	0.135	0.134	0.132	0.125	0.125	0.124	0.110
Oesophagus	0.05	0.176 ± 0.039	0.166	0.168	0.163	0.161	0.147	0.149	0.147	0.147
BoneMarrow	0.12	0.137 ± 0.003	0.185	0.184	0.184	0.179	0.121	0.123	0.123	0.121
BoneSurface	0.01	0.278 ± 0.009	0.240	0.240	0.247	0.247	0.380	0.383	0.379	0.369
EyeLens		0.693 ± 0.076	0.250	0.247	0.241	0.228	0.211	0.215	0.206	0.202
Pharynx		2.236 ± 0.190	3.232	3.216	3.206	3.161	3.107	2.982	3.103	2.563
Effective dose (mSv)		0.114 ± 0.002	0.115	0.115	0.113	0.109	0.110	0.111	0.113	0.110

Table 2.

Measurement from TLD and simulation results about FOV 4 × 4 cm

		Equivalent dose (mSv)
Organ	Tissue PHITS simulation weighting factor	TLD measurement	PHITS simulation
			each 1 degrees	each 2 degrees	each 5 degrees	each 10 degrees	each 20 degrees	each 30 degrees	each 45 degrees	each 90 degrees
Brain	0.01	0.092 ± 0.006	0.053	0.053	0.053	0.053	0.054	0.054	0.054	0.057
Salivary	0.01	0.993 ± 0.061	1.234	1.243	1.257	1.282	1.092	1.125	0.968	1.231
Thyroid	0.04	0.000 ± 0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
OralMucosa	0.12	0.080 ± 0.013	0.059	0.058	0.059	0.057	0.049	0.050	0.050	0.053
Skin	0.01	0.002 ± 0.000	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001
Oesophagus	0.05	0.004 ± 0.024	0.004	0.004	0.004	0.004	0.003	0.003	0.003	0.003
BoneMarrow	0.12	0.031 ± 0.004	0.022	0.022	0.022	0.022	0.028	0.027	0.027	0.028
BoneSurface	0.01	0.052 ± 0.005	0.072	0.073	0.074	0.076	0.072	0.070	0.070	0.097
EyeLens		0.143 ± 0.032	0.052	0.053	0.053	0.053	0.050	0.050	0.051	0.049
Pharynx		0.264 ± 0.054	0.366	0.365	0.367	0.366	0.374	0.373	0.364	0.370
Effective dose (mSv)		0.025 ± 0.001	0.024	0.024	0.024	0.024	0.022	0.022	0.020	0.024

TLD measurements

First, the calibration factor of the TLD (TLD MSO-S, Toreck, Kanagawa, Japan) was obtained. All 18 chips were located in the rotation centre and exposed by X-ray irradiation of 3D Accuitomo operating at 80 kV, 7 mA and 17.5 s under the maintenance mode, accompanied by the probe of the ionization chamber (Victoreen Model 500). Then, each TLD chip was measured with a TLD reader (Kyokko TLD reader 2500, Kyokko Denki Co. Ltd., Tokyo, Japan), and the calibration factor was obtained. Next, TLD chips were inserted into the Rando phantom as seven chips in the brain and each in the salivary gland, submandibular gland, sublingual gland, oral mucosa, thyroid, oesophagus, bone marrow, bone surface, skin surface and pharyngeal cavity, as indicated in Figure 3b. The phantom was subjected to CBCT scanning and the absorbed doses were obtained. The measurements were repeated three times and the data were obtained by averaging them. All the measurement processes were performed under light-emitting diode lights, avoiding the effects of ultraviolet rays. The equivalent dose for each organ was obtained from the absorbed dose multiplied by each calibration factor. The effective dose was calculated as the sum of all equivalent doses and the corresponding tissue-weighting factors (Tables 1 and 2).

Results

The calculation with each one degree in the simulation took approximately six hours in this study, and one set of 360° simulation required at least 2,160 h, or approximately three months per FOV. The estimated organ doses and effective doses from the Monte-Carlo simulations and those from the TLD measured values are listed in Tables 1 and 2 for the large (8 × 8 cm) and small (4 × 4 cm) FOV, respectively. The effective doses of the large and small FOV from the simulations were almost the same as those from the TLD measurements, although there were several differences in the itemized organs.

The data are illustrated in bar graphs as shown in Figure 4, which represent the values as the ratios against each degree. In the simulation of the large FOV (Figure 4a), the differences in values between doses were within ±10%. However, the organ doses of oral mucosa and bone marrow were significantly lower at more than 20°, and the doses in the thyroid, esophagus, and eye lens decreased by less than 10% when the steps were higher than 20° each. However, in the simulation of the small FOV (Figure 4b), the results for the 2–45° steps were within 10%, whereas the organ doses in the salivary, thyroid, oral mucosa and esophagus were low, reducing by 10% every 20°. Therefore, we determined that simulation at 5° and 10° is sufficient for estimating the effective doses using the large and small FOV, respectively.

Figure 4.

The comparison of effective doses by each degree calculations. (a) and (b) are the bar graphs for the large (8 × 8 cm) and the small (4 × 4 cm) field of view, respectively. The data are presented as the ratios against each 1°. The red lines indicate ±10% differences.

Based on these findings, we compared the effective dose using a large FOV versus multiple small FOVs covering the corresponding area, as indicated in Figure 5. We found that six small FOV scans were necessary to cover the same tooth area with one large FOV scanning. The simulations were performed at 10° intervals for small FOVs, and the results are shown in Table 3. The effective dose from six small FOV scans was approximately 1.2 times higher than that of the large one.

Figure 5.

The relationship between the large and the small field of views (FOVs) covering the full teeth area. We set one large and six small FOVs shown in axial (a), sagittal (b), and coronal (c) views.

Table 3.

Simulation results from each 10 degrees assuming full-jaw examination by six times of FOV of 4 × 4 cm and from two degrees one time of 8 × 8 cm

Organ six exams			One exam
	weighting facto	r with 4 × 4 cm	with 8 × 8 cm
Brain	0.01	0.683	0.240
Salivary	0.01	2.098	3.573
Thyroid	0.04	0.002	0.322
OralMucosa	0.12	0.347	0.291
Skin	0.01	0.006	0.139
Oesophagus	0.05	0.028	0.172
BoneMarrow	0.12	0.165	0.191
BoneSurface	0.01	0.120	0.311
EyeLens		0.378	0.255
Pharynx		0.962	3.529
Effective dose [mSv]		0.150	0.122

Discussion

In this study, we performed a Monte-Carlo simulation using a step-and-shoot method to estimate the effective doses in a CBCT examination. The data are shown in Tables 1 and 2, which demonstrate that the effective doses in the small and large FOVs from simulation were almost the same as those from TLD or radiochromic films measurements, which is consistent with previous reports.^{3,4,6–8,11–13,15} However, there were several differences in the itemized organs between the two methods. We consider this to be due to the following potential reasons. (1) Technical problems related to the measurements: A TLD chip or radiochromic films have a direction and energy dependency, and some fluctuation (there is an intra- or interchip difference sensitivity and a measurement needs a certain number of measurement points) to measure the absorbed dose. Hence, the data were generally expressed with standard deviations from a plurality of measurements. Considering 95% confidence intervals, the values would have ± 3.5% and ± 12.0% errors in the large and small FOVs, respectively. Based on this, PHITS specified an isotropic volume of 1 cm³ for this study, which favours data fluctuation to measure the absorbed dose and return one value from the Monte-Carlo simulation. The simulation always returns the same values based on the same random number table, and its reproducibility is expressed as a relative error that can be reduced by increasing the number of histories as necessary. In this study, all the values of relative errors were less than 0.1, which indicates that the calculations were “generally probable”.¹⁸ (2) Handling the Rando phantom: The measurements require careful phantom positioning, but it was sometimes difficult to set the same position in CBCT in three-dimensional directions even using external laser beams. While a PHITS can locate a voxel phantom specifying their coordinates in three dimensions, we can set the phantom to precisely the same place, or it is also possible to fine-tune its position. However, a PHITS must employ the virtual phantom after a conversion from the real phantom by CT, potentially causing differences from partial volume and/or the beam-hardening effect due to technical problems during CT imaging. To minimize this possibility, we used the maximum tube current and lowest pitch as possible for scanning, as indicated in the Materials and Methods. (3) CBCT simulation settings: We employed a relatively simple setting as the point source, the generic X-ray spectrum, and the lead collimation for realizing the real X-ray beam in 3D Accuitomo, as shown in Figure 1. However, we did not simulate the heterogeneity of the X-ray beam as a heel effect, a precise filtering, or continuous X-ray emission status in this study. Morant et al¹¹ simulated an X-ray tube originating from an electron generator colliding with a tungsten target, then bow-tie filtered it, and successfully reproduced the heel effect. Such an X-ray simulation is configurable, but the setting would be more complicated, and the computation time considerably longer. In fact, they needed to employ a high-speed computing device for calculations. This study only employed the prepared point source in PHITS with a generic X-ray spectrum from the textbook and a simple lead collimation set by manually measuring the field size. Hence, it should be noted that the measurements obtained from this simple method matches those obtained in previous studies using conventional TLD measurements. This method has an advantage in that it can be easily expanded to other CBCTs, only changing the tube voltage and tube current, the collimation size and the distance between the focus and subject, and can be performed in a shorter calculation time.

In this study, we attempted to optimize the number of steps and shoot procedures. This concept is important because no study to date has addressed this point in CBCT simulations. Morant et al modeled the iCAT CBCT and while they were able to completely simulate the operation of X-ray irradiation as described above, they employed a pulsed X-ray emission system. Furthermore, the calculations were performed for the number of pulses. Ernst et al¹² modeled 3D Accuitomo 170, which is a continuous X-ray emission type, similar to our study, but they employed the EGSnrc code. This simulator is commercially available with the egs cbct code specified for simulating cone beam CT scans. However, this code is not publicly available as it is still in the experimental stage, and the computation details are not open; hence, the calculation algorithm being used is unknown. Lee et al performed the simulation employing PCMXC, which is also a commercially available software with a very user-friendly graphical user interface and seems to select an angle setting for the calculation, but they did not attempt to consider the steps.²⁰ Therefore, we attempted to tackle this issue and determine optimized calculation numbers employing the step and shoot method. As a result, we determined that a simulation with every 5° and 10° would be sufficient to estimate the effective dose for the large and small FOV, respectively.

The results of this study allowed for the comparison of complicated exposure situations. Here, we compared the effective doses from one large FOV and six small FOVs covering the corresponding area (Figure 5), and they were only 20% of difference at 0.122 and 0.150 mSv, respectively (Table 3). Although the doses were similar, the two situations differed in the clinical sense. Six small FOVs examinations required a six-fold examination time that might be a weak point in hospital management, but they would be advantageous for image quality. This is because the small FOV causes fewer scattered radiations, benefits from magnified projection,²³ and is less susceptible to lower spatial resolution due to location dependencies.²⁴ Therefore, we recommend clinicians select a smaller FOV as much as possible.