Body-size-dependent phantom library constructed from ICRP mesh-type reference computational phantoms

Figure 1 shows the adult male and female MRCPs that were modified for the construction of the body-size-dependent phantom library. The heights and weights of the MRCPs are consistent with the reference values (i.e. male: 176 cm and 73 kg; female: 163 cm and 60 kg) (ICRP 2002). The MRCPs are in the tetrahedral-mesh format composed of ∼8.2 and ∼8.6 million tetrahedrons for the male and female phantom, respectively. The MRCPs are also given in the polygonal-mesh format for users who are interested in deforming the phantoms; in this case, the male and female phantoms are composed of ∼2.5 and ∼2.6 million triangle facets, respectively. The MRCPs contain 48 organs and tissues with 170 subregions, including all of the target and source regions required for effective dose calculation. The masses of all organs/tissues are matched to the reference values inclusive of blood contents (ICRP 2002, 2016a). Note that the MRCPs in the tetrahedral-mesh format can be directly implemented in general-purpose Monte Carlo codes such as Geant4 (Allison et al 2016), MCNP6 (Goorley et al 2012), and PHITS (Sato et al 2013), which is to say, without the voxelization process conventionally used for other mesh phantoms (Zhang et al 2009, Cassola et al 2010), fully maintaining the advantages of the mesh geometry in dose calculations (Yeom et al 2014, Kim et al 2018). Detailed information on the MRCPs can be found elsewhere (Kim et al 2018).

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Target height–weight grids and ten secondary anthropometric parameters were determined based on various anthropometric data. The height–weight grids were determined using the Continuous NHANES (1999–2014) database (https://www.cdc.gov/nchs/nhanes/index.htm) for adult male and female subjects aged from 20 to 50 years, as considered in the ICRP reference data (ICRP 2002). The determination was conducted by using an approach similar to that of (Geyer et al 2014). The subjects were binned by height increments of 5 cm from the 5th to 95th height percentiles in Gaussian distribution. Each height bin was parsed by weight increments of 5 kg, maintaining at least 10 subjects in each bin to assure statistical significance. The height–weight grids based on the NHANES database cannot cover some Asian people with very small body sizes. Therefore, we considered additional height–weight grids that had been determined based on the 7th Korean National Anthropometric Survey data (http://sizekorea.kr/). Figure 2 shows the determined height-weight grids containing 108 and 104 bins for adult males and females, respectively.

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Ten secondary anthropometric parameters (i.e. sitting height; head height, depth, and breadth; sagittal abdominal diameter; and upper-arm, waist, buttock, thigh, and calf circumferences) were determined by deriving regression equations as a function of height and weight from various anthropometric databases. The equations for the sagittal abdominal diameter and upper-arm, waist, thigh and calf circumferences were derived from the Continuous NHANES (1999–2014) database. The equations for the sitting height and buttock circumference, which are unavailable in the Continuous NHANES (1999–2014) database, were derived from the NHANES III (1988–1994) database. The equations for the head dimensions (i.e. head height, depth, and breadth), which are unavailable in the NHANES databases, were derived from other databases. That is, the data of the PeopleSize 2008 Professional software (https://www.openerg.com/psz/) were used for the head height, and the U.S. Army Anthropometric Survey (ANSUR II) database (Gordon et al 2014) was used for the head depth and breadth. The derived regression equations for all of the parameters are shown in table 1.

Table 1. Regression equations for secondary anthropometric parameters (Y) in centimeters as function of height (X_h) in centimeters and weight (X_w) in kilograms.

Anthropometric parameters	Male				Female
	$a$	$b$	$c$	${R^2}$	$a$	$b$	$c$	${R^2}$
Sitting height	0.3954	—	21.98	0.5937	0.4006	—	20.49	0.5990
Head height	0.05322	—	13.87	0.9977	0.04883	—	13.70	0.9980
Head depth	0.02380	0.01390	14.58	0.1945	0.02811	0.01538	13.35	0.1664
Head breadth	−0.008715	0.01524	15.65	0.1237	0.004085	0.009938	13.43	0.05599
Sagittal abdominal diameter	−0.1430	0.2012	29.97	0.8558	−0.1560	0.2090	30.79	0.8748
Upper-arm circumference	−0.1074	0.2102	34.89	0.8241	−0.1524	0.2599	37.02	0.8775
Waist circumference	−0.4719	0.7801	112.5	0.9011	−0.4100	0.7758	102.1	0.8651
Buttock circumference	−0.1275	0.5531	76.25	0.9033	−0.2088	0.7039	86.78	0.8999
Thigh circumference	−0.1038	0.3122	46.06	0.8188	−0.1102	0.3767	43.79	0.8168
Calf circumference	−0.0336	0.1873	29.09	0.7896	−0.0114	0.2078	24.66	0.7728

$$\begin{equation*}Y = a{X_h} + b{X_w} + c\end{equation*}$$

As an initial step in the construction of the phantom library, 'grid-center' and 'anchor' phantoms were constructed as basis/kernel models to be used for deformation to construct the phantom library (see section 2.4). The grid-center phantoms, representing the body size at the grid center (male: 175 cm and 100 kg; female: 165 cm and 95 kg), were constructed by deforming the MRCPs (male: 176 cm and 73 kg; female: 163 cm and 60 kg) following the body-size deformation procedure established by (Lee et al 2019). The grid-center phantoms were then deformed to construct a set of 10 anchor phantoms for each gender in various body-fat percentages (BF%s), covering all BF%s in the phantom library. For the construction of the anchor phantoms, the body shape of the grid-center phantoms was deformed to change the body weight (i.e. the BF%) while maintaining the standing height and all internal organs and tissues except for the breast adipose tissue. The breast adipose tissue, the amount of which was assumed to be in proportion to the BF, was additionally adjusted following the approach of (Lee et al 2019). The body weight according to the target BF% was determined by using the lean body mass (LBM; the body weight minus the body fat) formulas as a function of standing height and body weight, derived by (Deurenberg et al 1991) and (Frankenfield et al 2001). The anchor phantoms represent a typical body shape in accordance with the BF%, which was confirmed by an anatomist. The constructed grid-center and anchor phantoms are shown in figure 3.

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The grid-center and anchor phantoms were deformed to construct the phantom library. First, among the grid-center and anchor phantoms, one whose BF% is closest to that of the target phantom in the library was selected. The selected phantom was deformed again by using the deformation procedure of (Lee et al 2019). The deformation procedure can be divided into two main steps: (1) phantom scaling to match the target standing height, sitting height, head dimensions (head height, depth, and breadth), and LBM and (2) phantom adjustment to match the target values of all other anthropometric parameters, to redefine the interior skin structures (e.g. the 50 μm thick radiosensitive target layer), and to match the target mass of the breast adipose tissue. The first step (i.e. phantom scaling) can be easily automated, but this is not the case for the second step (i.e. phantom adjustment). (Lee et al 2019) manually conducted the second step to construct 18 percentile-specific phantoms, thus revealing this manual approach to be labor-intensive and time-consuming, which fact makes it indeed practically challenging to construct ∼200 body-size-dependent phantoms. This issue was fully overcome in the present study by developing and using an in-house C++ program for automatic phantom adjustment.

Figure 4 shows the overall workflow of the adjustment program. For an automatic phantom adjustment, the grid-center and anchor phantoms were segmented into eight regions (i.e. head, foot, upper-arm, waist, hip, thigh, calf, and remaining regions), as shown in figure 5. Accordingly, the phantoms scaled from the grid-center and anchor phantoms were also made of eight regions. First, the exterior body surface segmented into the upper-arm, waist, hip, thigh, and calf regions was adjusted to match the target values of the secondary anthropometric parameters (i.e. upper-arm, waist, buttock, thigh, and calf circumferences and sagittal abdominal diameter). For this adjustment, the facets of the body surface were moved by shifting a vertex in the direction averaged over the normal directions of all of the facets that include the shifting vertex. The movement step was empirically determined as one-fifth of the radius deviation between two circles, the circumferences of which were assumed by the phantom's secondary anthropometric parameters and the target values. For each movement, the program checked to determine if there was any intersection between facets, using the Intersection function in the computational geometry algorithms library (CGAL, https://www.cgal.org/). If an intersection was detected, the involved facets were moved back to the previous locations. The movement was repeated until the phantom's secondary anthropometric parameters were matched to the target values within 5% difference. Likewise, the exterior body surface segmented into the remaining regions was adjusted to match the target body weight within 2% difference; the head and foot regions were not adjusted to maintain the standing heights which had been matched during the first step (i.e. phantom scaling). After the adjustment of the exterior body surface, the adjusted surface was replicated to create three additional surfaces. Then, one of the surfaces was uniformly shrunk to redefine the interior skin surface so that the skin mass was matched to the target value within 1% difference. The other two surfaces also were uniformly shrunk to redefine the skin target layer at a depth of 50–100 μm from the exterior body surface. Finally, the breast adipose tissue was enlarged or shrunk to match the target mass within the 1% difference by repeatedly moving the facets of the breast adipose tissue in the manner done for the adjustment of the exterior body surface. The adjustment program took 16.3 to 45.2 h (24.6 h on average) per phantom with one thread of the Intel® Xeon® CPU E5-2698 v4 (@2.20 GHz with 40 cores (two hyper-threads per core) and 256 GB RAM) in CentOS Linux release 7.3.1611 (Core).

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Monte Carlo (MC) dose calculations were performed with some selected phantoms from the developed library for external photon exposures in order to determine the influence of body size on dose calculation. To that end, organ/tissue doses calculated using three male phantoms in different body heights (H165W80, H175W80, and H190W80) were compared to see the dosimetric influence of the body height. Organ/tissue doses calculated using three female phantoms in different body weights (H165W45, H165W65, and H165W140) were also compared to see the dosimetric influence of the body weight. The following describes details of MC simulations, according to the RECORDs guideline (Sechopoulos et al 2018). For the MC dose calculations, the selected phantoms in the tetrahedral-mesh format were implemented in the Geant4 MC code (version 10.04, released in December 2017) (Allison et al 2016) by using the G4Tet class, following the implementation procedure of (Yeom et al 2014). The phantoms were assumed to be in vacuum and irradiated by mono-energetic broad-parallel photon beams in three directions (antero-posterior (AP), postero-anterior (PA), and right-lateral (RLAT)). The beam-energy points considered in ICRP Publication 116 (ICRP 2010), ranging from 10 keV to 10 GeV, were used. The number of primary particles varied from 10⁷ to 10¹⁰ depending on the energies and body sizes to keep statistical relative errors for all the calculated organ/tissue doses below 5%. Variance reduction techniques were not used in the simulations. The photon beams were simulated, via the G4VUserPrimaryGeneratorAction class, by modeling a 100-cm-radius disk source uniformly emitting photons in the normal direction. Figure 6 shows, as an example, the M_H175W80 phantom irradiated by photon beams in the AP and RLAT geometries. The average absorbed doses for six organs and tissues (i.e. red bone marrow (RBM), colon, lung, stomach, breasts, and gonads) having high tissue-weighting factors (≥ 0.08) (ICRP 2007) were calculated. The absorbed doses for all of the organs and tissues except for the RBM were directly calculated using the G4PSEnergyDeposit class. The RBM absorbed doses were calculated using the dedicated scoring class (Yeom et al 2016b) based on the fluence-to-absorbed-dose response functions (DRFs) derived from micron CT images (Johnson et al 2011). Note that the small and complex structure of the RBM could not be explicitly modeled in the MRCPs (Yeom et al 2016b) used for the construction of the phantom library. The physics library of G4EmLivermorePhysics was used to transport photons and secondary electrons with a secondary range cut value of 1 mm. The simulations were performed on the same server computer with the Intel® Xeon® CPU E5-2698 v4 (@ 2.20 GHz with 40 cores (two hyper-threads per core) and 256 GB RAM) in CentOS Linux release 7.3.1611 (Core). The compiler used was GCC 7.2.0.

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Additional MC simulations were performed to calculate the average absorbed doses for six organs and tissues of the male and female phantoms in three different body weights (male: H175W60, H175W90, and H175W130; female: H165W60, H165W90, and H165W130). In order to determine the dose differences between the two libraries, the calculated organ/tissue doses were compared with those produced by (Chang et al 2018) using the corresponding body-size phantoms from the body-size-dependent phantom library developed in collaboration between the University of Florida and the National Cancer Institute (UF/NCI) (Geyer et al 2014).

The body-size-dependent phantom library constructed in the present study is shown in figure 7. The library contains 108 adult male phantoms and 104 adult female phantoms, covering the body sizes of most Caucasian and Asian populations. The male phantoms cover standing heights from 160 to 190 cm and body weights from 50 to 155 kg. The female phantoms cover standing heights from 150 to 175 cm and body weights from 40 to 150 kg. The standing height, sitting height, and head dimensions of the phantoms were matched to the target values within the 0.1% difference. The body weight of the phantoms was matched to the target value within the 2% difference. All of the other anthropometric parameters of the phantoms (i.e. sagittal abdominal diameter and upper-arm, waist, buttock, thigh, and calf circumferences) were matched to the target values within 5% difference. The masses of all of the organs and tissues of the phantoms were automatically determined by the phantom scaling process, except for the skin and breast adipose tissue, the masses of which were matched to the target values within 1% difference.

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The variation in organ/tissue masses for 13 randomly selected organs and tissues (i.e. colon, lungs, stomach, breasts, gonads, urinary bladder, oesophagus, liver, thyroid, brain, salivary glands, skin, and residual soft tissue (RST)) is shown in figure 8 by means of organ/tissue mass ratios to adult male and female MRCPs. Most of the organs and tissues, those located in the trunk, show a similar variation, their ratios ranging from 0.73 to 1.57 for males and 0.72 to 1.66 for females; this is because these organs/tissues were scaled strictly in proportion to the LBM. The variation for the brain is the smallest, its ratios ranging from 0.91 to 1.17 for males and 0.92 to 1.16 for females, which is because the organs and tissues located in the head were scaled in proportion to the head dimensions. The variation of the RST is the largest, its ratio ranging from 0.50 to 4.00 for males and 0.55 to 3.98 for females. Note that the RST mainly consists of adipose tissues, showing the greatest variation depending on the body sizes.

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Figure 9 shows the variation in organ/tissue depths for 11 randomly selected organs and tissues (i.e. colon, lungs, stomach, breasts, gonads, urinary bladder, oesophagus, liver, thyroid, brain, and salivary glands) from the front, back, and right by means of organ/tissue depth differences with respect to adult male and female MRCPs. It can be seen that the organs/tissues of library phantoms are generally located deeper than those of the MRCPs for both the male and female, which is because the MRCPs have smaller body sizes than most phantoms in the library. Several organs/tissues (e.g. colon and urinary bladder) of all or almost all the female library phantoms tend to be especially deeper from the front than those of the female MRCP; this is because significant modifications were made in several body regions of female library phantoms to match the target values of anthropometric parameters. Note that the MRCPs were developed directly from the CT images of individuals, possibly not satisfying target values of anthropometric parameters corresponding to their standing heights and body weights.

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Figure 10 shows the ratios of the organ/tissue doses of M_H165W80 and M_H190W80 to those of M_H175W80 for the AP, PA, and RLAT geometries. For the photon energies >0.1 MeV, the ratios tend to be close to unity (mostly between 0.9 and 1.1), which means that the organ/tissue doses among the three phantoms are generally similar within the 10% differences. Relatively large differences up to 30% can be seen at the gonad doses between M_H165W80 and M_H175W80 for the PA geometry and energies >20 MeV. For the photon energies ⩽0.1 MeV, the ratios for most cases are significantly different from unity, and the differences tend to increase as the photon energy decreases. The ratios between M_H165W80 and M_H175W80 are smaller than unity, which means that the organ/tissue doses of M_H165W80 are lower than those of M_H175W80. In contrast, the ratios between M_H190W80 and M_H175W80 are greater than unity, which means that the organ/tissue doses of M_H190W80 are higher than those of M_H175W80. These results demonstrate that the organ/tissue doses tend to increase as the standing height increases, which can be explained by the fact that the thicknesses of the overlying tissues from the body surface to the organs/tissues tend to decrease with increasing standing height, because the standing height with a fixed body weight is in inverse proportion to the BF%.

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Figure 11 plots the ratios of the organ/tissue doses of F_H165W45 and F_H165W140 to those of F_H165W65 for the AP, PA, and RLAT geometries. For the photon energies ⩽0.1 MeV, it can also be seen that the ratios are significantly different from unity and that the differences tend to increase by up to several orders of magnitude as the energy decreases. The ratios between F_H165W45 and the F_H165W65 are greater than unity, which means that the organ/tissue doses of F_H165W45 are greater than those of F_H165W65. Contrastingly, the ratios between F_H165W140 and F_H165W65 are smaller than unity, which means that the organ/tissue doses of F_H165W140 are lower than those of F_H165W65. These results clearly demonstrate that the organ/tissue doses tend to decrease as the body weight (mainly body fat) increases, due to the increase in the thicknesses of the overlying tissues from the body surface to the organs/tissues. For the energies >0.1 MeV, the ratios are generally in the range from 0.7 to 2, showing that the dose differences are much less significant than those for the energies ⩽0.1 MeV. Interestingly, for the energies >10 MeV, the opposite dose-difference trend due to body weight was observed; that is, the organ/tissue doses tend to increase even though the body weight increased. This can be explained by the fact that such high energy photons tend to create dose build-up regions by deeper depths and, thus, to deliver greater absorbed doses to the deeper-lying organs/tissues of a heavier person.

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Figure 12 plots the ratios of the organ/tissue doses of the phantoms of the same body size (male: H175W60, H175W90, and H175W130; female: H165W60, H165W90, and H165W130) between the MRCP-based phantom library developed in the present study and the UF/NCI phantom library (Chang et al 2018). For the energies >0.1 MeV, the ratios are generally close to unity (mostly between 0.9 and 1.1), meaning that the two libraries provide similar organ/tissue doses for the same body size. Relatively large differences can be seen only for the female breasts, in which the breast doses of the MRCP-based phantoms are greater than those of the UF/NCI phantoms by a factor of about 2 in most cases. For the energies ⩽0.1 MeV, the ratios significantly deviate from unity for most cases, which deviations dramatically increase as the energy decreases by up to several orders of magnitude. That is, the two phantoms, despite having the same body size, provide significantly different organ/tissue doses, which differences are associated with different organ/tissue locations and depths across the different phantom libraries, as stemming from the different original phantoms (MRCPs vs. UF/NCI phantoms). This result raises an important issue: when using the MRCP-based phantom library as well as other existing phantom libraries (Geyer et al 2014, Akhavanallaf et al 2019) for individual dose reconstructions, one should keep in mind that dosimetric uncertainties due to anatomical differences between the phantoms and individuals always exist and would be large, especially for exposure scenarios involving kilovoltage photon beams.

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