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. Author manuscript; available in PMC: 2024 Mar 18.
Published in final edited form as: Biomed Phys Eng Express. 2019 Sep 23;5(6):065002. doi: 10.1088/2057-1976/ab2850

Dosimetric impact of voxel resolutions of computational human phantoms for external photon exposure

Choonsik Lee 1, Andreu Badal 2, Yeon Soo Yeom 1, Keith Griffin 1, Dayton McMillan 1
PMCID: PMC10948017  NIHMSID: NIHMS1950936  PMID: 38500848

Abstract

Several research teams have developed computational phantoms in polygonal-mesh (PM) and/or Non-Uniform Rational B-Spline format, but it has not been systematically evaluated if the existing voxel phantoms are still dosimetrically valid. We created three voxel phantoms with the resolutions of 1,000, 125, and 1 mm3 and simulated the irradiation in antero-posterior geometry with photons of 0.1, 1, and 10 MeV using voxel Monte Carlo codes, and compared the energy deposition to their organs/tissues with the values from the original PM phantom using mesh Monte Carlo codes. The coefficient of variation in energy deposition overall showed about five-fold decrease as the voxel resolution increased but differences were mostly less than 5% for any voxel resolution. We conclude that PM phantoms and mesh Monte Carlo techniques may not be necessary for external photon exposure (0.1 – 10 MeV) and the existing voxel phantoms can provide enough dosimetric accuracy in those exposure conditions.

1. Introduction

Since their introduction in the 1960s, the digital models of human anatomy, called computational human phantoms (Xu 2014), combined with Monte Carlo radiation transport techniques have been actively used for radiation dose calculations in a variety of research fields including radiation protection and medical physics. Computational human phantoms have evolved from simplified stylized (or mathematical) phantoms via voxel (or tomographic) phantoms to hybrid (or boundary representation) phantoms (Xu 2014). The stylized phantoms based on mathematical equations are flexible but not realistic enough to represent complex anatomical human structures, whereas the voxel phantoms based on tomographic radiological images are anatomically realistic but cannot be flexibly modified due to the nature of voxel structure (i.e., 3D number matrix). Those limitations of the previous phantoms are overcome by the latest hybrid phantoms (Lee et al 2010, Geyer et al 2014, Segars et al 2013, Xu et al 2007, Lee et al 2007, Sun et al 2013, Kim et al 2011a, Zhang et al 2009). The hybrid phantoms are developed using radiological images, just like voxel phantoms, but their anatomical structures are modeled by polygonal-mesh (PM) and/or Non-Uniform Rational B-Spline (NURBS) surfaces.

Hybrid phantoms have two major advantages over the previous stylized or voxel phantoms due to the unique formats. First, the hybrid phantoms are so flexible that the dimension and shape of their organs and whole body can be easily deformed (Lee et al 2008, Su et al 2012, Cassola et al 2010, Vazquez et al 2014). Therefore, it is possible to adjust organ volume or body dimension to match reference data. Second, the surface format makes it possible to model very thin radiosensitive layers within human anatomy, which cannot be easily modeled in voxel phantoms due to the limitation of voxel resolution. Several studies have reported the results of organ and tissue dose comparison between voxel and hybrid phantoms and highlighted dose difference for external and internal radiation in some exposure scenarios (Yeom et al 2013, Nguyen et al 2015, Yeom et al 2016). The International Commission on Radiological Protection (ICRP) has been converting the previous ICRP reference adult male and female voxel phantoms (ICRP 2009) into PM format for more accurate dosimetry calculations (Kim et al 2018).

However, hybrid phantoms are not always compatible with the existing Monte Carlo radiation transport codes (Kainz et al 2019). Hybrid phantoms in NURBS format cannot be combined with Monte Carlo codes, while hybrid phantoms in PM format can be imported into only a few Monte Carlo codes such as penMesh (Badal et al 2009), Geant4 (Allison et al 2016), and MCNP6 (Goorley et al 2012). In addition, computational efficiency for tracking the radiation propagation in PM geometry is much lower than in voxel geometry (Kim et al 2011b). Although the efficiency can be significantly improved by converting PM phantoms to tetrahedral mesh (TM) format (Yeom et al 2014), a large amount of computer memory is required and only few Monte Carlo codes such as Geant4 and PHITS (Sato et al 2018) can handle the TM geometry (Yeom et al 2019). In contrast to hybrid phantoms, voxel phantoms are compatible with most Monte Carlo radiation transport codes. Therefore, it is common practice to convert hybrid phantoms into voxel format before performing Monte Carlo simulations. The voxelization process discretizes the anatomy into a uniform 3D grid of voxels, of which size determines the resolution of the resulting voxel phantoms. Smaller voxels reproduce the original anatomy with better fidelity than larger voxels but require more computer memory and longer simulation time. Even though voxel size is essential to the accuracy of the simulation results and the required computational resources, there are no guidelines established on the selection of the optimal voxel size for different dosimetry applications.

The current study was intended to evaluate dosimetric performance of voxel phantoms with different voxel resolutions by comparing the dosimetry results from voxel and PM versions of an adult male hybrid phantom exposed to external photon beams. We created three voxel phantoms consisting of cubic voxels with the voxel resolutions of 1,000, 125, and 1 mm3 and simulated the irradiation in antero-posterior (AP) geometry with monoenergetic photons of 0.1, 1, and 10 MeV using a voxel Monte Carlo radiation transport code. We compared the energy deposition to major organs and skeletal sites from the three voxel phantoms with the values calculated from the original PM phantom using a mesh Monte Carlo radiation transport code.

2. Materials and Methods

2.1. Adult male hybrid phantom

We adopted the adult male hybrid phantom developed in collaboration between the University of Florida and the National Cancer Institute (NCI) (Lee et al 2010, Hurtado et al 2012). The phantom was developed from the head computed tomography (CT) images of an 18-year-old male patient and the torso CT images of a 36-year-old male patient, which was then combined with the arm and leg models developed from the CT images of an 18-year-old male patient. The organ volume and body dimension were adjusted to match the reference data from the ICRP Publication 89 (ICRP 2002, p 2002). The organs and tissues in the phantom are described by using NURBS format except for skeletons made of PM format. To conduct the current study, we converted the NURBS-format organ models into PM format for mesh Monte Carlo simulations, and then voxelized (Lee et al 2007) the PM phantom into three voxel phantoms with the voxel resolution of 1,000, 125, and 1 mm3, each voxel represented by a cube with the dimension of each side, 10, 5, and 1 mm.

2.2. Monte Carlo radiation transport

Monte Carlo radiation transport simulations in the three voxel phantoms were conducted using a general purpose Monte Carlo code, MCNPX2.7 (Pelowitz 2011). Assuming that charged particle equilibrium would be broken for thin walled organs at the photon energies greater than 1 MeV, we tracked the secondary electrons not relying on kerma approximation scoring for all energies.

Radiation transport within the PM phantom was performed using a triangle mesh geometry-based Monte Carlo code, penMesh (Badal et al 2009). penMesh is an extension of the penEasy (Sempau et al 2011) code, and is based on the PENELOPE (Sempau et al 1997, Salvat et al 2015) x ray and electron atomic interaction physics library. While penEasy can track radiation in a geometry described by voxels and analytic quadric surfaces, penMesh tracks radiation across objects described by triangle meshes. An octree data structure is used in penMesh to efficiently sort the triangles in space and minimize the number of ray-triangle intersections that need to be checked at every step of the simulation. Because of the octree structure, the number of meshes in the phantom and the size of the triangles in the meshes (mesh resolution) do not substantially affect the simulation time.

Before comparing the results from MCNPX and penMesh, we checked if the physics models in the two Monte Carlo codes make a difference in the dosimetry results. Since penMesh cannot read voxel phantoms and MCNPX cannot read PM phantoms, we adopted the penEasy (Sempau et al 2011) code which is based on the same physics model built in penMesh. Energy deposition (MeV/photon) was calculated for the three voxel phantoms with the resolution of 1,000, 125, and 1 mm3 exposed to 0.1, 1, and 10 MeV photons in AP geometry using the two Monte Carlo codes, MCNPX and penEasy. A total of 108 photons were launched in each simulation to reduce statistical relative errors to less than 1% for all organs and bone sites.

2.3. Comparison of energy deposition

We calculated energy deposition (MeV/photon) to major organs and trabecular bones in the three voxel phantoms using MCNPX2.7 and the PM phantom using penMesh exposed to photons with the energies of 0.1, 1, and 10 MeV in AP irradiation geometry. Broad parallel photon beams were generated to fully cover the whole body of the phantoms. For the comparison of energy deposition between the voxel and PM phantoms, we categorized major organs into two groups based on their volumes: between 300 – 2,000 cm3 (brain, heart, kidney, liver, and lung) and between 100 – 300 cm3 (pancreas and spleen). We included the tissue distributed across the whole body (muscle) and walled organs (colon wall, small intestine wall, and stomach wall) in the comparison. We also compared energy deposition to trabecular region. Trabecular bones are covered by thin cortical bone layers in the PM phantom, but these layers may not be fully represented in the voxel phantoms, especially the ones with lower voxel resolutions (e.g., 1,000 mm3). We reported the energy deposition to the following major bone sites each of which contains more than 10% of total active bone marrow (ICRP 2002): cranium, ribs, vertebra, sacrum, os coxae, and upper femurs.

3. Results

3.1. Voxel and PM phantoms

Figure 1 shows the perspective views of the three adult male voxel phantoms with the voxel resolutions of 1,000, 125, and 1 mm3, and the adult male PM phantom. The voxel phantoms contained 371,246, 2,609,334, and 300,590,640 voxels for the resolutions of 1,000, 125, and 1 mm3, respectively. The smooth appearance of the PM phantom (Figure 1d) is decreasingly preserved in the voxel phantoms with lower resolutions.

Figure 1.

Figure 1.

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Perspective views of the adult male voxel phantoms with the voxel resolutions of (a) 1,000 mm3, (b) 125 mm3, and (c) 1 mm3, and (d) the original adult male PM phantom before voxelization.

Transversal views at the level of the liver, stomach, and spleen of the voxel and PM phantoms are shown in Figure 2. It is noted that as the voxel resolution decreases from 1 mm3 to 1,000 mm3, the walled organs and cortical bone layers become disconnected and show holes.

Figure 2.

Figure 2.

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Transversal views of the adult male voxel phantoms with the resolutions of (a) 1,000 mm3, (b) 125 mm3, and (c) 1 mm3 used for MCNPX, and (d) the PM phantom used for penMesh with major organs and tissues indexed.

Figure 3 shows the percent difference of the organ and trabecular bone volumes between the three voxel phantoms at different resolutions (1,000, 125, and 1 mm3) and the PM phantom. We used the organ and tissue volumes of the PM phantom as reference and calculated the percent difference as (voxel/mesh – 1) × 100. The voxel phantom with the lowest resolution (1,000 mm3) over- or under-estimates the organ volumes of the PM phantom by up to 4% (heart) but the difference is reduced down to 2% for all organs in the 125 mm3 resolution voxel phantom. The 1 mm3 voxel phantom shows agreement less than 0.5% for all organs. The cortical bone volumes show a similar trend of reduction in differences as the resolution of the voxel phantoms increases (Figure 3b). Cranium cortical bone, for example, shows the difference of −32% in the 1,000 mm3 voxel phantom, which was reduced down to 4% in the 1 mm3 voxel phantom.

Figure 3.

Figure 3.

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Percent difference of the volumes of (a) major organs and tissues and (b) cortical bones between the three voxel phantoms with different resolutions (1,000, 125, and 1 mm3) and PM phantom. Note that the difference for spleen, os coxae and upper femur at the lowest resolution was zero. Percent difference (%) = (voxel/mesh - 1) × 100.

3.2. Comparison of physics models between MCNPX and penMesh

The number of photon histories processed per second in voxels were 6.4x104, 3.3x104, and 1.3x104 in MCNPX and 3.5x104, 3.4x104, and 2.5x104 in penEasy, for 1000, 125, and 1 mm3 resolutions at 10 MeV, respectively. As a reference, the corresponding penMesh simulations ran at 4.0x104 histories/sec. We used the penEasy results as reference and calculated percent difference as (MCNPX/penEasy −1) × 100. The percent differences between the two codes for the three voxel phantoms with the resolution of 1,000, 125, and 1 mm3 were −0.28%, −0.09%, and −0.06%, respectively, when averaged over the organs and all photon energies. As an example, Table 1 tabulates the percent difference in organ energy deposition between MCNPX and penEasy for 1 MeV photon. The percent differences for the 1,000, 125, and 1 mm3 voxel phantoms averaged across the organs are −0.4%, −0.4%, and −0.3%, respectively. We confirmed that the difference caused by the two physics models in MCNPX and penMesh is less than 0.3% on average. This result is consistent with the findings in the AAPM Report 195 (Sechopoulos et al 2015), which reported a 0.8% difference between MCNPX and PENELOPE in organ dose estimation in a computed tomography examination (case 5) with a 120 kVp x ray source.

Table 1.

Percent difference* in organ energy deposition between MCNPX and penEasy calculated for the three voxel phantoms exposed to 1 MeV photon in antero-posterior irradiation geometry.

Organs Voxel resolution (mm3)
1,000 125 1
Muscle −0.71% −0.76% −0.74%
Brain 1.45% 0.09% −0.86%
Heart −2.57% −0.97% −0.08%
Kidney −0.08% −0.66% 0.13%
Liver 0.62% 0.36% 0.58%
Lung −1.60% −0.75% −1.07%
Pancreas 1.18% −1.47% −1.38%
Spleen 1.15% 1.28% 1.98%
Colon Wall −1.60% −0.63% 0.49%
Small Intestine Wall −0.81% 0.12% −1.60%
Stomach Wall −1.34% −1.05% −0.77%
Average all organs −0.39% −0.40% −0.30%
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*

Percent difference (%) = (MCNPX/penEasy – 1) × 100

3.3. Comparison of energy deposition between voxel and PM phantoms

Table 2 shows the differences in energy deposition between the three voxel phantoms and PM phantom for the organs and tissues in different categories. The differences overall decreased as the voxel resolution increased. Figure 4 shows the ratio of energy deposition in the 1,000, 125, and 1 mm3 resolution voxel phantoms to those in the PM phantom for 1 MeV photons in (a) the distributed tissues, small and large organs, (b) walled organs, and (c) trabecular bones. As shown in Figure 4a, the coefficient of variation (COV) across the organs decreases from 4.4% to 1.4% when the voxel resolution increases from 1,000 mm3 to 1 mm3. The 1,000 mm3 voxel phantom underestimates the energy deposition in the muscle of the PM phantom by 10% but the difference reduces to about 2% when the voxel resolution is increased to 1 mm3. All organs overall show the similar trend while the difference is mostly within 5%. In case of the walled organs (Figure 4b), COV decreases from 4.2% to 0.5% as the voxel resolution increases. Comparison for the energy deposition in trabecular bones (Figure 4c) shows that COV reduces from 6.8% (1,000 mm3 resolution) to 5.6% (1 mm3 resolution).

Table 2.

Difference in energy deposition between the voxel (1000, 125, and 1 mm3 resolutions) and PM phantoms for distributed tissue, large organs, small organs, walled organs, and major trabecular bones for the photon energies of 0.1, 1, and 10 MeV.

0.1 MeV 1 MeV 10 MeV
Category Organs 1000 125 1 1000 125 1 1000 125 1
Distributed Muscle 0.888 0.938 0.963 0.897 0.955 0.983 0.936 0.989 1.006
Large Brain 0.990 0.966 0.960 1.026 1.005 0.992 1.023 1.015 1.002
Heart 1.049 1.001 0.998 1.030 1.013 1.011 1.057 1.010 1.019
Kidney 0.973 0.986 0.981 0.979 0.987 0.998 1.009 1.005 1.011
Liver 1.006 1.003 1.006 1.006 0.998 1.003 1.023 1.016 1.012
Lung 0.951 0.962 0.964 0.982 0.993 0.991 0.985 0.994 0.985
Small Pancreas 0.982 0.981 0.997 1.023 0.988 0.985 1.009 1.005 1.014
Spleen 1.018 1.015 1.023 0.991 1.007 1.023 1.042 1.039 1.045
Walled Colon W 0.976 0.983 0.989 0.986 1.015 1.015 1.009 1.020 1.023
SI W 1.013 0.963 0.991 1.055 1.021 1.004 1.038 0.990 1.001
Stomach W 0.938 0.965 0.992 0.978 1.004 0.996 0.970 1.001 1.040
Skeleton Cranium 1.112 1.332 1.311 0.914 1.123 1.114 0.923 1.157 1.153
Ribs 1.083 0.973 0.954 1.095 0.995 0.982 1.095 0.995 0.982
Vertebrae-T 0.960 0.884 0.933 0.994 0.943 0.978 0.994 0.943 0.978
Vertebrae-L 0.827 0.928 0.886 0.911 1.004 0.999 0.911 1.004 0.999
Sacrum 0.755 0.770 0.741 1.000 0.980 0.935 1.000 0.980 0.935
Os Coxae 0.861 0.886 0.883 0.930 0.983 0.994 0.930 0.983 0.994
Upper femur 0.859 0.866 0.861 0.943 0.976 0.967 0.943 0.976 0.967
Average difference 4.22% 3.32% 3.15% 1.44% 0.06% 0.17% 0.57% −0.68% −0.92%
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Figure 4.

Figure 4.

Figure 4.

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Comparison of energy deposition between the voxel and PM phantoms for (a) distributed tissue (muscle) and small/large organs, (b) walled organs, and (c) major trabecular bone.

4. Discussion

Several research teams have developed computational human phantoms in polygonal-mesh (PM) and/or Non-Uniform Rational B-Spline (NURBS) format (Xu 2014), but it has not been systematically evaluated if the existing voxel phantoms with various voxel resolutions are still dosimetrically valid for some irradiation scenarios. The current study was intended to evaluate the dosimetric impact of different voxel resolutions in the adult male voxel phantom by comparing their energy deposition for external photon beams with the values calculated for the same phantom in a PM format.

As expected, we observed the original smooth appearance in the PM phantom is not well preserved in lower resolution voxel phantoms (Figure 1 and Figure 2). Nevertheless, the voxelization process (Lee et al 2007) faithfully preserved the original volume of the organs and tissues so that the overall volume difference for major organs was within 4% (Figure 3a), whereas very thin layer such as cortical bones show greater difference over 30% in lowest voxel resolution (Figure 3b). Note that most of the existing voxel phantoms (Xu 2014) have resolutions between the 1 and 100 mm3; for example, the voxel resolution of the early voxel phantoms such as Golem (Zankl and Wittmann 2001) and KORMAN (Lee and Lee 2004) were 34.6 mm3 and 40 mm3, respectively. The comparison results in the current study are applicable to most voxel phantoms available to date.

We reported that the finer voxel resolution overall decreases difference in energy deposition between voxel and PM phantoms (Figure 4). Nevertheless, the difference in energy deposition is less than 5% in case of the voxel phantom with the resolution of 125 mm3, which is courser than voxel phantoms commonly used in practical applications. This small change in energy deposition is consistent with the small change in total organ volume reported in Figure 3. Note that the organs in the phantom are defined as a uniform material, and the inaccuracy introduced by the voxelization process affects only the small part of the organ boundary, not necessarily the total volume. If the organ volume is preserved after voxelization, and the thickness of the organ is much larger than a voxel, it is reasonable that the total energy deposition in the organ will be similar at different resolutions (for very small organs, such as the eye lens, the voxel size needs to be small enough to preserve the volume). As reported in Table 2, the energy depositions for 125 mm3 are very similar to 1 mm3, within ±1% of the difference to the mesh results for most organs. Figure 4c suggests that active bone marrow dose derived from the energy deposition to the trabecular bone sites in the voxel phantoms will not significantly over- or under-estimate the PM phantom-based values. We conclude that the existing voxel phantoms and voxelized versions of the hybrid phantoms coupled with voxel-based Monte Carlo codes can provide sufficient dosimetric accuracy for external photon exposure scenarios (0.1 – 10 MeV energy range) typically encountered in radiation protection applications.

The current study has the following limitations. First, the results are only valid for external photon beams and not necessarily for other radiation types such as electrons, which are reported to produce more prominent difference between voxel and PM phantoms (Yeom et al 2016). We are currently working on the systematic comparison for external electron beams as a follow-up study. Second, in the current study, the dose to the walled organs was measured over the whole thickness of the walls, which are simplified models of the thin layers defined in the ICRP Publication 89 (ICRP 2002) as radiosensitive. However, it may be more meaningful to investigate the impact of voxel resolution on dose to very thin radiosensitive layers (e.g., 50 micro-meter-think skin target layer) when an internal radiation source is distributed inside the organ contents. It is impossible to describe such a thin layer using even the finest voxel resolution used in the current study, 1 mm3. PM phantoms may be uniquely beneficial in the case of thin radiosensitive layers. Finally, we conducted the current study for the AP irradiation geometry and the adult male phantom as a representative exposure case, assuming that the general tendency of the dosimetric influence by the different voxel resolutions observed in the representative case should be similar in other idealized irradiation geometries although the degree of the influence might be somewhat different. Based on the organ depth distribution from the body surface (Griffin et al. in preparation), we found that the depth distributions for the organs we adopted in the current study are similar between AP and PA (between 3 and 20 cm) but they are different from those for RLAT and LLAT (between 3 and 40 cm). More investigation may be required for lateral irradiations, but our findings are considered valid at least for PA geometry.

5. Conclusion

In the current study, we evaluated the dosimetric impact of three different voxel resolutions in the adult male voxel phantom by comparing the energy deposition to major organs and tissues in the phantoms for external photon beams with the values from the same phantom in a PM format. This is one of few studies that systematically quantified the dosimetric errors induced by the voxel phantoms with various voxel resolutions. We conclude that PM phantoms combined with mesh Monte Carlo radiation transport techniques may not be necessary for external photon exposure scenarios (0.1 – 10 MeV energy range) and the existing voxel phantoms can provide enough dosimetric accuracy in those exposure conditions. Future works include the extension of the analysis to external electrons and internal dosimetry of thin radiosensitive layers. It would be also informative to investigate the dosimetric impact of different voxelization algorithms especially in coarse resolution voxel phantoms.

Acknowledgement

This research was funded by the intramural research program of the National Institutes of Health (NIH), National Cancer Institute, Division of Cancer Epidemiology and Genetics. The contents are solely the responsibility of the authors and does not necessarily represent the official views of the NIH. This work utilized the computational resources of the NIH High-Performance Computing Biowulf cluster (http://biowulf.nih.gov).

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