Phantom construction and conversion

Currently, the voxel phantom stands as the predominant human anatomy model employed in radiation dose assessment. For precise dose assessment in intricate workplaces, it is vital to produce phantoms that offer adjustable sizes and postures. Such malleable models can be crafted using the Boundary Representation (BREP) geometric definition methods, which can take the form of nonuniform rational B-splines (NURBS), polygon meshes, or a combination thereof. Relative to voxel models, the BREP model offers a broader range of deformation operations. It can represent new anatomical structures for staff or patients even in the absence of comprehensive whole-body image data [23]. For the purpose of this work, all BREP models, which are expressed as polygon-mesh phantoms before final computations, are termed ’polygon-mesh phantom’.

Direct calculations on polygon mesh phantoms are unfeasible. Typically, they are converted into either voxels or tetrahedrons to facilitate particle transport [24, 25]. As of now, THUDose_PD supports two such conversion techniques. However, given that tetrahedralization is not the focal point of this study, only the voxelization process is elucidated.

For the voxel phantom, THUDose_PD can import data in a binary file format. Pertinent files include both a configuration file and binary file. Details, such as phantom’s size, voxel’s resolution, and phantom’s central coordinates, are specified in the configuration file. Each voxel’s value corresponds to a material index within a predefined list, indicating its material classification.

For polygon-mesh phantoms, THUDose_PD offers a transformation procedure, termed voxelization. This method converts a three-dimensional object’s geometric representation into a voxel format that closely mirrors the original. The resulting data captures both the surface and the inner geometric details. For rapid voxelization, THUDose_PD employs OpenGL and utilizes the fragment shader in the rendering process to transition the intersection of triangles and voxels into sampling points. In parallel, computing techniques expedite the voxelization outcomes.

To enhance clinical efficacy, precise radiation dose evaluations based on actual patient CT scans are paramount. To this end, a phantom construction module was developed to load DICOM files, extract HU values, and subsequently transform them into densities and materials for ensuing calculations.

Particle transportation and source definition

The THUDose_PD physical process is based on the THUDose physical model, facilitating the simulation and transport of photons, electrons, neutrons, protons, and heavy ions. The program has predefined the eight irradiation types highlighted in ICRU Publication 95: antero-posterior (AP), posterior-anterior (PA), left lateral (LLAT), right lateral (RLAT), rotational (ROT), isotropic (ISO), superior hemisphere semi-isotropic (SS-ISO), and inferior hemisphere semi-isotropic (IS-ISO). For X-ray radiography, which is prevalent in medical applications, the source has been parameterized. Users simply define the source axis distance, deflection angle, and field size to initiate vertebral tract sampling. In the context of CT, a butterfly filter specific to CT machines was developed to introduce a CT source [26]. Additionally, the program supports phase-space files for radiation field simulations and user-defined source parameters. Beyond these external exposure scenarios, the software offers two methodologies for internal exposure dose assessment: a swift computation approach based on specific absorbed fraction (SAF) values determined via the Monte Carlo algorithm and a more detailed method reliant on the nuclide spectrum.

Dose calculation algorithms

The software offers three calculation modes: external, internal, and environmental external radiation dose assessments [27]. Each mode facilitates computations of organ dose, effective dose, and three-dimensional dose distribution. Organ doses can be directly calculated by utilizing voxels for Monte Carlo transport. Furthermore, to support three-dimensional radiation dose evaluations, THUDose_PD offers both voxel tally and mesh tally modes. In the voxel tally mode, when the input geometry is presented in voxels, the software generates a three-dimensional matrix identical in size to the geometry. It records physical quantities in each voxel grid and saves them in the respective element of the output matrix. This output matrix represents the three-dimensional statistical outcomes of the required physical quantities. Additionally, when there is a discrepancy between geometric and tally resolutions, data can be documented in the mesh tally mode, which derives from the G4MeshKernelRect class.

The calculations for organ and effective doses occur in the dose assessment module, termed as dose postprocessing. The aim here is to ascertain radiation-sensitive organ doses and then compute the effective dose, taking into account the tissue weight factor. Moreover, the software includes dose conversion coefficient computing capabilities, offering a theoretical foundation for radiation protection dose evaluations.

Assessing the dose for the red bone marrow is both vital and challenging in external radiation dose evaluations. THUDose_PD adopts distinct methodologies for dose computations for typical organs and the red bone marrow. For organs excluding the red bone marrow, an average dose methodology is employed, as detailed in Eqs. (1)–(2): $D=\frac{\text{d}\overline{ϵ}}{\text{d}m}\mathrm{,}$ (1) $D_{\text{T}}=\frac{1}{m_{\text{T}}}{\displaystyle {\int }_{m_{\text{T}}}}D\text{d}m\mathrm{,}$ (2) where $\text{d}\overline{ϵ}$ denotes the mean energy imparted by ionizing radiation to matter of mass dm, D denotes the absorbed dose, and m_T denotes the mass of an organ or tissue. These two equations were used to calculate the average absorbed dose of organ T, D_T. Furthermore, THUDose_PD was used to directly count the energy deposition to obtain the absorbed dose of the organs with the exception of the red marrow and endosteum.

For the red bone marrow, THUDose_PD provides three evaluation methods.

Direct method The approach considers the average dose of bones containing red marrow as the representative dose for the red marrow itself, termed as the bone-specific weighted average dose. This is computed as per the following formula, Eq. (3): $D_{\text{RBM}}=\frac{E_{\text{RBM}}}{m_{\text{RBM}}}=\frac{E_{\text{Bone}}\times r_{\text{RBM}}}{m_{\text{RBM}}}$ (3) The variable D_RBM represents the absorbed dose of the red bone marrow, while m_RBM signifies the mass of the red bone marrow. E_RBM and E_bone denote the energy deposits in the red bone marrow and bone, respectively. Lastly, r_RBM stands for the mass ratio of the red bone marrow to the bone.

3CFs-improved method Given that the equilibrium condition between the red bone marrow and trabecular bone is not met in phantoms, the S factor (or KS factor) is employed to calculate the dose of voxelized red bone marrow, termed the 3CFs method. Liu et al. [28] later refined this approach, resulting in the 3CFs-improved method. The absorbed dose D_RMB for the overall red bone marrow is the mass-weighted average of the red bone marrow dose at various locations. The associated formulas are presented in Eq. (4): $\begin{array}{l}{D}_{\text{RBM}}^i=\\ D_{\text{SPA}}^i\cdot \frac{{\displaystyle \int }{\left(\frac{{\mu }_{\text{en}}}{\rho }\left(E\right)\right)}_{\text{RBM}}\varphi \left(E\right)KS\left(E\right)E\cdot \text{d}E}{{\displaystyle \int }{\left(\frac{{\mu }_{\text{en}}}{\rho }\left(E\right)\right)}_{\text{SPA}}\varphi \left(E\right)E\cdot \text{d}E}\mathrm{,}\end{array}$ (4) where $D_{\text{RMB}}^i$ and $D_{\text{SPA}}^i$ denote the absorbed doses of the red bone marrow and spongiosa in bone i, the KS factor adopts the KS data of 44-year-old adults, E and ϕ(E) denote the photon energy and fluence in the spongiosa, respectively. ${\overline{D}}_{\text{RBM}}={\displaystyle \sum _i{R}^i}\cdot D_{RBM}^i$ (5) The final average dose to the total red marrow is provided by Eq. (5), where Ri denotes the ratio of the mass of red marrow in bone i to the total mass of red marrow.

Dose-response function method calculated with dose-response function method [29], as follows, Eq. (6-7): $D\left(r_{\text{T}}\mathrm{,}x\right)={\displaystyle {\int }_E}\text{Φ}\left(E\mathrm{,}{r}_{\text{S}}\mathrm{,}x\right)R\left(r_{\text{T}}\leftarrow r_{\text{S}}\mathrm{,}x\mathrm{,}E\right)\text{d}E\mathrm{,}$ (6) $D_{\text{skel}}\left(r_{\text{T}}\right)={\displaystyle \sum _x\frac{m(r_{\text{T}}\mathrm{,}x)}{m(r_{\text{T}})}}D\left(r_{\text{T}}\mathrm{,}x\right)\mathrm{.}$ (7) Bone-specific absorbed dose per particle fluence (Gy⋅cm²) to red bone marrow and endosteum is a function of particle energy and skeletal region, i.e., $R\left(r_{\text{T}}\leftarrow r_{\text{S}}\mathrm{,}x\mathrm{,}E\right)$ in Eq. (6). The fluence of particles of energy E in the source tissue r_S of bone site x, Φ(E,r_S,x), was simulated by THUDose_PD. The absorbed dose to tissue r_T (red bone marrow) at bone site x was calculated using Eq. (6). Additionally, Eq. (7) is used to obtain the average absorbed dose of red marrow, where m(r_T,x) and m(r_T) denote the mass of tissue r_T at bone site x and the total mass of r_T, respectively.

For internal radiation dose computation, the software offers a quick estimation mode grounded on SAF values alongside a more detailed computation mode. The detailed approach utilizes Monte Carlo simulation, relying on the organ’s nuclide spectrum. This strategy accommodates various models, working positions, and nuclide residence durations, employing the organ nuclide spectrum for the Monte Carlo simulation. Subsequently, the software calculates the equivalent and effective doses committed to the organs irradiated within the phantom. However, given this aspect is beyond the main scope of this research, it will not be extensively discussed here.

Three-dimensional visualization

THUDose facilitates the visualization of geometry and particle trajectories in the ‘wrl’ format, compatible with most three-dimensional software. Moreover, THUDose_PD enhances the three-dimensional visualization module, offering windows in four distinct views: perspective, front, side, and top. This advanced view supports the customization of visible slices and adjusts the displayed dose value ranges. For CAD geometries and polygon-mesh phantoms, THUDose_PD allows imports in the ‘ply’ format and offers the ability to display components in a variety of colors. When it comes to voxel phantoms, THUDose_PD features a display function for binary formats, where each organ can be distinctively showcased using a unique color set. In the realm of dose assessment, it is often pivotal to merge the geometry (or phantom) with the dose distribution, aiding in pinpointing high-dose locations and facilitating radiation risk analyses. THUDose_PD’s visualization module presents a solution that concurrently visualizes both geometry and dose distribution. The integration of isodose lines further aids users in their analyses. Furthermore, while organ doses are often rendered as non-intuitive tables or datasets, THUDose_PD revolutionizes this by offering three-dimensional visualizations of organ doses, enabling the display of specific organs to streamline user comparisons and in-depth analyses.

Benchmark against ICRP publications

The external irradiation benchmarking leveraged insights from ICRP publication 116. This evaluation contrasted dose conversion coefficients for ISO irradiation with monoenergetic photons and AP irradiation with monoenergetic neutrons. The internal irradiation benchmarking drew from the research of Zankl et al. [30, 31], which examined the SAF values of organs when subjected to electron and photon irradiation.

ICRP Publication 116 deduces reference conversion coefficients for both the effective dose and organ-absorbed doses under various external exposure conditions. This is based on the ICRP reference phantoms for both genders. It offers data from external beams of monoenergetic photons, electrons, positrons, and neutrons with configurations such as AP, PA, LLAT, RLAT, ROT, and ISO. In our assessment, the focus was on validating dose conversion coefficients specifically for the ICRP reference male, choosing monoenergetic photons and neutrons ranging from 10 keV to 10 GeV for the process.

Zankl et al. employed the ICRP reference male and the EGSnrc Monte Carlo program to deduce SAF values for photons and electrons, considering varied source organs and target organs. To ascertain the precision of SAF values derived using THUDose_PD, the ICRP reference male served as the basis for calculating the SAF values for electrons moving from the kidney to three distinct organs: the kidney itself, the adrenals, and the liver. The outcomes of this exercise were juxtaposed against Zankl’s findings.

Polygon-mesh phantom voxelization

The polygon-mesh phantom was crafted by demarcating the organ boundaries of the voxel phantom using three-dimensional visualization software. This formed polygon mesh phantom boasts flexibility, allowing adjustments in height, weight, and posture. Once tailored, the modified polygon-mesh phantom was then imported into THUDose_PD for dose calculations by transforming it back into a voxel phantom. Illustrating this with the Chinese polygon mesh reference male phantom (CRAM_S) as a case in point, the steps for voxelization can be seen in Fig. 3.

Fig. 3Full-screen View

Flow chart of the voxelization operation in THUDose_PD.

First, the polygon-mesh phantom was adjusted using the three-dimensional modeling software Rhino to realize the target size and posture. Layers were added and named for each organ. The Python plug-in of Rhino was used to write scripts for batch export based on the polygon mesh phantom in *.3dm form. Then, each organ was exported as an stl file with the same file name as the organ layer, and simultaneously the stl file list was exported, i.e., * .lst text file, in which the file names are sorted from the largest to the smallest organ volume.

Subsequently, preparation of a phantom information file is necessary. This file should detail the index and anticipated weight of each organ. Moreover, during the post-processing phase of dose calculations — particularly when merging residual tissues — it is essential to identify the group to which an organ belongs. This type of information is then saved in a text file, denoted as (*. organmassOrg.txt).

The previously prepared files were then loaded into THUDose_PD. Users can set their preferred voxel size, expressed in millimeters (mm). Once the conversion mode is chosen, the program permits a maximum permissible deviation from the intended organ weight. It is worth noting that all organs are converted in descending order of size. Given this approach, conflicts may arise when smaller-volume organs intersect with larger ones. To address such conflicts, the program offers three resolution methods: overwriting, retaining, and randomizing

overwrite ‘Overwrite’ refers to the region where the conflict occurs is covered by the small volume organ that is converted later.

keep ‘Keep’ denotes that the current conversion result is maintained, and the small volume organ that will be converted later avoids the conflict area.

random ‘Random’ means that in conflict areas, small-volume organs are randomly covered.

The maximum deviation was used to ensure the upper limit of deviation between the voxelized organ mass and expected mass. The algorithm is realized by a loop that combines the corrosion and dilation algorithms. In this study, a polygon-mesh phantom CRAM_S with a height of 170 cm and weight of 63 kg was voxelized. In the THUDose_PD parameter configuration, the voxel resolution is 1.74 mm × 1.741 mm × 1.000 mm, the conversion mode is selected as ’overwrite,’ and the maximum deviation is set to 2%. The results of the output voxel phantom, CRAM, were compared for organ mass and tested for the efficiency of the entire conversion process.

Three-dimensional dose assessment

A three-dimensional depiction of an indoor work environment was evaluated across several layers: the combined visualization of ray traces with geometry, integrated display of phantom files with three-dimensional dose distribution, and independent portrayal of phantom organ doses.

For the ray trace and geometry visualization test, a newborn phantom undergoing radiography was used. This phantom was subjected to a vertebral photon beam in an AP configuration. The distance between the source and the phantom’s back was set at 100 cm, with a radiation field measuring 12.5 cm × 17.4 cm. To examine the integrated visualization of phantoms with three-dimensional dose distributions, and the distinct portrayal of organ doses, an external irradiation scenario was simulated using an isotropic point source. The chosen phantom for this test was a reference Chinese adult male. Positioned directly in front of the phantom was a ¹³⁷Cs point source, emitting energy at 661 keV. The three-dimensional dose distributions and organ doses were concurrently scored and then utilized in the visualization tests