Assessment of doses from incorporated bone-seeking radionuclides plays an essential role in predicting radiogenic risks for individuals residing in contaminated areas. Strontium isotopes are among the most common of these radionuclides, which can be released into the environment both through global fallout and other technogenic radiation incidents. ⁹⁰Sr is a long-lived, bone-seeking, beta-emitting radionuclide; its accumulation in bone tissue leads to chronic irradiation of the red bone marrow (RBM), thereby increasing the risk of developing leukemia [1–4].

Assessment of doses from strontium isotopes involves the use of biokinetic and dosimetric models. A biokinetic model was previously developed at the Ural Scientific and Practical Center for Radiation Medicine (Russia).1 This model simulates the transport processes of Sr within the body; the output of this model is the specific activity of Sr in bone tissue. The dosimetric model enables calculation of dose conversion factors (DF) from the specific activity of the radionuclide in bone tissue to the absorbed dose rate in RBM (Gy/s) [5]. Such models are developed based on the creation of computational phantoms, representing 3D models that simulate the spatial arrangement and composition of media in which radiation transport will subsequently be simulated. Developing such phantoms for beta-emitters is a challenging task due to the necessity of adequately describing both the linear dimensions of bones and their microstructure.

Modern phantoms used for the internal dosimetry of strontium are based on the analysis of medical images of human skeletons2 [6–10]. Consequently, such phantoms have a significant limitation for their use in cohort studies. Indeed, due to the limited amount of autopsy material, they do not allow for the assessment of uncertainties associated with the variability of skeletal dimensions and microarchitecture within a population.

An alternative approach consists in the parametric method of stochastic modeling of bone structures, referred to as stochastic parametric skeletal dosimetry (SPSD) modeling [11]. This approach, developed at the Ural Scientific and Practical Center for Radiation Medicine (Russia), estimates the phantom parameters based on published bone measurement results rather than using medical images. The extensive body of literature enables assessment of the variability in skeletal characteristics within a population and the associated DF variability.

Previous publications [12–16] were the first to present the parameters of skeletal phantoms for newborns, one-year-old, 5-year-old, and 10-year-old children, as well as for adult males and females. The skeletal regions with active hematopoiesis are identical in 15-year-olds and adults. Furthermore, many skeletal regions in 15-year-old individuals are similar in shape and microstructural characteristics to those in adults. For this reason, phantoms for 15-year-old male and female adolescents were developed based on adult phantoms; in other words, some parameters for 15-year-old phantoms were set equal to those for adults. Similar to adults, sexual dimorphism assessment is also important for 15-year-olds. Thus, this our study represents a new stage in the development of computational phantoms for different age groups.

In this work, we aim to develop computational phantoms of the skeleton for 15-year-old male and female adolescents for assessing doses in RBM from incorporated beta-emitting radionuclides.

The stages of phantom development did not differ from those for other age groups [11]. The primary stage involved identifying the modeling objects, i.e., skeletal regions with active hematopoiesis, and estimating the mass fraction of RBM in each such a region. Subsequently, linear dimensions and bone microstructural characteristics were estimated based on literature data. Following this, each modeled skeletal region was subdivided into smaller parts. A computational phantom was generated for each such a part.

The RBM mass fraction in various skeletal bones was estimated based on published data [17]. Within the SPSD approach, not the entire skeleton is modeled, but only its regions containing RBM. This rule also applies to individual bones; that is, only their parts containing RBM were modeled. Accordingly, based on MRI study results [18–23], the distribution of RBM within the bones was assessed.

The phantom parameters for 15-year-old male and female adolescents, similar to those for other age groups, included average values of bone microstructural parameters, i.e., trabecular thickness (Tb. Th.), mean trabecular separation (Tb. Sp.), and the bone volume fraction (BV/TV) [24]. Bone and segment dimensions, as well as cortical bone layer thickness (Ct. Th.), were also phantom parameters. We estimated all these parameters based on measurement results obtained using histomorphometry and micro-computed tomography (micro-CT) and published in the respective literature.

Literature data were collected and analyzed according to a previously described methodology [24]. The parameters of the adult male and female phantoms [16] were used for those skeletal regions for which no published data were found. Measurement results from bones of Caucasians and Mongoloids were included in the analysis, given that these ethnic groups are representative of the Ural region for the age range of 13–17 years.

Bone microarchitecture parameters were estimated using the published data obtained by histomorphometry and micro-CT. Cortical bone thickness was assessed based on published measurement results obtained using CT, micro-CT, and micrometer gauges. Linear bone dimensions were estimated from published measurement results utilizing anatomical boxes, ultrasonography, radiographic studies, and CT.

In the absence of sexual dimorphism in the studied bone characteristics, datasets for both sexes were pooled. In such cases, the bone segment was modeled independently of sex. In other instances, phantoms for different sexes were modeled separately.

Each skeletal region with active hematopoiesis was subdivided into smaller parts — segments. All segments feature homogeneous bone microarchitecture and cortical layer thickness and are described by simple geometric shapes [25]. A basic phantom bone segment (BPS) was modeled for each segment. The segmentation was performed such that each segment possessed a homogeneous microarchitecture and a homogeneous cortical layer thickness. For BPSs represented by elongated cylinders or elongated/flat rectangular parallelepipeds, only the portion of BPS whose maximum linear dimensions reached 30 mm was modeled. Further increasing the maximum size of such a BPS does not affect the DF [26]. Thus, segmentation permits accounting for heterogeneous microarchitecture and cortical thickness within a bone, reduces the size of the phantoms (thereby enabling higher resolution), and improves simulation accuracy.

The density and chemical composition of the modeled media (mineralized bone and bone marrow) were identical for all BPSs and were estimated based on literature sources [27][28]. The generation of BPSs was performed using the Trabecula software application developed in our laboratory [29]. A BPS consists of three media: bone marrow (BM) — the target tissue, as well as cortical bone (CB) and trabecular bone (TB) — two separate source tissues.

Trabecular bone was modeled as a 3D network of bone strands — trabeculae — whose spatial arrangement and thickness were randomly selected within the bounds of bone microarchitecture parameter variability estimated from published data [30–34]. Bone marrow is located in the spaces between the trabeculae, and cortical bone (CB) encases the trabecular bone (TB) externally as a continuous layer with a specified thickness. The voxel size for each BPS was adjusted such that it did not exceed 70% of Tb. Th. and ranged within 50–140 μm [29]. The volumes of the media comprising the phantom were calculated in the Trabecula software.

Phantoms created using the SPSD approach enable the assessment of DF uncertainties associated with the variability of skeletal characteristics within a population. For this purpose, sets of supplementary phantoms of bone segment (SPS) were modeled for each BPS. While the BPS was modeled with average parameter values, the parameter values for the SPS were randomly sampled within the boundaries of the minimum and maximum measured values of their variability. The method for uncertainty assessment was described in detail in [35].

Skeletal regions with active hematopoiesis in a 15-year-old adolescent, bone segmentation, and cross-sections of individual segments using the clavicle as an example are presented in the figure.

Figure prepared by the authors

Fig. Skeletal regions with active hematopoiesis for a 15-year-old male adolescent and their segmentation illustrated using the clavicle: (a) skeleton of a 15-year-old (regions modeled with active hematopoiesis are highlighted in blue); (b) clavicle (bone segments are outlined by dashed lines); (c) diagram of bone division into basic phantoms of bone segments (BPS) and their linear parameters; (d) BPS of the clavicle in voxel representation, cross section (voxels simulating mineralized bone are shown in black, bone marrow is shown in white)

The set of skeletal regions with active hematopoiesis for 15-year-olds did not differ from that for adults; however, there are differences in the RBM distribution among these regions, as demonstrated in Table 1.

Table 1 shows that the skeleton of 15-year-olds comprises 12 skeletal regions with active hematopoiesis, with the RBM mass fraction ranging 1.0–18.6%. No sexual dimorphism was observed in the RBM distribution within the skeleton.

The elemental composition of the modeled media is equivalent to that in adults [16] and was estimated based on published data [28]. We used the measurement results published for the density of the cortical bone layer in 15-year-olds [27] as the density for both CB and TB (1.85 g/cm³). The BM density was assumed to be 1.0 g/cm³ [28].

No significant sexual dimorphism was found in bone microarchitecture characteristics [26]; therefore, data from males and females were pooled. Table 2 presents the microarchitecture parameter values for the BPS of 15-year-old male and female adolescents.

The variability ranges of bone microarchitecture parameters within a bone were used to set the characteristics of the 3D trabecular network model, thereby enhancing its realism. For 15-year-old adolescents, no such variability values were found; therefore, these values were assumed to be the same as for adults [36].

The linear dimensions and cortical layer thickness adopted for the BPS of 15-year-old male and female adolescents are presented in Table 3. The data sources used to obtain these parameters are presented in [24].

Unlike bone microstructural parameters, the linear dimensions of several bones depend on sex; therefore, their dimensions were estimated separately for males and females. The SPSD phantoms of the skeleton for 15-year-old male and female adolescents consist of 46 BPSs, of which 14 segments are specific to males, another 14 are specific to females, and 32 segments were modeled identically for both sexes, as shown in Table 3. The sacrum was the most segmented skeletal region with active hematopoiesis. It comprised 10 BPSs, while a single BPS was used to model both the humerus and the skull.

The basic phantoms of bone segments (BPS) for a 15-year-old adolescent are mostly shaped as cylinders or rectangular parallelepipeds. Their dimensions ranged 3.5–66 mm. Sexual dimorphism is characteristic of many BPSs, with the greatest differences observed in the inferior part of the superior pubic ramus, at the level of 66%. The cortical bone layer of the modeled phantoms ranged from 0.3 mm (cervical vertebral bodies) to 2.3 mm (proximal end of the femur). BV/TV varied 12–52%, trabecular thickness ranged 0.1–0.29 mm, and the trabecular separation was 0.45–1.4 mm (Table 4).

The population variability of individual linear phantom dimensions ranged from 3% (cervical vertebral bodies) to 36% (inferior pubic ramus), with an average of 30% across all dimensions of all BPSs. The greatest variability in the cortical bone layer thickness was estimated for the sternum — 44%, while the smallest was for the cervical vertebral bodies — 3%. On average, the variability of Ct. Th. was 27%. For microarchitecture parameters, this indicator ranged from 6% to 42%. The volume of the generated SPSs ranged 23–264% of the BPS volume.

We used approximately 100 literature sources describing bone samples (> 5000) from 4592 individuals [24] to estimate the parameters of phantoms for 15-year-old male and female adolescents. A total of 197 parameters characterizing linear dimensions and 138 parameters characterizing the microstructure of the skeletal bones were evaluated to construct these phantoms. As mentioned earlier, some parameters for the phantoms of 15-year-old male and female adolescents were set equal to those for adults, specifically microarchitecture parameters for the clavicle, ribs, scapula, skull, cervical vertebrae, and sternum, as well as linear dimensions for the femoral neck, humerus, pelvic bones, and ribs.

By the age of 15, ossification processes are complete in many skeletal regions, and these regions were modeled using the same set of segments as for adults, although with different parameters. These include the femur, humerus, pelvic bones, sacrum, skull, ribs, and scapula. On the other hand, some skeletal regions modeled for adults were not modeled for 15-year-olds, such as the articular processes and arches of the thoracic and lumbar vertebrae. Consequently, the skeletal phantom for 15-year-old male and female adolescents consists of a smaller number of segments than adult phantoms, but a greater number than phantoms for younger children.

The RBM distribution in 15-year-olds is similar to that in adults; however, the RBM fraction in the vertebrae is greater in adults than in 15-year-olds, while the RBM fraction in the femur and humerus is, conversely, smaller.

The BV/TV for the BPS of 15-year-olds averages 20%, which is slightly higher than that for adults (17.3%). Age-related changes in Tb. Th. are insignificant, whereas Tb. Sp. for 15-year-olds is 18% lower than for adults. Table 4 presents a comparison of the media volumes within the BPS for 15-year-old male and female adolescents, as well as for adult males and females.

Due to their smaller linear dimensions, the total volume of the BPS for 15-year-old adolescents is 21% less than that for adults. The sexual dimorphism in the average BPS volumes was 11%, and for individual segments, it reached 73% (ribs 11–12).

The present work is the sixth in a series of articles devoted to the parameters of computational skeletal phantoms for humans of different ages and sexes. In this article, we provide a description of SPSD phantoms of the skeleton for 15-year-old male and female adolescents. The phantoms consist of 46 BPSs. For 14 out of the 46 segments, sexual dimorphism in linear dimensions was taken into account.

Based on the assessment of parameter variability, 12 SPSs were generated for each BPS. The DF calculated for the SPSs will be used to assess their population variability.

The generated phantoms can be applied for the internal dosimetry of bone-seeking beta-emitters in the population, as well as for the dosimetry of other beta-emitting radionuclides, including those used in radionuclide therapy, such as ⁸⁹Sr, ³²P, ¹⁸⁶Re, ¹⁸⁸Re, and ¹¹⁷mSn.

Further research will focus on DF calculating, as well as on developing computational phantoms for the internal dosimetry of bone-seeking radionuclides during the intrauterine period.

Authors’ contributions. All the authors confirm that they meet the ICMJE criteria for authorship. The most significant contributions were as follows: Pavel A. Sharagin — acquisition, analysis and interpretation of data; drafting and revising the article; Evgenia I. Tolstykh — research methodology development; article revision; Elena A. Shishkina — research concept development; article revision.

1. Currently entitled the South Ural Federal Research and Clinical Center for Medical Biophysics. 2. Pafundi D. Image-based skeletal tissues and electron dosimetry models for the ICRP reference pediatric age series. Dissertation for PhD Degree. University of Florida; 2009.