After entering the body, bone-seeking radionuclides accumulate in the mineralized bone tissue and cause local red bone marrow (RBM) exposure, which can lead to grave medical consequences. Thus, for example, the increased risk of leukemia and the development of chronic radiation syndrome in people from the cohort of the Techa River contaminated with radionuclides in 1950s are largely attributed to ingestion of strontium isotopes (^89,90Sr) [1–4]. It was strontium isotopes that were the main sources of the RBM internal exposure in these people. Thus, improvement of dosimetry methods for bone-seeking radionuclides can help prepare for potential emergency situations related to radioactive contamination of the environment and represents an important challenge of radiobiology and radiation protection. Biokinetic and dosimetric models are used to estimate the absorbed dose to RBM. Biokinetic ones are used to assess specific radionuclide activity in the source tissue (skeletal bones). Such models simulate metabolic processes in the body allowing one to estimate the ingested radionuclide fraction in various organs, particularly in the bones, depending on its quantity and time after ingestion [5]. The dose conversion factors (DF) for conversion of specific radionuclide activity in the source tissue (skeleton) into the absorbed dose rate in the target tissue (RBM) are used to calculate the dose to RBM. DF represents a dosimetric model output. The computational skeletal dosimetry phantoms representing surrogates of real body tissues and describing relative positions of the source (bone) and target (RBM) tissues, in which radiation transport is simulated, are used to simulate the exposure geometry. The existing computational phantoms for RBM dosimetry are based on the analysis of a limited number of post mortem bone CT images [6–12]. The use of such phantoms makes it impossible to consider individual variability in bone size and microstructure, as well as the associated uncertainty in the DF estimates. As an alternative, Stochastic Parametric Skeletal Dosimetry (SPSD) modeling, the original parametric method for stochastic bone structure modeling, was developed in the Urals Research Center for Radiation Medicine [13, 14]. The SPSD phantom parameters are based on the numerous published measurement results of real bones in people of different ages. A lot of statistics reported in the papers used enable estimation of uncertainties associated with individual variability in the skeletal parameters. A phantom is a virtual model of simple geometric shape. A computational phantom is filled with spongiosa (a combination of trabecular bone and bone marrow) and covered with a dense layer of cortical bone. RBM, trabecular bone and cortical bone were modeled as distinct media constituting the phantom. Such complex model is a simplified representation of the real bone that is well suited for internal dosimetry from the boneseeking beta emitters [13, 14]. The model consistency was demonstrated in the reported numerical experiments [13, 15, 16] yielding the energy curves for SPSD phantoms that were matched to the published data.

When the environment is contaminated with bone-seeking radionuclides (e.g. contamination of the Techa River), these can be ingested by people of different ages (from newborns to adults) [1–3, 17]. That is why it is important to develop phantoms for various age groups. We have already created phantoms representing skeletons of a newborn [18] and a 1-year-old child [19] within the framework of the SPSD approach.

The study was aimed to develop a computational phantom representing a 5-year-old child’s skeleton for estimation of doses to RBM from the beta emitting radionuclides incorporated in the bone. This study represents the next stage of work on the development of a set of reference man computational phantoms for various age groups.

METHODS

Phantoms were created using the original SPSD method previously used to create phantoms representing a newborn [17] and a 1-year-old child [18].

Only the bone fragments containing RBM, i.e. skeletal sites with active hematopoiesis (hematopoietic sites), determined in accordance with the published data on the RBM distribution across the skeleton, were modeled within the framework of the SPSD methodology [20].

The SPSD phantom of the skeletal hematopoietic sites consists of a set of smaller phantoms, the Bone Phantom Segments (BPS) of a simple geometric shape with homogenous bone tissue microarchitecture and cortical layer thickness, describing distinct skeletal bone sites. Such segmentation simplifies the modeling process and enables estimation of the bone microarchitecture heterogeneity within a single hematopoietic site. BPS parameters are based on the published data. The segmentation process details are provided in the earlier reports [13, 21].

Parameters of phantoms included the mineralized bone tissue and bone marrow (simulated media) chemical composition and density, along with the geometry of the source and target tissues comprised in the modeled bone fragment.

Chemical composition and density of the simulated media determined based on the published data were used in all phantoms representing a 5-year-old child [22, 23].

To describe relative position and geometry of tissues inside the bone, we assessed linear dimensions, cortical layer thickness (Ct. Th.), and microarchitecture characteristics for each modeled bone site.

To assess morphometric parameters of the phantoms representing a 5-year-old child, we reviewed articles published in peer-reviewed journals, atlases, manuals, monographs, and dissertations. We also reviewed digital resources containing collections of x-ray images. To perform analysis, we collected the measurement results of individuals/samples that were considered to be healthy by the authors and had no disorders resulting in bone deformities. Ethnicity: Caucasians and Mongoloids, since these groups are typical of the Urals region. The subjects’ age was 3–7 years.

In this study, the following bone microarchitecture characteristics were assessed based on the published data: trabecular thickness (Tb. Th.), trabecular separation (Tb. Sp.), bone fraction in the spongiosa volume (BV/TV). We considered the measurement data of skeletal bones obtained using various techniques: micrometers, osteometric board, ultrasound and radiography, as well as computed tomography (CT). Histomorphometry and microCT data were used to estimate the trabecular bone parameters (Tb. Th., Tb. Sp., BV/TV) and the cortical layer thickness.

Average estimates of bone characteristics were taken as computational phantom parameters. When the published data on individual measurements were available, we combined these data to calculate the means and standard deviations (SD). When the measurement results of groups of people were averaged, a weighting factor (W_N) for each group considering the number of subjects (N) was introduced: W_N = 1, when N ≥ 25; W_N = N/25, when N < 25. Methods to select and assess the published data were previously discussed in detail in [24–26].

A voxel BPS was constructed for each segment using the original Trabecula software [27]. The BPS voxels imitated either mineralized bone, or bone marrow (BM), depending on the voxel center position in the phantom.

Trabecular bone (TB) and cortical bone (CB) were considered as source tissues, while bone marrow (BM) was considered as target tissue. BM was evenly distributed across the trabeculae in the BPS. Voxel size selected individually for each phantom did not exceed 70% of trabecular thickness and varied between 50–200 µm in the generated phantoms [27, 28]. The source and target tissue volumes were automatically calculated in the Trabecula software for each BPS.

Hematopoietic sites of a 5-year-old child, segmentation and BPS generated are provided in figure (exemplified by the scapula).

To simulate population variability in the size and microstructure characteristics for each BPS, 12 Supplementary Phantom Segments (SPS) were created with the bone micro- and macro-structure parameters randomly selected within the range of their individual variability (within the limits of minimum and maximum measured values).

RESULTS

The main hematopoietic sites of the 5-year-old child’s skeleton and the mass fraction of RBM in these sites were determined based on the MRI data (tab. 1) [20].

The skeleton of a 5-year-old child includes 14 hematopoietic sites for simulation (tab. 1). The share of RBM in these sites in the total skeletal RBM content varies from 0.9% to 18.1%. Distribution of RBM within each hematopoietic site was also determined based on the published MRI data [29–33].

Chemical composition of the simulated media was selected based on ICRP data for adults (tab. 2) [22].

The mineralized bone tissue density estimated based on the cortical bone density measured in 5-year-old children was 1.80 g/cm³ [23]. The RBM density was taken equal to the water density (1 g/cm³) [22].

The spongiosa parameters were assessed based on the published data; the analysis and calculation of average population value of the spongiosa parameters were described in detail in [26]. The BPS micro-architecture parameter values for a 1-year-old child are provided in tab. 3.

The linear dimensions and thickness of the cortical layer assumed/used for the BPS representing a 5-year-old child are provided in tab. 4.

The phantom representing skeletal hematopoietic sites of a 5-year-old child consists of 43 BPS (tab. 4). A different number of BPS was used to describe these, depending on the shape of the simulated hematopoietic site: 1 (ribs) to 9 (sacrum).

As in phantoms representing skeletons of people of other ages, most BPS of a 5-year-old child are cylinders and rectangular parallelepipeds; BSP size is within 3–75 mm. The minimum Ct. Th. value was reported for the sternal BPS (0.1 mm), while the maximum value was reported for the femoral diaphysis (3.7 mm). The spongiosa parameters varied greatly. The BV/TV ratio of BPS was 13–52%, Tb. Th. was 0.09–0.29 mm, and Tb. Sp. was 0.48–0.98 mm (tab. 3).

The average individual variability of the BPS dimensional parameters was 14%; the highest variability value was reported for the ribs (35%), while the lowest value was reported for the distal part of the humerus (3%). The average cortical layer thickness was 26%, with the maximum value of 35% reported for the sacral segments and the minimum value of 7% reported for bodies of the cervical vertebrae. The average variability of spongiosa parameters was 18%, with the minimum value of 2% and maximum value of 70%.

Variability values were used for SPS modeling. SPS volume varies greatly, it can differ from the BPS volume by a factor of three, both upwards and downwards. In our future studies, DFs will be calculated for both BPS and SPS. Standard deviation of DFs calculated for SPS from DFs calculated for BPS will characterize the DF population variability.

DISCUSSION

Comparison of the modeling outcome with the masses of real bones was performed for the newborn in order to confirm the methodological approach accuracy. We have found no masses or volumes of the wet bones of 5-year-old children, that is why we cannot compare the modeling outcome with the real bones. The existing computational phantoms obtained by scanning autopsy material are non-parametric, that is why it is impossible to compare parameters of these phantoms with the SPSD phantom parameters. For most bones, it is also impossible to compare the characteristics of phantoms obtained as a result of their generation (masses of simulated media) with the published phantom masses, since only skeletal sites with active hematopoiesis are modeled within the framework of the SPSD approach, not the entire skeleton. The SPSD phantom masses (sums of masses of all segments comprised in the phantom) were compared with the published data for the bones, which were modeled as a whole: pelvic bones and the clavicle of a 5-year-old child [7, 12]. The comparison showed that the difference between the phantom masses reported in the published papers and the SPSD phantom masses did not exceed 20%.

It makes sense to assess age-related changes in the characteristics of phantoms representing a newborn, 1-year-old and 5-year-old children. The phantom representing a skeleton of a 5-year-old child consists of a larger number of BPS than the phantoms representing skeletons of younger children. This is associated with the processes underlying cartilage mineralization that are intense within the first five years of life; in particular, vertebral processes and the sternum have undergone significant mineralization by the age of 5. Furthermore, the process of the RBM substitution with adipose tissue in the tubular bone diaphysis is not over yet in children of this age, that is why BPS were modeled for these sites. Significant changes in the RBM distribution across the skeleton occur by the age of 5. Thus, children of this age have a significantly lower mass fraction of RBM in the skull compared to 1-year-old children (28.7% vs. 18.1%), furthermore, fraction of RBM in other skeletal segments is increased. The BPS micro-structure parameters show little changes. The cortical layer thickness significantly increases during this period; all the modeled skeletal segments become covered with the cortical layer by the age of 5, in contrast to phantoms representing a newborn and a 1-year-old child. In the period from the age of one to five years, the size of all parts of the skeleton increases significantly. Comparison of the volumes of phantoms representing skeletal segments of 1-year-old and 5-year-old children exemplified by the distal part of the femur, clavicle, bodies of the cervical and lumbar vertebrae is provided in tab. 5.

As shown in tab. 5, the volumes of simulated media of a 5-year-old child largely exceed those of the 1-year-old child. The increase in the source tissue volume for this period is 3.26-fold and 2.78-fold for TB and CB, respectively. The CB volume increase is 3.03-fold. The total BPS volume of a 5-year-old child is on average 2.8 times larger than the volume of the phantom representing a 1-year-old child.

We expect that such age-related changes will have a significant impact on the average DF of the skeleton and, therefore, on the dose rate. The increase in the BPS linear dimensions can have the greatest effect on the DF for strontium incorporated in the trabecular bone. Previous studies have shown that the larger the BPS size, the greater the chance is of absorbing energy from the incorporated radionuclide within the phantom, not outside it [15, 16]. The opposite pattern is typical of strontium in the cortical bone: the larger the phantom size, the lower the likelihood of energy transfer from the source incorporated on the outer cortical layer to the target (RBM) is. Thus, when the BPS size increases, one can expect the increase in DF for ^89,90Sr in the trabecular bone and decrease in DF for Sr in the cortical bone.

The phantom parameters provided (tab. 3, tab. 4) can be integrated in the Trabecula software to generate voxel phantoms. Modeling of radiation transport using voxel phantoms will make it possible to assess DFs for bone-seeking beta emitters, thereby allowing one to determine the RBM absorbed dose rate.

CONCLUSIONS

The study resulted in the development of computational phantoms representing the main skeletal sites of a 5-yearold child with active hematopoiesis. These phantoms were developed using the same method, as for the newborn and 1-year-old child. The phantoms modeled imitate bone tissue structure, while the sets of phantoms simulate population variability in the size of structures of distinct bones. The provided phantom representing a 5-year-old child will be used to calculate DFs for ^89,90Sr, which, in turn, are essential for estimates of adjusted coefficients linking individual radionuclide uptake and dose to RBM, which will help to improve dose estimates for the Urals region residents. As the way forward, we also plan to create SPSD phantoms representing skeletons of people of other age groups: 10 year-olds, 15-year-olds and adults. SPSD phantoms can be used for the incorporated bone-seeking beta emitter dosimetry in the population, in case of radionuclide contamination of the environment, as well as for dosimetry from other bone-seeking beta emitters, including those used in radionuclide therapy, such as ⁸⁹Sr, ³²P, ¹⁸⁶Re, ¹⁸⁸Re, ¹¹⁷mSn.