Radionuclide incorporation in a human body could lead to internal exposure of tissues and organs. One of the most radiosensitive organs is the haematopoietically active bone marrow (AM). Found inside skeletal cavities, AM cells are the main target for bone-seeking radionuclides that accumulate in mineralized bone tissue. The most dangerous of the radionuclides are ^89,90Sr. These very radionuclides were the key source of AM exposure for the residents of the Techa riverside settlements, contaminated with radioactive substances in the 1950s. Mean AM dose absorbed in the course of a lifetime in the Techa River Cohort members was 0.35 Gy, but in some people it exceeded 1 Gy and could reach 7 Gy, which resulted in a chronic radiation syndrome development and raised the risk of leukemia [1–4]. The contribution to the AM dose was 61–94% and 2.5–3.2% of ⁹⁰Sr and ⁸⁹Sr, respectively [5]. Among the exposed individuals are people of various ages, including small children. Dose assessment for the exposed population could help to prepare for potential radiation emergencies. The methods of dosimetric modeling that were used previously to estimate AM dose are outdated [6]. More accurate data on AM doses received by the members of the Southern Urals population exposed to radiation cohort (SUPER cohort) would allow better assessment of the radiation-related risks of leukemias [7]. Estimation of the AM doses requires assessment of the radionuclide specific activity in the source tissue and calculation of the dose conversion factor (DF) from specific activity of a radionuclide in the source to the absorbed dose rate in a target.

Biokinetic models that describe distribution and transfer of a radionuclide through the tissues of the body after its ingress are used to estimate radionuclide specific activity [5]. DF is calculated using dosimetric modeling. It involves simulating the transfer of radiation resulting from strontium isotopes decay in the source tissue (bone) and energy absorption in AM (the target tissue), taking into account the exposure geometry. That is why an important part of dosimetric modeling is the elaboration of computational bone phantoms. They are surrogates of the real body tissues (AM and bone) that describe the geometry of source and target tissues and allow simulation of radiation transfer. It should be noted that the current approaches to modeling shape and structure of the bone are based on the analysis of postmortem computed tomography (CT) images of individual bone segments [6, 8–12]. The use of autopsy material limits the number of samples used to estimate the parameters of phantoms and makes it impossible to account for individual variability of size of human bones. 

An original parametric method of stochastic modeling of bone structures, SPSD modeling (SPSD — stochastic parametric skeletal dosimetry), was developed at the Urals Research Center for Radiation Medicine [13]. SPSD modeling implies determination of parameters of the phantoms based on numerous published bone measurements. It allows accounting for the uncertainties due to the variability of skeletons in different people. The inside of a computational bone phantom is filled with spongiosa, which is a combination of trabecular bone and AM. And its outside bears a dense layer of cortical bone. The trabecular bone is modeled as a grid of rod-like trabeculae. Such model is a simplified representation of a real bone, yet it is suitable for internal dosimetry of bone-seeking beta-emitters [13]. The previously published numerical experiments [14, 15] demonstrate adequacy of the model; these experiments yielded energy dependences for SPSD phantoms that were compared to the published data [12].

The current study is devoted to the elaboration of a computational phantom of a one-year-old child's skeleton. It is the next step in the series of studies on the development of a set of computational phantoms of a reference man of different age. Previously, we published a paper covering the development of the computational phantom of a newborn's skeleton [16].

The objective of the study is the elaboration of a computational phantom of skeleton of a one-year-old child to estimate AM doses due to beta-emitting radionuclides incorporated in the bone.

METHODS

The phantoms were created using the original SPSD method. For dosimetric modeling, we selected only the skeletal sites with active hematopoiesis. A set of hematopoietic sites were identified based on the published data on AM distribution inside the skeleton [17]. SPSD phantom of skeletal hematopoietic sites consists of a set of smaller phantoms, which are basic phantoms of bone segment (BPS) of simple geometry. They describe individual sites of the skeletal bones. The approach to determination of BPS parameters (based on the previously published data) is given below. 

We studied papers in peer-reviewed journals, atlases, manuals, monographs and dissertations as sources of data on dimensional characteristics of bones of a one-year-old child. This set was completed with electronic resources containing collections of X-ray images. The measurements of people/ samples that the authors qualified as healthy without diseases leading to bone deformation were collected for the analysis. The ethnicities considered were Caucasians and Mongoloids, as these groups are common in the Ural region. The age of the children ranged from 9 months to 2 years.

Relying on the published data, for every hematopoietic site we assessed linear dimensions and thickness of the cortical bone layer (Ct.Th), as well as bone microarchitecture characteristics: trabeculae thickness (Tb.Th), trabecular separation (Tb.Sp.), bone volume fraction of spongiosa (BV/TV). The linear skeletal bone measurements obtained using callipers, osteometric boards, ultrasound and X-ray examinations, and CT were studied.  Histomorphometry and micro-CT data were used to assess the parameters of trabecular bone (Tb.Th, Tb.Sp, BV/TV) and cortical layer thickness.

Averaged estimates of bone characteristics were taken as parameters for digital phantoms. If published papers containing data on individual measurements were available, we combined them and calculated arithmetic means and standard deviations (SD). When the data on the study of the groups of people were averaged, then for each group we used a weighting factor, (W_N), that factored in the number (N) of samples: W_N = 1 if N ≥ 25; W_N = N/25 if N < 25. The methods of selection and analysis of the published data were described in detail in previous publications [18–21].

Having acquired the datasets presenting population-average characteristics of bone size and shape, we divided each hematopoietic site into small segments of simple geometric shape with homogeneous bone microarchitecture and cortical layer thickness. Such segmentation allows accounting for heterogeneity of structure of trabecular and cortical bone inside a single hematopoietic site and simplifies modeling. The process of segmentation has been described in detail in [18, 19].

Each phantom includes descriptions of the modeled media and geometry of source and target tissues. Bone marrow (BM) and mineralized bone tissue (part of trabecular and cortical bone) are the media constituting BPS. Chemical composition and density of the modeled media were determined based on the previously published data [22] and applied for all phantoms of a one-year-old child.

For each segment a voxel BPS was generated in the Trabecula [23] software. Depending on the position of the center of the voxel in the phantom, voxels imitate either mineralized bone or bone marrow (BM). We regarded trabecular bone (TB) and cortical bone (CB) as source tissues, and bone marrow (BM) as a detector tissue. BM was uniformly distributed between trabeculae inside the BPS. Voxel sizes differed phantom to phantom, but did not exceed 70% of the trabecula thickness [23, 24]. In the modeled phantoms, the size of the voxel varied in the range from 50 to 200 µm. Trabecula software automatically calculated the volumes of source and detector tissues for each BPS.

Hematopoietic sites of a one-year-old child, division into segments and modeled BPS are demonstrated on the example of the humerus (figure).

To simulate population variability of dimensions and microstructure characteristics, we generated 12 SPSs (supplementary phantoms) for each BPS with mean parameter values. The parameters of these SPSs were selected at random, within the range of their individual variability (within the limits of minimum and maximum values of the measurements).

RESULTS

The main hematopoietic sites in a one-year-old child's skeleton and the AM mass fraction therein, were determined in accordance with the MRI data [17] (tab. 1).

According to tab. 1, skeleton of a one-year-old child includes 13 hematopoietic sites for modeling. The AM mass fraction therein ranges from 0.9 to 28.7% of its total mass fraction in the body.

 As is the case with a newborn [16], the following parts of the skeleton were not modeled: epiphysis of the tubular bone, sternum, craniofacial bones and vertebral processes (cervical, thoracic, lumbar), because, according the published data [26–31], they either contain very little AM or consist of cartilage tissue.

Table 2 (tab. 2) presents chemical composition of the modeled media; we selected the values based on the ICRP data [22] for adults.

The density of mineralized bone tissue was calculated based on the published measurement results of the cortical bone density of one-year-old children [25]; it made up 1.70 g/cm³. As for the red bone marrow, its density was taken as equal to that of water, 1 g/cm³ [16].

The parameters of spongiosa were also determined based on the published data; their analysis and calculation of population-average spongiosa parameters were described in detail in [21]. Table 3 (tab. 3) presents the values of the BPSs microarchitecture parameters of a one-year-old child.

Table 4 (tab. 4) presents linear dimensions and cortical layer thickness assumed for BPSs of a one-year-old child.

The phantom of hematopoietic sites of a newborn's skeleton consists of 39 BPSs (tab. 4). Depending on the shape of the simulated hematopoietic sites, we used different amount of BPSs to describe them: from 1 (ribs) to 9 (sacrum).

For the most part, BPSs were modeled by cylinders and rectangular parallelepipeds. The size of the phantoms varies widely, from 2.7 to 35.8 mm. Phantoms describing spinal column have no cortical layer due to the fact that the ossification process is incomplete (Table 4). Bodies of femur and tibia have the highest values of Ct.Th for the BPS of a one-year-old child: 2.3 mm. In the first year of life, bones of the cranial vault ossify intensively and the fontanelles close up, therefore, as opposed to those of a newborn, BPSs representing cranial vault of a one-year-old child are covered with a cortical bone layer. The spongiosa parameters differed significantly for different BPSs. The BV/TV ratio in BPSs varies from 14 to 52%, Tb.Th value — from 0.09 to 0.29 mm, Tb.Sp value — from 0.48 to 0.98 mm (tab. 3).

Individual variability of the BPSs dimensional parameters on the average made up 14%, with the highest value belonging to the scapula acromion (42%) and the lowest — to the acetabulum of pubic bone (3%). On the average variability of the cortical layer thickness made up 20%, with the maximum 47% variability for iliac ala. The mean variability of spongiosa parameters was 25%, with minimum and maximum values 9% and 52%, respectively.

The variability values were used to model the SPSs. Their volumes vary widely; they can be 3-fold larger or smaller than those of the BPSs. Further on, we shall calculate DF both for BPSs and SPSs. Mean square deviation of DF calculated for SPSs from those calculated for BPS will characterize the population variability of the DF.

DISCUSSION

In the study devoted to the modeling of a newborn’s skeleton [16], we have demonstrated that the weight of the generated phantoms correspond to the weight of real bones. We could not make such a comparison for the phantom of a one-year-old child's skeleton due to lack of data on weight of the respective wet bones in the available literature. However, it is interesting to compare skeletal phantoms of a one-year-old child and a newborn. In general, the former includes more BPSs than the latter, which counts 34 of them. This is due to the ossification and increase in the size of sacrum, which required additional segmentation of the ilium. At the same time, in the bones of hands and feet, yellow bone marrow replaces AM already in the first year of life, which means these segments are not modeled when a one-year-old child's phantom is elaborated.

Naturally, the volume of similar BPSs increases with age, along with the size of the bones. The comparison of the volume of the phantoms of the skeletal sites of a newborn and oneyear old child based on the example of distal femur, clavicle, cervical and lumbar vertebral bodies is given in tab. 5.

The volume of BPSs in the phantom of a one-year-old child is significantly higher than in that of a newborn (tab. 5). The volumes of the modeled media also increase in the vast majority of phantoms. Interestingly, if the source tissue volume (TB and CB) increases 1.5 times on the average, the volume of the target tissue increases in 4.5 times. The drop in the volume of trabecular bone (TB) in the lumbar vertebral body phantoms is explained by the decreasing BV/TV ratio: according to the published data, it goes down from 0.45 to 0.14 (tab. 3). In most BPSs, the volume of CB increases significantly, 2.3-fold on the average, in the first year of life, with the exception of BPSs of vertebral bodies. On the average, the total volume of BPSs for a one-year-old child is 2.4 times larger than that for a newborn.

CONCLUSIONS

As a result of this study computational phantoms of the main sites of a one-year-old child's skeleton with active hematopoiesis were created. We developed these phantoms using the same methods as for the phantoms of a newborn. The generated phantoms simulate bone tissue structure and population variability of the size of individual bone structure. The presented phantom of a one-year-old child will be used to calculate DF for ^89,90Sr, which in turn are necessary to estimate refined factors linking individual intake of the radionuclide and the AM dose, which will help to improve dose estimates for residents of the Ural region. It should be noted that the phantom developed with the help of SPSD could be used to calculate DF for other bone-seeking beta emitters, including those used in radionuclide therapy, such as ⁸⁹Sr, ³²P, ¹⁸⁶Re, ¹⁸⁸Re, ¹¹⁷mSn. Our plans include generation of SPSD skeletal phantoms for other age groups: 5-year, 10-year, 15-year old children and adults. SPSD phantoms can be used for dosimetry of incorporated bone-seeking betaemitters in the population in situations when the environment is contaminated with radionuclides.