Internal exposure of the red bone marrow (RBM) due to bone-seeking radionuclides may lead to serious health effects for a human body. The most dangerous and wide-spread bone-seeking radionuclides are ^89,90Sr. These elements could be found in the composition of the global radioactive fallouts as a result of the nuclear weapon testing. They also got into the environment due to some other radiation incidents [1]. For example, strontium isotopes were present in the composition of the radioactive releases into the Techa River in 1950s leading to their accumulation in the bodies of the residents of territories along the river [2–5]. It was ^89,90Sr that were the main sources of the RBM exposure for the members of the Techa River Cohort. Estimation of doses from these radionuclides is a challenging task. It involves biokinetic modeling of the radionuclide turnover to evaluate its concentration in a bone (source-tissue) [6], as well as dosimetric modeling which allows assessing the dose conversion factors (DF) from the radionuclide activity in a bone to the absorbed dose rate in RBM. Dosimetric models imitate the location of the source-tissue and target-tissue relative each other. At present computational phantoms (3D models of the skeleton and RBM) serve the function of such models. The radiation transfer is imitated inside these phantoms. Modern skeletal phantoms to estimate RBM doses are based on the analysis of the computer tomography (CT) images of the skeletons of very few deceased people [7–13].

Limited amount of biopsy material does not allow assessing the uncertainties associated with the variability of the size and micro-architecture of the skeleton within the population. As an alternative URCRM has developed an original parametric method of stochastic modeling of bone structures — SPSD-modeling (Stochastic parametric skeletal dosimetry) [14, 15]. Within the framework of this approach, it is suggested that numerous published measurement results of morphometric and hystomorphometric studies of the bones should be used as model parameters. High degree of statistical significance of the published measurement results makes it possible to estimate uncertainties associated with the individual variability of the skeletal parameters.

SPSD-phantom of a skeleton as a whole is a set of small phantom segments. These are the digital models of simple geometric shape filled with trabecular bone with RBM located in the inter-trabecular cavities. Some part of the phantom surfaces is covered with the layer of solid cortical bone. Thus, SPSD-phantoms contain two source-tissues: trabecular and cortical bone and one target-tissue — RBM. This model suits perfectly the internal dosimetry of bone-seeking beta-emitters [14, 15]. Model adequacy is supported by good agreement of the calculated energy dependences for the SPSD-phantoms and similar dependences described in some published research [14, 16, 17].

In case of population exposure, the radionuclides may enter a body of a person of various age. For example, radioactive contamination of the Techa River led to the exposure of residents in the age-range from newborns to elderly people [2–4, 18]. To estimate doses to RBM for all age groups we have previously developed SPSD-phantoms representing the skeleton of a new-born [19], one-year-old [20], and five-year-old child [21]. The objective of the current study is to develop computational phantoms representing the skeleton of a ten-year-old child to estimate RBM doses from beta-emitting radionuclides incorporated in a bone. The study is yet another step in the work aimed at the development of a set of computational phantoms of a standard man for different age groups.

METHODS

Computational phantom of a ten-year-old child was generated within the framework of SPSD method similarly to the phantoms for younger age groups [14]. The method consists of the following steps:
1) evaluation of the RBM distribution within the skeleton, identification of the modeled sites of the skeleton with active hematopoiesis (hematopoietic sites);
2) measuring linear dimensions and micro-structure parameters of the modeled bones based on the published data;
3) hematopoietic site segmentation;
4) voxel phantom generation for every segment.

Bone marrow distribution within the skeleton of 10-years-old child was evaluated using ICRP-data [13], which based on results of MRI-research [22].

In total the analysis included 11,927 measurement results of the bone samples [23, 24]. To measure the morphometric parameters of the phantoms of a ten-year-old child, manuscripts published in peer-reviewed journals, atlases, manuals, monographs, and dissertations were studied as well as digital resources containing collections of x-ray images. The measurement results of individuals/samples that the authors considered to be healthy and having no disorders resulting in bone deformities were used for the analysis. Ethnicity: Caucasians and Mongoloids, since these groups are typical of the Urals region. The subjects’ age was 8–12 years.

Histomorphometry and micro-CT data were used to estimate the parameters of trabecular bone (Tb. Th., Tb. Sp., BV/TV) and cortical layer thickness. The following properties of the bone micro-architecture were evaluated: trabecular thickness (Tb. Th.), trabecular separation (Tb. Sp.), bone volume to total spongiosa volume relation (BV/TV). The data of the linear dimension measurement results of the skeletal bones were examined with the help of various techniques: micrometers, osteometric boards, ultrasound scans and radiography, as well as computed tomography (CT).

Within each skeletal site with active hematopoiesis the bones are subdivided into relatively small segments. The so-called Bone Phantom Segments (BPS) was modeled for every segment [25, 26]. Each segment should have relatively homogeneous microarchitecture and cortical layer thickness. Segments should be described by simple geometric shapes (cylinder, rectangular parallelepiped, etc.). Such subdivision allows taking into account the micro-architecture heterogeneity inside a bone. Moreover, relatively small size of the segments makes it possible to generate the phantoms imitating them with rather high resolution.

Averaged estimates of bone characteristics were taken as computational phantom parameters. If the published data on individual measurements were available, they were combined to calculate the means and standard deviations (SD). When the measurement results of groups of people were averaged, a weighting factor (WN) which took account of the number of subjects (N) was introduced for each group: WN = 1, when N ≥ 25; WN = N/25, when N < 25. Methods to select and assess the published data were previously described in detail in [23].

Linear dimensions and parameters of the bone micro-architecture influence the geometry of source and target tissue in BPS. They were determined for each segment separately. In addition to these parameters, the chemical composition and density of the modeled media were determined based on the published research data [27, 28] and were used for all the BPS of a ten-year-old child.

A voxel BPS was generated for each segment using the original Trabecula software [29]. Every voxel in a BPS imitates either mineralized bone, or bone marrow (BM), depending on the voxel center position in a phantom.

Trabecular (TB) and cortical bone (CB) were considered as source tissues, while bone marrow (BM) was viewed as target tissue. BM was uniformly distributed across the trabeculae in the BPS. Voxel size was selected individually for each phantom. It did not exceed 70% of trabecular thickness and varied in the range 50–200 μm [29, 30]. The modeled media volumes were calculated for each BPS using the Trabecula software package.

Hematopoietic sites of a ten-year-old child, segmentation process and generated BPS are given in figure (exemplified by the tibia).

SPSD method allows simulating the population variability of the micro-structure sizesand characteristics for every BPS. With this objective in view, 12 Supplementary Phantom Segments (SPS) were created for every BPS 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

Skeletal sites with active hematopoiesis of the skeleton of a ten-year-old child and RBM mass fraction in these sites have been determined based on the ICRP data [22] and are provided in tab. 1.

As it can be seen from tab. 1, the skeleton of a ten-year-old child has 13 hematopoietic sites. RBM mass fraction in these sites varies from 0.9% to 18.1% of the total RBM content in the skeleton. In addition, distribution of RBM within each hematopoietic site was determined based on the published MRI data [31–36].

Chemical composition of the modeled media was obtained based on the ICRP data for adults (tab. 2) [25].

The density of mineral bone tissue has been estimated based on the measurement results of the cortical bone thickness in children aged 10 and is equal to 1.85 g/cm3 [26]. It has been assumed that RBM density is equal to that of water (1 g/cm3) [25].

Bone micro-structure characteristics were evaluated based on the published research data. A detailed description of their analysis and calculation of the population-average were given in [23]. Micro-architecture parameter values for the BPS of a ten-year-old child are provided in tab. 3.

Linear dimensions and values of cortical layer thickness assumed for the BPS of a ten-year-old child are given in tab. 4.

As it is shown in tab. 4 the phantom of hematopoietic sites of a ten-year-old child skeleton consists of 38 BPS. The number of BPS within a hematopoietic site depended on its shape and varied from 1 (ribs) to 9 (pelvic bones).

Most of the BPSs of a ten-year-old child were represented by cylinders and rectangular parallelepipeds. Their linear dimensions were within the range from 3 to 88 mm. The minimum Ct. Th. value was reported for the BPSs of the vertebra (0.2 mm). It differed tenfold from the maximum value assumed for the proximal end of the femora (2.2 mm). Bone micro-architecture parameters also varied widely. BV/TV value in BPS varies in the range 14-52%, Tb. Th — from 0.12 mm to 0.29 mm, Tb. Sp. — from 0.46 mm to 1 mm (tab. 3).

On the average, individual variability of the BPS linear dimensions made up 12%. The greatest variability was reported for the iliac bone (30%), the least — for the lateral border of scapula. The cortical layer thickness of the bone varied within the range from 7% (cervical vertebra) to 62% (sternum). On the average, it made up 24%. The variability of the micro-structure parameters was within the range 6–42%, and on the average it was 19%. The obtained values of the variability parameters of the phantoms were used to model SPS. The volume of the SPS could differ from the volume of the BPS more than 3 times both upwards or downwards. Calculation of the DF for the BPSs and SPSs will make it possible to evaluate DF population variability as a mean-square deviation of the DF values calculated for SPS from those calculated for the BPS.

DISCUSSION

The phantom of a skeleton of a ten-year-old child has less BPSs than that of a five-year-old child. It could be explained by the fact that RBM has been substituted by yellow bone marrow in the tubular bone diaphyses, therefore these skeletal sites were not modeled. At the age of 10 the greatest RBM fraction is located in the pelvic bones and femora as compared to the younger age groups when the greatest amount of RBM is reported for the cranial bones. Also, at this age 29% of the total RBM is reported for the segments of the spine and sacrum. Micro-structure parameters of the BPS change little as compared to the phantom of a five-year-old child. There is a tendency to a decrease in BV/TV and Tb.Th, and an increase in Tb. Sp. Over a 5-year period, i.e. by the age of 10, the cortical layer thickness has increased by 20% in any given BPS. The age-dependent changes in the characteristics of the phantoms could be demonstrated by comparing the volumes of the simulated media. tab. 5 shows the comparison of the volume of the skeletal sites of five- and ten-year old child on the example of the distal end of the femur, clavicle, cervical and lumbar vertebra.

It has been shown in tab. 5 that the volume of the modeled media of a ten-year-old child exceeds that for a five-year-old one, which reflects the growth of the skeletal bones. The source-tissue volume increased on the average 1.96 times for TB, and 1.48 times for the CB. The total volume of the BPS increased 1.6 times over a 5-year period (from the age of 5 till 10). Over the same period of time the total volume of the CB increased only 1.3 times. It is due to the cessation of the hematopoiesis in skeletal sites with high Ct.Th. (the middle of the diaphyses of the long tubular bones). We expect that such age-dependent dynamics of the phantom characteristics will result in the decrease of the DF from Sr incorporated in the cortical bone.

In the course of the future studies the phantom parameters (tab. 3, tab. 4) provided in this manuscript will be integrated into the Trabecula software package to generate voxel phantom. The simulation of the energy transfer in these phantoms will allow estimating he DF for the bone-seeking beta-emitters, which gives an opportunity to estimate the RBM absorbed dose rate.

CONCLUSIONS

As a result of the conducted study computational phantoms of the main skeletal sites with active hematopoiesis have been developed for a ten-year-old child. These phantoms were elaborated based on the SPSD method similar to the phantoms developed for other age groups. The obtained phantoms imitate the structure of the bone tissue. These sets demonstrate the population variability of the dimensions of the structure of certain skeletal bones. The provided phantom representing a ten-year-old child will further be used to calculate DF for ^89,90Sr, which in their turn are necessary for the assessment of the improved coefficients linking the individual radionuclide intake to dose to RBM. It will enable the dose estimates improvement for the residents of the Urals region. For the future studies we plan to develop SPSD-phantoms of the skeleton of men and women aged 15, and for adults. The given phantoms could be used for the dosimetry of incorporated bone-seeking beta-emitters in the population, in case of the contamination of the environment with radionuclides, and for the dosimetry of other beta-emitting radionuclides including those used in radionuclide therapy, such as ⁸⁹Sr, ³²P, ¹⁸⁶Re, ¹⁸⁸Re, ¹¹⁷mSn.