Active marrow (AM) exposure due to internal radiation from man-made bone-seeking radionuclides can lead to grave medical consequences. Such exposure can occur both as part of radionuclide therapy and due to  radionuclides have been released into the environment as a result of nuclear weapons testing or radiation accidents. Radioactive contamination of the Techa River in the 1950s led to exposure AM of riverside village residents to doses of about 0.35 Gy, which caused chronic radiation syndrome [1–4] and an increased risk of leukemia. The main sources of AM internal exposure were the bone-seeking beta emitters ^89,90Sr [2]. This demonstrates that improvement of AM dosimetry from incorporated ⁹⁰Sr is an urgent task of radiobiology and radiation protection. ⁹⁰Sr dosimetry includes biokinetic modeling to estimate its distribution in body tissues and calculate the specific activity of ⁹⁰Sr in the source tissues, as well as dosimetric modeling of energy transfer from the source tissue (bone) to the target tissue (AM). The results of dosimetric modeling are dose factors (DF), which allow converting the specific activity of the incorporated radiation source into the absorbed dose rate in the target tissue. An important step in dosimetric modeling is the development of computational phantoms, i.e., a representative digital representation of source and target tissue geometries in which researchers can model the radiation transport. The bone is an object of modelling when constructing phantoms for AM dosimetry. The dosimetric bone model is a simplified representation of a real bone; it consists of a solid cortical bone layer that covers the phantom from the outside, whereas the spongiosa fills the model from the inside. Spongiosa is a set of trabecular bone, which modeled as a network of rod-like trabeculae and the AM located between them. Currently, there are several approaches for modeling the shape and structure of bone, based on the analysis of computed tomography (CT) images [5–9]. These methods require pathoanatomic material and do not allow taking into account the individual variability of the size of human bones. Instead, in the Urals Research  Centre for Radiation Medicine” was developed an original parametric method for stochastic modeling of bone structures, known as SPSD modeling (stochastic parametric skeletal dosimetry) [10]. This method is based on the use of published averaged measurements of bone structures as phantom parameters, thus avoiding using of autopsy material, and assessing uncertainties associated with skeletal variability in different individuals.

The aim of this study is to develop a computational phantom of newborn skeleton for AM dosimetry from incorporated ⁹⁰Sr.

METHODS

The original SPSD technique was used for the skeleton modeling. In the frame of this approach, only skeletal areas with active hematopoiesis, i.e., those containing AM (hematopoietic sites), are modeled. The SPSD phantom of skeletal hematopoietic sites consist of a set of smaller phantoms — the Bone Phantom Segments (BPS) of a simple geometric shape, describing individual skeletal bone sites. Each phantom includes a description of the simulated media and a description of the source and target tissue geometries.

The modeled skeletal sites with active hemopoiesis (hemopoietic sites) were identified according to published data on AM distribution.

Each BPS consists of mineralized bone tissue and AM. To simulate the transport of energy in these two medias, we determined their chemical composition and density according to published data. These characteristics were used as parameters for all phantoms.

We evaluated parameters characterizing irradiation geometry for each BPS: linear bone dimensions, cortical layer thickness (Ct.Th), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp.), bone fraction in spongiosa volume (BV/TV). We evaluated the listed parameters based on published data. To assess the characteristics of bone geometry, articles in peer-reviewed publications, atlases, manuals, monographs and theses were considered. Also, we analyzed electronic resources containing collections of X-rays. The results of measurements of people/samples, which the authors identified as healthy and without diseases leading to bone deformation, were taken for analysis. Ethnically people/samples belonged to Caucasians and Mongolians due to the fact that these groups are characteristic of the population of the Ural region. We considered data from measurements of skeletal bones using various techniques: micrometers, anatomical boxes, ultrasound and radiological studies, CT (for linear dimensions and Ct.Th), histomorphometry and micro-CT — for microarchitecture parameters (Tb.Th, Tb.Sp, BV/TV). Averaged estimates of bone characteristics were taken as parameters of digital phantoms. If published data on individual measurements were available, we combined them and calculated arithmetic means and standard deviations (SDs). In the case of averaging the results of studies of groups of people, we would introduce a weighting coefficient (Wn), which took into account the number (n) of the studied subjects: Wn = 1, if n ≥ 25; Wn = n/25 if n < 25. Methods for the selection and analysis of literature data are described in detail [11–14].

Based on the average values of the selected parameters for each bone segment, using the original Trabecula software [15] a computational phantom in voxel form — Bone Phantom Segment (BPS ) was generated. BPS is a model of a simple geometric shape (rectangular parallelepiped, cylinder, prism, etc.), filled inside with spongiosa and on the outside covered with a cortical layer, as shown by the example of the phantom of the iliac bone of a newborn (fig. 1).  

Each phantom element (AM, trabecula, cortical layer) was imitated by a set of three-dimensional elements – voxels – from which simulated structures were composed. Each voxel imitate either mineralized bone or bone marrow (BM), depending on the location of the voxel center in the phantom. As source tissues, the dosimetric model considers trabecular bone (TB) and cortical bone (CB) separately, and bone marrow is considered as a target tissue, assuming that AM is uniformly distributed inside the BPS. The voxel size differed between phantoms, did not exceed 70% of the trabecula thickness [15, 16], and varied from 50 to 200 μm. Volumes of source and target tissues were automatically calculated in Trabecula software for each voxel phantom.

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

RESULTS

The main hematopoietic sites of a newborn’s skeleton and the mass fraction of AM in them were determined according to the data of MRI studies [17] and are presented in tab. 1. 

The phantom of skeletal hematopoietic sites of a newborn baby includes 14 hematopoietic sites. AM content of these varies from 1.7 to 28.2%.

Hematopoietic sites include bone regions that were not modeled in the SPSD approach. So, epiphyses of long bones were not modeled, since they are mostly composed of cartilage tissue [18–22]. We did not model the bones of the facial skull, since its share compared to the brain is about 13%, and a significant part of the body of the maxilla and mandibula is occupied by developing teeth [33–35]. Besides, vertebral processes were not modeled, since only small ossification centers are observed in newborns [23].

The chemical composition of the simulated medias was selected based on ICRP data for adults [19]. The chemical composition of bone tissue and the AM used for all BPS is presented in tab. 2. 

The density of mineralized bone tissue was estimated based on the results of measurements of the cortical bone density of newborns [24] and is 1.65 g/cm³. The density of the red bone marrow was taken equal to the density of water (1 g/cm³) [25].

We estimated the parameters of the spongiosa microarchitecture based on published data already described in detail [14]. The linear dimensions and thickness of the cortical layer as BPS parameters are presented in tab. 3. 

Thus, the phantom of skeletal hematopoietic sites of a newborn consist of 34 BPSs. Depending on the form of the simulated hematopoietic site, it may include 1 (ribs) to 5 (sacrum) BPSs. Most of the BPSs are cylinders and rectangular parallelepipeds. The sizes of phantoms vary widely: from 2 to 33 mm. As shown in tab. 3, not all phantoms are covered with a cortical layer, which is associated with an incomplete process of ossification of the spine and skull bones. The highest Ct.Th value for a newborn is characteristic of the diaphysis of the femur (1.7 mm).

DISCUSSION

To test the adequacy of the SPSD approach, we performed a comparison of simulated phantoms and real bones. There are unique data on the mass of wet mineralized bones obtained during the study of 40 full-term newborns [68]. Masses corresponding to the sizes of phantoms were calculated as the sum of the volumes of simulated medias (BM, TB, CB) multiplied by their density.

A comparison of the measured bone masses and masses of SPSD phantoms (calculated as the sum of the masses of the segments describing the bone) is shown in fig. 2.

As can be seen from the comparison, the masses corresponding to the sizes of SPSD phantoms in most cases fall within the range of standard deviation of the values obtained by the author of the compared work [68], that is, they correspond well to the masses of real bones.

A feature of the SPSD phantom is the generation by the BPS of a simple geometric shape, that is, a simplified representation of the real shape of the bone site. A simplified representation can result in biased estimates of simulation results. As mentioned earlier, BPS is modeled with mean population parameter values, and SPS parameters were randomly selected within their population variability range. As a result, the simulated bone segment is "inside" a set of SPSs geometric shapes. The variance of the DF set calculated for SPS reflects the effect of variability in bone size, shape, and microstructure.

CONCLUSIONS

As a result of the work, computational phantoms of the main skeletal sites with active hematopoiesis for a newborn were generated. The simulated phantom imitate the structure of bone tissue as well as the variability of skeletal parameters within a population. The phantom fits well with measurements of the newborn's real bones. The phantom is used to improve the the Techa River dosimetry system. In the future, SPSD phantoms will be created for other age groups: 1 year, 5 years, 10 years, 15 years, adults and for the human fetus at 24 weeks of pregnancy. SPSD phantoms can be used for dosimetry of other bone-seeking beta emitters including used in radionuclide therapy such as ⁸⁹Sr, ³²P, ¹⁸⁶Re, ¹⁸⁸Re, ^117mSm.