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A Three-Dimensional Transport Model for Determining Absorbed Fractions of Energy for Electrons Within Trabecular Bone

Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, Florida

Correspondence: For correspondence or reprints contact: Wesley E. Bolch, PhD, Department of Nuclear and Radiological Engineering, University of Florida, Gainesville, FL 32611-8300.

ABSTRACT

Bone marrow is generally the dose-limiting organ of concern in radioimmunotherapy and in radionuclide palliation of bone pain. However, skeletal dosimetry is complicated by the intricate nature of its microstructure, which can vary greatly throughout skeletal regions. In this article, a new three-dimensional electron transport model for trabecular bone is introduced, based on Monte Carlo transport and on bone microstructure information for several trabecular bone sites. Methods: Marrow cavity and trabecular chord length distributions originally published by Spiers et al. were randomly sampled to create alternating regions of bone, endosteum and marrow during the three-dimensional transport of single electrons. For the marrow spaces, explicit consideration of the site-specific elemental composition was made in the transport calculations based on the percentage of active and inactive marrow in each region. The electron transport was performed with the EGS4 electron transport code and the parameter reduced electron-step transport algorithm. Electron absorbed fractions of energy were tabulated for seven adult trabecular bone sites, considering three source and target regions: the trabecular marrow space (IMS), the trabecular bone endosteum (TBE) and the trabecular bone volume (TBV). Results: For all source-target combinations, the absorbed fraction was seen to vary widely within the skeleton. These variations can be directly attributed to the differences in the trabecular microstructure of the different skeletal regions. For many source-target combinations, substantial energy dependence was seen in the calculated absorbed fraction, a factor not considered in values recommended by the International Commission on Radiological Protection (ICRP). A one-dimensional model of electron transport in trabecular bone, based on range-energy relation ships, was also developed to verify the three-dimensional transport model and to evaluate differences between the two modeling approaches. Differences of 10%–15% were seen, particularly at low electron energies. In the case of a TBV source and a TMS target (or vice versa), differences >50% were seen in the absorbed fraction. Conclusion: The three-dimensional model of electron transport in trabecular bone allows improved estimates of skeletal absorbed fractions. The model highlights both the regional and the energy dependency of the absorbed fraction not previously considered in the ICRP model.

Key Words: dosimetry • trabecular bone • absorbed fractions • Monte Carlo transport • EGS4

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