Surface area overestimation within three-dimensional digital images and its consequence for skeletal dosimetry

The most recent methods for trabecular bone dosimetry are based on Monte Carlo transport simulations within three-dimensional (3D) images of real human bone samples. Nuclear magnetic resonance and micro-computed tomography have been commonly used as imaging tools for studying trabecular microstructure. In order to evaluate the accuracy of these techniques for radiation dosimetry, a previous study was conducted that showed an overestimate in the absorbed fraction of energy for low-energy electrons emitted within the marrow space and irradiating the bone trabeculae. This problem was found to be related to an overestimate of the surface area of the true bone-marrow interface within the 3D digital images, and was identified as the surface-area effect. The goal of the present study is to better understand how this surface-area effect occurs in the case of single spheres representing individual marrow cavities within trabecular bone. First, a theoretical study was conducted which showed that voxelization of the spherical marrow cavity results in a 50% overestimation of the spherical surface area. Moreover, this overestimation cannot be reduced through a reduction in the voxel size (e.g., improved image resolution). Second, a series of single-sphere marrow cavity models was created with electron sources simulated within the sphere (marrow source) and outside the sphere (bone trabeculae source). The series of single-sphere models was then voxelized to represent 3D digital images of varying resolution. Transport calculations were made for both marrow and bone electron sources within these simulated images. The study showed that for low-energy electrons (< 100 keV), the 50% overestimate of the bone-marrow interface surface area can lead to a 50% overestimate of the cross-absorbed fraction. It is concluded that while improved resolution will not reduce the surface area effects found within 3D image-based transport models, a tenfold improvement in current image resolution would compensate the associated errors in cross-region absorbed fractions for low-energy electron sources. Alternatively, other methods of defining the bone-marrow interface, such as with a polygonal isosurface, would provide improvements in dosimetry without the need for drastic reductions in image voxel size.