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

Abstract

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.

The UF series of tomographic computational phantoms of pediatric patients

“…The lower image resolution in z direction ͑CT slice thickness͒ generates a slightly stair-stepped surface of the external features of the older phantoms and their internal organs, with a corresponding overestimate of their sur-face area. 28 Previous studies from both Jones 29 and Zankl, 30 however, indicate that these voxelized organ surfaces do not significantly influence dosimetry results for photon irradiations. The rather unsmooth surfaces near the abdomen of the 9-month phantom are thought to be due to breathing artifacts introduced during the CT scan.…”

Lognormal Distribution of Cellular Uptake of Radioactivity: Monte Carlo Simulation of Irradiation and Cell Killing in 3-Dimensional Populations in Carbon Scaffolds

“…However, because of the jagged representation of the boundary between voxels, this segmentation does not preserve the surface area of the interface between the 2 media. This voxel effect has consequences for dosimetric assessment using Monte Carlo transport and is especially important for low-energy electrons (35). At a 6-mm voxel size, the effect is pronounced for electron energies below 20 keV (e.g., for electrons emitted by 3 H or 125 I).…”

Comparison of NMR simulations of porous media derived from analytical and voxelized representations

“…It is well known that the process of discretizing an analytically defined surface inevitably leads to errors because a continuous surface is truncated into a finite number of bins [19][20][21]. Table 1 describes results obtained from the discretization of a pore using different voxel sizes.…”

“…Peter et al [19] found that discretization of actual phantom geometry yielded inaccurate simulations compared to those obtained with analytical phantoms in their Monte-Carlo simulations for nuclear biomedical application. Rajon et al [20,21] emphasized that image voxelization overestimates the surface area of the bone-marrow interface, thereby leading to errors in cross-dose to bone as high as 25% for some low-energy beta emitters. They also found that the overestimation cannot be reduced through reduction of the voxel size (e.g., improved image resolution).…”