Voxel size effects in three‐dimensional nuclear magnetic resonance microscopy performed for trabecular bone dosimetry

Abstract

An important problem in internal dosimetry is the assessment of energy deposition by beta particles within trabecular regions of the skeleton. Recent dosimetry methods for trabecular bone are based on Monte Carlo particle transport simulations within three-dimensional (3D) images of real human bone samples. Nuclear magnetic resonance (NMR) microscopy is a 3D imaging technique of choice due to the large signal differential between bone tissue and the water-filled marrow cavities. Image voxel sizes currently used in NMR microscopy are between 50 microm and 100 microm, but the images are time consuming to acquire and can only be performed at present for in vitro samples. It is therefore important to evaluate what resolution is best suitable in order to properly characterize the trabecular microstructure, to adequately predict the tissue dosimetry, and to minimize imaging time. In this work, a mathematical model of trabecular bone, composed of a distribution of spherical marrow cavities, was constructed. The mathematical model was subsequently voxelized with different voxel sizes (16 microm to 1,000 microm) to simulate 3D NMR images. For each image, voxels are assigned to either bone or marrow according to their enclosed marrow fraction. Next, the images are coupled to the EGS4 electron transport code and absorbed fractions to bone and marrow are calculated for a marrow source of monoenergetic electrons. Radionuclide S values are also determined for the voxelized images with results compared to data calculated for the pure mathematical sample. The comparison shows that for higher energy electrons (>400 keV), good convergence of the results is seen even within images of poor resolution. Above 400 keV, a voxel resolution as large as 300 microm results in dosimetry errors below 5%. For low-energy electrons and high-resolution images, the self-dose to marrow is also determined to within 5% accuracy. Nevertheless, increased voxelization of the image overestimates the surface area of the bone-marrow interface leading to errors in the cross-dose to bone as high as 25% for some low-energy beta emitters.

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

“…44 The principle is to calculate the volume fraction of each voxel inside the sphere. If this volume fraction exceeds 0.5, the voxel is assigned to marrow; otherwise, it is assigned to bone.…”

MIRD Pamphlet No. 25: MIRDcell V2.0 Software Tool for Dosimetric Analysis of Biologic Response of Multicellular Populations

“…However, there have been dramatic improvements in dosimetry models that reflect the substructure of organs as well as tissue elements within them (3)(4)(5). These models rely on improved nuclear medicine imaging capabilities that facilitate determination of activity within the voxels that represent tissue elements that are about 0.2-1 cm 3 in volume (6)(7)(8)(9). However, even these improved approaches assume that all cells within the tissue element receive essentially the same absorbed dose.…”

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).…”