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

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 μ m and 100 μ m , 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 μ m to 1000 μ m ) 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 μ m 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.