Skeletal dosimetry: A hyperboloid representation of the bone-marrow interface to reduce voxel effects in three-dimensional images of trabecular bone

Radiation damage to the hematopoietic bone marrow is clearly defined as the limiting factor to the development of internal emitter therapies. Current dosimetry models rely on chord-length distributions measured through the complex microstructure of the trabecular bone regions of the skeleton in which most of the active marrow is located. Recently, Nuclear Magnetic Resonance (NMR) has been used to obtain high-resolution three-dimensional (3D) images of small trabecular bone samples. These images have been coupled with computer programs to estimate dosimetric parameters such as chord-length distributions, and energy depositions by monoenergetic electrons. This new technique is based on the assumption that each voxel of the image is assigned either to bone tissue or to marrow tissue after application of a threshold value. Previous studies showed that this assumption had important consequences on the outcome of the computer calculations. Both the chord-length distribution measurements and the energy deposition calculations are subject to voxel effects that are responsible for large discrepancies when applied to mathematical models of trabecular bone.;The work presented in this dissertation proposes first a quantitative study of the voxel effects. Consensus is that the voxelized representation of surfaces should not be used as direct input to dosimetry computer programs. Instead we need a new technique to transform the interfaces into smooth surfaces. The Marching Cube (MC) algorithm was used and adapted to do this transformation. The initial image was used to generate a continuous gray-level field throughout the image. The interface between bone and marrow was then simulated by the iso-gray-level surface that corresponds to a predetermined threshold value. Calculations were then performed using this new representation. Excellent results were obtained for both the chord-length distribution and the energy deposition measurements. Voxel effects were reduced to an acceptable level and the discrepancies found when using the voxelized representation of the interface were reduced to a few percent. We conclude that this new model should be used every time one performs dosimetry estimates using NMR images of trabecular bone samples.