A hyperboliod representation of the bone–marrow interface within 3D NMR images of trabecular bone: applications to skeletal dosimetry

Abstract

Recent advances in physical models of skeletal dosimetry utilize high-resolution NMR microscopy images of trabecular bone. These images are coupled to radiation transport codes to assess energy deposition within active bone marrow irradiated by bone- or marrow-incorporated radionuclides. Recent studies have demonstrated that the rectangular shape of image voxels is responsible for cross-region (bone-to-marrow) absorbed fraction errors of up to 50% for very low-energy electrons (<50 keV). In this study, a new hyperboloid adaptation of the marching cube (MC) image-visualization algorithm is implemented within 3D digital images of trabecular bone to better define the bone–marrow interface, and thus reduce voxel effects in the assessment of cross-region absorbed fractions. To test the method, a mathematical sample of trabecular bone was constructed, composed of a random distribution of spherical marrow cavities, and subsequently coupled to the EGSnrc radiation code to generate reference values for the energy deposition in marrow or bone. Next, digital images of the bone model were constructed over a range of simulated image resolutions, and coupled to EGSnrc using the hyperboloid MC (HMC) algorithm. For the radionuclides 33P, 117mSn, 131I and 153Sm, values of S(marrow←bone) estimated using voxel models of trabecular bone were shown to have relative errors of 10%, 9%, <1% and <1% at a voxel size of 150 µm. At a voxel size of 60 µm, these errors were 6%, 5%, <1% and <1%, respectively. When the HMC model was applied during particle transport, the relative errors on S(marrow←bone) for these same radionuclides were reduced to 7%, 6%, <1% and <1% at a voxel size of 150 µm, and to 2%, 2%, <1% and <1% at a voxel size of 60 µm. The technique was also applied to a real NMR image of human trabecular bone with a similar demonstration of reductions in dosimetry errors.