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.

Presently, skeletal dosimetry models utilized in clinical medicine simulate electron path lengths through skeletal regions based upon distributions of linear chords measured across bone trabeculae and marrow cavities. In this work, a human thoracic vertebra has been imaged via nuclear magnetic resonance (NMR) spectroscopy yielding a three-dimensional voxelized representation of this skeletal site. The image was then coupled to the radiation transport code EGS4 allowing for 3D tracing of electron paths within its true 3D structure. The macroscopic boundaries of the trabecular regions, as well as the cortex of cortical bone surrounding the bone site, were explicitly considered in the voxelized transport model. For the case of a thoracic vertebra, energy escape to the cortical bone became significant at source energies exceeding approximately 2 MeV. Chord-length distributions were acquired from the same NMR image, and subsequently used as input for a chord-based dosimetry model. Differences were observed in the absorbed fractions given by the chord-based model and the voxel transport model, suggesting that some of the input chord distributions for the chord-based models may not be accurate. Finally, this work shows that skeletal mass estimates can be made from the same NMR image in which particle transport is performed. This feature allows one to determine a skeletal S-value using absorbed fraction and mass data taken from the same anatomical tissue sample. The techniques developed in this work may be applied to a variety of skeletal sites, thus allowing for the development of skeletal dosimetry models at all skeletal sites for both males and females and as a function of subject age.

Radiation dose estimates to the trabecular region of the skeleton are of primary importance due to recent advancements in nuclear medicine. Establishing methods for accurately calculating dose in these regions is difficult due to the complex microstructure of this anatomic site and the typical ranges of beta-particles in both bone and marrow tissues. At the present time, models of skeletal dosimetry used in clinical medicine rely upon measured distributions of straight-line path lengths (chord lengths) through bone and marrow regions. This work develops a new three-dimensional, digital method for acquiring these distributions within voxelized images. In addition, the study details the characteristics of measuring chord distributions within digital images and provides a methodology for avoiding undesirable pixel or voxel effects. The improved methodology has been applied to a digital image (acquired via NMR microscopy) of the trabecular region of a human thoracic vertebra. The resulting chord-length distributions across both bone trabeculae and bone marrow cavities were found to be in general agreement with those measured in other studies utilizing different methods. In addition, this study identified that bone and marrow space chord-length distributions are not statistically independent, a condition implicitly assumed within all current skeletal dosimetry models of electron transport. The study concludes that the use of NMR microscopy combined with the digital measurement techniques should be used to further expand the existing Reference Man database of trabecular chord distributions to permit the development of skeletal dosimetry models which are more age and gender specific.

Investigations at the University of Leeds under the direction of F.W. Spiers in the early 1960s through the late 1970s established the first comprehensive assessment of marrow dose conversion factors (DCFs) for beta-emitting radionuclides within the volume or on the surface of trabecular bone. These DCFs were subsequently used in deriving radionuclide S values for skeletal tissues published in MIRD Pamphlet No. 11. Eckerman re-evaluated this work and extended the methods of Spiers to radionuclides within the marrow to provide DCFs for fifteen skeletal regions in computational models representing individuals of six different ages. These results were used in the MIRDOSE3 software. Bouchet et al. used updated information on regional bone and marrow masses, as well as 3D electron transport techniques, to derive radionuclide S values in skeletal regions of the adult. Although these two efforts are similar in most regards, the models differ in three respects in: (1) the definition of the red marrow region, (2) the definition of a surface source of activity, and (3) the assumption applied in transporting electrons through the trabecular endosteum. In this study, a review of chord-based skeletal models is given, followed by a description of the differences in the Eckerman and Bouchet et al. transport models. Finally, new data from NMR microscopy and radiation transport in trabecular bone is applied to address item (1) above. Dose conversion factors from MIRD 11, the Eckerman model, the Bouchet et al. model, and a revised model are compared for several radionuclides important to internal emitter therapy.

In 1995, the International Commission on Radiological Protection (ICRP) issued ICRP Publication 70 which provided an extensive update to the physiological and anatomical reference data for the skeleton of adults and children originally issued in ICRP Publication 23. Although ICRP Publication 70 has been a valuable document in the development of reference voxel computational phantoms, additional guidance is needed for dose assessment in the skeletal tissues beyond that given in ICRP Publication 30. In this study, a computed tomography (CT) and micro-CT-based model of the skeletal tissues is presented, which considers (1) a 50-microm depth in marrow for the osteoprogenitor cells, (2) electron escape from trabecular spongiosa to the surrounding cortical bone, (3) cortical bone to trabecular spongiosa cross-fire for electrons and (4) variations in specific absorbed fraction with changes in bone marrow cellularity for electrons. A representative data set is given for electron dosimetry in the craniofacial bones of the adult male.