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.