Theoretical analysis of error propagation in triple-energy absorptiometry: application to measurement of lead in bone in vivo

Bone densitometry using x-ray spectra

In contrast to the two distinct energy regions that are involved in dual-energy x-ray absorptiometry for bone densitometry, the complete spectrum of a beam transmitted through two layers of different materials is utilized in this study to calculate the areal density of each material. Test objects constructed from aluminum and Plexiglas were used to simulate cortical bone and soft tissue, respectively. Solid-state HPGe (high-purity germanium) detectors provided high-resolution x-ray spectra over an energy range of approximately 20-80 keV. Areal densities were obtained from spectra using two methods: a system of equations for two spectral regions and a nonlinear fit of the entire spectrum. Good agreement with the known areal densities of aluminum was obtained over a wide range of PMMA thicknesses. The spectral method presented here can be used to decrease beam hardening at a small number of bodily points selected for examination.

Quantification of breast density with dual energy mammography: a simulation study

Breast density, the percentage of glandular breast tissue, has been identified as an important yet underutilized risk factor in the development of breast cancer. A quantitative method to measure breast density with dual energy imaging was investigated using a computer simulation model. Two configurations to measure breast density were evaluated: the usage of monoenergetic beams and an ideal detector, and the usage of polyenergetic beams with spectra from a tungsten anode x-ray tube with a detector modeled after a digital mammography system. The simulation model calculated the mean glandular dose necessary to quantify the variability of breast density to within 1/3%. The breast was modeled as a semicircle 10 cm in radius with equal homogenous thicknesses of adipose and glandular tissues. Breast thicknesses were considered in the range of 2-10 cm and energies in the range of 10-150 keV for the two monoenergetic beams, and 20-150 kVp for spectra with a tungsten anode x-ray tube. For a 4.2 cm breast thickness, the required mean glandular doses were 0.183 microGy for two monoenergetic beams at 19 and 71 keV, and 9.85 microGy for two polyenergetic spectra from a tungsten anode at 32 and 96 kVp with beam filtrations of 50 microm Rh and 300 microm Cu for the low and high energy beams, respectively. The results suggest that for either configuration, breast density can be precisely measured with dual energy imaging requiring only a small amount of additional dose to the breast. The possibility of using a standard screening mammogram as the low energy image is also discussed.