Dual energy x-ray absorptiometry: the effects of beam hardening on bone density measurements

X-ray tubes have superseded radionuclide sources for dual photon absorptiometry of the spine and hip. However, the use of a polyenergetic spectrum is a potential source of error for x-ray absorptiometers since beam hardening may result in a nonlinear measurement scale for bone mineral density (BMD). A quantitative study of the effects of beam hardening on measurements made with a commercial dual energy x-ray scanner has been performed. Bone was represented by layers of aluminum of linearly increasing thickness which were scanned under water thicknesses ranging from 0 to 25 cm to represent different body thicknesses of soft tissue. Beam hardening had two effects on measured BMD: (i) at a constant true BMD, measured BMD varied with water thickness; (ii) at a constant water thickness, the BMD scale was not precisely linear. For conditions appropriate to spine and hip studies (BMD) values in the range 0.7 to 1.4 g/cm2 and body thickness between 15 and 25 cm) the maximum deviation of measured BMD from a linear scale was 0.023 g/cm2, while the root-mean-square deviation (0.01 g/cm2) was comparable to the measurement precision for a spine or femoral neck scan (about 1%). The largest departures from linearity were found to occur at the thinnest water thicknesses for BMD values in the range 0.2 to 0.6 g/cm2. The effect of scale nonlinearity on the results of longitudinal studies was examined: for a spine scan at 20-cm body thickness, measured changes in BMD slightly overestimated the true change and implied an error of 0.15%/year for a measurement of a true rate of loss of 3% year in a postmenopausal woman.