Bone mineral densitometry with x-ray and radionuclide sources: a theoretical comparison

Two methods of dual-photon absorptiometry (DPA) utilizing an x-ray tube instead of a radionuclide source have recently been introduced. In one method kVp switching is employed and two transmitted intensities at each pixel are determined. In the other method, K-edge filtration combined with a single kVp spectrum is used, but photons in two energy windows are counted. We present a theoretical analysis of the two methods, focusing on a figure of merit which is essentially the exposure efficiency (the precision for a given entrance exposure) and tube loading. We also compare their exposure efficiencies to theoretical limits that no DPA system can exceed. Our study indicates that the K-edge-filtered method is more exposure efficient by about a factor of 2. The switched-kVp method requires less heat units per scan by about a factor of 3. A hybrid K-edge switched-kVp method is suggested which achieves the same exposure efficiency as the K-edge-filtered method at lesser tube loading. Our theoretical model is based on published x-ray spectra and attenuation coefficients and is in good agreement with other simulation work. It is of interest that a point source of Gd-153 would be even more exposure efficient, achieving about 90% of the theoretical limit. However, in practice, the Gd source is of finite size and limited strength, and consequently the radionuclide method cannot achieve as good a precision as either x-ray method in similar scan times.