A theoretical analysis of the accuracy of single-energy CT bone-mineral measurements.

A relationship has been derived between the in vivo concentration of calcium hydroxyapatite and the in vitro concentration of K2HPO4 solution in a single-energy quantitative computed tomography (QCT) bone-mineral determination. Under certain simplifying assumptions this relationship is linear. The gradient term has been calculated as a function of scanner effective energy using the measured variation of solvent water density with K2HPO4 concentration; it ranges from 1.17 at 60 keV to 1.21 at 80 keV. The intercept term has been calculated as a function of effective energy, patient age and trabecular bone volume (TBV) by modelling the constituents of whole trabecular bone and using published normal composition data. It varies from about 15 to 25 mg cm-3 at an effective energy of 70 keV and within a TBV range of 5 to 20%. This intercept term may be used as an additive correction which improves the accuracy of single-energy QCT results without significant loss of precision. However, the method is limited by the uncertainties of tissue composition in an individual patient.