On two-parameter models of photon cross sections: Application to dual-energy CT imaging



The goal of this study is to evaluate the theoretically achievable accuracy in estimating photon cross sections at low energies (201000keV) from idealized dual-energy x-ray computed tomography (CT) images. Cross-section estimation from dual-energy measurements requires a model that can accurately represent photon cross sections of any biological material as a function of energy by specifying only two characteristic parameters of the underlying material, e.g., effective atomic number and density. This paper evaluates the accuracy of two commonly used two-parameter cross-section models for postprocessing idealized measurements derived from dual-energy CT images. The parametric fit model (PFM) accounts for electron-binding effects and photoelectric absorption by power functions in atomic number and energy and scattering by the Klein–Nishina cross section. The basis-vector model (BVM) assumes that attenuation coefficients of any biological substance can be approximated by a linear combination of mass attenuation coefficients of two dissimilar basis substances. Both PFM and BVM were fit to a modern cross-section library for a range of elements and mixtures representative of naturally occurring biological materials (Z=220). The PFM model, in conjunction with the effective atomic number approximation, yields estimated the total linear cross-section estimates with mean absolute and maximum error ranges of 0.6%–2.2% and 1%–6%, respectively. The corresponding error ranges for BVM estimates were 0.02%–0.15% and 0.1%–0.5%. However, for photoelectric absorption frequency, the PFM absolute mean and maximum errors were 10.8%–22.4% and 29%–50%, compared with corresponding BVM errors of 0.4%–11.3% and 0.5%–17.0%, respectively. Both models were found to exhibit similar sensitivities to image-intensity measurement uncertainties. Of the two models, BVM is the most promising approach for realizing dual-energy CT cross-section measurement.