title: On two-parameter models of photon cross sections: application to dual-energy CT imaging.
abstract: The goal of this study is to evaluate the theoretically achievable accuracy in estimating photon cross sections at low energies (20-1000 keV) 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 = 2-20). 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.
authors.affiliation: Department of Radiation Oncology, Virginia Commenwealth University, Richmond, Virginia 23284, USA. jwilliamson@mcvh-vcu.edu
authors.forename: Jeffrey F
authors.initials: JF
authors.lastname: Williamson
authors.forename: Sicong
authors.initials: S
authors.lastname: Li
authors.forename: Slobodan
authors.initials: S
authors.lastname: Devic
authors.forename: Bruce R
authors.initials: BR
authors.lastname: Whiting
authors.forename: Fritz A
authors.initials: FA
authors.lastname: Lerma
mesh_terms: D015502:Absorptiometry, Photon / Q000379:methods*; D000465:Algorithms; D019412:Anatomy, Cross-Sectional / Q000379:methods*; D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000379:methods; D008954:Models, Biological; D017785:Photons; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*