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.

A stoichiometric calibration method for dual energy computed tomography

“…As reported in several studies (e.g., see ref. [51,52]), the thyroid is difficult to model due to its content in iodine which makes it highly sensitive to the energy spectrum due to the photoelectric effect dominance for low energies. respectively.…”

“…At the basis of the stoichiometric calibration of Schneider et al (1996), the parametrization of Jackson and Hawkes [19] relies on Mayneord's power law [26,44] and is limited when it comes to modelling the photoelectric effect in human tissues containing high-Z materials, such as bone [51] or the thyroid [52]. Other problems also arise with the attempt to consistently defining the EAN using a power law, as the choice of the exponent is arbitrary [3,23,37].…”

Dimensionality and noise in energy selective x‐ray imaging

“…Gingold and Hasegawa 15 and Williamson et al 16 not only study the intrinsic dimensionality but also use sensitivity analysis with the partial derivatives of the basis set coefficients to include errors in the measurements. Gingold and Hasegawa compare the errors using two monoenergetic spectra with energies in low and high bands to the sensitivity analysis.…”

Alternating Minimization Algorithms for Transmission Tomography

“…They and Williamson, et al [42] describe methods to recover the relative partial densities using monoenergetic approximations to the scans and linear inversions.…”