TY - JOUR

T1 - On two-parameter models of photon cross sections

T2 - Application to dual-energy CT imaging

AU - Williamson, Jeffrey F.

AU - Li, Sicong

AU - Devic, Slobodan

AU - Whiting, Bruce R.

AU - Lerma, Fritz A.

N1 - Funding Information:
This work was supported in part by Grants No. CA R01-46640 and CA R01-75371 awarded by the National Institutes of Health. The authors are indebted to two Virginia Commonwealth University summer work/study students, Suresh Joel (Department of Biomedical Engineering) and James Liang (School of Medicine), who contributed significantly to the MATLAB codes used for data analysis in this project.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Basis-vector model

KW - Dual-energy x-ray computed tomography

KW - Monte Carlo simulation

KW - Parametric fit model

KW - Photon cross section

UR - http://www.scopus.com/inward/record.url?scp=33750549467&partnerID=8YFLogxK

U2 - 10.1118/1.2349688

DO - 10.1118/1.2349688

M3 - Article

C2 - 17153391

AN - SCOPUS:33750549467

SN - 0094-2405

VL - 33

SP - 4115

EP - 4129

JO - Medical physics

JF - Medical physics

IS - 11

ER -