Counting Loss Correction of Energy-Resolving Photon Counting Detector for Medical Imaging Based on Simulation of the Energy Transportations of the X-Rays

Analysis of X-ray energies made available by energy-resolving photon counting detectors (ERPCDs) will derive novel quantitative X-ray images based on accurate material identification, in which information on true X-ray attenuation must be analyzed. However, in practical applications under high counting rates, this information is distorted by the counting loss caused by pulse pileup and dead time. In this study, we aimed to propose a counting loss correction algorithm. The correction is performed by converting the measured “counting rate values” into those expected in ideal measurement conditions. Because the degree of the counting loss relates to the shape of the energy spectrum, our algorithm considers X-ray penetration in objects with various effective atomic numbers <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left(\mathrm{Z}_{\text{eff }} \mathrm{s}\right)$</tex> and the detector response. The expected counting rates were derived by simulating X-ray spectra by considering the beam hardening effect and the detector response. To consider the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex> dependence, correction curves related to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$6.5&lt;\mathrm{Z}_{\text{eff }}&lt;13$</tex> were virtually generated from experimentally obtained correction curves for polymethyl methacrylate (PMMA, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}=6.5)$</tex> and aluminum <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\text{Al}, \mathrm{Z}_{\text{eff }}=13)$</tex>. In the correction process, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex> was firstly assumed, and the corresponding correction curve was tentatively applied to the measured counting rate of the unknown object. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex> was then determined by a previously reported material identification algorithm. Finally, a properly corrected condition was determined based on the principle that the derived <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex> should match the tentatively assumed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex>. Experimental verification was performed by measuring PMMA, Al, and their bilayer structures <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathrm{Z}_{\text{eff }}=8.5-10.5)$</tex> having mass thicknesses of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1-10 ~\mathrm{g} / \text{cm}^{2}$</tex> with our prototype detector. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}$</tex> images can be derived with an accuracy of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{eff }}+/-1$</tex>. Our counting loss correction method will contribute to high-precision quantitative analysis using ERPCD.