A cascaded model of spectral distortions due to spectral response effects and pulse pileup effects in a photon-counting x-ray detector for CT

Purpose: Energy discriminating, photon-counting detectors (PCDs) are an emerging technology for computed tomography (CT) with various potential benefits for clinical CT. The photon energies measured by PCDs can be distorted due to the interactions of a photon with the detector and the interaction of multiple coincident photons. These effects result in distorted recorded x-ray spectra which may lead to artifacts in reconstructed CT images and inaccuracies in tissue identification. Model-based compensation techniques have the potential to account for the distortion effects. This approach requires only a small number of parameters and is applicable to a wide range of spectra and count rates, but it needs an accurate model of the spectral distortions occurring in PCDs. The purpose of this study was to develop a model of those spectral distortions and to evaluate the model using a PCD (model DXMCT-1; DxRay, Inc., Northridge, CA) and various x-ray spectra in a wide range of count rates. Methods: The authors hypothesize that the complex phenomena of spectral distortions can be modeled by: (1) separating them into count-rate independent factors that we call the spectral response effects (SRE), and count-rate dependent factors that we call the pulse pileup effects (PPE), (2) developing separate models for SRE and PPE, and (3) cascading the SRE and PPE models into a combined SRE+PPE model that describes PCD distortions at both low and high count rates. The SRE model describes the probability distribution of the recorded spectrum, with a photo peak and a continuum tail, given the incident photon energy. Model parameters were obtained from calibration measurements with three radioisotopes and then interpolated linearly for other energies. The PPE model used was developed in the authors' previous work [K. Taguchi et al., "Modeling the performance of a photon counting x-ray detector for CT: Energy response and pulse pileup effects," Med. Phys. 38(2),