A framework to model charge sharing and pulse pileup for virtual imaging trials of photon-counting CT

Objective. This study describes the development, validation, and integration of a detector response model that accounts for the combined effects of x-ray crosstalk, charge sharing, and pulse pileup in photon-counting detectors. Approach. The x-ray photon transport was simulated using Geant4, followed by analytical charge sharing simulation in MATLAB. The analytical simulation models charge clouds with Gaussian-distributed charge densities, which are projected on a 3x3 pixel neighborhood of interaction location to compute detected counts. For pulse pileup, a prior analytical method for redistribution of energy-binned counts was implemented for delta pulses. The x-ray photon transport and charge sharing components were validated using experimental data acquired on the CdTe-based Pixirad-1/Pixie-III detector using monoenergetic beams at 26, 33, 37, and 50 keV. The pulse pileup implementation was verified with a comparable Monte Carlo simulation. The model output without pulse pileup was used to generate spatio-energetic response matrices for efficient simulation of scanner-specific photon-counting CT (PCCT) images with DukeSim, with pulse pileup modeled as a post-processing step on simulated projections. For analysis, images for the Gammex multi-energy phantom and the XCAT chest phantom were simulated at 120 kV, both with and without pulse pileup for a range of doses (27-1344 mAs). The XCAT images were evaluated qualitatively at 120 mAs, while images for the Gammex phantom were evaluated quantitatively for all doses using measurements of attenuation coefficients and Calcium concentrations. Main results. Reasonable agreement was observed between simulated and experimental spectra with Mean Absolute Percentage Error Values (MAPE) between 10% and 31% across all incident energies and detector modes. The increased pulse pileup from increased dose affected attenuation coefficients and calcium concentrations, with an effect on calcium quantification as high as MAPE of 28%. Significance. The presented approach demonstrates the viability of the model for enabling VITs to assess and optimize the clinical performance of PCCT.