Spatio-energetic cross-talk in photon counting detectors: Numerical detector model (PcTK) and workflow for CT image...

The interpixel cross-talk of energy-sensitive photon counting x-ray detectors (PCDs) has been studied and an analytical model (version 2.1) has been developed for double-counting between neighboring pixels due to charge sharing and K-shell fluorescence x-ray emission followed by its reabsorption (Taguchi K, et al., Medical Physics 2016;43(12):6386-6404). While the model version 2.1 simulated the spectral degradation well, it had the following problems that has been found to be significant recently: (1) The spectrum is inaccurate with smaller pixel sizes; (2) the charge cloud size must be smaller than the pixel size; (3) the model underestimates the spectrum/counts for 10-40 keV; and (4) the model version 2.1 cannot handlen-tuple-counting withn > 2 (i.e., triple-counting or higher). These problems are inherent to the design of the model version 2.1; therefore, we developed a new model and addressed these problems in this study.

We propose a new PCD cross-talk model (version 3.2; Pc TK for "photon counting toolkit") that is based on a completely different design concept from the previous version. It uses a numerical approach and starts with a 2-D model of charge sharing (as opposed to an analytical approach and a 1-D model with version 2.1) and addresses all of the four problems. The model takes the following factors into account: (1) shift-variant electron density of the charge cloud (Gaussian-distributed), (2) detection efficiency, (3) interactions between photons and PCDs via photoelectric effect, and (4) electronic noise. Correlated noisy PCD data can be generated using either a multivariate normal random number generator or a Poisson random number generator. The effect of the two parameters, the effective charge cloud diameter (d₀ ) and pixel size (d_pix ), was studied and results were compared with Monte Carlo simulations and the previous model version 2.1. Finally, a script for the workflow for CT image quality assessment has been developed, which started with a few material density images, generated material-specific sinogram (line integrals) data, noisy PCD data with spectral distortion using the model version 3.2, and reconstructed PCD- CT images for four energy windows.

The model version 3.2 addressed all of the four problems listed above. The spectra withd_pix  = 56-113 μm agreed with that of Medipix3 detector withd_pix  = 55-110 μm without charge summing mode qualitatively. The counts for 10-40 keV were larger than the previous model (version 2.1) and agreed with MC simulations very well (root-mean-square difference values with model version 3.2 were decreased to 16%-67% of the values with version 2.1). There were many non-zero off-diagonal elements withn-tuple-counting withn > 2 in the normalized covariance matrix of 3 × 3 neighboring pixels. Reconstructed images showed biases and artifacts attributed to the spectral distortion due to the charge sharing and fluorescence x rays.

We have developed a new PCD model for spatio-energetic cross-talk and correlation between PCD pixels. The workflow demonstrated the utility of the model for general or task-specific image quality assessments for the PCD- CT.Note: The program (Pc TK) and the workflow scripts have been made available to academic researchers. Interested readers should visit the website (pctk.jhu.edu) or contact the corresponding author.