In-silico Modeling, Optimization, and Harmonization of Photon-Counting Detector Computed Tomography

Abstract

Purpose: To develop, validate, and demonstrate a customizable photon-counting detector computed tomography (PCD-CT) model for optimizing energy settings and generating harmonized virtual monoenergetic images to enhance spectral separation, inter- and intra-scanner consistency, and material imaging accuracy. Methods: For the development, validation and utility-demonstration, a customizable simulation model, DukeCounter, was developed to replicate real PCD-CT systems. Photon transport and crosstalk in PCDs were modeled using Monte Carlo simulations, and charge sharing was implemented using an analytical Gaussian charge cloud model. The fundamental interactions in PCDs including photoelectric absorption, Compton and fluorescence x-ray scatterings, charge cloud formation, and charge diffusion and repulsion were modeled. Spatio-energetic detector responses were generated for face-on CdTe-, CZT-, GaAs-, and edge-on Si-based PCDs. These responses, combined with standardized scanner parameters, were integrated into a CT simulator to create virtual DukeCounter PCD-CT scanners. The framework was benchmarked against experimental data from a clinical CdTe-based PCD-CT scanner across three dose levels. To demonstrate its utility, three pilot studies were conducted using a computational ACR phantom for task-generic image quality assessment, an XCAT model with bronchitis and emphysema for COPD biomarker extraction, and an XCAT with liver lesions for lesion detectability analysis.For the PCD-CT optimization, CdTe-, CZT-, and Si-based PCD-CT scanners were modeled using an in-silico imaging framework by incorporating scanner geometries and validated spatio-energetic detector responses of DukeCounter to account for inter-pixel and inter-energy crosstalk and noise correlation. Using these models, two energy settings (thresholding and binning), two dose levels, and two sizes of a cylindrical phantom containing inserts with various concentrations of calcium, iodine, and gadolinium were simulated. The tube voltage (120 kV), pitch (1), gantry rotation speed (0.5 rot/second), and reconstruction settings were held constant across all acquisitions. Quantitative metrics including the separability index (s’) and contrast-to-noise ratio (CNR) were determined. Energy settings were ranked based on the s’, and the rank-sum method with a Friedman test was used to determine the optimal setting.For the PCD-CT harmonization, in-silico models of CdTe-, CZT-, and Si-based PCD-CT scanners were simulated to generate four energy-bin CT images for both multi-material cylindrical and anthropomorphic (XCAT) phantoms. Images were acquired across four exposure levels (50, 100, 200, 400 mAs), three helical pitches (0.8, 1.0, 1.2), and two reconstruction kernels (Hann and Ram-Lak), while keeping other parameters constant. Ground-truth VMIs (in HU) were generated from the known linear attenuation coefficients at energies 30 to 90 keV (5 keV intervals). A conditional U-Net architecture was trained to predict a target-energy VMI given the four energy-bin images and an encoded energy level as inputs. The model was trained on 75% of data, validated on 15%, and tested on 10%. Quantitative performance was assessed using root mean square error (RMSE), mean absolute percentage difference (MAPD), structural similarity index measure (SSIM), and voxel-wise Bland-Altman analyses across scanners and acquisition conditions.Results: From the PCD modeling study, the simulated charge cloud size increased with energy and was more pronounced in Si due to its low atomic number. The detector response across a 3×3-pixel neighborhood varied with PCD material, design, and energy threshold settings. Validation results demonstrated strong agreement between simulated and real ACR images. For the 20-keV-threshold images, the mean relative difference (MRD) in f50 of MTF was 4.15%1.21 for air and 2.54%2.08 for bone, and the MRD in fav of NPS was 0.83%0.97. The MRDs in noise magnitude were 2.65%1.68, 3.05%1.97, and 2.78%1.79 for the 20-keV-threshold, 65-keV-threshold, and 70-keV-VMI images, respectively. The MRDs in CT number for the same image types were 0.03%0.03, 0.11%0.09, 0.11%0.05 for air, and 1.85%0.20, 1.84%0.55, 0.50%0.36 for polyethylene. DukeCounter-generated images showed that task-generic and task-specific image qualities were influenced by PCD materials, designs, and energy threshold settings. GaAs-based DukeCounter exhibited the highest image noise, the largest error in COPD biomarker quantification, and the lowest performance in liver lesion detection, under consistent acquisition and reconstruction settings.From the PCD-CT optimization study, the optimal energy settings varied primarily with phantom size and material pairs to separate (Ca-I, Ca-Gd, I-Gd) rather than dose level. When aggregated across all imaging tasks and conditions, the optimal energy settings were 30-65 keV and 20-35-50-70 keV for two- and four-threshold CdTe-, 20-35-50-70 keV for four-threshold CZT-, and 5-35-50-80-120 keV for four-bin Si-based PCD-CT systems. Four-threshold CdTe showed significantly higher s’ performance than two-threshold (mean difference of 0.87 ± 1.57, p < 0.001). Four-threshold CZT performed slightly but consistently better than CdTe (mean difference of 0.11  0.28, p < 0.001).From the PCD-CT harmonization study, the conditional U-Net model achieved high quantitative and structural accuracy in generating harmonized VMIs across all scanners and imaging conditions for both cylindrical and XCAT phantoms. For cylindrical phantoms, the mean RMSE and MAPD were 8.5  4.4 HU and 11.1  4.3 % for CdTe-, 9.4  3.8 HU and 11.2  3.6 % for CZT-, and 12.2  6.9 HU and 16.4  8.0 % for Si-based PCD-CT scanners. For the XCAT phantom, performance was comparable (RMSE = 12.1-13.2 HU and MAPD = 11.8-16.0 %), improving at higher exposure levels (RMSE = 11.9  5.3 HU, MAPD = 11.2  5.2 % at 400 mAs). Voxel-wise Bland–Altman analysis revealed minimal bias (< 3 HU) and tight 95% limits of agreement ( 17 HU) between scanner pairs, confirming inter-scanner harmonization. Structural similarity between predicted and ground-truth VMIs was high (SSIM = 0.96-0.99), demonstrating high spatial and spectral fidelity across all imaging conditions.Conclusion:A customizable, modular simulation framework was developed to model spatio-energetic detector responses for various PCD materials and designs. The detector responses were integrated into a CT simulation pipeline to build DukeCounter PCD-CT systems. The framework’s utility was demonstrated through task-specific assessments of image quality and clinical performance of DukeCounter systems using XCAT phantoms. This approach enables systematic PCD-CT design evaluation and optimization, supporting translational research in medical imaging by reducing the cost, time, and radiation burden of physical experiments.The s-prime optimization work presented a simulation-based framework for optimizing PCD-CT scanners and provided clinically translatable energy settings to advance the clinical adoption of PCD-CT and support accurate, standardized spectral imaging.The proposed conditional U-Net effectively learns the nonlinear mapping between multi-energy PCD-CT data and corresponding VMIs across various scanners and acquisition protocols. By leveraging realistic, physics-informed in-silico datasets that provide ground-truth mappings, this framework offers a computationally efficient, data-driven pipeline for harmonized VMI generation. The approach eliminates the need for scanner-specific calibrations or material-basis selection and provides standardized, scanner-agnostic spectral imaging, advancing the clinical translation and quantitative reliability of PCD-CT.