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Photon-counting CT (PCCT) is an emerging imaging technology with potential improvements in quantification and rendition of micro-structures due to its smaller detector sizes. The aim of this study was to assess the performance of a new PCCT scanner (NAEOTOM Alpha, Siemens) in quantifying clinically relevant bone imaging biomarkers for characterization of common bone diseases. We evaluated the ability of PCCT in quantifying microarchitecture in bones compared to conventional energy-integrating CT. The quantifications were done through virtual imaging trials, using a 50 percentile BMI male virtual patient, with a detailed model of trabecular bone with varied bone densities in the lumbar spine. The virtual patient was imaged using a validated CT simulator (DukeSim) at CTDI vol of 20 and 40 mGy for three scan modes: ultra-high-resolution PCCT (UHR-PCCT), high-resolution PCCT (HR-PCCT), and a conventional energy-integrating CT (EICT) (FORCE, Siemens). Further, each scan mode was reconstructed with varying parameters to evaluate their effect on quantification. Bone mineral density (BMD), trabecular volume to total bone volume (BV/TV), and radiomics texture features were calculated in each vertebra. The most accurate BMD measurements relative to the ground truth were UHR-PCCT images (error: 3.3% ± 1.5%), compared to HR-PCCT (error: 5.3% ± 2.0%) and EICT (error: 7.1% ± 2.0%). UHR-PCCT images outperformed EICT and HR-PCCT. In BV/TV quantifications, UHR-PCCT (errors of 29.7% ± 11.8%) outperformed HR-PCCT (error: 80.6% ± 31.4%) and EICT (error: 67.3% ± 64.3). UHR-PCCT and HR-PCCT texture features were sensitive to anatomical changes using the sharpest kernel. Conversely, the texture radiomics showed no clear trend to reflect the progression of the disease in EICT. This study demonstrated the potential utility of PCCT technology in improved performance of bone quantifications leading to more accurate characterization of bone diseases.