Establishing error bounds for internal calibration of quantitative computed tomography

Opportunistic computed tomography (CT) scans, which can assess relevant osteoporotic bones of interest, offer a potential solution for identifying osteoporotic individuals. CT scans usually do not contain calibration phantoms, so internal calibration methods have been developed to create a voxel-specific density calibration that can be used in opportunistic CT. It remains a challenge, however, to account for potential sources of error in internal calibration, such as beam hardening or heterogeneous internal reference tissues. The purpose of this work was to introduce our internal calibration method that accounts for these variations and to estimate error bounds for the bone mineral density (BMD) measurements taken from internally calibrated scans. The error bounds are derived by incorporating a combination of a Monte Carlo simulation and standard error propagation into our previously established internal calibration method. A cohort of 138 clinical abdominal CT scans were calibrated for BMD assessment with a phantom placed in the field of view and used as the ground truth. Our modified internal calibration method provided error bounds on the same images and was tested to contain the ground truth phantom-calibrated BMD. This was repeated using 10 different internal reference tissue combinations to explore how error bounds are affected by the choice of internal tissue referents. We found that the tissue combination of air, skeletal muscle, and cortical bone yielded the most accurate BMD estimates while maintaining error bounds that were sufficiently conservative to account for sources of error such as beam hardening and heterogeneous tissue samples. The mean difference between the phantom BMD and the BMD resulting from the tissue combination of air, skeletal muscle and cortical bone was 2.12 mg/cc (0.06% BMD error) and 1.13 mg/cc (0.02 % BMD error) for the left and right femur, respectively. Providing error bounds for internal calibration provides a method to explore the influence of internal reference tissues and confidence for BMD estimates.