Technical Note: Exploring the limit for the conversion of energy-subtracted CT number to electron density for high-atomic-number materials

Purpose: For accurate tissue inhomogeneity correction in radiotherapy treatment planning, the authors had previously proposed a novel conversion of the energy-subtracted CT number to an electron density (ΔHU–ρ_e conversion), which provides a single linear relationship between ΔHU and ρ_e over a wide ρ_e range. The purpose of this study is to address the limitations of the conversion method with respect to atomic number (Z) by elucidating the role of partial photon interactions in the ΔHU–ρ_e conversion process. Methods: The authors performed numerical analyses of the ΔHU–ρ_e conversion for 105 human body tissues, as listed in ICRU Report 46, and elementary substances with Z = 1–40. Total and partial attenuation coefficients for these materials were calculated using the XCOM photon cross section database. The effective x-ray energies used to calculate the attenuation were chosen to imitate a dual-source CT scanner operated at 80–140 kV/Sn under well-calibrated and poorly calibrated conditions. Results: The accuracy of the resultant calibrated electron density,ρ_e^cal, for the ICRU-46 body tissues fully satisfied the IPEM-81 tolerance levels in radiotherapy treatment planning. If a criterion of ρ_e^cal/ρ_e − 1 is assumed to be within ±2%, the predicted upper limit of Z applicable for the ΔHU–ρ_e conversion under the well-calibrated condition is Z = 27. In the case of the poorly calibrated condition, the upper limit of Z is approximately 16. The deviation from the ΔHU–ρ_e linearity for higher Z substances is mainly caused by the anomalous variation in the photoelectric-absorption component. Conclusions: Compensation among the three partial components of the photon interactions provides for sufficient linearity of the ΔHU–ρ_e conversion to be applicable for most human tissues even for poorly conditioned scans in which there exists a large variation of effective x-ray energies owing to beam-hardening effects arising from the mismatch between the sizes of the object and the calibration phantom