Accurate effective atomic number determination with polychromatic grating-based phase-contrast computed tomography

The demand for quantitative medical imaging is increasing in the ongoing digitalization. Conventional computed tomography (CT) is energy-dependent and therefore of limited comparability. In contrast, dual-energy CT (DECT) allows for the determination of absolute image contrast quantities, namely the electron density and the effective atomic number, and is already established in clinical radiology and radiation therapy. Grating-based phase-contrast computed tomography (GBPC-CT) is an experimental X-ray technique that also allows for the measurement of the electron density and the effective atomic number. However, the determination of both quantities is challenging when dealing with polychromatic GBPC-CT setups. In this paper, we present how to calculate the effective atomic numbers with a polychromatic, laboratory GBPC-CT setup operating between 35 and 50\,kVp. First, we investigated the accuracy of the measurement of the attenuation coefficients and electron densities. For this, we performed a calibration using the concept of effective energy. With the reliable experimental quantitative values, we were able to evaluate the effective atomic numbers of the investigated materials using a method previously shown with monochromatic X-ray radiation. In detail, we first calculated the ratio of the electron density and attenuation coefficient, which were experimentally determined with our polychromatic GBPC-CT setup. Second, we compared this ratio with tabulated total attenuation cross sections from literature values to determine the effective atomic numbers. Thus, we were able to calculate two physical absolute quantities -- the electron density and effective atomic number -- that are in general independent of the specific experimental conditions like the X-ray beam spectrum or the setup design.