Combined effects of pulse pile-up and energy response in energy-resolved, photon-counting computed tomography

The very high x-ray flux rates employed in today´s human computed tomography (CT) scanners in order to keep scanning times at a conveniently low level constitute the most challenging obstacle to the advent of clinical, photon-counting (spectral) CT. Even with most sophisticated, application-specific, energy-discriminating, photon-counting readout electronics, designed for room-temperature semi-conductor sensors like CdTe or CZT, the effects of spectral degradation due to pulse pile-up, i.e., count rate losses and gains will have to be taken into account in a clinical setting. The energy registered in a first-order pile-up event (superposition of two pulses) depends strongly on the energies of the two primaries involved, the difference in their arrival times and the spectral detector response behavior. We present an analytic model for the number of expected counts in binned photon-counting detectors, which is based on work by Wielopolski and Gardner and takes into account the combined effects of a spectral detector response function and 1^st order pulse pile-up. The analytic model is validated by means of Monte-Carlo simulations and is applied to a simulation of a clinical spectral CT scenario in the context of K-edge imaging of a high-atomic number element as a contrast material. The artifacts in the reconstructed single-bin images and their manifestation in material-decomposed images are discussed and interpreted in terms of gains and losses of counts due to pile-up. Finally, we discuss the shortcomings of the model like the limitation to 1^st order pile-up and the inherent restriction of the Wielopolski-Gardner model to peak pile-up.