Modeling the performance of a photon counting x‐ray detector for CT: Energy response and pulse pileup effects

Abstract

Purpose:Recently, photon counting x-ray detectors ͑PCXDs͒ with energy discrimination capabilities have been developed for potential use in clinical computed tomography ͑CT͒ scanners. These PCXDs have great potential to improve the quality of CT images due to the absence of electronic noise and weights applied to the counts and the additional spectral information. With high count rates encountered in clinical CT, however, coincident photons are recorded as one event with a higher or lower energy due to the finite speed of the PCXD. This phenomenon is called a "pulse pileup event" and results in both a loss of counts ͑called "deadtime losses"͒ and distortion of the recorded energy spectrum. Even though the performance of PCXDs is being improved, it is essential to develop algorithmic methods based on accurate models of the properties of detectors to compensate for these effects. To date, only one PCXD ͑model DXMCT-1, DxRay, Inc., Northridge, CA͒ has been used for clinical CT studies. The aim of that study was to evaluate the agreement between data measured by DXMCT-1 and those predicted by analytical models for the energy response, the deadtime losses, and the distorted recorded spectrum caused by pulse pileup effects. Methods: An energy calibration was performed using 99m Tc ͑140 keV͒, 57 Co ͑122 keV͒, and an x-ray beam obtained with four x-ray tube voltages ͑35, 50, 65, and 80 kVp͒. The DXMCT-1 was placed 150 mm from the x-ray focal spot; the count rates and the spectra were recorded at various tube current values from 10 to 500 A for a tube voltage of 80 kVp. Using these measurements, for each pulse height comparator we estimated three parameters describing the photon energy-pulse height curve, the detector deadtime , a coefficient k that relates the x-ray tube current I to an incident count rate a by a = k ϫ I, and the incident spectrum. The mean pulse shape of all comparators was acquired in a separate study and was used in the model to estimate the distorted recorded spectrum. The agreement between data measured by the DXMCT-1 and those predicted by the models was quantified by the coefficient of variation ͑COV͒, i.e., the root mean square difference divided by the mean of the measurement. Results: Photon energy versus pulse height curves calculated with an analytical model and those measured using the DXMCT-1 were in agreement within 0.2% in terms of the COV. The COV between the output count rates measured and those predicted by analytical models was 2.5% for deadtime losses of up to 60%. The COVs between spectra measured and those predicted by the detector model were within 3.7%-7.2% with deadtime losses of 19%-46%. Conclusions: It has been demonstrated that the performance of the DXMCT-1 agreed exceptionally well with the analytical models regarding the energy response, the count rate, and the recorded spectrum with pulse pileup effects. These models will be useful in developing methods to compensate for these effects in PCXD-based clinical CT systems.

Dimensionality and noise in energy selective x‐ray imaging

“…The CRLB is applicable with nonidealized detectors if good models 28,29 of detector noise are available. These models can be used with the CRLB to determine the effects of nonideal detector performance on dimensionality, to optimize the detectors, and to develop estimators that provide efficient performance.…”

“…The independent Poisson distribution is a valid statistical model if the detector is quantum noise limited and pulse pileup is negligible. 28,29 The quantum-noise limited assumption means that electronic noise and other system imperfections are much smaller than photon counting noise.…”

Vision 20/20: Single photon counting x‐ray detectors in medical imaging

“…Simple models, such as linear corrections or self-convolution, 80 are not accurate for modeling complex mechanisms of distortion. Various pulse pileup models have been developed, 35,[81][82][83][84] and we have developed a model 83,84 that satisfies the accuracy, efficiency, and ability to handle a large number of coincidence requirements for high input count rates. The pulse pileup model accounts for the (bipolar) shape of the pulse, the distribution function of time intervals between random events, and the transmitted spectrum as the probability density function.…”

“…10). 84 The coefficients of variation (i.e., the root mean square difference divided by the mean of measure- FIG. 10.…”

Breast tissue decomposition with spectral distortion correction: A postmortem study

“…49,[54][55][56] The benefits of photon-counting detectors in material identification can be substantially deteriorated with the presence of such spectral distortions, especially for the investigated three-material decomposition where the x-ray attenuation difference of the three components are very small. In current study, we initially investigated the accuracy of dual energy decomposition based on raw images, which utilized all detected photons.…”