Cammin Jochen, Xu Jennifer, Barber William C, Iwanczyk Jan S, Hartsough Neal E, Taguchi Katsuyuki
Division of Medical Imaging Physics, The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, Maryland 21287.
Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21287.
Med Phys. 2014 Apr;41(4):041905. doi: 10.1118/1.4866890.
Energy discriminating, photon-counting detectors (PCDs) are an emerging technology for computed tomography (CT) with various potential benefits for clinical CT. The photon energies measured by PCDs can be distorted due to the interactions of a photon with the detector and the interaction of multiple coincident photons. These effects result in distorted recorded x-ray spectra which may lead to artifacts in reconstructed CT images and inaccuracies in tissue identification. Model-based compensation techniques have the potential to account for the distortion effects. This approach requires only a small number of parameters and is applicable to a wide range of spectra and count rates, but it needs an accurate model of the spectral distortions occurring in PCDs. The purpose of this study was to develop a model of those spectral distortions and to evaluate the model using a PCD (model DXMCT-1; DxRay, Inc., Northridge, CA) and various x-ray spectra in a wide range of count rates.
The authors hypothesize that the complex phenomena of spectral distortions can be modeled by: (1) separating them into count-rate independent factors that we call the spectral response effects (SRE), and count-rate dependent factors that we call the pulse pileup effects (PPE), (2) developing separate models for SRE and PPE, and (3) cascading the SRE and PPE models into a combined SRE+PPE model that describes PCD distortions at both low and high count rates. The SRE model describes the probability distribution of the recorded spectrum, with a photo peak and a continuum tail, given the incident photon energy. Model parameters were obtained from calibration measurements with three radioisotopes and then interpolated linearly for other energies. The PPE model used was developed in the authors' previous work [K. Taguchi et al., "Modeling the performance of a photon counting x-ray detector for CT: Energy response and pulse pileup effects," Med. Phys. 38(2), 1089-1102 (2011)]. The agreement between the x-ray spectra calculated by the cascaded SRE+PPE model and the measured spectra was evaluated for various levels of deadtime loss ratios (DLR) and incident spectral shapes, realized using different attenuators, in terms of the weighted coefficient of variation (COVW), i.e., the root mean square difference weighted by the statistical errors of the data and divided by the mean.
At low count rates, when DLR < 10%, the distorted spectra measured by the DXMCT-1 were in agreement with those calculated by SRE only, with COVW's less than 4%. At higher count rates, the measured spectra were also in agreement with the ones calculated by the cascaded SRE+PPE model; with PMMA as attenuator, COVW was 5.6% at a DLR of 22% and as small as 6.7% for a DLR as high as 55%.
The x-ray spectra calculated by the proposed model agreed with the measured spectra over a wide range of count rates and spectral shapes. The SRE model predicted the distorted, recorded spectra with low count rates over various types and thicknesses of attenuators. The study also validated the hypothesis that the complex spectral distortions in a PCD can be adequately modeled by cascading the count-rate independent SRE and the count-rate dependent PPE.
能量分辨型光子计数探测器（PCD）是一种新兴的计算机断层扫描（CT）技术，对临床CT具有多种潜在益处。由于光子与探测器的相互作用以及多个重合光子的相互作用，PCD测量的光子能量可能会发生畸变。这些效应会导致记录的X射线光谱失真，进而可能在重建的CT图像中产生伪影，并影响组织识别的准确性。基于模型的补偿技术有可能解决这些畸变效应。这种方法只需要少量参数，适用于广泛的光谱和计数率，但它需要一个准确的PCD光谱畸变模型。本研究的目的是建立一个光谱畸变模型，并使用PCD（型号DXMCT-1；DxRay公司，加利福尼亚州北岭）和各种X射线光谱在广泛的计数率范围内对该模型进行评估。
作者假设光谱畸变的复杂现象可以通过以下方式建模：（1）将它们分为我们称为光谱响应效应（SRE）的计数率无关因素和我们称为脉冲堆积效应（PPE）的计数率相关因素；（2）分别为SRE和PPE建立模型；（3）将SRE和PPE模型级联成一个组合的SRE+PPE模型，该模型描述了低计数率和高计数率下的PCD畸变。SRE模型根据入射光子能量描述记录光谱的概率分布，包括一个光电峰和一个连续谱尾部。模型参数通过使用三种放射性同位素的校准测量获得，然后针对其他能量进行线性插值。所使用的PPE模型是作者在之前的工作中开发的[K. Taguchi等人，“用于CT的光子计数X射线探测器性能建模：能量响应和脉冲堆积效应”，《医学物理》38(2)，1089-1102（2011）]。通过级联SRE+PPE模型计算的X射线光谱与测量光谱之间的一致性，针对不同的死时间损失率（DLR）和入射光谱形状进行了评估，这些形状通过使用不同的衰减器实现，评估指标为加权变异系数（COVW），即由数据的统计误差加权的均方根差除以平均值。
在低计数率下，当DLR<10%时，DXMCT-1测量的畸变光谱仅与SRE计算的光谱一致，COVW小于4%。在较高计数率下，测量光谱也与级联SRE+PPE模型计算的光谱一致；以聚甲基丙烯酸甲酯（PMMA）作为衰减器，在DLR为22%时COVW为5.6%，在DLR高达55%时低至6.7%。
所提出的模型计算的X射线光谱在广泛的计数率和光谱形状范围内与测量光谱一致。SRE模型预测了在各种类型和厚度的衰减器下低计数率时的畸变记录光谱。该研究还验证了以下假设：通过将计数率无关的SRE和计数率相关的PPE级联，可以充分模拟PCD中的复杂光谱畸变。
