Department of Radiology, The University of Chicago, Chicago, Illinois, USA.
Department of Biomedical Engineering, Marquette University and Medical College of Wisconsin, Milwaukee, Wisconsin, USA.
Med Phys. 2022 Oct;49(10):6368-6383. doi: 10.1002/mp.15942. Epub 2022 Aug 31.
Calibration of photon-counting detectors (PCDs) is necessary for quantitatively accurate spectral computed tomography (CT), but the calibration process can be complicated by nonlinear flux-dependent physical factors such as pulse pile-up.
This work develops a method for spectral sensitivity calibration of a PCD-based spectral CT system that incorporates nonlinear flux dependence and can thus be employed at high photon flux.
A calibration model for the spectral response and polynomial flux dependence is proposed, which incorporates prior x-ray source spectrum and PCD models and that has a small set of parameters for adjusting to the spectral CT system of interest. The model parameters are determined by fitting transmission data from a known object of known composition: a step-wedge phantom composed of different thicknesses of aluminum, a bone equivalent, and polymethyl methacrylate (PMMA), a soft-tissue equivalent. This fitting employs Tikhonov regularization, and the regularization strength and the polynomial order for the intensity modeling are determined by bias and variance analysis. The spectral calibration and nonlinear intensity correction is validated on transmission measurements through a third material, Teflon, at different x-ray photon flux levels.
The nonlinear intensity dependence is determined to be accurately accounted for with a third-order polynomial. The calibrated spectral CT model accurately predicts Teflon transmission to within 1% for flux levels up to 50% of the detector maximum.
The proposed PCD calibration method enables accurate physical modeling necessary for quantitative imaging in spectral CT. Furthermore, the model applies to high flux settings so that acquisition times will not be limited by restricting the spectral CT system to low flux levels.
光子计数探测器（PCD）的校准对于定量准确的光谱计算机断层扫描（CT）是必要的，但校准过程可能会因非线性通量相关的物理因素（如脉冲堆积）而变得复杂。
本工作开发了一种用于基于 PCD 的光谱 CT 系统的光谱灵敏度校准方法，该方法纳入了非线性通量依赖性，因此可以在高光子通量下使用。
提出了一种光谱响应和多项式通量依赖性的校准模型，该模型纳入了先前的 X 射线源谱和 PCD 模型，并且具有少量的参数可用于调整感兴趣的光谱 CT 系统。模型参数通过拟合已知成分的已知物体的透射数据来确定：一个由不同厚度的铝、骨等效物和聚甲基丙烯酸甲酯（PMMA，软组织等效物）组成的阶梯状楔形体。该拟合采用 Tikhonov 正则化，并且强度建模的正则化强度和多项式阶数通过偏差和方差分析确定。光谱校准和非线性强度校正通过在不同的 X 射线光子通量水平下通过第三种材料聚四氟乙烯（Teflon）进行透射测量来验证。
确定非线性强度依赖性准确地用三阶多项式来描述。校准后的光谱 CT 模型准确地预测了 Teflon 的透射率，在高达探测器最大通量的 50%的通量水平下，误差在 1%以内。
所提出的 PCD 校准方法实现了光谱 CT 中定量成像所需的精确物理建模。此外，该模型适用于高通量设置，因此不会通过将光谱 CT 系统限制在低通量水平来限制采集时间。
