Division of Imaging and Applied Mathematics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, Maryland 20993-0002, USA.
Med Phys. 2010 Jun;37(6):2593-605. doi: 10.1118/1.3397462.
Accurate models of detector blur are crucial for performing meaningful optimizations of three-dimensional (3D) x-ray breast imaging systems as well as for developing reconstruction algorithms that faithfully reproduce the imaged object anatomy. So far, x-ray detector blur has either been ignored or modeled as a shift-invariant symmetric function for these applications. The recent development of a Monte Carlo simulation package called MANTIS has allowed detailed modeling of these detector blur functions and demonstrated the magnitude of the anisotropy for both tomosynthesis and breast CT imaging systems. Despite the detailed results that MANTIS produces, the long simulation times required make inclusion of these results impractical in rigorous optimization and reconstruction algorithms. As a result, there is a need for detector blur models that can be rapidly generated.
In this study, the authors have derived an analytical model for deterministic detector blur functions, referred to here as point response functions (PRFs), of columnar CsI phosphor screens. The analytical model is x-ray energy and incidence angle dependent and draws on results from MANTIS to indirectly include complicated interactions that are not explicitly included in the mathematical model. Once the mathematical expression is derived, values of the coefficients are determined by a two-dimensional (2D) fit to MANTIS-generated results based on a figure-of-merit (FOM) that measures the normalized differences between the MANTIS and analytical model results averaged over a region of interest. A smaller FOM indicates a better fit. This analysis was performed for a monochromatic x-ray energy of 25 keV, a CsI scintillator thickness of 150 microm, and four incidence angles (0 degrees, 15 degrees, 30 degrees, and 45 degrees).
The FOMs comparing the analytical model to MANTIS for these parameters were 0.1951 +/- 0.0011, 0.1915 +/- 0.0014, 0.2266 +/- 0.0021, and 0.2416 +/- 0.0074 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. As a comparison, the same FOMs comparing MANTIS to 2D symmetric Gaussian fits to the zero-angle PRF were 0.6234 +/- 0.0020, 0.9058 +/- 0.0029, 1.491 +/- 0.012, and 2.757 +/- 0.039 for the same set of incidence angles. Therefore, the analytical model matches MANTIS results much better than a 2D symmetric Gaussian function. A comparison was also made against experimental data for a 170 microm thick CsI screen and an x-ray energy of 25.6 keV. The corresponding FOMs were 0.3457 +/- 0.0036, 0.3281 +/- 0.0057, 0.3422 +/- 0.0023, and 0.3677 +/- 0.0041 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. In a previous study, FOMs comparing the same experimental data to MANTIS PRFs were found to be 0.2944 +/- 0.0027, 0.2387 +/- 0.0039, 0.2816 +/- 0.0025, and 0.2665 +/- 0.0032 for the same set of incidence angles.
The two sets of derived FOMs, comparing MANTIS-generated PRFs and experimental data to the analytical model, demonstrate that the analytical model is able to reproduce experimental data with a FOM of less than two times that comparing MANTIs and experimental data. This performance is achieved in less than one millionth the computation time required to generate a comparable PRF with MANTIS. Such small computation times will allow for the inclusion of detailed detector physics in rigorous optimization and reconstruction algorithms for 3D x-ray breast imaging systems.
准确的探测器模糊模型对于进行有意义的三维（3D）X 射线乳房成像系统优化以及开发真实再现成像物体解剖结构的重建算法至关重要。到目前为止，X 射线探测器模糊要么被忽略，要么在这些应用中被建模为具有平移不变对称功能的函数。最近开发的名为 MANTIS 的蒙特卡罗模拟包允许详细建模这些探测器模糊功能，并证明了断层合成术和乳房 CT 成像系统的各向异性的幅度。尽管 MANTIS 产生了详细的结果，但所需的长模拟时间使得在严格的优化和重建算法中包含这些结果是不切实际的。因此，需要能够快速生成的探测器模糊模型。
在这项研究中，作者推导出了一种用于柱状 CsI 磷光体屏幕的确定性探测器模糊函数（PRF）的解析模型，这里称为点响应函数（PRF）。该解析模型与 X 射线能量和入射角有关，并利用 MANTIS 的结果间接包括了复杂的相互作用，这些相互作用没有明确包含在数学模型中。一旦推导出数学表达式，就通过基于测量归一化差异的二维（2D）拟合来确定系数的值，该归一化差异是在感兴趣区域内对 MANTIS 和分析模型结果进行平均得到的。较小的 FOM 表示更好的拟合。对于 25keV 的单色 X 射线能量、150 微米的 CsI 闪烁体厚度和四个入射角（0 度、15 度、30 度和 45 度）进行了此分析。
对于这些参数，将解析模型与 MANTIS 进行比较的 FOM 分别为 0.1951 +/- 0.0011、0.1915 +/- 0.0014、0.2266 +/- 0.0021 和 0.2416 +/- 0.0074，用于 0 度、15 度、30 度和 45 度。相比之下，将 MANTIS 与零角 PRF 的二维对称高斯拟合进行比较的相同 FOM 分别为 0.6234 +/- 0.0020、0.9058 +/- 0.0029、1.491 +/- 0.012 和 2.757 +/- 0.039，用于相同的入射角集。因此，解析模型比二维对称高斯函数更能匹配 MANTIS 结果。还与 170 微米厚的 CsI 屏幕和 25.6keV 的 X 射线能量的实验数据进行了比较。相应的 FOM 分别为 0.3457 +/- 0.0036、0.3281 +/- 0.0057、0.3422 +/- 0.0023 和 0.3677 +/- 0.0041，用于 0 度、15 度、30 度和 45 度。在之前的一项研究中，将相同的实验数据与 MANTIS PRF 进行比较的 FOM 分别为 0.2944 +/- 0.0027、0.2387 +/- 0.0039、0.2816 +/- 0.0025 和 0.2665 +/- 0.0032，用于相同的入射角集。
将 MANTIS 生成的 PRF 和实验数据与解析模型进行比较的两组衍生 FOM 表明，解析模型能够以不到与 MANTIS 和实验数据进行比较的两倍的 FOM 重现实验数据。在不到生成可比 PRF 所需的百万分之一的计算时间内实现了这种性能。如此小的计算时间将允许在 3D X 射线乳房成像系统的严格优化和重建算法中包含详细的探测器物理。
