Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD, 21205, USA.
Department of Radiology, University of California, Davis, Davis, CA, 95616, USA.
Med Phys. 2021 Jun;48(6):2772-2789. doi: 10.1002/mp.14820. Epub 2021 Apr 16.
The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three-dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone-beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two-dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT.
Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi-wire tool for measurement of the axial plane MTF [denoted as , where is the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g., = 45°, denoted as ]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C-arm with CBCT capability, showing that yields an informative one-dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide "isotropic" resolution was evaluated by quantitative comparison of MTF at various .
All three test tools provided consistent measurement of , and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane ( ) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C-arm system exhibited non-isotropic spatial resolution with conventional non-isotropic 1D apodization filters (i.e., frequency cutoff filters) - which is common in CBCT - and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non-isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D ).
Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Experiments on a CBCT C-arm validated many intuitive aspects of 3D spatial resolution and quantified the extent to which a CBCT system may be considered to have isotropic resolution. Measurement of ) provided a practical 1D measure of the underlying 3D MTF characteristics and is extensible to other CT or CBCT systems offering high, isotropic spatial resolution.
调制传递函数（MTF）被广泛用作医学成像系统空间分辨率的客观指标。尽管在计算机断层扫描（CT）和锥形束 CT（CBCT）中三维（3D）各向同性空间分辨率的能力有所提高，但此类系统的 MTF 评估通常仅在轴向平面中报告，并且缺乏用于评估完全 3D 空间分辨率特性的实用方法。本研究综述了二维（2D）和 3D 扩展函数的基本理论关系，并报告了用于分析 CBCT 中 3D MTF 的实用方法和测试工具。
在共同的符号框架内回顾了 2D 和 3D MTF 测量的基本方面，并报告了三个具有分析代码的 MTF 测试工具，并在网上提供（https://istar.jhu.edu/downloads/）：（a）用于测量轴向平面中 MTF 的多线工具[表示为 ，其中 是轴向平面外的测量角度]作为轴向平面中位置的函数;（b）用于在 3D 傅立叶域中测量任何方向 MTF 的楔形工具[例如 = 45°，表示为 ];和（c）用于在 3D 傅立叶域中测量任何或所有方向 MTF 的球体工具。在具有 CBCT 功能的移动 C 臂上进行了实验，结果表明 提供了整体 3D 空间分辨率特性的信息丰富的一维（1D）表示，捕获了可能在常规分析中错过的 3D MTF 的重要特性。研究了各向异性滤波器和探测器读出模式的影响，并通过比较各种 处的 MTF 定量评估了系统可以说是提供“各向同性”分辨率的程度。
所有三个测试工具都提供了一致的 的测量结果，楔形和球体工具展示了如何在轴向平面（ ）之外的方向测量 MTF，可以揭示常规轴向 MTF 测量无法发现的空间分辨率特性。与球体工具相比，楔形工具由于改进的采样而降低了统计测量误差，并且球体工具证明了从单次扫描中可以在任何或所有方向（在零锥体外）进行 MTF 测量。由于常见于 CBCT 的非各向同性 1D 平滑滤波器（即频率截止滤波器），C 臂系统表现出非各向同性的空间分辨率，并且实现各向同性 2D 平滑导致可量化的各向同性 MTF。类似地，非对称像素 binning 模式也对 3D MTF 施加了非各向同性效应，并且在每种情况下都可以通过对 1D 的一维（1D）测量来观察整体 3D MTF 特性。
在一个一致的框架内提出了三个测试工具和相应的 MTF 分析方法，用于以适合常规实用测量的方式分析 3D 空间分辨率特性。在 CBCT C 臂上进行的实验验证了 3D 空间分辨率的许多直观方面，并量化了 CBCT 系统可能被认为具有各向同性分辨率的程度。 的测量提供了基础 3D MTF 特性的实用 1D 度量，并且可扩展到提供高各向同性空间分辨率的其他 CT 或 CBCT 系统。
