An Accessible Analytical Approach to Characterize the Modulation Transfer Function of Fluoroscopic Systems
Abstract
Purpose
Improve accessibility of Modulation Transfer Function (MTF) metrics for implementing routine quality control (QC) of fluoroscopes.
Methods
Typical MTF curve evaluation involves edge-spread function (ESF) binning, discrete differentiation, and discrete Fourier transformation. This numerical method varies in implementation and struggles with low-CNR edges common in fluoroscopic images. To address these issues, a model-based method was devised involving one step: fitting the ESF to a predefined sigmoid function. To narrow scope, this investigation only considered sigmoids that 1) are defined by one parameter α, the steepness of the sigmoid at inflection, and 2) have mathematical derivatives and subsequent Fourier transforms defined by elementary functions. Five sigmoids were discovered to meet such criteria; these were respectively nicknamed Boltzmann, Gaussian, Gudermann, Laplacian, and Lorentzian. To assess real-world performance of each model, 347 fluoro loops of a tin swatch phantom were acquired by 19 fluoroscopes. The last frame of each loop was isolated, ESF pixel data was obtained, and a sigmoid model was fit via least-squares regression. Per fluoroscope, each model’s precision was indicated by a low interquartile-range/median (IQR/M) for α. Under the model-based approach, traditional MTF metrics MTF50, MTF20, MTF10, and MTFa scale linearly with α, so their IQR/M is equivalent.
Results
Four out of five sigmoid models demonstrated better precision than the numerical method described in IEC 62220-1-1:2015. Across fluoroscopes, the median IQR/M of each model’s α were the following: Boltzmann: 0.45; Gaussian: 0.36; Gudermann: 0.42; Laplacian: 0.47; Lorentzian: 1.94. By comparison, the median IQR/M of IEC MTF50 was 1.21.
Conclusion
The model-based method provides accessible spatial resolution measurement suited for routine fluoroscopic QC. The simplicity facilitates standardization, having less degrees of freedom in implementation than numerical methods. Numerical methods prioritize accuracy; the model-based method retains relative accuracy, excels in precision, and is more efficient for evaluation of clinical image quality.