Theory, method, and test tools for determination of 3D MTF characteristics in cone-beam CT

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.