Modified Z-resolution protocol for digital breast tomosynthesis

The EUREF protocol measures the z-resolution of a digital breast tomosynthesis (DBT) system via a ball bearing's (BB) point-spread function (PSF) and is quantified as the full-width at half-maximum (FWHM) of the associated artifact spread function (ASF). PSF is largely governed by the apparent angle ( $\alpha$ ), defined as the radian angle subtended by the BB across the X-ray sources, which in turn depends on the BB's location and acquisition geometry. Under fixed DBT geometry and reconstruction conditions, the FWHM is therefore expected to follow a predictable spatial trend. However, we found that the EUREF protocol does not consistently reproduce this behavior; it fails to capture the gradual rise in FWHM for anteriorly displaced BBs expected from a narrowing $\alpha$ (with which FWHM is inversely correlated) and exhibits a systematic bias to the stochastic noise in the reconstruction image.

The purpose of this work was to develop a z-resolution metric that more rigorously reflects the underlying local PSF's $\alpha$ without incurring a sensitivity to stochastic noise. We propose a protocol that uses multiplanar reconstruction to track the oblique BB signal in its natural spatial scale, uses means instead of maxima to generate the ASF, and employs a functional fit to estimate the FWHM more robustly-hereafter referred to as the Modified Protocol.

The protocol was evaluated using analytically simulated and experimentally acquired DBT reconstructions of BBs displaced anteriorly and superiorly and compared against the EUREF protocol. The percent change in FWHM due to stochastic noise was used to quantify systematic noise susceptibility. The strength of the anti-correlation between FWHM and apparent angle α was used to assess each protocol's agreement with the PSF geometry.

By demonstrating a consistent linear anti-correlation between FWHM and α for both superior and anterior BB displacements, the Modified protocol faithfully captures the spatial variation in PSF. The Modified protocol also substantially reduces the noise-induced FWHM shift-by 98% in simulations and 84% in physical experiments-relative to the EUREF protocol.

The EUREF protocol exhibits systematic errors which can limit its reliability in characterizing the z-resolution. Our Modified protocol mitigates these shortcomings and restores concordance between measured z-resolution and the underlying local PSF geometry ( $\alpha$ ), while also improving precision by reducing the susceptibility to stochastic noise. The Modified protocol thus offers an alternative to the existing EUREF framework, providing a z-resolution metric that serves as a more reliable surrogate for the PSF while remaining more robust to image noise.