Correspondence: Reply to ‘Quantitative evaluation of X-ray dark-field images for microcalcification analysis in mammography'

Scherer et al.1 claim that the phantom study in our Article2 might not reliably model real microcalcifications in human breast and referred to previous publications3–5 to emphasize that the scattering signal depends on particle grain sizes. Specifically, they mention Michel et al.’s simulation results6, which report a larger scattering signal of calcium hydroxyapatite compared with calcium oxalate dihydrate (more generally calcium oxalate in Michel et al.), contradicting our phantom results. First, we want to emphasize that our Article focused on isolated, single microcalcifications instead of clustered microcalcifications as studied in Michel et al.6, which is a special clinical occurrence. The formation process of microcalcifications in human breast is very complex and not fully understood7,8. To the best of our knowledge, the internal structure of isolated microcalcifications remains unknown. Previous works3–5 investigating scattering signals as recorded by grating interferometers are all based on simplified, diluted sphere particles models. While we agree that such approaches can reflect the scattering signal formation to a certain extent, it has not been demonstrated whether they can reliably deal with both types of microcalcifications, especially considering that the two types have different crystalline structures. We are aware of the difficulties of simulating actual microcalcifications in human breast, as well as the potential differences between the simulants we used and the real microcalcifications. The aim of the phantom experiment was to show that for realistically approximated chemical composition (based on Haka et al.9) and unknown (but very likely different) scattering behaviour of the simulants, our method could discriminate between them with excellent selectivity. The discrepancy between our phantom results and Michel et al.’s numerical simulation might well come from the fact that their work is based on the assumption that the calcium oxalate has the same concentration and grain size as the hydroxyapatite. Although this assumption does not hold in real samples6, it indeed demonstrates the influence of the microcalcifications’s structure on the scattering signal. We are currently working on the further exploration and exact determination of the internal structure of real microcalcifications to better understand its contribution to the recorded scattering signal. Scherer et al. pointed out our mistake in the data processing of biopsy and mastectomy samples. Despite the principle description and corresponding formula in our Article are correct, the contribution of the underlying breast tissue was inadvertently neglected in the computation. In the following, we explain in other words what has been described in the section ‘Non-invasive microcalcifications classification’ in the original Article. We introduce the quantity noted as r-ratio and defined in equation (4) as r1⁄4 c s m, where s and m refer to the scattering and absorption signals of the microcalcifications, taking into account the contribution of the underlying breast tissue, while c is a systemdependent constant. It follows that s1⁄4s sb and m1⁄4m mb, where s, m, sb and mb correspond to the total scattering, total absorption, breast tissue scattering and breast tissue absorption signals, respectively. The numerical determination of the s and m signals is obtained with an image processing algorithm, involving the segmentation of the microcalcification, its localization and the determination of its (projected) size and immediate neighbourhood. When calculating the r-ratio, both the absorption and scattering contributions from the underlying breast tissue should be taken into account, but were inadvertently neglected in the original Article. Amended versions of the original Figs 3d and 5f (Figs 1 and 2, respectively) and original Supplementary Fig. 1b (Fig. 3) appear below. The r-ratio values for all the DOI: 10.1038/ncomms10868 OPEN