Modeling and simulation of diffusion and reaction processes during the staining of tissue sections on slides

Histological slides are an important tool in the diagnosis of tumors as well as of other diseases that affect cell shapes and distributions. Until now, the research concerning an optimal staining time has been mainly done empirically. In experimental investigations, it is often not possible to stain an already-stained slide with another stain to receive further information. To overcome these challenges, in the present paper a continuum-based model was developed for conducting a virtual (re-)staining of a scanned histological slide. This model is capable of simulating the staining of cell nuclei with the dye hematoxylin (C.I. 75,290). The transport and binding of the dye are modeled (i) along with the resulting RGB intensities (ii). For (i), a coupled diffusion–reaction equation is used and for (ii) Beer–Lambert’s law. For the spatial discretization an approach based on the finite element method (FEM) is used and for the time discretization a finite difference method (FDM). For the validation of the proposed model, frozen sections from human liver biopsies stained with hemalum were used. The staining times were varied so that the development of the staining intensity could be observed over time. The results show that the model is capable of predicting the staining process. The model can therefore be used to perform a virtual (re-)staining of a histological sample. This allows a change of the staining parameters without the need of acquiring an additional sample. The virtual standardization of the staining is the first step towards universal cross-site comparability of histological slides. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00418-022-02118-9.