Hereditary diffuse gastric cancer (HDGC) evolution depends on E-cadherin dysfunction [2, 1]. We demonstrate experimentally that the low E-cadherin expression strongly correlates with basal epithelial extrusion. Using three different mathematical models, we explore computationally how differential adhesion of the mutated cell to the ECM fibres and epithelial tissue geometry regulates basal extrusion. We introduce a novel phase-field model to describe epithelial tissue dynamics and its interaction with the ECM, and use this model in tandem with a vertex model and a dissipative particle dynamics simulation of epithelial tissues. In these simulations, we observe that the adhesion to the matrix strongly accelerates basal extrusion, thus expecting that, in the progression of HDGC, an increase in cell-ECM adhesion will play an important role. We further observe that the curvature of the epithelial tissue, which increases the mutated cell exposure to the ECM and the mechanical stress imposed on the cell, facilitates the initial steps of cell extravasation. The implementation of different mathematical modelling strategies that yield comparable results strengthens the confidence in these predictions, thus suggesting novel avenues to explore experimentally [3]. [1] U. Carvallaro, G. Christofori: Cell adhesion and signalling by cadherins and Ig-CAMs in cancer, Nature Publishing Group 2, pp. 118-132 (2004). DOI: 10.1038/nrc1276 [2] B. Angst, C. Marcozzi, and M. Magee: The cadherin superfamily: diversity in form and function, The Company of Biologists Ltd 4, pp 629-641. DOI: 10.1242/jcs.114.4.629 [3] S. Melo, P. Guerrero, M. Moreira, J. R. Bordin, F. Carneiro, P. Carneiro, M. B. Dias, J. Carvalho, J. Figueiredo, R. Seruca, R. Travasso: The ECM and tissue architecture are major determinants of early invasion mediated by E-cadherin dysfunction, Communications Biology 6, 1132 (2023). D.O.I: 10.1038/s42003-023-05482-x