“…Moreover, Gallinato et al [35] have proposed a mixture model of breast cancer cell invasion whereby the presence of the basement membrane of the milk ducts is taken into account by imposing nonlinear Kedem-Katchalsky interface conditions [19,28,29,51,55,70] at the interface between the tumour and the host region. In the setting of Gallinato et al [35], such transmission conditions lead the normal velocity of the cells and the cell volume fraction to be continuous across the basement membrane, which is not necessarily the case. Finally, Arduino & Preziosi [11] and Giverso et al [37] have presented a number of multiphase models of cancer cell migration and invasion through the ECM.…”