Numerical predictions of endothelial gaps formation: modelling the metastatic spread of cancer

Cancer or immune cells within the vasculature may usually interact with the endothelial cells through which they can transmigrate. In fact, cancer and immune cells are the most common cells that usually transmigrate presenting different strategies. In inflammation it is assumed that leukocytes interact with the endothelial cells of the vasculature, weakening the VE-cadherin-mediated cell-cell junctions and subsequently inducing the gap formation between the endothelial cells. Although there are not many numerical models that have simulated this process of cell transmigration in the endothelial layers, a couple of previous models have focused on that topic. On the one hand, a particle-based model was proposed by Ramis-Conde et al (2009) in which authors assume that the tumour cell interacts with endothelial cells weakening these junctions. On the other hand, Cao et al (2016) proposed a chemo-mechanical model assuming that the limiting condition for transmigration is the deformation characteristics of the nucleus in the tumour cells. However, more recently, Escribano et al (2019) proposed that endothelial gap formation occurs spontaneously without interaction with transmigrating cells. To test this assumption authors elaborated a novel particle-based model to investigate how contractile and protrusive cell forces in the endothelium are able to regulate gap formation. To simulate cell-cell junctions, a force-based model was considered, assuming a catch-bond constitutive law. This model is able to predict the formation of endothelial gaps between cells preferentially at vertices according to experimental measurements.