A novel 3D atomistic-continuum cancer invasion model: In silico simulations of an in vitro organotypic invasion assay

A genuinely hybrid, multiscale 3D cancer invasion and metastasis modelling framework

“…Thus, the evolution equation for MMPs density is given by with constants D E , . Note that equation (4.1) describes the evolution of soluble MMPs that are secreted in the local extracellular microenvironment and we do not account in (4.1) for membrane-bound MMPs such as MT1-MMP [2, 43, 44]. Although, the presence of MT1-MMP has been suggested in [43], to be a necessary and sufficient factor for the migration of MCCs.…”

“…At this stage, the values are scaled to the proper biological range. Figure source and reference [2].…”

“…In this context, we have previously proposed in [1, 2], a hybrid mathematical modelling framework that is capable of capturing the dynamic transitions between these phenotypes and shedding light on their underlying mechanisms. By combining deterministic and stochastic mathematical modelling frameworks, our hybrid approach is able to account for the heterogeneous nature of cancer cells, the complex macroscopic dynamics, and the stochasticity inherent in cellular migration.…”

“…Previous hybrid model. The hybrid model that we present in this paper is an extension of a previously proposed hybrid model detailed in [1,2]. Here, we provide a brief overview of the model.…”

Multiscale Modeling of Glioma Invasion: From Receptor Binding to Flux-Limited Macroscopic PDEs

“…This strategy together with the limited fluxes in the model allows for large time increments in the computations. For more details on the method we refer the reader to [37,36,54], where the same numerical approach was applied to similar 2D advection-reaction-diffusion problems, and to [55,22], where it was applied in a 2D and 3D hybrid atomistic-macroscopic cancer invasion model. The algorithms were implemented in MATLAB [45] and the visualizations were produced by MATLAB [45] and PARAVIEW [1].…”