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Description
Invasion, one of the hallmarks of cancer, is a complex process involving numerous interactions between cancer cells and the extracellular matrix, facilitated by matrix degrading enzymes (MDEs). It was demonstrated experimentally that there are two important types of MDEs, membrane-bound and diffusible metalloproteinases, involved in cancer invasion. To analyse the impact of those two types of MDEs on cancer invasion, we formulate a microscopic cell-scale model for the degradation of the extra-cellular matrix by matrix degrading enzymes produced by cancer cells. Using tools from the theory of homogenisation we propose a macroscopic tissue-level model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble MDEs. For the macroscopic model we prove the well-posedness result and propose a finite element method for the numerical approximation. Simulation results illustrate the role of the bound and soluble enzymes in cancer invasion processes.
