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Is it Necessary to Model the Matrix Degrading Enzymes for Simulating Tumour Growth?

We propose a hybrid continuum–discrete model to simulate tumour growth on a microscopic scale. The lattice– based spatio–temporal model consists of reaction–diffusion equations that describe interactions between cancer cells and their microenvironment. The components that are typically considered are usually nutrients, like oxygen and glucose, matrix degrading enzymes (MDE) and the extracellular matrix (ECM). The in–vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. Thus, the aim is to describe the processes on the basis of simplified mathematical approaches, which depict realistic results at the same time. In this work we discuss if we have to model the MDEs or if the ECM can be modelled directly depending on the cancer cells distribution. Comparing the results for modelling the tumour growth with the common choice and with the simplified model without MDE, we observe almost similar results. The model without MDE allows for a straightforward, fast and accurate implementation.