Thermodynamically constrained averaging theory for cancer growth modelling*

In Systems Biology, network models are often used to describe intracellular mechanisms at the cellular level. The obtained results are difficult to translate into three dimensional biological systems of higher order. The multiplicity and time dependency of cellular system boundaries, mechanical phenomena and spatial concentration gradients affect the intercellular relations and communication of biochemical networks. These environmental effects can be integrated with our promising cancer modelling environment, that is based on thermodynamically constrained averaging theory (TCAT). Especially, the TCAT parameter viscosity can be used as critical player in tumour evolution. Strong cell-cell contacts and a high degree of differentiation make cancer cells viscous and support compact tumour growth with high tumour cell density and accompanied displacement of the extracellular material. In contrast, dedifferentiation and losing of cell-cell contacts make cancer cells more fluid and lead to an infiltrating tumour growth behaviour without resistance due to the ECM. The fast expanding tumour front of the invasive type consumes oxygen and the limited oxygen availability behind the invasive front results automatically in a much smaller average tumour cell density in the tumour core. The proposed modelling technique is most suitable for tumour growth phenomena in stiff tissues like skin or bone with high content of extracellular matrix.