Multiphase modelling of desmoplastic tumour growth

•Mathematical model and simulations of solid, desmoplastic tumour growth.•Analysis of spatially independent solutions.•Application of Level Set Method for heterogeneous initial conditions.

It is well-known that the microenvironment of solid tumours is a significant component of the processes of tumour growth and invasion. Interactions between tumour cells and stromal components play a crucial role in tumour progression as well as suppression. We describe a mathematical model of tumour growth within a host tissue which takes into account both cell-extracellular matrix interactions and tissue compression effects. This multiphase model consisting of three coupled partial differential equations captures the dynamics of tumour progression, particularly of a desmoplastic tumour (i.e. a tumour rich in fibrous connective tissue). The model is analysed in terms of stability in a spatially homogenous case. Computer simulations agree with the biological picture of the disease and may help to understand the process leading to the pathology.