A Novel Mathematical Approach for Modelling of Cancer Invasion in Tissue

A Novel Mathematical Approach for Modelling of Cancer Invasion in Tissue

In this paper, we consider a relatively simple mathematical model of cancer cell invasion of tissue (extracellular matrix), which focuses on the role of a generic matrix degrading enzyme such as the urokinase-type plasminogen activator (uPA). The model consists of a system of reaction-diffusion-taxis partial differential equations describing the interactions cancer cells, the matrix degrading enzyme and the host tissue. The results of the study showed that the tumor heterogeneity can be comprehensively explained by the numerical complicated dynamics proposed in the current research. Furthermore, the performed computations of the model equations yield dynamic, heterogeneous spatio-temporal solutions, which correspondingly demonstrate the potential of such a simple model in describing and subsequent interpretation of the cancer cell progression and invasion.

In this paper, we consider a relatively simple mathematical model of cancer cell invasion of tissue (extracellular matrix), which focuses on the role of a generic matrix degrading enzyme such as the urokinase-type plasminogen activator (uPA). The model consists of a system of reaction-diffusion-taxis partial differential equations describing the interactions cancer cells, the matrix degrading enzyme and the host tissue. The results of the study showed that the tumor heterogeneity can be comprehensively explained by the numerical complicated dynamics proposed in the current research. Furthermore, the performed computations of the model equations yield dynamic, heterogeneous spatio-temporal solutions, which correspondingly demonstrate the potential of such a simple model in describing and subsequent interpretation of the cancer cell progression and invasion.