A multi-layered hybrid model for cancer cell invasion.

In this article, a hybrid model is developed based on multi-scale concept for solid  tumour cell invasion into a healthy tissue. Our aim is to study the tumour heterogeneity due to the geometry of a growing tumour caused by the phenotypic transformations of cells. In this context, an early vascular growth is considered after angiogenesis. Hence, the microenvironment of the solid tumour is rich of oxygen and nutrients. It is also considered that epidermal growth factor (EGF) is distributed into the surrounding extracellular matrix (ECM) of the tumour. The developed multi-layered model consists of three layers: intracellular or subcellular, cellular, and extracellular or tissue layer. The model integrates the events that occur simultaneously in these three layers to identify the underlying diversity. Here, every cell is represented as an agent. Characteristics of an agent are controlled by its intracellular protein expressions and its surrounding microenvironment. A mature proliferative or migratory or hybrid cell agent spawn two indistinguishable children unless it may convert into other phenotype due to influence of the microenvironment. Further, a simple cell cycle model is adapted which is influenced by EGF-EGFR signalling pathway and the external oxygen and nutrients. Moreover, migratory and hybrid cells secrete several matrix degrading enzymes (MDEs) which remodel the ECM for tumour invasion locally. Several biomechanical forces are considered that simultaneously act on the cancer cells. The outcome of the model is very similar to the results reported in earlier studies. The model shows the characteristics of cancer invasion that include sustainable proliferation by ignoring growth suppressor signals and reproduction of cancer cells at abnormal proportion, restrict apoptosis, and invade into the surrounding tissue. As the simulation parameters get modified due to different biochemical and biophysical processes, the robustness of the model is determined. It is found that only a number of proliferative cells are moderately sensitive to the parameters and others are less-sensitive.