3D models of the dynamics of cancer cells under external pressure

Skin cancer is one of the most frequent cancers worldwide. Recently, it has been shown that the tumor proliferation rate in skin and its dynamics can be changed by an osmotic pressure. However, these findings are rather unstructured. A weak pressure can slow down the tumor growth, while a very high pressure can, on the contrary, lead to accelerated growth and metastases. The magnitude and spatial distribution of osmotic pressures in tumors at present cannot be measured experimentally. Therefore, it is of particular interest to find appropriate models that would simulate the effects of additional osmotic pressures in skin and assess the features of its implementation. In this paper, we suggest an improved model based on the principles of the conventional hydrodynamic model for macrophase separations, which allows one to include not only the properties of healthy and cancer cells but also the microenvironment. We study and analyze the proliferation of cancer cells in 3D models of the epidermal layer of skin under an osmotic pressure. There are two suggested 3D models that are based on the same principles: (1) cellular cubic lattice and (2) cell spheroid. This allows expanding the application of the model depending on a given task. Here, we are focused on the study of melanoma at an early stage when there are not many cancer cells. Additional compressive and expansive pressures are added to the central part of the system. Both systems demonstrate similar results in slowing down the rate of tumor growth with a small pressure.