Conditions of acceleration and deceleration of the cancer cell growth under osmotic pressure

In this paper, we study a pattern formation in the epidermal layer of skin during tumor development and appearance of a binary surface consisting of healthy and cancer cells forming Turing patterns under external osmotic pressure. The basic methodology of introducing the external influences, for example, time-targeted drug therapy or radiation exposure, influence of electromagnetic fields, laser radiation or other tumor-targeting physical influences act differently in different phases of the cell cycle. In some cases, this can lead to a slowdown in the growth of cancer cells, and sometimes vice versa. Therefore, it is of particular interest to choose the right parameters such as starting time of external pressure, its magnitude and duration depending on the cell cycle of developing cancer cells. We propose a biologically inspired model that allows us to simulate the growth of cancer cells under conditions of osmotic pressure. We divide this growth into two phases. The first is characterized by active cell division, and the second by their growth. In this article, we introduce two types of pressure: short-term and long-term, and looked at what this leads to in different phases. We have found an interesting result, that there are some resonant points in time both in the first and second phases, when the introduction of additional pressure leads to the most significant slowdown in the growth of cancer cells.