Modelling the effect of osmotic pressure on cancer cell growth: The role of area size and duration of exposure

Background and Objectives: One of the new and effective methods for treating skin cancer and other proliferative diseases, such as psoriasis, is phototherapy, but there is a problem of limiting the penetration of radiation into the depths of the tissue caused by the multiple scattering of the light waves. This problem can be solved by introducing optical clearing agents, many of which are hyperosmotic. In turn, the action of hyperosmotic agents can cause side effects that are induced by the appearance of additional external pressure, which can both increase and decrease the proliferation rate of cancer cells. Materials and Methods: In this work, numerical simulations of a two-dimensional model of an epidermal cell layer on a basal membrane under conditions of additional external pressure are performed. The paper studies the influence of the size of the area of localization of additional pressure, its magnitude and duration of exposure on the proliferation of cancer cells in the area of a binary surface consisting of healthy and cancer cells. Results: Studies were carried out at twofold and fivefold increase of pressure in the selected area (2 kPa and 5 kPa). The influence of the moment of introduction of additional pressure and its duration is also considered in this work. We have determined the parameters at which the rate of cancer cell proliferation slows down. It has been shown that the most pronounced inhibition occurs when applying an additional pressure of 2 kPa in the 1 $\times$ 1 mm region (the size of the entire system is 2 $\times$ 2 mm). The studies were carried out at a twofold and fivefold increase in pressure in the selected area (2 kPa and 5 kPa). Here we have also studied the effect of the duration of exposure if its introduction began at different moments t$_0$ of Phase 1. It has been shown that for t$_0$ = 240 the dependence of area covered by cancer cells $\Phi$ on the duration of short-term pressure is nonlinear, and for t$_0$ = 400 this dependence is linear, and the longer impact causes the slowdown of $\Phi$ growth.