Pattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions

TL;DR

This study uses numerical simulations to explore how cancer cell proliferation and hydrodynamic interactions influence skin cancer pattern formation, revealing microphase separation and pattern diversity consistent with clinical observations.

Contribution

The paper introduces a modified Model H incorporating logistic growth and mechanical friction, demonstrating microphase separation and pattern diversity in skin cancer modeling.

Findings

Cancer pattern formation depends on proliferation rate and hydrodynamic strength.

Microphase separation occurs due to cancer cell proliferation.

Different cancer patterns can be generated by varying parameters.

Abstract

We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer cells and also a mechanical friction between dermis and epidermis. Importantly, our model exhibits a microphase separation due to the proliferation of cancer cells. By numerically solving the time evolution equations of the cancer composition and its velocity, we show that the phase separation kinetics strongly depends on the cell proliferation rate as well as on the strength of hydrodynamic interactions. A steady state diagram of cancer patterns is established in terms of these two dynamical parameters and some of the patterns correspond to clinically observed cancer patterns. Furthermore, we examine in detail the time evolution of the average composition of cancer cells and the characteristic length of the microstructures. Our results demonstrate that different sequence of cancer patterns can be obtained by changing the proliferation rate and/or hydrodynamic interactions.