Surface tension-driven boundary growth in tumour spheroids

TL;DR

This paper models tumour spheroid growth driven by surface tension and elasticity, revealing how elastocapillary interactions influence boundary expansion and residual stress, validated by experimental data.

Contribution

It introduces a hyperelastic boundary accretion model incorporating surface tension effects, providing new insights into tumour boundary mechanics and growth behavior.

Findings

Tumour spheroids open when cut, even without residual stress.

Residual stress amplifies tumour opening due to elastocapillary effects.

Model estimates surface tension acting on tumour spheroids.

Abstract

Growing experimental evidence highlights the relevant role of mechanics in the physiology of solid tumours, even in their early stages. While most of the mathematical models describe tumour growth as a volumetric increase of mass in the bulk, in vitro experiments on tumour spheroids have demonstrated that cell proliferation occurs in a thin layer at the boundary of the cellular aggregate. In this work, we investigate how elasticity and surface tension interact during the development of tumour spheroids. We model the spheroid as a hyperelastic material undergoing boundary accretion, where the newly created cells are deformed by the action of surface tension. This growth leads to a frustrated reference configuration, resulting in the appearance of residual stress. Our theoretical framework is validated using experimental results from the literature. Like fully developed tumours, spheroids open when subjected to radial cuts. Remarkably, this behaviour is observed even in newly formed spheroids, which lack residual stress. Through both analytical solutions and numerical simulations, we show that this phenomenon is driven by elastocapillary interactions, where the residual stress developed in grown spheroids amplifies the tumour opening. Our model's outcomes align with experimental observations and allow us to estimate the surface tension acting on tumour spheroids.