Influence of initial residual stress on growth and pattern creation for a layered aorta

TL;DR

This study explores how initial residual stress influences growth patterns in layered arteries, revealing its dominant role over geometry and material properties in pattern formation and offering insights for biomedical tissue engineering.

Contribution

It extends volume growth theory to account for existing residual stresses, demonstrating their significant impact on tissue growth and pattern evolution in arteries.

Findings

Initial residual stress greatly affects pattern development.

Residual stress influences residual stress accumulation more than geometry.

Initial residual stress can be used to control tissue patterning.

Abstract

Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters. Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering.