Homeostatic Kinematic Growth Model for Arteries -- Residual Stresses and Active Response

TL;DR

This paper introduces a novel kinematic growth model for arteries that incorporates residual stresses and active smooth muscle responses, enabling realistic simulation of arterial growth and behavior under physiological conditions.

Contribution

The paper presents new evolution equations for arterial growth that avoid instability issues and integrate active muscle response, improving the realism of arterial growth modeling.

Findings

Accurately reproduces in vivo stress distributions in arteries.

Aligns well with experimental data from rat cerebral arteries.

Demonstrates stable and realistic growth simulations.

Abstract

A simple kinematic growth model for muscular arteries is presented which allows the incorporation of residual stresses such that a homeostatic in-vivo stress state under physiological loading is obtained. To this end, new evolution equations for growth are proposed, which avoid issues with instability of final growth states known from other kinematric growth models. These evolution equations are connected to a new set of growth driving forces. By introducing a formulation using the principle Cauchy stresses, reasonable in vivo stress distributions can be obtained while ensuring realistic geometries of arteries after growth. To incorporate realistic Cauchy stresses for muscular arteries under varying loading conditions, which appear in vivo, e.g., due to physical activity, the growth model is combined with a newly proposed stretch-dependent model for smooth muscle activation. To account for the changes of geometry and mechanical behavior during the growth process, an optimization procedure is described which leads to a more accurate representation of an arterial ring and its mechanical behavior after the growth-related homogenization of the stresses is reached. Based thereon, parameters are adjusted to experimental data of a healthy middle cerebral artery of a rat showing that the proposed model accurately describes real material behavior. The successful combination of growth and active response indicates that the new growth model can be used without problems for modeling active tissues under various conditions.