Three-dimensional numerical simulation of soft-tissue wound healing using constrained-mixture anisotropic hyperelasticity and gradient-enhanced damage mechanics

Abstract

Healing of soft biological tissues is the process of self-recovery or self-repair after injury or damage to the extracellular matrix (ECM). In this work, we assume that healing is a stress-driven process, which works at recovering a homeostatic stress metric in the tissue by replacing the damaged ECM with a new undamaged one. For that, a gradient-enhanced continuum healing model is developed for three-dimensional anisotropic tissues using the modified anisotropic Holzapfel–Gasser–Ogden constitutive model. An adaptive stress-driven approach is proposed for the deposition of new collagen fibres during healing with orientations assigned depending on the principal stress direction. The intrinsic length scales of soft tissues are considered through the gradient-enhanced term, and growth and remodelling are simulated by a constrained-mixture model with temporal homogenization. The proposed model is implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three numerical examples have been achieved to illustrate the performance of the proposed model in simulating the healing process with various damage situations, converging towards stress homeostasis. The orientations of newly deposited collagen fibres and the sensitivity to intrinsic length scales are studied through these examples, showing that both have a significant impact on temporal evolutions of the stress distribution and on the size of the damage region. Applications of the approach to carry out in silico experiments of wound healing are promising and show good agreement with existing experiment results.

Sensitivity analysis of non‐local damage in soft biological tissues

“…The first advantage of the presented model is that it can assess nonlocal damage with uncertain material parameters, including internal length scales. In our previous works, 12,13 it was proved that the internal length scales have obvious effects on the localization of damage, for example, a larger internal length scales lead to a larger lower level of damage and activated zone. In this paper, the influence of uncertain internal length scales can be analyzed by the proposed model.…”

“…In this part, series of tests on 286 elements are performed. The mesh‐dependence had been already examined in our previous works 12,13 . Here we investigate the influence of the shear modulus and the internal length scales on the damage analysis in deterministic problem.…”

“…The developed damage models can be divided into three approaches 9 : (1) models based on continuum damage mechanics, (2) models based on the theory of pseudo‐elasticity, and (3) the softening hyperelasticity approach. Among the continuum damage models, a gradient‐enhanced non‐local damage model was proposed by Dimitrijevic and Hackl, 10,11 and a nonlocal continuum healing model that combines the gradient‐enhanced damage model and a temporally homogenized growth and remodeling model was originally presented in our previous works 12,13 . This model has the following advantages: (1) good mesh independence is achieved in the simulation of damage evolution with growth and remodeling; and (2) the nonlocal damage process is realized by introducing the gradient‐enhanced variable, thus allowing the effect of internal length scales of soft tissues to be considered.…”

Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

“…Since the density does not change during the damaging phase, it corresponds to the initial collagen density. Note that the contribution of collagen to the strain energy per unit volume ( 10) is not further divided into a contribution for damaged and intact collagen, as has been done, e.g., by He et al (2019) and Zuo et al (2020).…”

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

“…Tissue remodeling is governed by laws of production and degradation for each constituent based on stress states. This type of model has been used to predict different tissue adaptations such as aneurysm growth for instance by Baek et al ( 2006 ); Alberto Figueroa et al ( 2009 ); Watton and Hill ( 2009 ); Zeinali-Davarani and Baek ( 2012 ); Valentín et al ( 2013 ); Cyron et al ( 2016 ); Braeu et al ( 2017 ); Famaey et al ( 2018 ); Latorre and Humphrey ( 2018b ), and Mousavi et al ( 2019 ) or wound healing by Zuo et al ( 2020 ). However, to the best of our knowledge, the constrained mixture theory has never been used to model healing after arterial clamping.…”