Gradient-enhanced continuum models of healing in damaged soft tissues

TL;DR

This paper introduces two novel gradient-enhanced non-local models for simulating healing in soft tissues, capturing the influence of intrinsic length scales and enabling more accurate finite element analysis of tissue repair processes.

Contribution

The study presents the first gradient-enhanced continuum models for soft tissue healing, incorporating non-local variables and implemented in Abaqus for numerical simulations.

Findings

Models successfully simulate healing in soft tissues.

Application demonstrated in balloon angioplasty scenarios.

Models capture non-local effects in tissue repair.

Abstract

Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length-scales in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced con-stitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user sub-routine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.