A thermodynamic framework for unified continuum models for the healing of damaged soft biological tissue

TL;DR

This paper develops a unified thermodynamic continuum damage model for simulating soft tissue healing, eliminating the need for ad hoc equations and providing a more concise, universal framework validated through numerical examples.

Contribution

It introduces a thermodynamics-based continuum damage model for tissue healing that inherently captures key parameters without additional equations.

Findings

Model aligns well with existing healing data

Effective in simulating arterial tissue repair

Applicable to various soft tissue healing scenarios

Abstract

When they are damaged or injured, soft biological tissues are able to self-repair and heal. Mechanics is critical during the healing process, as the damaged extracellular matrix (ECM) tends to be replaced with a new undamaged ECM supporting homeostatic stresses. Computational modeling has been commonly used to simulate the healing process. However, there is a pressing need to have a unified thermodynamics theory for healing. From the viewpoint of continuum damage mechanics, some key parameters related to healing processes, for instance, the volume fraction of newly grown soft tissue and the growth deformation, can be regarded as internal variables and have related evolution equations. This paper is aiming to establish this unified framework inspired by thermodynamics for continuum damage models for the healing of soft biological tissues. The significant advantage of the proposed model is that no \textit{ad hoc} equations are required for describing the healing process. Therefore, this new model is more concise and offers a universal approach to simulate the healing process. Three numerical examples are provided to demonstrate the effectiveness of the proposed model, which is in good agreement with the existing works, including an application for balloon angioplasty in an arteriosclerotic artery with a fiber cap.