Modelling approaches for evaluating multiscale tendon mechanics

Abstract

Tendon exhibits anisotropic, inhomogeneous and viscoelastic mechanical properties that are determined by its complicated hierarchical structure and varying amounts/organization of different tissue constituents. Although extensive research has been conducted to use modelling approaches to interpret tendon structure–function relationships in combination with experimental data, many issues remain unclear (i.e. the role of minor components such as decorin, aggrecan and elastin), and the integration of mechanical analysis across different length scales has not been well applied to explore stress or strain transfer from macro- to microscale. This review outlines mathematical and computational models that have been used to understand tendon mechanics at different scales of the hierarchical organization. Model representations at the molecular, fibril and tissue levels are discussed, including formulations that follow phenomenological and microstructural approaches (which include evaluations of crimp, helical structure and the interaction between collagen fibrils and proteoglycans). Multiscale modelling approaches incorporating tendon features are suggested to be an advantageous methodology to understand further the physiological mechanical response of tendon and corresponding adaptation of properties owing to unique in vivo loading environments.

Experimental evaluation of multiscale tendon mechanics

“…In our recent work, the distal region of bovine DDFT, which contains higher PG content, showed greater shear stresses than the proximal region with lower PG content . Additionally, a multi‐fibril model, which incorporated a chondroitin‐6‐sulphate side chain to mimic discontinuous fibril assembly in mature tendons, showed consistent failure stresses and elastic modulus with experimental data . However, other theoretical models and experiment results question this hypothesis.…”

“…Collagen crimp has been proposed to contribute to strain‐stress non‐linearity by stretching as a result of small tensile forces at low strains, and function as something of a shock absorber . Another hypothesis is that the recoil or crimp of collagen fibers is potentially maintained by elastic fibers, which have been observed within the hierarchical tendon structure …”

“…Schematic of the multiscale tendon hierarchical structure (adapted, with permission, from Fang et al Schematic of full tendon taken, with permission, from Handsfield et al). IFM, interfascicular matrix.…”

A generalized inelastic modeling concept for soft fibrous tissues

“…The IFM consists of small diameter fibrils, wrapping bigger diameter fibrils, and proteoglycans . PGs are made of a core protein (CP) to which glycosaminoglycan (GAG) side chains are covalently bonded …”

Integrated multiscale biomaterials experiment and modelling: a perspective

“…Although this has been recognized for decades, many important mysteries persist relating to understanding of the fibres themselves and of their mesoscale interactions. As reviewed by Fang & Lake [9], the field has gradually progressed from simple phenomenological models to intricate structural models that account for details of fibre response, architecture and interactions. This issue presents several major advances in this area, and highlights open challenges.…”