Parameter optimization for the visco-hyperelastic constitutive model of tendon using FEM

Microstructural modeling of Achilles Tendon biomechanics focusing on bone insertion site

The interface between the Achilles Tendon (AT) and calcaneus comprises soft and hard connective tissues. Such interfaces are vulnerable to mechanical damage. Tendon to Bone Insertion Region (TBIR) has unique microstructural characteristics for reinforcement. This region constitutes almost 10% of the AT's distal end. The rest of the tendon (tendon proper) has longitudinal fiber orientation with no mineral content. Although, the TBIR lacks longitudinally organized fibers and at the same time, incorporates mineral molecules. In this study, a 3D computational model of the TBIR proposed to underline several reinforcement mechanisms. The obtained results showed that off-axis alignment of fibers, when coupled with the mineral deposition, shifts the stress concentration region to the tendon proper. In the case of altering each parameter individually, probable failure observed in the bone interface, which causes complications in surgical procedure or during healing. A gradual increase of mineral compensates for the stiffness mismatch between the AT and calcaneus. The proposed computational framework illustrated the complementary roles of fiber orientation and mineral molecules: nearly transverse orientation of fibers alleviated the stress concentration locally, while mineral deposition directly enhanced the TBIR stiffness.

Quantification of Internal Stress-Strain Fields in Human Tendon: Unraveling the Mechanisms that Underlie Regional Tendon Adaptations and Mal-Adaptations to Mechanical Loading and the Effectiveness of Therapeutic Eccentric Exercise

By virtue of their anatomical location between muscles and bones, tendons make it possible to transform contractile force to joint rotation and locomotion. However, tendons do not behave as rigid links, but exhibit viscoelastic tensile properties, thereby affecting the length and contractile force in the in-series muscle, but also storing and releasing elastic stain energy as some tendons are stretched and recoiled in a cyclic manner during locomotion. In the late 90s, advancements were made in the application of ultrasound scanning that allowed quantifying the tensile deformability and mechanical properties of human tendons in vivo. Since then, the main principles of the ultrasound-based method have been applied by numerous research groups throughout the world and showed that tendons increase their tensile stiffness in response to exercise training and chronic mechanical loading, in general, by increasing their size and improving their intrinsic material. It is often assumed that these changes occur homogenously, in the entire body of the tendon, but recent findings indicate that the adaptations may in fact take place in some but not all tendon regions. The present review focuses on these regional adaptability features and highlights two paradigms where they are particularly evident: (a) Chronic mechanical loading in healthy tendons, and (b) tendinopathy. In the former loading paradigm, local tendon adaptations indicate that certain regions may “see,” and therefore adapt to, increased levels of stress. In the latter paradigm, local pathological features indicate that certain tendon regions may be “stress-shielded” and degenerate over time. Eccentric exercise protocols have successfully been used in the management of tendinopathy, without much sound understanding of the mechanisms underpinning their effectiveness. For insertional tendinopathy, in particular, it is possible that the effectiveness of a loading/rehabilitation protocol depends on the topography of the stress created by the exercise and is not only reliant upon the type of muscle contraction performed. To better understand the micromechanical behavior and regional adaptability/mal-adaptability of tendon tissue it is important to estimate its internal stress-strain fields. Recent relevant advancements in numerical techniques related to tendon loading are discussed.

Modelling approaches for evaluating multiscale tendon mechanics

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.

A fibre-reinforced poroviscoelastic model accurately describes the biomechanical behaviour of the rat Achilles tendon

Background

Computational models of Achilles tendons can help understanding how healthy tendons are affected by repetitive loading and how the different tissue constituents contribute to the tendon’s biomechanical response. However, available models of Achilles tendon are limited in their description of the hierarchical multi-structural composition of the tissue. This study hypothesised that a poroviscoelastic fibre-reinforced model, previously successful in capturing cartilage biomechanical behaviour, can depict the biomechanical behaviour of the rat Achilles tendon found experimentally.

Materials and Methods

We developed a new material model of the Achilles tendon, which considers the tendon’s main constituents namely: water, proteoglycan matrix and collagen fibres. A hyperelastic formulation of the proteoglycan matrix enabled computations of large deformations of the tendon, and collagen fibres were modelled as viscoelastic. Specimen-specific finite element models were created of 9 rat Achilles tendons from an animal experiment and simulations were carried out following a repetitive tensile loading protocol. The material model parameters were calibrated against data from the rats by minimising the root mean squared error (RMS) between experimental force data and model output.

Results and Conclusions

All specimen models were successfully fitted to experimental data with high accuracy (RMS 0.42-1.02). Additional simulations predicted more compliant and soft tendon behaviour at reduced strain-rates compared to higher strain-rates that produce a stiff and brittle tendon response. Stress-relaxation simulations exhibited strain-dependent stress-relaxation behaviour where larger strains produced slower relaxation rates compared to smaller strain levels. Our simulations showed that the collagen fibres in the Achilles tendon are the main load-bearing component during tensile loading, where the orientation of the collagen fibres plays an important role for the tendon’s viscoelastic response. In conclusion, this model can capture the repetitive loading and unloading behaviour of intact and healthy Achilles tendons, which is a critical first step towards understanding tendon homeostasis and function as this biomechanical response changes in diseased tendons.