Modelling approaches for evaluating multiscale tendon mechanics

Biomechanics of soft biological tissues and organs, mechanobiology, homeostasis and modelling

The human body consists of many different soft biological tissues that exhibit diverse microstructures and functions and experience diverse loading conditions. Yet, under many conditions, the mechanical behaviour of these tissues can be described well with similar nonlinearly elastic or inelastic constitutive relations, both in health and some diseases. Such constitutive relations are essential for performing nonlinear stress analyses, which in turn are critical for understanding physiology, pathophysiology and even clinical interventions, including surgery. Indeed, most cells within load-bearing soft tissues are highly sensitive to their local mechanical environment, which can typically be quantified using methods of continuum mechanics only after the constitutive relations are determined from appropriate data, often multi-axial. In this review, we discuss some of the many experimental findings of the structure and the mechanical response, as well as constitutive formulations for 10 representative soft tissues or organs, and present basic concepts of mechanobiology to support continuum biomechanical studies. We conclude by encouraging similar research along these lines, but also the need for models that can describe and predict evolving tissue properties under many conditions, ranging from normal development to disease progression and wound healing. An important foundation for biomechanics and mechanobiology now exists and methods for collecting detailed multi-scale data continue to progress. There is, thus, considerable opportunity for continued advancement of mechanobiology and biomechanics.

The effect of enzymatic GAG degradation on transverse shear properties of porcine cornea

The structural integrity of cornea depends on properties of its extracellular matrix, mainly a mixture of collagen fibers and soluble proteoglycans (PGs). PGs are macromolecules of negatively charged sulphated glycosaminoglycans (GAGs) covalently attached to a protein core. GAGs appear as bridges between adjacent collagen fibers and could facilitate force transfer between them. Furthermore, GAGs are responsible for corneal hydration by attracting and maintaining water molecules into the extracellular matrix. Based on these observations, GAGs are expected to be essential for biomechanical properties of cornea. The primary objective of the present study was to determine the effects of GAGs on shear properties of cornea. For this purpose, GAGs were enzymatically removed from porcine corneal disks by keratanase II enzyme. After confirming the successful removal of GAGs by histochemical methods, torsional rheometry was performed to characterize the shear stiffness of GAG-depleted samples as a function of axial strain. It was found that the shear modulus of all samples was a function of applied shear strain and compressive strain. Beyond the range of linear viscoelastic response, the average complex shear modulus decreased with increasing the shear strain. Increasing the axial strain from 0% to 40% significantly increased the average complex shear modulus of corneal disks in all groups. Finally, the enzyme treatment with keratanase II enzyme significantly decreased the shear stiffness. The experimental measurements were discussed in terms of microstructural and compositional properties of corneal extracellular matrix and it was concluded that GAGs play a significant role in defining shear properties of cornea.

Estimation of the biaxial tensile behavior of ovine esophageal tissue using artificial neural networks

Diseases of the esophagus affect its function and often lead to replacement of long sections of the organ. Current healing methods involve the use of bioscaffolds processed from other animal models. Although the properties of these animal models are not exactly the same as those of the human esophagus, they nevertheless present a reasonable means of assessing the biomechanical properties of the esophageal tissue. Besides, sheep bear many similarities physiologically to humans and they also suffer from same diseases as humans. The morphology of their esophagus is also comparable to that of humans. Thus, in the study, an ovine esophagus was studied. Studies on the planar biaxial tests of the gross esophageal anatomy are limited. The composite nature of the gross anatomy of the esophagus makes the application of structure-based models such as Holzapfel-type models very difficult. In current studies the tissue is therefore often separated into specific layers with substantial collagen content. The effects of adipose tissue and other non-collagenous tissue often make the mechanical behavior of the esophagus widely diverse and unpredictable using deterministic structure-based models. Thus, it may be very difficult to predict its mechanical behavior. In the study, an NARX neural network was used to predict the stress-strain response of the gross anatomy of the ovine esophagus. The results show that the NARX model was able to achieve a correlation above 99.9% within a fitting error margin of 16%. Therefore, the use of artificial neural networks may provide a more accurate way of predicting the biaxial stress-strain response of the esophageal tissue, and lead to further improvements in the design and development of synthetic replacement materials for esophageal tissue.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Guidelines for ex vivo mechanical testing of tendon

Tendons are critical for the biomechanical function of joints. Tendons connect muscles to bones and allow for the transmission of muscle forces to facilitate joint motion. Therefore, characterizing the tensile mechanical properties of tendons is important for the assessment of functional tendon health and efficacy of treatments for acute and chronic injuries. In this guidelines paper, we review methodological considerations, testing protocols, and key outcome measures for mechanical testing of tendons. The goal of the paper is to present a simple set of guidelines to the nonexpert seeking to perform tendon mechanical tests. The suggested approaches provide rigorous and consistent methodologies for standardized biomechanical characterization of tendon and reporting requirements across laboratories.

An indentation-based framework for probing the glycosaminoglycan-mediated interactions of collagen fibrils

Microscale deformation processes, such as reorientation, buckling, and sliding of collagen fibrils, determine the mechanical behavior and function of collagenous tissue. While changes in the structure and composition of tendon have been extensively studied, the deformation mechanisms that modulate the interaction of extracellular matrix (ECM) constituents are not well understood, partly due to the lack of appropriate techniques to probe the behavior. In particular, the role of glycosaminoglycans (GAGs) in modulating collagen fibril interactions has remained controversial. Some studies suggest that GAGs act as crosslinkers between the collagen fibrils, while others have not found such evidence and postulate that GAGs have other functions. Here, we introduce a new framework, relying on orientation-dependent indentation behavior of tissue and computational modeling, to evaluate the shear-mediated function of GAGs in modulating the collagen fibril interactions at a length scale more relevant to fibrils compared to bulk tests. Specifically, we use chondroitinase ABC to enzymatically deplete the GAGs in tendon; measure the orientation-dependent indentation response in transverse and longitudinal orientations; and infer the microscale deformation mechanisms and function of GAGs from a microstructural computational model and a modified shear-lag model. We validate the modeling approach experimentally and show that GAGs facilitate collagen fibril sliding with minimal crosslinking function. We suggest that the molecular reconfiguration of GAGs is a potential mechanism for their microscale, strain-dependent viscoelastic behavior. This study reveals the mechanisms that control the orientation-dependent indentation response by affecting the shear deformation and provides new insights into the mechanical function of GAGs and collagen crosslinkers in collagenous tissue.

Mimicking the Hierarchical Organization of Natural Collagen: Toward the Development of Ideal Scaffolding Material for Tissue Regeneration

Biological materials found in living organisms, many of which are proteins, feature a complex hierarchical organization. Type I collagen, a fibrous structural protein ubiquitous in the mammalian body, provides a striking example of such a hierarchical material, with peculiar architectural features ranging from the amino acid sequence at the nanoscale (primary structure) up to the assembly of fibrils (quaternary structure) and fibers, with lengths of the order of microns. Collagen plays a dominant role in maintaining the biological and structural integrity of various tissues and organs, such as bone, skin, tendons, blood vessels, and cartilage. Thus, "artificial" collagen-based fibrous assemblies, endowed with appropriate structural properties, represent ideal substrates for the development of devices for tissue engineering applications. In recent years, with the ultimate goal of developing three-dimensional scaffolds with optimal bioactivity able to promote both regeneration and functional recovery of a damaged tissue, numerous studies focused on the capability to finely modulate the scaffold architecture at the microscale and the nanoscale in order to closely mimic the hierarchical features of the extracellular matrix and, in particular, the natural patterning of collagen. All of these studies clearly show that the accurate characterization of the collagen structure at the submolecular and supramolecular levels is pivotal to the understanding of the relationships between the nanostructural/microstructural properties of the fabricated scaffold and its macroscopic performance. Several studies also demonstrate that the selected processing, including any crosslinking and/or sterilization treatments, can strongly affect the architecture of collagen at various length scales. The aim of this review is to highlight the most recent findings on the development of collagen-based scaffolds with optimized properties for tissue engineering. The optimization of the scaffolds is particularly related to the modulation of the collagen architecture, which, in turn, impacts on the achieved bioactivity.

Three-Dimensional Quantification of Collagen Microstructure During Tensile Mechanical Loading of Skin

Skin is a heterogeneous tissue that can undergo substantial structural and functional changes with age, disease, or following injury. Understanding how these changes impact the mechanical properties of skin requires three-dimensional (3D) quantification of the tissue microstructure and its kinematics. The goal of this study was to quantify these structure-function relationships via second harmonic generation (SHG) microscopy of mouse skin under tensile mechanical loading. Tissue deformation at the macro- and micro-scale was quantified, and a substantial decrease in tissue volume and a large Poisson’s ratio was detected with stretch, indicating the skin differs substantially from the hyperelastic material models historically used to explain its behavior. Additionally, the relative amount of measured strain did not significantly change between length scales, suggesting that the collagen fiber network is uniformly distributing applied strains. Analysis of undeformed collagen fiber organization and volume fraction revealed a length scale dependency for both metrics. 3D analysis of SHG volumes also showed that collagen fiber alignment increased in the direction of stretch, but fiber volume fraction did not change. Interestingly, 3D fiber kinematics was found to have a non-affine relationship with tissue deformation, and an affine transformation of the micro-scale fiber network overestimates the amount of fiber realignment. This result, along with the other outcomes, highlights the importance of accurate, scale-matched 3D experimental measurements when developing multi-scale models of skin mechanical function.

Structure, composition and fibril-reinforced poroviscoelastic properties of bovine knee ligaments and patellar tendon

Tissue-level stress-relaxation of ligaments and tendons in the toe region is characterized by fast and long-term relaxations and an increase in relaxation magnitude with strain. Characterizing the compositional and structural origins of these phenomena helps in the understanding of mechanisms of ligament and tendon function and adaptation in health and disease. A three-step tensile stress-relaxation test was conducted on dumbbell-shaped pieces of bovine knee ligaments and patellar tendon (PT) (n = 10 knees). Their mechanical behaviour was characterized by a fibril-reinforced poroviscoelastic material model, able to describe characteristic times and magnitudes of fast and long-term relaxations. The crimp angle and length of tissues were measured with polarized light microscopy, while biochemical contents were determined by colorimetric biochemical methods. The long-term relaxation time was longer in the anterior cruciate ligament (ACL) and PT compared with collateral ligaments (p < 0.05). High hydroxyproline content predicted greater magnitude and shorter time of both fast and long-term relaxation. High uronic acid content predicted longer time of long-term relaxation, whereas high crimp angle predicted higher magnitude of long-term relaxation. ACL and PT are better long-term stabilizers than collateral ligaments. The long-term relaxation behaviour is affected or implied by proteoglycans and crimp angle, possibly relating to slow structural reorganization of the tissue.

Comparison of material models for anterior cruciate ligament in tension: from poroelastic to a novel fibril-reinforced nonlinear composite model

Computational models of the knee joint are useful for evaluating stresses and strains within the joint tissues. However, the outcome of those models is sensitive to the material model and material properties chosen for ligaments, the collagen reinforced tissues connecting bone to bone. The purpose of this study was to investigate different compositionally motivated material models and further to develop a model that can accurately reproduce experimentally measured stress-relaxation data of bovine anterior cruciate ligament (ACL). Tensile testing samples were extracted from ACLs of bovine knee joints (N = 10) and subjected to a three-step stress-relaxation test at the toe region. Data from the experiments was averaged and one average finite element model was generated to replicate the experiment. Poroelastic and different fibril-reinforced poro(visco)elastic material models were applied, and their material parameters were optimized to reproduce the experimental force-time response. Material models with only fluid flow mediated relaxation were not able to capture the stress-relaxation behavior (R² = 0.806, 0.803 and 0.938). The inclusion of the viscoelasticity of the fibrillar network improved the model prediction (R² = 0.978 and 0.976), but the complex stress-relaxation behavior was best captured by a poroelastic model with a nonlinear two-relaxation-time strain-recruited viscoelastic fibrillar network (R² = 0.997). The results suggest that in order to replicate the multi-step stress-relaxation behavior of ACL in tension, the fibrillar network formulation should include the complex nonlinear viscoelastic phenomena.

Multi-Scale Loading and Damage Mechanisms of Plantaris and Rat Tail Tendons

Tendinopathy, degeneration of the tendon that leads to pain and dysfunction, is common in both sports and occupational settings, but multi-scale mechanisms for tendinopathy are still unknown. We recently showed that micro-scale sliding (shear) is responsible for both load transfer and damage mechanisms in the rat tail tendon; however, the rat tail tendon is a specialized non-load-bearing tendon, and thus the load transfer and damage mechanisms are still unknown for load-bearing tendons. The objective of this study was to investigate the load transfer and damage mechanisms of load-bearing tendons using the rat plantaris tendon. We demonstrated that micro-scale sliding is a key component for both mechanisms in the plantaris tendon, similar to the tail tendon. Namely, the micro-scale sliding was correlated with applied strain, demonstrating that load was transferred via micro-scale sliding in the plantaris and tail tendons. In addition, while the micro-scale strain fully recovered, the micro-scale sliding was non-recoverable and strain-dependent, and correlated with tissue-scale mechanical parameters. When the applied strain was normalized, the % magnitudes of non-recoverable sliding was similar between the plantaris and tail tendons. Statement of clinical significance: Understanding the mechanisms responsible for the pathogenesis and progression of tendinopathy can improve prevention and rehabilitation strategies and guide therapies and the design of engineered constructs. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:1827-1837, 2019.

Tendon Tissue Engineering: Effects of Mechanical and Biochemical Stimulation on Stem Cell Alignment on Cell-Laden Hydrogel Yarns

Fiber-based approaches hold great promise for tendon tissue engineering enabling the possibility of manufacturing aligned hydrogel filaments that can guide collagen fiber orientation, thereby providing a biomimetic micro-environment for cell attachment, orientation, migration, and proliferation. In this study, a 3D system composed of cell-laden, highly aligned hydrogel yarns is designed and obtained via wet spinning in order to reproduce the morphology and structure of tendon fascicles. A bioink composed of alginate and gelatin methacryloyl (GelMA) is optimized for spinning and loaded with human bone morrow mesenchymal stem cells (hBM-MSCs). The produced scaffolds are subjected to mechanical stretching to recapitulate the strains occurring in native tendon tissue. Stem cell differentiation is promoted by addition of bone morphogenetic protein 12 (BMP-12) in the culture medium. The aligned orientation of the fibers combined with mechanical stimulation results in highly preferential longitudinal cell orientation and demonstrates enhanced collagen type I and III expression. Additionally, the combination of biochemical and mechanical stimulations promotes the expression of specific tenogenic markers, signatures of efficient cell differentiation towards tendon. The obtained results suggest that the proposed 3D cell-laden aligned system can be used for engineering of scaffolds for tendon regeneration.

Multiscale mechanical effects of native collagen cross-linking in tendon

The hierarchical structure of tendon allows for attenuation of mechanical strain down decreasing length scales. While reorganization of collagen fibers accounts for microscale strain attenuation, cross-linking between collagen molecules contributes to deformation mechanisms at the fibrillar and molecular scales. Divalent and trivalent enzymatic cross-links form during the development of collagen fibrils through the enzymatic activity of lysyl oxidase (LOX). By establishing connections between telopeptidyl and triple-helical domains of adjacent molecules within collagen fibrils, these cross-links stiffen the fibrils by resisting intermolecular sliding. Ultimately, greater enzymatic cross-linking leads to less compliant and stronger tendon as a result of stiffer fibrils. In contrast, nonenzymatic cross-links such as glucosepane and pentosidine are not produced during development but slowly accumulate through glycation of collagen. Therefore, these cross-links are only expected to be present in significant quantities in advanced age, where there has been sufficient time for glycation to occur, and in diabetes, where the presence of more free sugar in the extracellular matrix increases the rate of glycation. Unlike enzymatic cross-links, current evidence suggests that nonenzymatic cross-links are at least partially isolated to the surface of collagen fibers. As a result, glycation has been proposed to primarily impact tendon mechanics by altering molecular interactions at the fiber interface, thereby diminishing sliding between fibers. Thus, increased nonenzymatic cross-linking decreases microscale strain attenuation and the viscous response of tendon. In conclusion, enzymatic and nonenzymatic collagen cross-links have demonstrable and distinct effects on the mechanical properties of tendon across different length scales.

Multiscale Mechanical Evaluation of Human Supraspinatus Tendon Under Shear Loading After Glycosaminoglycan Reduction

Proteoglycans (PGs) are broadly distributed within many soft tissues and, among other roles, often contribute to mechanical properties. Although PGs, consisting of a core protein and glycosaminoglycan (GAG) sidechains, were once hypothesized to regulate stress/strain transfer between collagen fibrils and help support load in tendon, several studies have reported no changes to tensile mechanics after GAG depletion. Since GAGs are known to help sustain nontensile loading in other tissues, we hypothesized that GAGs might help support shear loading in human supraspinatus tendon (SST), a commonly injured tendon which functions in a complex multiaxial loading environment. Therefore, the objective of this study was to determine whether GAGs contribute to the response of SST to shear, specifically in terms of multiscale mechanical properties and mechanisms of microscale matrix deformation. Results showed that chondroitinase ABC (ChABC) treatment digested GAGs in SST while not disrupting collagen fibers. Peak and equilibrium shear stresses decreased only slightly after ChABC treatment and were not significantly different from pretreatment values. Reduced stress ratios were computed and shown to be slightly greater after ChABC treatment compared to phosphate-buffered saline (PBS) incubation without enzyme, suggesting that these relatively small changes in stress values were not due strictly to tissue swelling. Microscale deformations were also not different after ChABC treatment. This study demonstrates that GAGs possibly play a minor role in contributing to the mechanical behavior of SST in shear, but are not a key tissue constituent to regulate shear mechanics.

Experimental evaluation of multiscale tendon mechanics

Tendon's primary function is a mechanical link between muscle and bone. The hierarchical structure of tendon and specific compositional constituents are believed to be critical for proper mechanical function. With increased appreciation for tendon importance and the development of various technological advances, this review paper summarizes recent experimental approaches that have been used to study multiscale tendon mechanics, includes an overview of studies that have evaluated the role of specific tissue constituents, and also proposes challenges/opportunities facing tendon study. Tendon has been demonstrated to have specific structural characteristics (e.g., multi-level hierarchy, crimp pattern, helix) and complex mechanical properties (e.g., non-linearity, anisotropy, viscoelasticity). Physical mechanisms including uncrimping, fiber sliding, and collagen reorganization have been shown to govern tendon mechanical responses under both static and dynamic loading. Several tendon constituents with relatively small quantities have been suggested to play a role in its mechanics, although some results are conflicting. Further research should be performed to understand the interplay and communication of tendon mechanical properties across levels of the hierarchical structure, and further show how each of these components contribute to tendon mechanics. The studies summarized and discussed in this review have helped elucidate important aspects of multiscale tendon mechanics, which is a prerequisite for analyzing stress/strain transfer between multiple scales and identifying key principles of mechanotransduction. This information could further facilitate interpreting the functional diversity of tendons from different species, different locations, and even different developmental stages, and then better understand and identify fundamental concepts related to tendon degeneration, disease, and healing. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:1353-1365, 2017.

Hierarchical Spring-Block Model for Multiscale Friction Problems

A primary issue in biomaterials science is to design materials with ad hoc properties, depending on the specific application. Among these properties, friction is recognized as a fundamental aspect characterizing materials for many practical purposes. Recently, new and unexpected frictional properties have been obtained by exploiting hierarchical multiscale structures, inspired by those observed in many biological systems. In order to understand the emergent frictional behavior of these materials at the macroscale, it is fundamental to investigate their hierarchical structure, spanning across different length scales. In this article, we introduce a statistical multiscale approach, based on a one-dimensional formulation of the spring-block model, in which friction is modeled at each hierarchical scale through the classical Amontons-Coulomb force with statistical dispersion on the friction coefficients of the microscopic components. By means of numerical simulations, we deduce the global statistical distributions of the elementary structure at micrometric scale and use them as input distributions for the simulations at the next scale levels. We thus study the influence of microscopic artificial patterning on macroscopic friction coefficients. We show that it is possible to tune the friction properties of a hierarchical surface and provide some insight on the mechanisms involved at different length scales.

Multiscale mechanical integrity of human supraspinatus tendon in shear after elastin depletion

Human supraspinatus tendon (SST) exhibits region-specific nonlinear mechanical properties under tension, which have been attributed to its complex multiaxial physiological loading environment. However, the mechanical response and underlying multiscale mechanism regulating SST behavior under other loading scenarios are poorly understood. Furthermore, little is known about the contribution of elastin to tendon mechanics. We hypothesized that (1) SST exhibits region-specific shear mechanical properties, (2) fiber sliding is the predominant mode of local matrix deformation in SST in shear, and (3) elastin helps maintain SST mechanical integrity by facilitating force transfer among collagen fibers. Through the use of biomechanical testing and multiphoton microscopy, we measured the multiscale mechanical behavior of human SST in shear before and after elastase treatment. Three distinct SST regions showed similar stresses and microscale deformation. Collagen fiber reorganization and sliding were physical mechanisms observed as the SST response to shear loading. Measures of microscale deformation were highly variable, likely due to a high degree of extracellular matrix heterogeneity. After elastase treatment, tendon exhibited significantly decreased stresses under shear loading, particularly at low strains. These results show that elastin contributes to tendon mechanics in shear, further complementing our understanding of multiscale tendon structure-function relationships.

Integrated multiscale biomaterials experiment and modelling: a perspective

Advances in multiscale models and computational power have enabled a broad toolset to predict how molecules, cells, tissues and organs behave and develop. A key theme in biological systems is the emergence of macroscale behaviour from collective behaviours across a range of length and timescales, and a key element of these models is therefore hierarchical simulation. However, this predictive capacity has far outstripped our ability to validate predictions experimentally, particularly when multiple hierarchical levels are involved. The state of the art represents careful integration of multiscale experiment and modelling, and yields not only validation, but also insights into deformation and relaxation mechanisms across scales. We present here a sampling of key results that highlight both challenges and opportunities for integrated multiscale experiment and modelling in biological systems.