Incorporating plasticity of the interfibrillar matrix in shear lag models is necessary to replicate the multiscale mechanics of tendon fascicles

Mechanical Models of Collagen Networks for Understanding Changes in the Failure Properties of Aging Skin

Skin undergoes mechanical alterations due to changes in the composition and structure of the collagenous dermis with aging. Previous studies have conflicting findings, with both increased and decreased stiffness reported for aging skin. The underlying structure-function relationships that drive age-related changes are complex and difficult to study individually. One potential contributor to these variations is the accumulation of nonenzymatic crosslinks within collagen fibers, which affect dermal collagen remodeling and mechanical properties. Specifically, these crosslinks make individual fibers stiffer in their plastic loading region and lead to increased fragmentation of the collagenous network. To better understand the influence of these changes, we investigated the impact of nonenzymatic crosslink changes on the dermal microstructure using discrete fiber networks representative of the dermal microstructure. Our findings suggest that stiffening the plastic region of collagen's mechanical response has minimal effects on network-level stiffness and failure stresses. Conversely, simulating fragmentation through a loss of connectivity substantially reduces network stiffness and failure stress, while increasing stretch ratios at failure.

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.

Mouse Achilles tendons exhibit collagen disorganization but minimal collagen denaturation during cyclic loading to failure

While overuse is a prominent risk factor for tendinopathy, the fatigue-induced structural damage responsible for initiating tendon degeneration remains unclear. Denaturation of collagen molecules and collagen fiber disorganization have been observed within certain tendons in response to fatigue loading. However, no studies have investigated whether these forms of tissue damage occur in Achilles tendons, which commonly exhibit tendinopathy. Therefore, the objective of this study was to determine whether mouse Achilles tendons undergo collagen denaturation and collagen fiber disorganization when cyclically loaded to failure. Consistent with previous testing of other energy-storing tendons, we found that cyclic loading of mouse Achilles tendons produced collagen disorganization but minimal collagen denaturation. To determine whether the lack of collagen denaturation is unique to mouse Achilles tendons, we monotonically loaded the Achilles and other mouse tendons to failure. We found that the patellar tendon was also resistant to collagen denaturation, but the flexor digitorum longus (FDL) tendon and tail tendon fascicles were not. Furthermore, the Achilles and patellar tendons had a lower tensile strength and modulus. While this may be due to differences in tissue structure, it is likely that the lack of collagen denaturation during monotonic loading in both the Achilles and patellar tendons was due to failure near their bony insertions, which were absent in the FDL and tail tendons. These findings suggest that mouse Achilles tendons are resistant to collagen denaturation in situ and that Achilles tendon degeneration may not be initiated by mechanically-induced damage to collagen molecules.

Age-dependent mechanical properties of tail tendons in wild-type and mimecan gene-knockout mice - A preliminary study

Mimecan, or osteoglycin, belongs to the family of small leucine-rich proteoglycans. In connective tissues mimecan is implicated in the development and maintenance of normal collagen fibrillar organization. Since collagen fibrils are responsible for tissue reinforcement, the absence of mimecan could lead to abnormal tissue mechanical properties. Here, we carried out a preliminary investigation of possible changes in the mechanical properties of tendons in mice lacking a functional mimecan gene, as a function of age. Tail tendons were dissected from mimecan gene knockout (KO) and wild type (WT) mice at ages 1, 4 and 8 months and mechanical properties evaluated using a microtensile testing equipment. Mimecan gene knockout resulted in changes in tendon elasticity- and fracture-related properties. While tendons of WT mice exhibited enhanced mechanical properties with increasing age, this trend was notably attenuated in mimecan KO tendons, with the exception of fracture strain. When genotype and age were considered as cross factors, the diminution in the mechanical properties of mimecan KO tendons was significant for yield strength, modulus and fracture strength. This effect appeared to affect the mice at 4 month old. These preliminary results suggest that mimecan may have a role in regulating age-dependent mechanical function in mouse tail tendon.

Mechanical Stimulation via Muscle Activity Is Necessary for the Maturation of Tendon Multiscale Mechanics During Embryonic Development

During embryonic development, tendons transform into a hypocellular tissue with robust tensile load-bearing capabilities. Previous work suggests that this mechanical transformation is due to increases in collagen fibril length and is dependent on mechanical stimulation via muscle activity. However, the relationship between changes in the microscale tissue structure and changes in macroscale tendon mechanics is still unclear. Additionally, the specific effect of mechanical stimulation on the multiscale structure-function relationships of developing tendons is also unknown. Therefore, the objective of this study was to measure the changes in tendon mechanics and structure at multiple length scales during embryonic development with and without skeletal muscle paralysis. Tensile testing of tendons from chick embryos was performed to determine the macroscale tensile modulus as well as the magnitude of the fibril strains and interfibrillar sliding with applied tissue strain. Embryos were also treated with either decamethonium bromide or pancuronium bromide to produce rigid or flaccid paralysis. Histology was performed to assess changes in tendon size, spacing between tendon subunits, and collagen fiber diameter. We found that the increase in the macroscale modulus observed with development is accompanied by an increase in the fibril:tissue strain ratio, which is consistent with an increase in collagen fibril length. Additionally, we found that flaccid paralysis reduced the macroscale tendon modulus and the fibril:tissue strain ratio, whereas less pronounced effects that were not statistically significant were observed with rigid paralysis. Finally, skeletal paralysis also reduced the size of collagen fibril bundles (i.e., fibers). Together, these data suggest that more of the applied tissue strain is transmitted to the collagen fibrils at later embryonic ages, which leads to an increase in the tendon macroscale tensile mechanics. Furthermore, our data suggest that mechanical stimulation during development is necessary to induce structural and mechanical changes at multiple physical length scales. This information provides valuable insight into the multiscale structure-function relationships of developing tendons and the importance of mechanical stimulation in producing a robust tensile load-bearing soft tissue.

The influence of glycosaminoglycan proteoglycan side chains on tensile force transmission and the nanostructural properties of Achilles tendons

This study investigates the nanostructural mechanisms that lie behind load transmission in tendons and the role of glycosaminoglycans (GAGs) in the transmission of force in the tendon extracellular matrix. The GAGs in white New Zealand rabbit Achilles tendons were enzymatically depleted, and the tendons subjected to cyclic loading at 6% strain for up to 2 hr. A nanoscale morphometric assessment of fibril deformation under strain was linked with the decline in the tendon macroscale mechanical properties. An atomic force microscope (AFM) was employed to characterize the D-periodicity within and between fibril bundles (WFB and BFB, respectively). By the end of the second hour of the applied strain, the WFB and BFB D-periodicities had significantly increased in the GAG-depleted group (29% increase compared with 15% for the control, p < .0001). No statistically significant differences were found between WFB and BFB D-periodicities in either the control or GAG-depleted groups, suggesting that mechanical load in Achilles tendons is uniformly distributed and fairly homogenous among the WFB and BFB networks. The results of this study have provided evidence of a cycle-dependent mechanism of damage accumulation. The accurate quantification of fibril elongation (measured as the WFB and BFB D-periodicity lengths) in response to macroscopic applied strain has assisted in assessing the complex structure-function relationship in Achilles tendon.

A microstructural model of tendon failure

Collagen fibrils are the most important structural component of tendons. Their crimped structure and parallel arrangement within the tendon lead to a distinctive non-linear stress-strain curve when a tendon is stretched. Microstructural models can be used to relate microscale collagen fibril mechanics to macroscale tendon mechanics, allowing us to identify the mechanisms behind each feature present in the stress-strain curve. Most models in the literature focus on the elastic behaviour of the tendon, and there are few which model beyond the elastic limit without introducing phenomenological parameters. We develop a model, built upon a collagen recruitment approach, that only contains microstructural parameters. We split the stress in the fibrils into elastic and plastic parts, and assume that the fibril yield stretch and rupture stretch are each described by a distribution function, rather than being single-valued. By changing the shapes of the distributions and their regions of overlap, we can produce macroscale tendon stress-strain curves that generate the full range of features observed experimentally, including those that could not be explained using existing models. These features include second linear regions occurring after the tendon has yielded, and step-like failure behaviour present after the stress has peaked. When we compare with an existing model, we find that our model reduces the average root mean squared error from 4.53MPa to 2.29MPa, and the resulting parameter values are closer to those found experimentally. Since our model contains only parameters that have a direct physical interpretation, it can be used to predict how processes such as ageing, disease, and injury affect the mechanical behaviour of tendons, provided we can quantify the effects of these processes on the microstructure.

The differences in viscoelastic properties of subtendons result from the anatomical tripartite structure of human Achilles tendon - ex vivo experimental study and modeling

The human Achilles tendon (AT) is a hierarchical structure macroscopically composed of three subtendons originating from the soleus (SOL) and gastrocnemius (GL, GM) muscles. According to recent reports, the divisible structure of the AT together with diverse material properties of its subtendons are suspected as a probable cause of non-homogeneous stress and strain distribution occurring in loaded AT. Despite numerous investigations on human AT, there is still relatively little knowledge regarding mechanical properties of subtendon-level hierarchy, which is crucial in fully understanding the multiscale relationship which governs tendon mechanics. In this paper we present the first ex vivo study conducted on SOL, GL, and GM subtendons of human AT. We investigate differences in viscoelastic properties of SOL, GM, and GL subtendons in terms of tensile modulus, mechanical hysteresis as well as stress relaxation observed at two different values of strain. Our results show that the most significant differences in mechanical properties exist between subtendon attached to the soleus muscle (SOL) and subtendons originating from the two heads of the gastrocnemius muscle (GM and GL). We used our experimental results to calibrate three different constitutive models: the hyperelastic Yeoh model with power-law flow, the microstructurally motivated Holzapfel-Gasser-Ogden model enhanced with strain-dependent Berström-Boyce flow and the phenomenological elasto-viscoplastic Arruda-Boyce-based model with strain-dependent Berström-Boyce flow supplemented with component representing matrix response. All calibrated models may be applied to commercial FEA software as a sufficient solution for rapid mechanical response modeling of human AT subtendons or for the purpose of future development of comprehensive patient-specific models of human lower limbs. STATEMENT OF SIGNIFICANCE: The divisible structure of the Achilles tendon together with diverse material properties of its subtendons are suspected as a probable cause of non-homogeneous stress and strain distribution occurring in loaded Achilles tendon. Despite numerous investigations on mechanical properties of Achilles tendon, there is still relatively little knowledge regarding mechanical properties of subtendon-level hierarchy, which is crucial in fully understanding the multiscale relationship which governs tendon mechanics. This study is the first reported ex vivo investigation conducted on SOL, GL, and GM human Achilles subtendons. We investigate differences in the viscoelastic properties of individual subtendons and demonstrate that the observed differences should be considered as muscle-dependent. Our experimental research is supported with a modeling study in which we calibrate three different constitutive models.

Combining polarized Raman spectroscopy and micropillar compression to study microscale structure-property relationships in mineralized tissues

Bone is a natural composite possessing outstanding mechanical properties combined with a lightweight design. The key feature contributing to this unusual combination of properties is the bone hierarchical organization ranging from the nano- to the macro-scale. Bone anisotropic mechanical properties from two orthogonal planes (along and perpendicular to the main bone axis) have already been widely studied. In this work, we demonstrate the dependence of the microscale compressive mechanical properties on the angle between loading direction and the mineralized collagen fibril orientation in the range between 0° and 82°. For this, we calibrated polarized Raman spectroscopy for quantitative collagen fibril orientation determination and validated the method using widely used techniques (small angle X-ray scattering, micro-computed tomography). We then performed compression tests on bovine cortical bone micropillars with known mineralized collagen fibril angles. A strong dependence of the compressive micromechanical properties of bone on the fibril orientation was found with a high degree of anisotropy for both the elastic modulus (E_a/E_t=3.80) and the yield stress (σ_a^y/σ_t^y=2.54). Moreover, the post-yield behavior was found to depend on the MCF orientation with a transition between softening to hardening behavior at approximately 50°. The combination of methods described in this work allows to reliably determine structure-property relationships of bone at the microscale, which may be used as a measure of bone quality.

Dependence of tendon multiscale mechanics on sample gauge length is consistent with discontinuous collagen fibrils

While collagen fibrils are understood to be the primary load-bearing elements in tendon, controversy still exists on how fibrils functionally transmit load from muscle to bone. Specifically, it's unclear whether fibrils are structurally continuous along the tendon length and bear load independently, or if they are discontinuous and transfer load through interfibrillar shear forces. To address this question, we investigated whether the multiscale mechanics of rat tail tendon fascicles is dependent on sample gauge length. We hypothesized that as the grip-to-grip length is reduced and approaches the length of the collagen fibrils, tendon fascicles will adopt a multiscale mechanical response consistent with structurally continuous fibrils. Our findings show that, for gauge lengths of 20 mm or greater, the local fibril strains are less than the bulk tissue strains, which can be explained by relative sliding between discontinuous collagen fibrils. In contrast, at a 5 mm gauge length, the fibril strains are equivalent to the applied tissue strains, suggesting that the collagen fibrils are structurally continuous between the grips. Additionally, the macroscale tissue modulus is increased at gauge lengths of 5 and 10 mm. Together, these data support the hypothesis that collagen fibrils in rat tail tendon fascicles are discontinuous and also suggest that their length is between 5 and 10 mm. This fundamental information regarding tendon structure-function relationships underscores the importance of the tissue components that transmit load between fibrils and is critical for understanding tendon pathology as well as establishing structural benchmarks for suitable tissue engineered replacements.

Helical fibrillar microstructure of tendon using serial block-face scanning electron microscopy and a mechanical model for interfibrillar load transfer

Tendon's hierarchical structure allows for load transfer between its fibrillar elements at multiple length scales. Tendon microstructure is particularly important, because it includes the cells and their surrounding collagen fibrils, where mechanical interactions can have potentially important physiological and pathological contributions. However, the three-dimensional (3D) microstructure and the mechanisms of load transfer in that length scale are not known. It has been postulated that interfibrillar matrix shear or direct load transfer via the fusion/branching of small fibrils are responsible for load transfer, but the significance of these mechanisms is still unclear. Alternatively, the helical fibrils that occur at the microstructural scale in tendon may also mediate load transfer; however, these structures are not well studied due to the lack of a three-dimensional visualization of tendon microstructure. In this study, we used serial block-face scanning electron microscopy to investigate the 3D microstructure of fibrils in rat tail tendon. We found that tendon fibrils have a complex architecture with many helically wrapped fibrils. We studied the mechanical implications of these helical structures using finite-element modelling and found that frictional contact between helical fibrils can induce load transfer even in the absence of matrix bonding or fibril fusion/branching. This study is significant in that it provides a three-dimensional view of the tendon microstructure and suggests friction between helically wrapped fibrils as a mechanism for load transfer, which is an important aspect of tendon biomechanics.

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.

Evaluating Plastic Deformation and Damage as Potential Mechanisms for Tendon Inelasticity using a Reactive Modeling Framework

Inelastic behaviors, such as softening, a progressive decrease in modulus before failure, occur in tendon and are important aspect in degeneration and tendinopathy. These inelastic behaviors are generally attributed to two potential mechanisms: plastic deformation and damage. However, it is not clear which is primarily responsible. In this study, we evaluated these potential mechanisms of tendon inelasticity by using a recently developed reactive inelasticity model (RIE), which is a structurally-inspired continuum mechanics framework that models tissue inelasticity based on the molecular bond kinetics. Using RIE, we formulated two material models, one specific to plastic deformation and the other to damage. The models were independently fit to published experimental tensile tests of rat tail tendons. We quantified the inelastic effects and compared the performance of the two models in fitting the mechanical response during loading, relaxation, unloading, and reloading phases. Additionally, we validated the models by using the resulting fit parameters to predict an independent set of experimental stress-strain curves from ramp-to-failure tests. Overall, the models were both successful in fitting the experiments and predicting the validation data. However, the results did not strongly favor one mechanism over the other. As a result, to distinguish between plastic deformation and damage, different experimental protocols will be needed. Nevertheless, these findings suggest the potential of RIE as a comprehensive framework for studying tendon inelastic behaviors.

Comparative multi-scale hierarchical structure of the tail, plantaris, and Achilles tendons in the rat

Rodent tendons are widely used to study human pathologies such as tendinopathy and repair, and to address fundamental physiological questions about development, growth, and remodeling. However, how the gross morphology and multi-scale hierarchical structure of rat tendons, such as the tail, plantaris, and Achilles tendons, compare with that of human tendons are unknown. In addition, there remains disagreement about terminology and definitions. Specifically, the definitions of fascicle and fiber are often dependent on diameter sizes, not their characteristic features, and these definitions impair the ability to compare hierarchical structure across species, where the sizes of the fiber and fascicle may change with animal size and tendon function. Thus, the objective of the study was to select a single species that is commonly used for tendon research (rat) and tendons with varying mechanical functions (tail, plantaris, Achilles) to evaluate the hierarchical structure at multiple length scales using histology, SEM, and confocal imaging. With the exception of the specialized rat tail tendon, we confirmed that in rat tendons there are no fascicles and the fiber is the largest subunit. In addition, we provided a structurally based definition of a fiber as a bundle of collagen fibrils that is surrounded by elongated cells, and this definition was supported by both histologically processed and unprocessed samples. In all rat tendons studied, the fiber diameters were consistently between 10 and 50 μm, and this diameter range appears to be conserved across larger species. Specific recommendations were made highlighting the strengths and limitations of each rat tendon as a research model. Understanding the hierarchical structure of tendon can advance the design and interpretation of experiments and development of tissue-engineered constructs.

In silico assessment of biomedical products: The conundrum of rare but not so rare events in two case studies

In silico clinical trials, defined as "The use of individualized computer simulation in the development or regulatory evaluation of a medicinal product, medical device, or medical intervention," have been proposed as a possible strategy to reduce the regulatory costs of innovation and the time to market for biomedical products. We review some of the the literature on this topic, focusing in particular on those applications where the current practice is recognized as inadequate, as for example, the detection of unexpected severe adverse events too rare to be detected in a clinical trial, but still likely enough to be of concern. We then describe with more details two case studies, two successful applications of in silico clinical trial approaches, one relative to the University of Virginia/Padova simulator that the Food and Drug Administration has accepted as possible replacement for animal testing in the preclinical assessment of artificial pancreas technologies, and the second, an investigation of the probability of cardiac lead fracture, where a Bayesian network was used to combine in vivo and in silico observations, suggesting a whole new strategy of in silico-augmented clinical trials, to be used to increase the numerosity where recruitment is impossible, or to explore patients' phenotypes that are unlikely to appear in the trial cohort, but are still frequent enough to be of concern.

Viscoelastic shear lag model to predict the micromechanical behavior of tendon under dynamic tensile loading

Owing to its viscoelastic nature, tendon exhibits stress rate-dependent breaking and stiffness function. A Kelvin-Voigt viscoelastic shear lag model is proposed to illustrate the micromechanical behavior of the tendon under dynamic tensile conditions. Theoretical closed-form expressions are derived to predict the deformation and stress transfer between fibrils and interfibrillar matrix while tendon is dynamically stretched. The results from the analytical solutions demonstrate that how the fibril overlap length and fibril volume fraction affect the stress transfer and mechanical properties of tendon. We find that the viscoelastic property of interfibrillar matrix mainly results in collagen fibril failure under fast loading rate or creep rupture of tendon. However, discontinuous fibril model and hierarchical structure of tendon ensure relative sliding under slow loading rate, helping dissipate energy and protecting fibril from damage, which may be a key reason why regularly staggering alignment microstructure is widely selected in nature. According to the growth, injury, healing and healed process of tendon observed by many researchers, the conclusions presented in this paper agrees well with the experimental findings. Additionally, the emphasis of this paper is on micromechanical behavior of tendon, whereas this analytical viscoelastic shear lag model can be equally applicable to other soft or hard tissues, owning the similar microstructure.

The Virtual Physiological Human: Ten Years After

Biomedical research and clinical practice are struggling to cope with the growing complexity that the progress of health care involves. The most challenging diseases, those with the largest socioeconomic impact (cardiovascular conditions; musculoskeletal conditions; cancer; metabolic, immunity, and neurodegenerative conditions), are all characterized by a complex genotype-phenotype interaction and by a "systemic" nature that poses a challenge to the traditional reductionist approach. In 2005 a small group of researchers discussed how the vision of computational physiology promoted by the Physiome Project could be translated into clinical practice and formally proposed the term Virtual Physiological Human. Our knowledge about these diseases is fragmentary, as it is associated with molecular and cellular processes on the one hand and with tissue and organ phenotype changes (related to clinical symptoms of disease conditions) on the other. The problem could be solved if we could capture all these fragments of knowledge into predictive models and then compose them into hypermodels that help us tame the complexity that such systemic behavior involves. In 2005 this was simply not possible-the necessary methods and technologies were not available. Now, 10 years later, it seems the right time to reflect on the original vision, the results achieved so far, and what remains to be done.

Evidence that interfibrillar load transfer in tendon is supported by small diameter fibrils and not extrafibrillar tissue components

Collagen fibrils in tendon are believed to be discontinuous and transfer tensile loads through shear forces generated during interfibrillar sliding. However, the structures that transmit these interfibrillar forces are unknown. Various extrafibrillar tissue components (e.g., glycosaminoglycans, collagens XII and XIV) have been suggested to transmit interfibrillar loads by bridging collagen fibrils. Alternatively, collagen fibrils may interact directly through physical fusions and interfibrillar branching. The objective of this study was to test whether extrafibrillar proteins are necessary to transmit load between collagen fibrils or if interfibrillar load transfer is accomplished directly by the fibrils themselves. Trypsin digestions were used to remove a broad spectrum of extrafibrillar proteins and measure their contribution to the multiscale mechanics of rat tail tendon fascicles. Additionally, images obtained from serial block-face scanning electron microscopy were used to determine the three-dimensional fibrillar organization in tendon fascicles and identify any potential interfibrillar interactions. While trypsin successfully removed several extrafibrillar tissue components, there was no change in the macroscale fascicle mechanics or fibril:tissue strain ratio. Furthermore, the imaging data suggested that a network of smaller diameter fibrils (<150 nm) wind around and fuse with their neighboring larger diameter fibrils. These findings demonstrate that interfibrillar load transfer is not supported by extrafibrillar tissue components and support the hypothesis that collagen fibrils are capable of transmitting loads themselves. Conclusively determining how fibrils bear load within tendon is critical for identifying the mechanisms that impair tissue function with degeneration and for restoring tissue properties via cell-mediated regeneration or engineered tissue replacements. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2127-2134, 2017.

Investigating mechanisms of tendon damage by measuring multi-scale recovery following tensile loading

Tendon pathology is associated with damage. While tendon damage is likely initiated by mechanical loading, little is known about the specific etiology. Damage is defined as an irreversible change in the microstructure that alters the macroscopic mechanical parameters. In tendon, the link between mechanical loading and microstructural damage, resulting in macroscopic changes, is not fully elucidated. In addition, tendon damage at the macroscale has been proposed to initiate when tendon is loaded beyond a strain threshold, yet the metrics to define the damage threshold are not determined. We conducted multi-scale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. At the microscale, we observe full recovery of the fibril strain and only partial recovery of the interfibrillar sliding, indicating that the damage initiates at the interfibrillar structures. We show that non-recoverable sliding is a mechanism for tendon damage and is responsible for the macroscale decreased linear modulus and elongated toe-region observed at the fascicle-level, and these macroscale properties are appropriate metrics that reflect tendon damage. We concluded that the inflection point of the stress-strain curve represents the damage threshold and, therefore, may be a useful parameter for future studies. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

STATEMENT OF SIGNIFICANCE

Tendon pathology is associated with mechanically induced damage. Damage, as defined in engineering, is an irreversible change in microstructure that alters the macroscopic mechanical properties. Although microstructural damage and changes to macroscale mechanics are likely, this link to microstructural change was not yet established. We conducted multiscale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. We showed that non-recoverable sliding between collagen fibrils is a mechanism for tendon damage. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

Mechanical function near defects in an aligned nanofiber composite is preserved by inclusion of disorganized layers: Insight into meniscus structure and function

The meniscus is comprised of circumferentially aligned fibers that resist the tensile forces within the meniscus (i.e., hoop stress) that develop during loading of the knee. Although these circumferential fibers are severed by radial meniscal tears, tibial contact stresses do not increase until the tear reaches ∼90% of the meniscus width, suggesting that the severed circumferential fibers still bear load and maintain the mechanical functionality of the meniscus. Recent data demonstrates that the interfibrillar matrix can transfer strain energy to disconnected fibrils in tendon fascicles. In the meniscus, interdigitating radial tie fibers, which function to stabilize and bind the circumferential fibers together, are hypothesized to function in a similar manner by transmitting load to severed circumferential fibers near a radial tear. To test this hypothesis, we developed an engineered fibrous analog of the knee meniscus using poly(ε-caprolactone) to create aligned scaffolds with variable amounts of non-aligned elements embedded within the scaffold. We show that the tensile properties of these scaffolds are a function of the ratio of aligned to non-aligned elements, and change in a predictable fashion following a simple mixture model. When measuring the loss of mechanical function in scaffolds with a radial tear, compared to intact scaffolds, the decrease in apparent linear modulus was reduced in scaffolds containing non-aligned layers compared to purely aligned scaffolds. Increased strains in areas adjacent to the defect were also noted in composite scaffolds. These findings indicate that non-aligned (disorganized) elements interspersed within an aligned network can improve overall mechanical function by promoting strain transfer to nearby disconnected fibers. This finding supports the notion that radial tie fibers may similarly promote tear tolerance in the knee meniscus, and will direct changes in clinical practice and provide guidance for tissue engineering strategies.

STATEMENT OF SIGNIFICANCE

The meniscus is a complex fibrous tissue, whose architecture includes radial tie fibers that run perpendicular to and interdigitate with the predominant circumferential fibers. We hypothesized that these radial elements function to preserve mechanical function in the context of interruption of circumferential bundles, as would be the case in a meniscal tear. To test this hypothesis, we developed a biomaterial analog containing disorganized layers enmeshed regularly throughout an otherwise aligned network. Using this material formulation, we showed that strain transmission is improved in the vicinity of defects when disorganized fiber layers were present. This supports the idea that radial elements within the meniscus improve function near a tear, and will guide future clinical interventions and the development of engineered replacements.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Collagenous Extracellular Matrix Biomaterials for Tissue Engineering: Lessons from the Common Sea Urchin Tissue

Scaffolds for tissue engineering application may be made from a collagenous extracellular matrix (ECM) of connective tissues because the ECM can mimic the functions of the target tissue. The primary sources of collagenous ECM material are calf skin and bone. However, these sources are associated with the risk of having bovine spongiform encephalopathy or transmissible spongiform encephalopathy. Alternative sources for collagenous ECM materials may be derived from livestock, e.g., pigs, and from marine animals, e.g., sea urchins. Collagenous ECM of the sea urchin possesses structural features and mechanical properties that are similar to those of mammalian ones. However, even more intriguing is that some tissues such as the ligamentous catch apparatus can exhibit mutability, namely rapid reversible changes in the tissue mechanical properties. These tissues are known as mutable collagenous tissues (MCTs). The mutability of these tissues has been the subject of on-going investigations, covering the biochemistry, structural biology and mechanical properties of the collagenous components. Recent studies point to a nerve-control system for regulating the ECM macromolecules that are involved in the sliding action of collagen fibrils in the MCT. This review discusses the key attributes of the structure and function of the ECM of the sea urchin ligaments that are related to the fibril-fibril sliding action-the focus is on the respective components within the hierarchical architecture of the tissue. In this context, structure refers to size, shape and separation distance of the ECM components while function is associated with mechanical properties e.g., strength and stiffness. For simplicity, the components that address the different length scale from the largest to the smallest are as follows: collagen fibres, collagen fibrils, interfibrillar matrix and collagen molecules. Application of recent theories of stress transfer and fracture mechanisms in fibre reinforced composites to a wide variety of collagen reinforcing (non-mutable) connective tissue, has allowed us to draw general conclusions concerning the mechanical response of the MCT at specific mechanical states, namely the stiff and complaint states. The intent of this review is to provide the latest insights, as well as identify technical challenges and opportunities, that may be useful for developing methods for effective mechanical support when adapting decellularised connective tissues from the sea urchin for tissue engineering or for the design of a synthetic analogue.

Tendon exhibits complex poroelastic behavior at the nanoscale as revealed by high-frequency AFM-based rheology

Tendons transmit load from muscle to bone by utilizing their unique static and viscoelastic tensile properties. These properties are highly dependent on the composition and structure of the tissue matrix, including the collagen I hierarchy, proteoglycans, and water. While the role of matrix constituents in the tensile response has been studied, their role in compression, particularly in matrix pressurization via regulation of fluid flow, is not well understood. Injured or diseased tendons and tendon regions that naturally experience compression are known to have alterations in glycosaminoglycan content, which could modulate fluid flow and ultimately mechanical function. While recent theoretical studies have predicted tendon mechanics using poroelastic theory, no experimental data have directly demonstrated such behavior. In this study, we use high-bandwidth AFM-based rheology to determine the dynamic response of tendons to compressive loading at the nanoscale and to determine the presence of poroelastic behavior. Tendons are found to have significant characteristic dynamic relaxation behavior occurring at both low and high frequencies. Classic poroelastic behavior is observed, although we hypothesize that the full dynamic response is caused by a combination of flow-dependent poroelasticity as well as flow-independent viscoelasticity. Tendons also demonstrate regional dependence in their dynamic response, particularly near the junction of tendon and bone, suggesting that the structural and compositional heterogeneity in tendon may be responsible for regional poroelastic behavior. Overall, these experiments provide the foundation for understanding fluid-flow-dependent poroelastic mechanics of tendon, and the methodology is valuable for assessing changes in tendon matrix compressive behavior at the nanoscale.

Novel human intervertebral disc strain template to quantify regional three-dimensional strains in a population and compare to internal strains predicted by a finite element model

Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4-L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81-99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1264-1273, 2016.

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.

Multiscale strain analysis of tendon subjected to shear and compression demonstrates strain attenuation, fiber sliding, and reorganization

The manner in which strains are passed down the hierarchical length scales of tendons dictates how cells within the collagen network regulate the tissue response to loading. How tendons deform in different hierarchical levels under shear and compression is unknown. The aims of this study were: (i) to evaluate whether specific regions of bovine deep digital flexor tendons exhibited different strain attenuation from macro to micro length scales, and (ii) to elucidate mechanisms responsible for tendon deformation under shear and compression. Samples from distal and proximal regions of flexor tendons were subjected to three-step incremental stress-relaxation tests. Images of tissue markers, photobleached lines on collagen fibers, and nuclei locations were collected before and after loading. Results showed that strain transfer was attenuated from tissue to local matrix under both shear and compression. Nuclear aspect ratios exhibited smaller changes for distal samples, suggesting that cells are more shielded from deformation in the distal region. Collagen fiber sliding was observed to contribute significantly in response to shear, while uncrimping and fiber reorganization were the predominant mechanisms under compression. This study provides insight into microscale mechanisms responsible for multiscale strain attenuation of tendons under non-tensile macroscale loading.

Quantification of Interfibrillar Shear Stress in Aligned Soft Collagenous Tissues via Notch Tension Testing

The mechanical function of soft collagenous tissues is largely determined by their hierarchical organization of collagen molecules. While collagen fibrils are believed to be discontinuous and transfer load through shearing of the interfibrillar matrix, interfibrillar shear stresses have never been quantified. Scaling traditional shear testing procedures down to the fibrillar length scale is impractical and would introduce substantial artifacts. Here, through the use of a novel microscopic variation of notch tension testing, we explicitly demonstrate the existence of interfibrillar shear stresses within tendon fascicles and provide the first measurement of their magnitude. Axial stress gradients along the sample length generated by notch tension testing were measured and used to calculate a value of 32 kPa for the interfibrillar shear stress. This estimate is comparable to the interfibrillar shear stress predicted by previous multiscale modeling of tendon fascicles, which supports the hypothesis that fibrils are discontinuous and transmit load through interfibrillar shear. This information regarding the structure-function relationships of tendon and other soft collagenous tissues is necessary to identify potential causes for tissue impairment with degeneration and provide the foundation for developing regenerative repair strategies or engineering biomaterials for tissue replacement.

ALIGNMENT OF CELLULAR FOCAL CONTACTS AND THEIR SHAPES BY SUBSTRATE ANISOTROPY

Cell adhesion to the extracellular matrix is accomplished by the clustering of receptor–ligand bonds into focal contacts on the cell-substrate interface. The contractile forces applied onto these focal contacts lead to elastic deformation of the surrounding, which results into a cellular mechanosensory capability that plays a key role in cell adhesion, spreading, and migration, among many others. The mechanosensitivity can be manipulated by the substrate anisotropy, by which focal contacts may align into certain directions so to minimize the total mechanical potential energy. Using the elastic anisotropic contact analysis, this work systematically analyzes the dependence of the alignment on the elastic anisotropy, and more importantly, the direction of the inclined contractile forces. The contact displacement fields are a complex function of the elastic constants, so simple analysis based on tensile or shear softest direction cannot properly predict the alignment orientation. It is also proved that if these focal contacts are of elongated shape, the major axis will be parallel to the alignment direction.

Micromechanical poroelastic finite element and shear-lag models of tendon predict large strain dependent Poisson's ratios and fluid expulsion under tensile loading

As tendons are loaded, they reduce in volume and exude fluid to the surrounding medium. Experimental studies have shown that tendon stretching results in a Poisson's ratio greater than 0.5, with a maximum value at small strains followed by a nonlinear decay. Here we present a computational model that attributes this macroscopic observation to the microscopic mechanism of the load transfer between fibrils under stretch. We develop a finite element model based on the mechanical role of the interfibrillar-linking elements, such as thin fibrils that bridge the aligned fibrils or macromolecules such as glycosaminoglycans (GAGs) in the interfibrillar sliding and verify it with a theoretical shear-lag model. We showed the existence of a previously unappreciated structure-function mechanism whereby the Poisson's ratio in tendon is affected by the strain applied and interfibrillar-linker properties, and together these features predict tendon volume shrinkage under tensile loading. During loading, the interfibrillar-linkers pulled fibrils toward each other and squeezed the matrix, leading to the Poisson's ratio larger than 0.5 and fluid expulsion. In addition, the rotation of the interfibrillar-linkers with respect to the fibrils at large strains caused a reduction in the volume shrinkage and eventual nonlinear decay in Poisson's ratio at large strains. Our model also predicts a fluid flow that has a radial pattern toward the surrounding medium, with the larger fluid velocities in proportion to the interfibrillar sliding.