In situ multi-level analysis of viscoelastic deformation mechanisms in tendon collagen

Effect of negative pressure therapy on the treatment response to scar thickness and viscoelasticity

Patients with scars face a grave threat to their mental and physical health. Negative pressure has been used for scar therapy in medical care and provides a microenvironment conducive to scar healing while stimulating cell regeneration. Negative pressure may disrupt scar tissue regeneration when the pressure is too high or too low, so finding a suitable negative pressure is important. We hypothesized that different negative pressure magnitudes would affect scar tissue properties differently. This research aimed to provide practical recommendations for scar therapy. This study used three negative pressures (-105 mmHg, -125 mmHg, and -145 mmHg) to compare scar material properties. We measured scar tissue thickness and viscoelasticity with a motor-driven ultrasound indentation system. According to the results of this study, scar thickness is most effectively reduced at a negative pressure of -105 mmHg. In comparison, scar viscoelasticity continuously increases at a negative pressure of -125 mmHg. Negative pressure therapy can be recommended to scar care clinics based on the results of this study.

In situ measurement of viscoelastic properties of cellular monolayers via graphene strain sensing of elastohydrodynamic phenomena

Recent advances recognize that the viscoelastic properties of epithelial structures play important roles in biology and disease modeling. However, accessing the viscoelastic properties of multicellular structures in mechanistic or drug-screening applications has challenges in repeatability, accuracy, and practical implementation. Here, we present a microfluidic platform that leverages elastohydrodynamic phenomena, sensed by strain sensors made from graphene decorated with palladium nanoislands, to measure the viscoelasticity of cellular monolayers in situ, without using chemical labels or specialized equipment. We demonstrate platform utility with two systems: cell dissociation following trypsinization, where viscoelastic properties change over minutes, and epithelial-to-mesenchymal transition, where changes occur over days. These cellular events could only be resolved with our platform's higher resolution: viscoelastic relaxation time constants of λ = 14.5 ± 0.4 s-1 for intact epithelial monolayers, compared to λ = 13.4 ± 15.0 s-1 in other platforms, which represents a 30-fold improvement. By rapidly assessing combined contributions from cell stiffness and intercellular interactions, we anticipate that the platform will hasten the translation of new mechanical biomarkers.

Adaptation of Fibril-Reinforced Poroviscoelastic Properties in Rabbit Collateral Ligaments 8 Weeks After Anterior Cruciate Ligament Transection

Ligaments of the knee provide stability and prevent excessive motions of the joint. Rupture of the anterior cruciate ligament (ACL), a common sports injury, results in an altered loading environment for other tissues in the joint, likely leading to their mechanical adaptation. In the collateral ligaments, the patterns and mechanisms of biomechanical adaptation following ACL transection (ACLT) remain unknown. We aimed to characterize the adaptation of elastic and viscoelastic properties of the lateral and medial collateral ligaments eight weeks after ACLT. Unilateral ACLT was performed in six rabbits, and collateral ligaments were harvested from transected and contralateral knee joints after eight weeks, and from an intact control group (eight knees from four animals). The cross-sectional areas were measured with micro-computed tomography. Stepwise tensile stress-relaxation testing was conducted up to 6% final strain, and the elastic and viscoelastic properties were characterized with a fibril-reinforced poroviscoelastic material model. We found that the cross-sectional area of the collateral ligaments in the ACL transected knees increased, the nonlinear elastic collagen network modulus of the LCL decreased, and the amount of fast relaxation in the MCL decreased. Our results indicate that rupture of the ACL leads to an early adaptation of the elastic and viscoelastic properties of the collagen fibrillar network in the collateral ligaments. These adaptations may be important to consider when evaluating whole knee joint mechanics after ACL rupture, and the results aid in understanding the consequences of ACL rupture on other tissues.

Nanoscale characterization of collagen structural responses to in situ loading in rat Achilles tendons

The specific viscoelastic mechanical properties of Achilles tendons are highly dependent on the structural characteristics of collagen at and between all hierarchical levels. Research has been conducted on the deformation mechanisms of positional tendons and single fibrils, but knowledge about the coupling between the whole tendon and nanoscale deformation mechanisms of more commonly injured energy-storing tendons, such as Achilles tendons, remains sparse. By exploiting the highly periodic arrangement of tendons at the nanoscale, in situ loading of rat Achilles tendons during small-angle X-ray scattering acquisition was used to investigate the collagen structural response during load to rupture, cyclic loading and stress relaxation. The fibril strain was substantially lower than the applied tissue strain. The fibrils strained linearly in the elastic region of the tissue, but also exhibited viscoelastic properties, such as an increased stretchability and recovery during cyclic loading and fibril strain relaxation during tissue stress relaxation. We demonstrate that the changes in the width of the collagen reflections could be attributed to strain heterogeneity and not changes in size of the coherently diffracting domains. Fibril strain heterogeneity increased with applied loads and after the toe region, fibrils also became increasingly disordered. Additionally, a thorough evaluation of radiation damage was performed. In conclusion, this study clearly displays the simultaneous structural response and adaption of the collagen fibrils to the applied tissue loads and provide novel information about the transition of loads between length scales in the Achilles tendon.

The Role of the Non-Collagenous Extracellular Matrix in Tendon and Ligament Mechanical Behavior: A Review

Tendon is a connective tissue that transmits loads from muscle to bone, while ligament is a similar tissue that stabilizes joint articulation by connecting bone to bone. The 70-90% of tendon and ligament's extracellular matrix (ECM) is composed of a hierarchical collagen structure that provides resistance to deformation primarily in the fiber direction, and the remaining fraction consists of a variety of non-collagenous proteins, proteoglycans, and glycosaminoglycans (GAGs) whose mechanical roles are not well characterized. ECM constituents such as elastin, the proteoglycans decorin, biglycan, lumican, fibromodulin, lubricin, and aggrecan and their associated GAGs, and cartilage oligomeric matrix protein (COMP) have been suggested to contribute to tendon and ligament's characteristic quasi-static and viscoelastic mechanical behavior in tension, shear, and compression. The purpose of this review is to summarize existing literature regarding the contribution of the non-collagenous ECM to tendon and ligament mechanics, and to highlight key gaps in knowledge that future studies may address. Using insights from theoretical mechanics and biology, we discuss the role of the non-collagenous ECM in quasi-static and viscoelastic tensile, compressive, and shear behavior in the fiber direction and orthogonal to the fiber direction. We also address the efficacy of tools that are commonly used to assess these relationships, including enzymatic degradation, mouse knockout models, and computational models. Further work in this field will foster a better understanding of tendon and ligament damage and healing as well as inform strategies for tissue repair and regeneration.

Strain rate induced toughening of individual collagen fibrils

The nonlinear mechanical behavior of individual nanoscale collagen fibrils is governed by molecular stretching and sliding that result in a viscous response, which is still not fully understood. Toward this goal, the in vitro mechanical behavior of individual reconstituted mammalian collagen fibrils was quantified in a broad range of strain-rates, spanning roughly six orders of magnitude, from 10^-4 to 35 s^-1. It is shown that the nonlinear mechanical response is strain rate sensitive with the tangent modulus in the linear deformation regime increasing monotonically from 214 ± 8 to 358 ± 11 MPa. More pronounced is the effect of the strain rate on the ultimate tensile strength that is found to increase monotonically by a factor of four, from 42 ± 6 to 160 ± 14 MPa. Importantly, fibril strengthening takes place without a reduction in ductility, which results in equivalently large increase in toughness with the increasing strain rate. This experimental strain rate dependent mechanical response is captured well by a structural constitutive model that incorporates the salient features of the collagen microstructure via a process of gradual recruitment of kinked tropocollagen molecules, thus giving rise to the initial "toe-heel" mechanical behavior, followed by molecular stretching and sustained intermolecular slip that is initiated at a strain rate dependent stress threshold. The model shows that the fraction of tropocollagen molecules undergoing straightening increases continuously during loading, whereas molecular sliding is initiated after a small fibril strain (1%-2%) and progressively increases with applied strain.

Nonlinear time-dependent mechanical behavior of mammalian collagen fibrils

The viscoelastic mechanical behavior of collagenous tissues has been studied extensively at the macroscale, yet a thorough quantitative understanding of the time-dependent mechanics of the basic building blocks of tissues, the collagen fibrils, is still missing. In order to address this knowledge gap, stress relaxation and creep tests at various stress (5-35 MPa) and strain (5-20%) levels were performed with individual collagen fibrils (average diameter of fully hydrated fibrils: 253 ± 21 nm) in phosphate buffered saline (PBS). The experimental results showed that the time-dependent mechanical behavior of fully hydrated individual collagen fibrils reconstituted from Type I calf skin collagen, is described by strain-dependent stress relaxation and stress-dependent creep functions in both the heel-toe and the linear regimes of deformation in monotonic stress-strain curves. The adaptive quasilinear viscoelastic (QLV) model, originally developed to capture the nonlinear viscoelastic response of collagenous tissues, provided a very good description of the nonlinear stress relaxation and creep behavior of the collagen fibrils. On the other hand, the nonlinear superposition (NSP) model fitted well the creep but not the stress relaxation data. The time constants and rates extracted from the adaptive QLV and the NSP models, respectively, pointed to a faster rate for stress relaxation than creep. This nonlinear viscoelastic behavior of individual collagen fibrils agrees with prior studies of macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. STATEMENT OF SIGNIFICANCE: Pure stress relaxation and creep experiments were conducted for the first time with fully hydrated individual collagen fibrils. It is shown that collagen nanofibrils have a nonlinear time-dependent behavior which agrees with prior studies on macroscale collagenous tissues, thus demonstrating consistent time-dependent behavior across length scales and tissue hierarchies. This new insight into the non-linear viscoelastic behavior of the building blocks of mammalian collagenous tissues may serve as the foundation for improved macroscale tissue models that capture the mechanical behavior across length scales.

Investigating the Fibrillar Ultrastructure and Mechanics in Keloid Scars Using In Situ Synchrotron X-ray Nanomechanical Imaging

Fibrotic scarring is prevalent in a range of collagenous tissue disorders. Understanding the role of matrix biophysics in contributing to fibrotic progression is important to develop therapies, as well as to elucidate biological mechanisms. Here, we demonstrate how microfocus small-angle X-ray scattering (SAXS), with in situ mechanics and correlative imaging, can provide quantitative and position-resolved information on the fibrotic matrix nanostructure and its mechanical properties. We use as an example the case of keloid scarring in skin. SAXS mapping reveals heterogeneous gradients in collagen fibrillar concentration, fibril pre-strain (variations in D-period) and a new interfibrillar component likely linked to proteoglycans, indicating evidence of a complex 3D structure at the nanoscale. Furthermore, we demonstrate a proof-of-principle for a diffraction-contrast correlative imaging technique, incorporating, for the first time, DIC and SAXS, and providing an initial estimate for measuring spatially resolved fibrillar-level strain and reorientation in such heterogeneous tissues. By application of the method, we quantify (at the microscale) fibrillar reorientations, increases in fibrillar D-period variance, and increases in mean D-period under macroscopic tissue strains of ~20%. Our results open the opportunity of using synchrotron X-ray nanomechanical imaging as a quantitative tool to probe structure–function relations in keloid and other fibrotic disorders in situ.

Microscale Creep and Stress Relaxation Experiments with Individual Collagen Fibrils

Nanoscale macromolecular biological structures exhibit time-dependent behavior, yet a quantitative understanding of their time-dependent mechanical behavior remains elusive, largely due to experimental challenges in attaining sufficient spatial and temporal resolution and control of stress or strain in conditions that guarantee their molecular integrity. To address this gap, an experimental methodology was developed to conduct creep and stress relaxation experiments with individual mammalian collagen fibrils. An image-based edge detection method implemented with high magnification optical microscopy and combined with closed-loop proportional-integral-derivative (PID) control was implemented and calibrated to apply constant force or stretch ratio values to individual collagen fibrils via a Microelectromechanical Systems (MEMS) device. This experimental methodology allowed for real-time control of uniaxial tensile stress or strain with 27 nm displacement resolution. The overall experimental system was tuned to apply step inputs with rise times below 0.5 s, less than 2.5% overshoot, and steady-state error less than 0.5%. Three individual collagen fibrils with diameters 101-121 nm were subjected to creep and stress relaxation tests in the range 4-20% engineering strain, under partially hydrated conditions. The collagen fibrils demonstrated non-linear viscoelastic behavior that was described well by the adaptive quasi-linear viscoelastic model. The results of this study demonstrate for the first time that mammalian collagen fibrils, the building blocks of connective tissues, exhibit nonlinear viscoelastic behavior in their partially hydrated state.

A mathematical model for viscoelastic properties of biological soft tissue

A quaternary viscoelastic structure model with two characteristic times is presented to describe the viscoelastic properties of parallel-fibered collagen tissue. The comparison results of model prediction and experimental data of rabbit medial collateral ligaments show that the model could accurately describe viscoelastic behavior such as stress-relaxation, strain-strengthening and creep of bio-soft-tissue within a small scope of errors. To study the biomechanical mechanism of viscoelasticity that biological soft tissue shows, the influence of model parameters on viscoelastic behavior of bio-soft-tissue is analyzed and researched, which indicated that the major influential elements of stress-relaxation in bio-soft-tissue are elastic modulus, relaxation time and strain rate of proteoglycan-rich matrix. The influence of elastic modulus of collagen fibers on stress-relaxation is not significant. However, the nonlinearity of stress-strain curve and viscoelastic behavior of bio-soft-tissue mostly depends on recruitment and reorientation of collagen fibers under external loading.

Reversible changes in the 3D collagen fibril architecture during cyclic loading of healthy and degraded cartilage

Biomechanical changes to the collagen fibrillar architecture in articular cartilage are believed to play a crucial role in enabling normal joint function. However, experimentally there is little quantitative knowledge about the structural response of the Type II collagen fibrils in cartilage to cyclic loading in situ, and the mechanisms that drive the ability of cartilage to withstand long-term repetitive loading. Here we utilize synchrotron small-angle X-ray scattering (SAXS) combined with in-situ cyclic loading of bovine articular cartilage explants to measure the fibrillar response in deep zone articular cartilage, in terms of orientation, fibrillar strain and inter-fibrillar variability in healthy cartilage and cartilage degraded by exposure to the pro-inflammatory cytokine IL-1β. We demonstrate that under repeated cyclic loading the fibrils reversibly change the width of the fibrillar orientation distribution whilst maintaining a largely consistent average direction of orientation. Specifically, the effect on the fibrillar network is a 3-dimensional conical orientation broadening around the normal to the joint surface, inferred by 3D reconstruction of X-ray scattering peak intensity distributions from the 2D pattern. Further, at the intrafibrillar level, this effect is coupled with reversible reduction in fibrillar pre-strain under compression, alongside increase in the variability of fibrillar pre-strain. In IL-1β degraded cartilage, the collagen rearrangement under cyclic loading is disrupted and associated with reduced tissue stiffness. These finding have implications as to how changes in local collagen nanomechanics might drive disease progression or vice versa in conditions such as osteoarthritis and provides a pathway to a mechanistic understanding of such diseases.

Statement of significance

Structural deterioration in biomechanically loaded musculoskeletal organs, e.g., joint osteoarthritis and back pain, are linked to breakdown and changes in their collagen-rich cartilaginous tissue matrix. A critical component enabling cartilage biomechanics is the ultrastructural collagen fibrillar network in cartilage. However, experimental probes of the dynamic structural response of cartilage collagen to biomechanical loads are limited. Here, we use X-ray scattering during cyclic loading (as during walking) on joint tissue to show that cartilage fibrils resist loading by a reversible, three-dimensional orientation broadening and disordering mechanism at the molecular level, and that inflammation reduces this functionality. Our results will help understand how changes to small-scale tissue mechanisms are linked to ageing and osteoarthritic progression, and development of biomaterials for joint replacements.

Biophotonic tools for probing extracellular matrix mechanics

The complex, hierarchical and heterogeneous biomechanics of the extracellular matrix (ECM) are central to the health of multicellular organisms. Characterising the distribution, dynamics and above all else origins of ECM biomechanics are challenges that have captivated researchers for decades. Recently, a suite of biophotonics techniques have emerged as powerful new tools to investigate ECM biomechanics. In this mini-review, we discuss how the non-destructive, sub-micron resolution imaging capabilities of Raman spectroscopy and nonlinear microscopy are being used to interrogate the biomechanics of thick, living tissues. These high speed, label-free techniques are implemented during mechanical testing, providing unprecedented insight into the compositional and structural response of the ECM to changes in the mechanical environment.

Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon

It is widely accepted that the nonlinear macroscopic mechanical behavior of soft tissue is governed by fiber straightening and re-orientation. Here, we provide a quantitative assessment of this phenomenon, by means of a continuum micromechanics approach. Given the negligibly small bending stiffness of crimped fibers, the latter are represented through a number of hypoelastic straight fiber phases with different orientations, being embedded into a hypoelastic matrix phase. The corresponding representative volume element (RVE) hosting these phases is subjected to “macroscopic” strain rates, which are downscaled to fiber and matrix strain rates on the one hand, and to fiber spins on the other hand. This gives quantitative access to the fiber decrimping (or straightening) phenomenon under non-affine conditions, i.e. in the case where the fiber orientations cannot be simply linked to the macroscopic strain state. In the case of tendinous tissue, such an RVE relates to the fascicle material with 50 μm characteristic length, made up of crimped collagen bundles and a gel-type matrix in-between. The fascicles themselves act as parallel fibers in a similar matrix at the scale of a tissue-related RVE with 500 μm characteristic length. As evidenced by a sensitivity analysis and confirmed by various mechanical tests, it is the initial crimping angle which drives both the degree of straightening and the shape of the macroscopic stress-strain curve, while the final linear portion of this curve depends almost exclusively on the collagen bundle elasticity. Our model also reveals the mechanical cooperation of the tissue’s key microstructural components: while the fibers carry tensile forces, the matrices undergo hydrostatic pressure.

Tendons exhibit greater resistance to tissue and molecular-level damage with increasing strain rate during cyclic fatigue

Musculoskeletal soft connective tissues are commonly injured due to repetitive use, but the evolution of mechanical damage to the tissue structure during repeated loading is poorly understood. We investigated the strain-rate dependence of mechanical denaturation of collagen as a form of structural microdamage accumulation during creep fatigue loading of rat tail tendon fascicles. We cycled tendons at three strain rates to the same maximum stress relative to their rate-dependent tensile strength. Collagen denaturation at distinct points during the fatigue process was measured by fluorescence quantification of collagen hybridizing peptide binding. The amount of collagen denaturation was significantly correlated with fascicle creep strain, independent of the cyclic strain rate, supporting our hypothesis that tissue level creep is caused by collagen triple-helix unfolding. Samples that were loaded faster experienced more creep strain and denaturation as a function of the number of loading cycles relative to failure. Although this increased damage capacity at faster rates may serve as a protective measure during high-rate loading events, it may also predispose these tissues to subsequent injury and indicate a mechanism of overuse injury development. These results build on evidence that molecular-level collagen denaturation is the fundamental mechanism of structural damage to tendons during tensile loading. STATEMENT OF SIGNIFICANCE: This study is the first to investigate the accumulation of denatured collagen in tendons throughout fatigue loading when the maximum stress is scaled with the applied strain rate. The amount of denatured collagen was correlated with creep strain, independent of strain rate, but samples that were cycled faster withstood greater amounts of denaturation before failure. Differential accumulation of collagen damage between fast and slow repetitive loading has relevance toward understanding the prevalence of overuse musculoskeletal injuries following sudden changes in activity level. Since collagen is a ubiquitous biological structural component, the basic patterns and mechanisms of loading-induced collagen damage in connective tissues are relevant for understanding injury and disease in other tissues, including those from the cardiovascular and pulmonary systems.

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils - such as fibrils from skin or corneal tissue.

Hierarchical ultrastructure: An overview of what is known about tendons and future perspective for tendon engineering

Abnormal tendons are rarely ever repaired to the natural structure and morphology of normal tendons. To better guide the repair and regeneration of injured tendons through a tissue engineering method, it is necessary to have insights into the internal morphology, organization, and composition of natural tendons. This review summarized recent researches on the structure and function of the extracellular matrix (ECM) components of tendons and highlight the application of multiple detection methodologies concerning the structure of ECMs. In addition, we look forward to the future of multi-dimensional biomaterial design methods and the potential of structural repair for tendon ECM components. In addition, focus is placed on the macro to micro detection methods for tendons, and current techniques for evaluating the extracellular matrix of tendons at the micro level are introduced in detail. Finally, emphasis is given to future extracellular matrix detection methods, as well as to how future efforts could concentrate on fabricating the biomimetic tendons.

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Summarize recent research on the structure and function of the extracellular matrix (ECM) components of tendons.

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Comments on current research methods concerning the structure of ECMs.

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Perspective on the future of multi-dimensional detection techniques and structural repair of tendon ECM components.

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.

Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals

Self-similar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractional-order derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractional-order temporal responses. We further expanded the fractal hyper-cell (FHC) viscoelasticity theory to investigate this spatio-temporal correlation. The FHC element was first compared with other material elements and spring–dashpot viscoelastic models, thereby highlighting its discrete and fractal nature. To demonstrate the utility of an FHC, tree-like, ladder-like and triangle-like FHCs were abstracted from human cartilage, tendons and muscle cross-sections, respectively. The duality and symmetry of the FHC element were further discussed, where operating the duality transformation generated new types of FHC elements, and the symmetry breaking of an FHC altered its fractional-order viscoelastic responses. Thus, the correlations between the staggering patterns of FHCs and their rheological power-law orders were established, and the viscoelastic behaviour of the multi-level FHC elements fitted well in stress relaxation experiments at both the macro- and nano-levels of the tendon hierarchy. The FHC element provides a theoretical basis for understanding the connections between structural degeneration of bio-tissues during ageing or disease and their functional changes.

Mineral and organic matrix composition at bone forming surfaces in postmenopausal women with osteoporosis treated with either teriparatide or zoledronic acid

The ability of bone to resist fracture is dependent on the composite nature of its mineral and organic matrix content. Teriparatide (TPTD) and zoledronic acid (ZOL) are approved anabolic and antiresorptive therapies, respectively, to reduce fracture risk in women with postmenopausal osteoporosis. In the SHOTZ study, postmenopausal women with osteoporosis were treated with TPTD (20 μg daily, subcutaneous) or ZOL (5 mg/year, intravenous infusion) for 24 months. Iliac crest biopsies were obtained at 6 months and again at 24 months from approximately one third of the original study cohort. To investigate the early effects of these two drugs on the quality of newly formed bone, we used vibrational spectroscopic techniques to analyze tetracycline-labelled transiliac biopsies obtained from participants at the 6-month time point. Raman spectra were acquired at forming trabecular and intra-cortical surfaces (identified by fluorescent double labels), to determine mineral, organic matrix, glycosaminoglycan, and tissue water content, as well as mineral maturity/crystallinity at three specific tissue ages (1-5, 15, and ≥25 days). Fourier transformed infrared microspectroscopy was used to determine pyridinoline/divalent collagen cross-link ratios. At 6 months, treatment with TPTD versus ZOL resulted in lower mineral and higher organic matrix content, increased tissue water content, and lower mineral/matrix, mineral maturity/crystallinity, glycosaminoglycan content, and pyridinoline/divalent enzymatic collagen cross-link ratio. Our results suggest that TPTD and ZOL have differential effects on material properties of newly formed bone at individual remodeling sites, highlighting their different mechanisms of action.

The mechanical characterization of blood vessels and their substitutes in the continuous quest for physiological-relevant performances. A critical review

During the last 50 years, novel biomaterials and tissue engineering techniques have been investigated to produce alternative vascular substitutes that recapitulate the unique elastic mechanical features of blood vessels. A large variation in mechanical characterization, including the test type, protocol, and data analysis, is present in literature which complicates the comparison among studies and prevents the blooming and the advancement of this field. In addition, a limited mechanical assessment of the substitute for the intended application is often provided. In this light, this review presents the mechanical environment of blood vessels, discusses their mechanical behavior responsible for the suited blood flow into the body (non-linearity, anisotropy, hysteresis, and compliance), and compares the mechanical properties reported in literature (obtained with compression, tensile, stress-relaxation, creep, dynamic mechanical analysis, burst pressure, and dynamic compliance tests). This perspective highlights that the mechanical properties extracted through conventional tests are not always suitable indicators of the mechanical performance during the working life of a vascular substitute. The available tests can be then strategically used at different stages of the substitute development, prioritizing the simplicity of the method at early stages, and the physiological pertinence at later stages, following as much as possible ISO standards in the field. A consistent mechanical characterization focused on the behavior to which they will be subdued during real life is one key and missing element in the quest for physiological-like mechanical performance of vascular substitutes.

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament (PDL), its mechanical behavior is very dependent on the type of loading (compressive versus tensile loading; static versus cyclic loading; uniaxial versus multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the PDL make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the PDL. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the PDL structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration.

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.

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.

The Effect of Strain Rate on the Stress Relaxation of the Pig Dermis: A Hyper-Viscoelastic Approach

The understanding of strain rate-dependent mechanical properties of the skin is important for accurate prediction of its biomechanics under different loading conditions. This study investigated the effect of strain rate, i.e., 0.025/s (low), 0.5/s (medium), and 1.25/s (high), ranging in the physiological loading rate of connective tissue, on the stress-relaxation response of the porcine dermis. Results show that in the initial phase of the relaxation, the value of stress relaxation (extent of relaxation) was found higher for high strain rate. However, the equilibrium stress was found strain rate independent. A Mooney-Rivlin-based five-term quasi-linear viscoelastic (QLV) model was proposed to determine the effect of strain rate on the stress-relaxation behavior of the porcine dermis. The value of relaxation modulus G1 and G2 were found higher for the high strain rate, whereas the reverse trend was observed for G3, G4, and G5. Moreover, the value of time constants τ1,τ2,τ3τ4, and τ5 were found higher for low strain rate. Statistical analysis shows no significant difference in the values of G5, τ4, and τ5 among the three strain rates. The proposed model was found capable to fit the stress-relaxation response of skin with great accuracy, e.g., root-mean-squared-error (RMSE) value equal to 0.015 ± 0.00012 MPa. Moreover, this hyper-viscoelastic model can be utilized: to quantify the effects of age and diseases on the skin; to simulate the stresses on sutures during large wound closure and impact loading.

Loading Rate Has Little Influence on Tendon Fascicle Mechanics

Mechanically, tendons behave like springs and store energy by stretching in proportion to applied stress. This relationship is potentially modified by the rate at which stress is applied, a phenomenon known as viscosity. Viscoelasticity, the combined effects of elasticity and viscosity, can affect maximum strain, the amount of stored energy, and the proportion of energy recovered (resilience). Previous studies of tendons have investigated the functional effects of viscoelasticity, but not at the intermediate durations of loading that are known to occur in fast locomotor events. In this study, we isolated tendon fascicles from rat tails and performed force-controlled tensile tests at rates between ∼10 MPa s^–1 to ∼80 MPa s^–1. At high rates of applied stress, we found that tendon fascicles strained less, stored less energy, and were more resilient than at low rates of stress (p = 0.007, p = 0.040, and p = 0.004, respectively). The measured changes, however, were very small across the range of strain rates studied. For example, the average strain for the slowest loading rate was 0.637% while it was 0.614% for the fastest loading. We conclude that although there is a measurable effect of loading rate on tendon mechanics, the effect is small and can be largely ignored in the context of muscle-actuated locomotion, with the possible exception of extreme muscle-tendon morphologies.

A Recruitment Model of Tendon Viscoelasticity That Incorporates Fibril Creep and Explains Strain-Dependent Relaxation

Soft tissues exhibit complex viscoelastic behavior, including strain-rate dependence, hysteresis, and strain-dependent relaxation. In this paper, a model for soft tissue viscoelasticity is developed that captures all of these features and is based upon collagen recruitment, whereby fibrils contribute to tissue stiffness only when taut. We build upon existing recruitment models by additionally accounting for fibril creep and by explicitly modeling the contribution of the matrix to the overall tissue viscoelasticity. The fibrils and matrix are modeled as linear viscoelastic and each fibril has an associated critical strain (corresponding to its length) at which it becomes taut. The model is used to fit relaxation tests on three rat tail tendon fascicles and predict their response to cyclic loading. It is shown that all of these mechanical tests can be reproduced accurately with a single set of constitutive parameters, the only difference between each fascicle being the distribution of their fibril crimp lengths. By accounting for fibril creep, we are able to predict how the fibril length distribution of a fascicle changes over time under a given deformation. Furthermore, the phenomenon of strain-dependent relaxation is explained as arising from the competition between the fibril and matrix relaxation functions.

Organic matrix quality discriminates between age- and BMD-matched fracturing versus non-fracturing post-menopausal women: A pilot study

Women with similar areal Bone Mineral Densities (BMD) may show divergent fracture incidence due to differences in bone quality. The hypothesis tested in the present pilot study is that postmenopausal (PM) women who have sustained osteoporotic fractures have altered organic matrix quality compared to those who have not. We used Raman microspectroscopy to analyze transiliac biopsies collected from fracturing (n = 6, mean age 62.5 ± 7.4 yrs; Cases) and non-fracturing PM women (n = 6, age- and BMD-matched; mean age 62.2 ± 7.3 yrs; Controls). Previous results show differences in intrinsic material properties by nanoindentation that are more homogenously distributed and could facilitate microcrack propagation in Cases, along with lower mineral carbonate/phosphate ratio by Fourier transform infrared spectroscopic imaging, and no differences in bone tissue mineralization by digitized microradiography. No differences between groups were seen by conventional histomorphometry. Spectra were acquired 2 μm away from previously performed nanoindents, in cortical and cancellous compartments. The determined parameters were: mineral to matrix ratio (MM), and nanoporosity (a surrogate for tissue water (TW)), glycosaminoglycan (GAG), pyridinoline (Pyd; trivalent enzymatic collagen cross-link), N(6)-carboxymethyllysine (CML; advanced glycation endproduct), and pentosidine (PEN; advanced glycation endproduct) content. ANCOVA indicated no differences in any of the spectroscopic outcomes between cancellous and cortical compartments. On the other hand, Cases had lower nanoporosity (TW) and GAG, and elevated Pyd, and CML content compared to Controls. In conclusion, the results of the present study indicate significant differences in organic matrix quality in PM women that sustain fragility fractures versus age- and BMD-matched controls, highlighting its importance as a potential independent determinant of fracture incidence.

Material properties and osteoporosis

The main clinical tool for the diagnosis and treatment of skeletal diseases such as osteoporosis is the determination of bone mineral density by dual x-ray absorptiometry. Although this outcome contributes to the determination of bone strength, the clinical evidence to date suggests that it does not correlate strongly with fracture incidence. The main reason for this discrepancy is the fact that several other bone properties, such as material properties, are not taken into account. This short review summarizes the reasons why material properties are important in the determination of bone strength and briefly discusses some of them as well as their influence on bone’s mechanical performance.

An Analysis of the Mechanical Properties of the Ponseti Method in Clubfoot Treatment

Congenital clubfoot is a complex pediatric foot deformity, occurring in approximately 1 in 1000 live births and resulting in significant disability, deformity, and pain if left untreated. The Ponseti method of manipulation is widely recognized as the gold standard treatment for congenital clubfoot; however, its mechanical aspects have not yet been fully explored. During the multiple manipulation-casting cycles, the tendons and ligaments on the medial and posterior aspect of the foot and ankle, which are identified as the rate-limiting tissues, usually undergo weekly sequential stretches, with a plaster of Paris cast applied after the stretch to maintain the length gained. This triggers extracellular matrix remodeling and tissue growth, but due to the viscoelastic properties of tendons and ligaments, the initial strain size, rate, and loading history will affect the relaxation behavior and mechanical strength of the tissue. To increase the efficiency of the Ponseti treatment, we discuss the theoretical possibilities of decreasing the size of the strain step and interval of casting and/or increasing the overall number of casts. This modification may provide more tensile stimuli, allow more time for remodeling, and preserve the mechanical integrity of the soft tissues.

In Situ Polyphosphate Nanoparticle Formation in Hybrid Poly(vinyl alcohol)/Karaya Gum Hydrogels: A Porous Scaffold Inducing Infiltration of Mesenchymal Stem Cells

The preparation and characterization of a porous hybrid cryogel based on the two organic polymers, poly(vinyl alcohol) (PVA) and karaya gum (KG), into which polyphosphate (polyP) nanoparticles have been incorporated, are described. The PVA/KG cryogel is prepared by intermolecular cross-linking of PVA via freeze-thawing and Ca2+-mediated ionic gelation of KG to form stable salt bridges. The incorporation of polyP as amorphous nanoparticles with Ca2+ ions (Ca-polyP-NP) is achieved using an in situ approach. The polyP constituent does not significantly affect the viscoelastic properties of the PVA/KG cryogel that are comparable to natural soft tissue. The exposure of the Ca-polyP-NP within the cryogel to medium/serum allows the formation of a biologically active polyP coacervate/protein matrix that stimulates the growth of human mesenchymal stem cells in vitro and provides the cells a suitable matrix for infiltration superior to the polyP-free cryogel. In vivo biocompatibility studies in rats reveal that already two to four weeks after implantation into muscle, the implant regions containing the polyP-KG/PVA material become replaced by initial granulation tissue, whereas the controls are free of any cells. It is proposed that the polyP-KG/PVA cryogel has the potential to become a promising implant material for soft tissue engineering/repair.

The Collagen Suprafamily: From Biosynthesis to Advanced Biomaterial Development

Collagen is the oldest and most abundant extracellular matrix protein that has found many applications in food, cosmetic, pharmaceutical, and biomedical industries. First, an overview of the family of collagens and their respective structures, conformation, and biosynthesis is provided. The advances and shortfalls of various collagen preparations (e.g., mammalian/marine extracted collagen, cell-produced collagens, recombinant collagens, and collagen-like peptides) and crosslinking technologies (e.g., chemical, physical, and biological) are then critically discussed. Subsequently, an array of structural, thermal, mechanical, biochemical, and biological assays is examined, which are developed to analyze and characterize collagenous structures. Lastly, a comprehensive review is provided on how advances in engineering, chemistry, and biology have enabled the development of bioactive, 3D structures (e.g., tissue grafts, biomaterials, cell-assembled tissue equivalents) that closely imitate native supramolecular assemblies and have the capacity to deliver in a localized and sustained manner viable cell populations and/or bioactive/therapeutic molecules. Clearly, collagens have a long history in both evolution and biotechnology and continue to offer both challenges and exciting opportunities in regenerative medicine as nature's biomaterial of choice.

Load transfer, damage, and failure in ligaments and tendons

The function of ligaments and tendons is to support and transmit loads applied to the musculoskeletal system. These tissues are often able to perform their function for many decades; however, connective tissue disease and injury can compromise ligament and tendon integrity. A range of protein and non-protein constituents, combined in a complex structural hierarchy from the collagen molecule to the tissue and covering nanometer to centimeter length scales, govern tissue function, and impart characteristic non-linear material behavior. This review summarizes the structure of ligaments and tendons, the roles of their constituent components for load transfer across the hierarchy of structure, and the current understanding of how damage occurs in these tissues. Disease and injury can alter the constituent make-up and structural organization of ligaments and tendons, affecting tissue function, while also providing insight to the role and interactions of individual constituents. The studies and techniques presented here have helped to understand the relationship between tissue constituents and the physical mechanisms (e.g., stretching, sliding) that govern material behavior at and between length scales. In recent years, new techniques have been developed to probe ever smaller length scales and may help to elucidate mechanisms of load transfer and damage and the molecular constituents involved in the in the earliest stages of ligament and tendon damage. A detailed understanding of load transfer and damage from the molecular to the tissue level may elucidate targets for the treatment of connective tissue diseases and inform practice to prevent and rehabilitate ligament and tendon injuries. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:3093-3104, 2018.

Unravelling the viscoelastic, buffer-like mechanical behavior of tendons: A numerical quantitative study at the fibril-fiber scale

We investigate the capacity of tendons to bear substantial loads by exploiting their hierarchical structure and the viscous nature of their subunits. We model and analyze two successive tendon scales: the fibril and fiber subunits. We present a novel method for bridging intra-scale experimental observations by combining a homogenization analysis technique with a Bayesian inference method. This allows us to infer elastic and viscoelastic moduli at the embedded fibril scale that are mechanically compatible with the experimental data observed at the fiber scale. We identify the rather narrow range of moduli values at the fibrillar scale that can reproduce the mechanical behavior of the fiber, while we quantify the viscoelastic contribution of the embedding, non-collagenous matrix substance. The computed viscoelastic moduli suggest that a great part of the stress relaxation capacity of tendons needs to be attributed to the embedding matrix substance of its inner components, classifying it as a primal load relaxation constituent.

Energy dissipation in mammalian collagen fibrils: Cyclic strain-induced damping, toughening, and strengthening

As the fundamental structural protein in mammals, collagen transmits cyclic forces that are necessary for the mechanical function of tissues, such as bone and tendon. Although the tissue-level mechanical behavior of collagenous tissues is well understood, the response of collagen at the nanometer length scales to cyclical loading remains elusive. To address this major gap, we cyclically stretched individual reconstituted collagen fibrils, with average diameter of 145 ± 42 nm, to small and large strains in the partially hydrated conditions of 60% relative humidity. It is shown that cyclical loading results in large steady-state hysteresis that is reached immediately after the first loading cycle, followed thereafter by limited accumulation of inelastic strain and constant initial elastic modulus. Cyclic loading above 20% strain resulted in 70% increase in tensile strength, from 638 ± 98 MPa to 1091 ± 110 MPa, and 70% increase in toughness, while maintaining the ultimate tensile strain of collagen fibrils not subjected to cyclic loading. Throughout cyclic stretching, the fibrils maintained a steady-state hysteresis, yielding loss coefficients that are 5-10 times larger than those of known homogeneous materials in their modulus range, thus establishing damping of nanoscale collagen fibrils as a major component of damping in tissues. STATEMENT OF SIGNIFICANCE: It is shown that steady-state energy dissipation occurs in individual collagen fibrils that are the building blocks of hard and soft tissues. To date, it has been assumed that energy dissipation in tissues takes place mainly at the higher length scales of the tissue hierarchy due to interactions between collagen fibrils and fibers, and in limited extent inside collagen fibrils. It is shown that individual collagen fibrils need only a single loading cycle to assume a highly dissipative, steady-state, cyclic mechanical response. Mechanical cycling at large strains leads to 70% increase in mechanical strength and values exceeding those of engineering steels. The same cyclic loading conditions also lead to 70% increase in toughness and loss properties that are 5-10 times higher than those of engineering materials with comparable stiffness.

Biomechanics show stem cell necessity for effective treatment of volumetric muscle loss using bioengineered constructs

Despite the regenerative capacity of muscle, tissue volume is not restored after volumetric muscle loss (VML), perhaps due to a loss-of-structural extracellular matrix. We recently demonstrated the structural and functional restoration of muscle tissue in a mouse model of VML using an engineered “bioconstruct,” comprising an extracellular matrix scaffold (decellularized muscle), muscle stem cells (MuSCs), and muscle-resident cells (MRCs). To test the ability of the cell-based bioconstruct to restore whole-muscle biomechanics, we measured biomechanical parameters in uninjured muscles, muscles injured to produce VML lesions, and in muscles that were injured and then treated by implanting either the scaffolds alone or with bioconstructs containing the scaffolds, MuSCs, and MRCs. We measured the active and passive forces over a range of lengths, viscoelastic force relaxation, optimal length, and twitch dynamics. Injured muscles showed a narrowed length-tension curve or lower force over a narrower range of muscle lengths, and increased passive force. When treated with bioconstructs, but not with scaffolds alone, injured muscles showed active and passive length-tension relationships that were not different from uninjured muscles. Moreover, injured muscles treated with bioconstructs exhibited reduced fibrosis compared to injured muscles either untreated or treated with scaffolds alone. The cell-based bioconstruct is a promising treatment approach for future translational efforts to restore whole-muscle biomechanics in muscles with VML lesions.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Contribution of the periosteum to mandibular distraction

Mandibular distraction is a surgical process that progressively lengthens bone. To improve the distraction procedure and devices, the load of distraction and the mechanical strain of soft tissues during the process must be determined. We tested the assumption that it could be the periosteum primarily opposing distraction. Therefore we assessed the mechanical properties of the human mandibular periosteum and compared the stress-strain data with the torque measured on the activator during a cadaveric mandibular distraction. A 20 mm horizontal mandibular distraction was performed in 7 cadavers using standard distractors. Torque was measured with a torquemeter placed on the activation rods of the devices, providing a load (L_t) for each millimeter of distraction. In parallel, 18 periosteum samples were harvested from 9 cadaver mandibles. Uniaxial tensile tests were performed on the specimens and an estimated load (L_c) was calculated using periosteal stress-strain data and mandibular dimensions. During the distraction process, we observed an increase of the load L_t from 11.6 to 50.6 N. The periosteum exhibited a nonlinear viscoelastic stress-strain relationship, typical of biological tissues composed of collagen and elastin. The median L_c and L_t were not significantly different for the first millimeter of distraction. We demonstrated the periosteum is primarily responsible for opposing the distraction load.

Fatigue of soft fibrous tissues: Multi-scale mechanics and constitutive modeling

In recent experimental studies a possible damage mechanism of collagenous tissues mainly caused by fatigue was disclosed. In this contribution, a multi-scale constitutive model ranging from the tropocollagen (TC) molecule level up to bundles of collagen fibers is proposed and utilized to predict the elastic and inelastic long-term tissue response. Material failure of collagen fibrils is elucidated by a permanent opening of the triple helical collagen molecule conformation, triggered either by overstretching or reaction kinetics of non-covalent bonds. This kinetics is described within a probabilistic framework of adhesive detachments of molecular linkages providing collagen fiber integrity. Both intramolecular and interfibrillar linkages are considered. The final constitutive equations are validated against recent experimental data available in literature for both uniaxial tension to failure and the evolution of fatigue in subsequent loading cycles. All material parameters of the proposed model have a clear physical interpretation.

STATEMENT OF SIGNIFICANCE

Irreversible changes take place at different length scales of soft fibrous tissues under supra-physiological loading and alter their macroscopic mechanical properties. Understanding the evolution of those histologic pathologies under loading and incorporating them into a continuum mechanical framework appears to be crucial in order to predict long-term evolution of various diseases and to support the development of tissue engineering.

A review of techniques for visualising soft tissue microstructure deformation and quantifying strain Ex Vivo

Many biological tissues have a complex hierarchical structure allowing them to function under demanding physiological loading conditions. Structural changes caused by ageing or disease can lead to loss of mechanical function. Therefore, it is necessary to characterise tissue structure to understand normal tissue function and the progression of disease. Ideally intact native tissues should be imaged in 3D and under physiological loading conditions. The current published in situ imaging methodologies demonstrate a compromise between imaging limitations and maintaining the samples native mechanical function. This review gives an overview of in situ imaging techniques used to visualise microstructural deformation of soft tissue, including three case studies of different tissues (tendon, intervertebral disc and artery). Some of the imaging techniques restricted analysis to observational mechanics or discrete strain measurement from invasive markers. Full-field local surface strain measurement has been achieved using digital image correlation. Volumetric strain fields have successfully been quantified from in situ X-ray microtomography (micro-CT) studies of bone using digital volume correlation but not in soft tissue due to low X-ray transmission contrast. With the latest developments in micro-CT showing in-line phase contrast capability to resolve native soft tissue microstructure, there is potential for future soft tissue mechanics research where 3D local strain can be quantified. These methods will provide information on the local 3D micromechanical environment experienced by cells in healthy, aged and diseased tissues. It is hoped that future applications of in situ imaging techniques will impact positively on the design and testing of potential tissue replacements or regenerative therapies. LAY DESCRIPTION: The soft tissues in our bodies, such as tendons, intervertebral discs and arteries, have evolved to have complicated structures which deform and bear load during normal function. Small changes in these structures can occur with age and disease which then leads to loss of function. Therefore, it is important to image tissue microstructure in 3D and under functional conditions. This paper gives an overview of imaging techniques used to record the deformation of soft tissue microstructures. Commonly there are compromises between obtaining the best imaging result and retaining the samples native structure and function. For example, invasive markers and dissecting samples damages the tissues natural structure, and staining or clearing (making the tissue more transparent) can distort tissue structure. Structural deformation has been quantified from 2D imaging techniques (digital image correlation) to create surface strain maps which help identify local tissue mechanics. When extended to 3D (digital volume correlation), deformation measurement has been limited to bone samples using X-ray micro-CT. Recently it has been possible to image the 3D structure of soft tissue using X-ray micro-CT meaning that there is potential for internal soft tissue mechanics to be mapped in 3D. Future application of micro-CT and digital volume correlation will be important for soft tissue mechanics studies particularly to understand normal function, progression of disease and in the design of tissue replacements.

Biological connective tissues exhibit viscoelastic and poroelastic behavior at different frequency regimes: Application to tendon and skin biophysics

In this study, a poroviscoelastic finite element model (FEM) was developed and used in conjunction with an AFM-based wide-bandwidth nanorheology system to predict the frequency-dependent mechanical behavior of tendon and dermis subjected to compression via nanoindentation. The aim was to distinguish between loading rates that are dominated by either poroelasticity, viscoelasticity, or the superposition of these processes. Using spherical probe tips having different radii, the force and tip displacement were measured and the magnitude, E^∗, and phase angle, ϕ, of the dynamic complex modulus were evaluated for mouse supraspinatus tendon and mouse dermis. The peak frequencies of the phase angle were associated with the characteristic time constants of poroelastic and viscoelastic material behavior. The developed FE model could predict the separate poroelastic and viscoelastic responses of these soft tissues over a 4 decade frequency range, showing good agreement with experimental results. We observed that poroelasticity was the dominant energy dissipation mechanism for mouse dermis and supraspinatus tendon at higher indentation frequencies (10² to 10⁴ Hz) whereas viscoelasticity was typically dominant at lower frequencies (<10² Hz). These findings show the underlying mechanical behavior of biological connective tissues and give insight into the role played by these different energy dissipation mechanisms in governing the function of these tissues at nanoscale.

STATEMENT OF SIGNIFICANCE

Soft biological tissues exhibit complex, load- and time-dependent mechanical behavior. Evaluating their mechanical behavior requires sophisticated experimental tools and numerical models that can capture the fundamental mechanisms governing tissue function. Using an Atomic-force-microscopy-based rheology system and finite element models, the roles of the two most dominant time-dependent mechanisms (poroelasticity and viscoelasticity) that govern the dynamic loading behavior of mouse skin and tendon have been investigated. FE models were able to predict and quantify the contribution of each mechanism to the overall dynamic response and confirming the presence of these two distinct mechanisms in the mechanical response. Overall, these results provide novel insight into the viscoelastic and poroelastic properties of mouse skin and tendon and promote better understanding of the underlying origins of each mechanism.

Nano-scale mechanisms explain the stiffening and strengthening of ligament tissue with increasing strain rate

Ligament failure is a major societal burden causing disability and pain. Failure is caused by trauma at high loading rates. At the macroscopic level increasing strain rates cause an increase in failure stress and modulus, but the mechanism for this strain rate dependency is not known. Here we investigate the nano scale mechanical property changes of human ligament using mechanical testing combined with synchrotron X-ray diffraction. With increasing strain rate, we observe a significant increase in fibril modulus and a reduction of fibril to tissue strain ratio, revealing that tissue-level stiffening is mainly due to the stiffening of collagen fibrils. Further, we show that the reduction in fibril deformation at higher strain rates is due to reduced molecular strain and fibrillar gaps, and is associated with rapid disruption of matrix-fibril bonding. This reduction in number of interfibrillar cross-links explains the changes in fibril strain; this is verified through computational modelling.

The hierarchical response of human corneal collagen to load

Fibrillar collagen in the human cornea is integral to its function as a transparent lens of precise curvature, and its arrangement is now well-characterised in the literature. While there has been considerable effort to incorporate fibrillar architecture into mechanical models of the cornea, the mechanical response of corneal collagen to small applied loads is not well understood. In this study the fibrillar and molecular response to tensile load was quantified using small and wide angle X-ray scattering (SAXS/WAXS), and digital image correlation (DIC) photography was used to calculate the local strain field that gave rise to the hierarchical changes. A molecular scattering model was used to calculate the tropocollagen tilt relative to the fibril axis and changes associated with applied strain. Changes were measured in the D-period, molecular tilt and the orientation and spacing of the fibrillar and molecular networks. These measurements were summarised into hierarchical deformation mechanisms, which were found to contribute at varying strains. The change in molecular tilt is indicative of a sub-fibrillar “spring-like” deformation mechanism, which was found to account for most of the applied strain under physiological and near-physiological loads. This deformation mechanism may play an important functional role in tissues rich in fibrils of high helical tilt, such as skin and cartilage.

Statement of Significance

Collagen is the primary mediator of soft tissue biomechanics, and variations in its hierarchical structure convey the varying amounts of structural support necessary for organs to function normally. Here we have examined the structural response of corneal collagen to tensile load using X-rays to probe hierarchies ranging from molecular to fibrillar. We found a previously unreported deformation mechanism whereby molecules, which are helically arranged relative to the axis of their fibril, change in tilt akin to the manner in which a spring stretches. This “spring-like” mechanism accounts for a significant portion of the applied deformation at low strains (<3%). These findings will inform the future design of collagen-based artificial corneas being developed to address world-wide shortages of corneal donor tissue.