Micromechanical analysis of native and cross-linked collagen type I fibrils supports the existence of microfibrils

Impact of changes in collagen construction and molecular state on integrin - binding properties

The interaction between the integrin and collagen is important in cell adhesion and signaling. Collagen, as the main component of extracellular matrix, is a base material for tissue engineering constructs. In tissue engineering, the collagen structure and molecule state may be altered to varying degrees in the process of processing and utilizing, thereby affecting its biological properties. In this work, the impact of changes in collagen structure and molecular state on the binding properties of collagen to integrin α2β1 and integrin specific cell adhesion were explored. The results showed that the molecular structure of collagen is destroyed under the influence of heating, freeze-grinding and irradiation, the triple helix integrity is reduced and molecular breaking degree is increased. The binding ability of collagen to integrin α2β1 is increased with the increase of triple helix integrity and decays exponentially with the increase of molecular breaking degree. The collagen molecular state can also influences the binding ability of collagen to cellular receptor. The collagen fibrils binding to integrin α2β1 and HT1080 cells is stronger than to collagen monomolecule. Meanwhile, the hybrid fibril exhibits a different cellular receptor binding performance from corresponding single species collagen fibril. These findings provide ideas for the design and development of new collagen-based biomaterials and tissue engineering research.

Failure in articular cartilage: Finite element predictions of stress, strain, and pressure under micro-indentation induced fracture

Articular cartilage is found at the distal end of long bones and is responsible for assisting in joint articulation. While articular cartilage has remarkable resistance to failure, once initially damaged, degeneration is nearly irreversible. Thus, understanding damage initiation is important. There are a few proposed mechanisms for articular cartilage failure initiation: (A) a single collagen fibril stress-based regime; (B) a rate-dependent regime captured by brittle failure at slow displacement rates (SDR) and ductile failure at fast displacement rates (FDR); and (C) a rate-dependent regime where failure is governed by pressurization fragmentation at SDR and governed by strain at FDR. The objective of this study was to use finite element (FE) models to provide evidence to support or refute these proposed failure mechanisms. Models were developed of microfracture experiments that investigated osmolarity (hypo-osmolar, normal osmolarity, and hyper-osmolar) and displacement rate (FDR and SDR) effects. Cartilage was modeled with a neo-Hookean ground matrix, strain-dependent permeability, nonlinear fibril reinforcement with viscoelastic fibril terms, and Donnan equilibrium swelling. Total stress, solid matrix stress, Lagrange strain, and fluid pressure were determined under the indenter tip at the moment of microfracture. Results indicated significant rate dependence across multiple outputs, which does not support (A) a single failure regime. Larger solid and fluid pressures at FDR than SDR did not support (C) a rate-dependent regime split by pressurization at SDR and strain at FDR. Consistent solid shear stresses at SDR and consistent third principal solid stresses at FDR support (B) the ductile-brittle failure regime. These findings help to shed light on the underlying mechanisms of articular cartilage failure, which have implications for the development of osteoarthritis.

Strain inhibition of bacterial collagenase is consistent with a collagen fibril uncrimping mechanism in rat tail tendons

Mechanical strain inhibits bacterial collagenase from cleaving collagen. Additionally, the toe region of a soft tissue's force-elongation curve arises from sequentially engaging collagen fibrils as the tissue lengthens. Together, these phenomena suggest that mechanical strain may gradually inhibit collagenase activity through a soft tissue's toe region. Therefore, this investigation sought to test this hypothesis. 92 rat tail tendon fascicles from 3 female sentinel animals underwent preliminary stiffness tests, and their force-elongation curves were fit to a collagen distribution model. This distribution-based model calculated the force magnitude corresponding to p% of collagen fibril engagement. Specimens were separated into one of five levels of p, and that level of force was maintained for two hours while being exposed to 0.054 U/mL of bacterial collagenase from C. histolyticum. The specimens were strained to failure following the creep test, and the relative reduction in stiffness was quantified to estimate the fraction of digested fibrils. Every 10% additional collagen engagement corresponded to a 6.3% (97% highest density interval: 4.3 - 8.4%) retention of stiffness, which indicated collagenase inhibition. The results of this investigation were consistent with a strain-inhibition hypothesis along with the established uncrimping mechanism in the toe region. These results support an interaction between mechanical strain and collagenolysis, which may be valuable for disease prevention or treatment.

Advanced-Glycation Endproducts: How cross-linking properties affect the collagen fibril behavior

Advanced-Glycation-Endproducts (AGEs) are known to be a major cause of impaired tissue material properties. In collagen fibrils, which constitute a major building component of human tissue, these AGEs appear as fibrillar cross-links. It has been shown that when AGEs accumulate in collagen fibrils, a process often caused by diabetes and aging, the mechanical properties of the collagen fibril are altered. However, current knowledge about the mechanical properties of different types of AGEs, and their quantity in collagen fibrils is limited owing to the scarcity of available experimental data. Consequently, the precise relationship between the nano-scale cross-link properties, which differ from type to type, their density in collagen fibrils, and the mechanical properties of the collagen fibrils at larger scales remains poorly understood. In our study, we use coarse-grained molecular dynamics simulations and perform destructive tensile tests on collagen fibrils to evaluate the effect of different cross-link densities and their mechanical properties on collagen fibril deformation and fracture behavior. We observe that the collagen fibril stiffens at high strain levels when either the AGEs density or the loading energy capacity of AGEs are increased. Based on our results, we demonstrate that this stiffening is caused by a mechanism that favors energy absorption via stretching rather than inter-molecular sliding. Hence, in these cross-linked collagen fibrils, the absorbed energy is stored rather than dissipated through friction, resulting in brittle fracture upon fibrillar failure. Further, by varying multiple AGEs nano-scale parameters, we show that the AGEs loading energy capacity is, aside from their density in the fibril, the unique factor determining the effect of different types of AGEs on the mechanical behavior of collagen fibrils. Our results show that knowing AGEs properties is crucial for a better understanding of the nano-scale origin of impaired tissue behavior. We further suggest that future experimental investigations should focus on the quantification of the loading energy capacity of AGEs as a key property for their influence on collagen fibrils.

The influence of AGEs and enzymatic cross-links on the mechanical properties of collagen fibrils

Collagen, one of the main building blocks for various tissues, derives its mechanical properties directly from its structure of cross-linked tropocollagen molecules. The cross-links are considered to be a key component of collagen fibrils as they can change the fibrillar behavior in various ways. For instance, enzymatic cross-links (ECLs), one particular type of cross-links, are known for stabilizing the structure of the fibril and improving material properties, while cross-linking AGEs (Advanced-Glycation Endproducts) have been shown to accumulate and impair the mechanical properties of collageneous tissues. However, the reasons for whether and how a given type of cross-link improves or impairs the material properties remain unknown, and the exact relationship between the cross-link properties and density, and the fibrillar behavior is still not well understood. Here, we use coarse-grained steered molecular models to evaluate the effect of AGEs and ECLs cross-links content on the deformation and failure properties of collagen fibrils. Our simulations show that the collagen fibrils stiffen at high strain levels when the AGEs content exceeds a critical value. In addition, the strength of the fibril increases with AGEs accumulation. By analyzing the forces within the different types of cross-links (AGEs and ECLs) as well as their failure, we demonstrate that a change of deformation mechanism is at the origin of these observations. A high AGEs content reinforces force transfer through AGEs cross-links rather than through friction between sliding tropocollagen molecules, which leads to failure by breaking of bonds within the tropocollagen molecules. We show that this failure mechanism, which is associated with lower energy dissipation, results in more abrupt failure of the collagen fibril. Our results provide a direct and causal link between increased AGEs content, inhibited intra-fibrillar sliding, increased stiffness, and abrupt fibril fracture. Therefore, they explain the mechanical origin of bone brittleness as commonly observed in elderly and diabetic populations. Our findings contribute to a better understanding of the mechanisms underlying impaired tissue behavior due to elevated AGEs content and could enable targeted measures regarding the reduction of specific collagen cross-linking levels.

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.

A coarse-grained molecular dynamics investigation of the role of mineral arrangement on the mechanical properties of mineralized collagen fibrils

Mineralized collagen fibrils (MCFs) comprise collagen molecules and hydroxyapatite (HAp) crystals and are considered universal building blocks of bone tissue, across different bone types and species. In this study, we developed a coarse-grained molecular dynamics (CGMD) framework to investigate the role of mineral arrangement on the load-deformation behaviour of MCFs. Despite the common belief that the collagen molecules are responsible for flexibility and HAp minerals are responsible for stiffness, our results showed that the mineral phase was responsible for limiting collagen sliding in the large deformation regime, which helped the collagen molecules themselves undergo high tensile loading, providing a substantial contribution to the ultimate tensile strength of MCFs. This study also highlights different roles for the mineralized and non-mineralized protofibrils within the MCF, with the mineralized groups being primarily responsible for load carrying due to the presence of the mineral phase, while the non-mineralized groups are responsible for crack deflection. These results provide novel insight into the load-deformation behaviour of MCFs and highlight the intricate role that both collagen and mineral components have in dictating higher scale bone biomechanics.

Mechanics of isolated individual collagen fibrils

Collagen fibrils are the fundamental structural elements in vertebrate animals and compose a framework that provides mechanical support to load-bearing tissues. Understanding how these fibrils initially form and mechanically function has been the focus of a myriad of detailed investigations over the last few decades. From these studies a great amount of knowledge has been acquired as well as a number of new questions to consider. In this review, we examine the current state of our knowledge of the mechanical properties of extant fibrils. We emphasize on the mechanical response and related deformation of collagen fibrils upon tension, which is the predominant load imposed in most collagen-rich tissues. We also illuminate the gaps in knowledge originating from the intriguing results that the field is still trying to interpret. STATEMENT OF SIGNIFICANCE: : Collagen is the result of millions of years of biological evolution and is a unique family of proteins, the majority of which provide mechanical support to biological tissues. Cells produce collagen molecules that self-assemble into larger structures, known as collagen fibrils. As simple as they appear under an optical microscope, collagen fibrils display a complex ultrastructural architecture tuned to the external forces that are imposed upon them. Even more complex is the way collagen fibrils deform under loading, and the nature of the mechanisms that drive their formation in the first place. Here, we present a cogent synthesis of the state-of-knowledge of collagen fibril mechanics. We focus on the information we have from in vitro experiments on individual, isolated from tissues, collagen fibrils and the knowledge available from in silico tests.

Instrument for tensile testing of individual collagen fibrils with facile sample coupling and uncoupling

Collagen is the major structural protein in human bodies constituting about 30% of the entire protein mass. Through a self-assembly process, triple helical collagen molecules assemble into high aspect-ratio fibers of tens to hundreds of nanometer diameter, known as collagen fibrils (CFs). In the last decade, several methods for tensile testing these CFs emerged. However, these methods are either overly time-consuming or offer low data acquisition bandwidth, rendering dynamic investigation of tensile properties impossible. Here, we describe a novel instrument for tensile testing of individual CFs. CFs are furnished with magnetic beads using a custom magnetic tweezer. Subsequently, CFs are lifted by magnetic force, allowing them to be picked-up by a microgripper structure, which is mounted on a cantilever-based interferometric force probe. A piezo-lever actuator is used to apply tensile displacements and to perform tensile tests of tethered CFs, after alignment. Once the mechanical tests are finished, CFs are removed from the microgripper by application of a magnetic field. Our novel instrument enables tensile tests with at least 25-fold increased throughput compared to tensile testing with an atomic force microscope while achieving force resolution (p-p) of 10 nN at a strain resolution better than 0.1%.

Exploring the Mechanical Properties and Performance of Type-I Collagen at Various Length Scales: A Progress Report

Collagen is the basic protein of animal tissues and has a complex hierarchical structure. It plays a crucial role in maintaining the mechanical and structural stability of biological tissues. Over the years, it has become a material of interest in the biomedical industries thanks to its excellent biocompatibility and biodegradability and low antigenicity. Despite its significance, the mechanical properties and performance of pure collagen have been never reviewed. In this work, the emphasis is on the mechanics of collagen at different hierarchical levels and its long-term mechanical performance. In addition, the effect of hydration, important for various applications, was considered throughout the study because of its dramatic influence on the mechanics of collagen. Furthermore, the discrepancies in reports of the mechanical properties of collagenous tissues (basically composed of 20-30% collagen fibres) and those of pure collagen are discussed.

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.

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.

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.

A quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues

The contribution presents an extension and application of a recently proposed finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelasticity to fibrous soft biological tissues and touches in particular upon computational aspects thereof. In line with theoretical framework presented by Dal (Int J Numer Methods Eng 117:118-140, 2019), the mixed variational formulation is extended to two families of fibers as often encountered while dealing with fibrous tissues. Apart from that, the purely Eulerian setting features the additive decomposition of the free energy function into volumetric, isotropic and anisotropic parts. The multiplicative split of the deformation gradient and all the outcomes thereof, e.g., unimodular invariants, are simply dispensed with in the three element formulations investigated, namely Q1, Q1P0 and the proposed Q1P0F0. For the quasi-incompressible response, the Q1P0 element formulation is briefly outlined where the pressure-type Lagrange multiplier and its conjugate enter the variational formulation as an extended set of variables. Using the similar argumentation, an extended Hu-Washizu-type mixed variational potential is introduced where the volume averaged squares of fiber stretches and associated fiber stresses are additional field variables. The resulting finite element formulation called Q1P0F0 is very attractive as it is based on mean values of the additional field variables at element level through integration over the element domain in a preprocessing step, earning the model vast utilization areas. The proposed approach is examined through representative boundary value problems pertaining to fibrous biological tissues. For all the cases studied, the proposed Q1P0F0 formulation elicits the most compliant mechanical response, thereby outperforming the standard Q1 and Q1P0 element formulations through mesh-refinement analyses. Results prompt further experimental investigations as to true deformation fields under biologically relevant loading conditions which would make the assessment of Q1P0 and Q1P0F0 more based on physical grounds.

Effect of the positional relationship between the interference screw and the tendon graft in the bone tunnel in ligament reconstruction

PURPOSE

To reveal the effects of the positional and length relationships between the interference screws (ISs) and the tendon graft in the bone tunnel on the fixation strength in ligament reconstruction.

METHODS

We compared three IS positions on the anterior (the Anterior group) or posterior (the Posterior group) or side (the Side group) of the tendon graft in relation to the pullout direction. The tendon graft was pulled at 0°, 30°, 60°, and 90° to the bone tunnel, and the maximum pullout load at each angle was compared among the groups. We also investigated the relationship between the length of the tendon graft and the length of the IS in the bone tunnel. The direction of the pullout force was the same as that of the Anterior group, and the maximum load was compared between groups in which the tendon graft was longer or shorter than the IS.

RESULTS

The maximum loads of the Anterior group were significantly greater than those of the Posterior and Side groups at the traction angles of 30° and 60°, respectively. An IS shorter than the tendon graft was found to provide significantly superior fixation strength compared to an IS longer than the tendon graft.

CONCLUSIONS

Better fixation strength was achieved when the IS was placed on the side of the anchorage tunnel on which the tendon graft was loaded and the IS was shorter than the tendon graft.

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.

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.

Rate-dependent adhesion of cartilage and its relation to relaxation mechanisms

Cartilage adhesion has been found to play an important role in friction responses in the boundary lubrication regime, but its underlying mechanisms have only been partially understood. This study investigates the rate dependence of adhesion from pre-to post-relaxation timescales of cartilage and its possible relation to relaxation responses of the tissue. Adhesion tests on cartilage were performed to obtain rate-dependent cartilage adhesion from relaxed to unrelaxed states and corresponding relaxation responses. The rate dependence of cartilage adhesion was analyzed based on experimental relaxation responses. Cartilage adhesion increased about 20 times from relaxed to unrelaxed states. This rate-dependent enhancement correlated well with the load relaxation responses in a characteristic time domain. These experimental results indicated that the degree of recovery (or relaxation) in the vicinity of contact during unloading governed the rate dependence of cartilage adhesion. In addition, the experimentally measured enhancement of adhesion was interpreted with the aid of computationally and analytically predicted adhesion trends in viscoelastic, poroviscoelastic, and cohesive contact models. Agreement between the experimental and predicted trends implied that the enhancement of cartilage adhesion originated from complex combinations of interfacial peeling and negative fluid pressure generated within the contact area during unloading. These findings enhance the current understanding of rate-dependent adhesion mechanisms explored within short time scales and thus could provide new insight into friction responses and stick-induced damage in cartilage.

Assessing collagen fibrils molecular damage after a single stretch-release cycle

Mechanical testing of connective tissues such as tendons and ligaments can lead to collagen denaturation even in the absence of macroscale damage. The following tensile loading protocols, ramp loading to failure, overloading and release, cyclic overloading and cyclic fatigue loading, all yield molecular damage in rat or bovine tendons. Single collagen fibrils extracted from the positional common digital extensor tendon of the forelimb also show molecular damage after tensile loading to failure. Using fibrils from the same source we assess changes to the molecular and supramolecular structure after tensile stress relaxation at strains between 4 and 22% followed by release. We observe no broken fibril and no significant change in D-band spacing. However, we observe significant binding of a fluorescent collagen hybridizing peptide to the fibrils indicating that collagen denaturation occurs in a strain dependent way for relaxation times between 1 s and 1500 s. We also show that peptide binding is associated with a decrease of the cross-sectional area of the fibrils providing an estimate of the dry volume loss due to molecular denaturation as well as an estimate of the mechanical energy density required, 25-110 MJ m^-3. In summary we show that collagen molecular damage can occur in the absence of fibril failure and without visible changes to the supramolecular structure.

Cartilage-on-cartilage cyclic loading induces mechanical and structural damage

Cartilage breaks down during mechanically-mediated osteoarthritis (OA). While previous research has begun to elucidate mechanical, structural and cellular damage in response to cyclic loading, gaps remain in our understanding of the link between cyclic cartilage loading and OA-like mechanical damage. Thus, the aim of this study was to quantify irreversible cartilage damage in response to cyclic loading. A novel in vitro model of damage through cartilage-on-cartilage cyclic loading was established. Cartilage was loaded at 1 Hz to two different doses (10,000 or 50,000 cycles) between -6.0 ± 0.2 MPa and -10.3 ± 0.2 MPa 1st Piola-Kirchhoff stress. After loading, mechanical damage (altered mechanical properties: elastic moduli and dissipated energy) and structural damage (surface damage and specimen thickness) were quantified. Linear and tangential moduli were determined by fitting the loading portion of the stress-strain curves. Dissipated energy was calculated from the area between loading and unloading stress-strain curves. Specimen thickness was measured both before and after loading. Surface damage was assessed by staining samples with India ink, then imaging the articular surface. Cyclic loading resulted in dose-dependent decreases in linear and tangential moduli, energy dissipation, thickness, and intact area. Collectively, these results show that cartilage damage can be initiated by mechanical loading alone in vitro, suggesting that cyclic loading can cause in vivo damage. This study demonstrated that with increased number of cycles, cartilage undergoes both tissue softening and structural damage. These findings are a first step towards characterizing the cartilage response to cyclic loading, which can ultimately provide important insight for delaying the initiation and slowing the progression of OA.

Mechanical properties, physiological behavior, and function of aponeurosis and tendon

During human movement, the muscle and tendinous structures interact as a mechanical system in which forces are generated and transmitted to the bone and energy is stored and released to optimize function and economy of movement and/or to reduce risk of injury. The present review addresses certain aspects of how the anatomical design and mechanical and material properties of the force-transmitting tissues contribute to the function of the muscle-tendon unit and thus overall human function. The force-bearing tissues are examined from a structural macroscopic point of view down to the nanoscale level of the collagen fibril. In recent years, the understanding of in vivo mechanical function of the force-bearing tissues has increased, and it has become clear that these tissues adapt to loading and unloading and furthermore that force transmission mechanics is more complex than previously thought. Future investigations of the force-transmitting tissues in three dimensions will enable a greater understanding of the complex functional interplay between muscle and tendon, with relevance for performance, injury mechanisms, and rehabilitation strategies.

Rate-dependent crack nucleation in cartilage under microindentation

This study investigates rate-dependent crack nucleation in cartilage under microindentation using a poroviscoelastic framework and nano/microscopic images. Localized crack failure was induced at known locations and at different loading rates via microindentation with an axisymmetric sphero-conical indenter. Finite element (FE) modeling was used to reproduce results of microindentation tests within a poroviscoelastic framework. Scanning electron microscopy (SEM) was used to examine nano- and microscale structural features of crack surfaces. Microindentation results showed rate-dependent crack nucleation in cartilage. In particular, critical total work required for crack nucleation was larger at the slow loading rate compared to the fast loading rate. FE results suggested that viscoelastic relaxation of cartilage was a major contributor to the rate dependency and that tensile stresses localized at the indenter tip was a governing factor in crack nucleation. SEM images combined with microindentation and FE results suggested that the solid matrix in the vicinity of the tip experienced relatively large relaxation and kinematic fiber rearrangement at the slow loading rate in comparison to the fast loading rate. These findings extend current understanding of rate-dependent failure mechanisms in cartilage.

Monte Carlo type Simulations of Mineralized Collagen Fibril based on Two Scale Asymptotic Homogenization

A multi-scale model for mineralized collagen fibril is proposed by taking into account the uncertainties associated with the geometrical properties of mineral phase and its distribution in the organic matrix. The asymptotic homogenization approach along with periodic boundary conditions has been used to derive the effective elastic moduli at two hierarchical length scales, namely: microfibril and mineralized collagen fibril. The uncertainties associated with the mineral plates have been directly included in the finite element mesh by randomly varying their sizes. A total 100 realizations for mineralized collagen fibril model with random distribution have been generated using an in-house MATLAB® code and Monte-Carlo type simulations have been performed under tension load to obtain the statistical equivalent modulus. The deformation response has been studied in both small (= 10%) and large (= 10%) strain regimes. The stress transformation mechanism has also been explored in microfibril which showed stress relaxation in the organic phase upon different stages of mineralization. The elastic moduli for microfibril under small and large strain have been obtained as 1.88 and 6.102 GPa, respectively, and have been used as input for upper scale homogenization procedure. Finally, the characteristic longitudinal moduli of the mineralized collagen fibril in the small and large strain regimes are obtained as 4.08 ± 0.062 and 12.93 ± 0.148 GPa, respectively. All the results are in good agreement to those obtained from previous experiments and molecular dynamics simulations in the literature with a significant reduction in the computational cost.

Evaluation of Mechanical Properties of Dimpled PET Fiber Fabricated by Electrospinning Method

Insufficient endothelialization of stent grafts tends to cause a problem of thrombosis formation. Because the structure of nanofibers, generally defined as fibers with a diameter below 1 μm, resembles the structure of an extracellular matrix, nanofibers are applied to scaffolds for regenerative medicine. Using nanofibers as the covering material of the stent graft can be expected to solve the problem of the stent graft. Previous studies have shown that a porous scaffold offers better surfaces to anchor and culture endothelial cells than a nonporous scaffold. Therefore, fibers with nanoorder dimples are expected to promote endothelialization. As a method of forming the dimple shape on the surface of the PET fiber, there is a method utilizing a difference in the volatilization rate of the solvent in the high humidity environment in the electrospinning method. For practical application of the stent graft to artificial blood vessels, the mechanical properties of the dimpled PET fiber should be clarified. In this study, the mechanical properties of single nanofibers and nonwoven fabrics of PET fibers with dimples on their surface were evaluated by tensile test. By forming the dimple shape on the fiber surface, the tensile strength of single PET fibers with dimples was 90 % lower than that of single PET fibers with a smooth surface. In the fabrication process of nonwoven fabric, the addition of EG delayed the volatilization of the PET solution, and the fibers adhered to each other. The bonding between the fibers contributed to the tensile strength of the nonwoven fabric.

Combining tensile testing and structural analysis at the single collagen fibril level

Tensile testing to failure followed by imaging is a simple way of studying the structure-function relationship of connective tissues such as skin, tendon, and ligament. However, interpretation of these datasets is complex due to the hierarchical structures of the tissues spanning six or more orders of magnitude in length scale. Here we present a dataset obtained through the same scheme at the single collagen fibril level, the fundamental tensile element of load-bearing tissues. Tensile testing was performed on fibrils extracted from two types of bovine tendons, adsorbed on a glass surface and glued at both ends. An atomic force microscope (AFM) was used to pull fibrils to failure in bowstring geometry. The broken fibrils were then imaged by AFM for morphological characterization, by second harmonic generation microscopy to assess changes to molecular packing, and by fluorescence microscopy after incubation with a peptide probe that binds specifically to denatured collagen molecules. This dataset linking stress-strain curves to post-failure molecular changes is useful for researchers modelling or designing functional protein materials.

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.

The Role of Network Architecture in Collagen Mechanics

Collagen forms fibrous networks that reinforce tissues and provide an extracellular matrix for cells. These networks exhibit remarkable strain-stiffening properties that tailor the mechanical functions of tissues and regulate cell behavior. Recent models explain this nonlinear behavior as an intrinsic feature of disordered networks of stiff fibers. Here, we experimentally validate this theoretical framework by measuring the elastic properties of collagen networks over a wide range of self-assembly conditions. We show that the model allows us to quantitatively relate both the linear and nonlinear elastic behavior of collagen networks to their underlying architecture. Specifically, we identify the local coordination number (or connectivity) 〈z〉 as a key architectural parameter that governs the elastic response of collagen. The network elastic response reveals that 〈z〉 decreases from 3.5 to 3 as the polymerization temperature is raised from 26 to 37°C while being weakly dependent on concentration. We furthermore infer a Young's modulus of 1.1 MPa for the collagen fibrils from the linear modulus. Scanning electron microscopy confirms that 〈z〉 is between three and four but is unable to detect the subtle changes in 〈z〉 with polymerization conditions that rheology is sensitive to. Finally, we show that, consistent with the model, the initial stress-stiffening response of collagen networks is controlled by the negative normal stress that builds up under shear. Our work provides a predictive framework to facilitate future studies of the regulatory effect of extracellular matrix molecules on collagen mechanics. Moreover, our findings can aid mechanobiological studies of wound healing, fibrosis, and cancer metastasis, which require collagen matrices with tunable mechanical properties.

Effects of maturation and advanced glycation on tensile mechanics of collagen fibrils from rat tail and Achilles tendons

Connective tissues are ubiquitous throughout the body and consequently affect the function of many organs. In load bearing connective tissues like tendon, the mechanical functionality is provided almost exclusively by collagen fibrils that in turn are stabilized by covalent cross-links. Functionally distinct tendons display different cross-link patterns, which also change with maturation, but these differences have not been studied in detail at the fibril level. In the present study, a custom built nanomechanical test platform was designed and fabricated to measure tensile mechanics of individual fibrils from rat tendons. The influence of animal maturity (4 vs. 16 week old rats) and functionally different tendons (tail vs. Achilles tendons) were examined. Additionally the effect of methylglyoxal (MG) treatment in vitro to form advanced glycation end products (AGEs) was investigated. Age and tissue type had no significant effect on fibril mechanics, but MG treatment increased strength and stiffness without inducing brittleness and gave rise to a distinct three-phase mechanical response corroborating that previously reported in human patellar tendon fibrils. That age and tissue had little mechanical effect, tentatively suggest that variations in enzymatic cross-links may play a minor role after initial tissue formation.

STATEMENT OF SIGNIFICANCE

Tendons are connective tissues that connect muscle to bone and carry some of the greatest mechanical loads in the body, which makes them common sites of injury. A tendon is essentially a biological rope formed by thin strands called fibrils made of the protein collagen. Tendon function relies on the strength of these fibrils, which in turn depends on naturally occurring cross-links between collagen molecules, but the mechanical influence of these cross-links have not been measured before. It is believed that beneficial cross-linking occurs with maturation while additional cross-linking with aging may lead to brittleness, but this study provides evidence that maturation has little effect on mechanical function and that age-related cross-linking does not result in brittle collagen fibrils.

In tendons, differing physiological requirements lead to functionally distinct nanostructures

The collagen-based tissues of animals are hierarchical structures: even tendon, the simplest collagenous tissue, has seven to eight levels of hierarchy. Tailoring tissue structure to match physiological function can occur at many different levels. We wanted to know if the control of tissue architecture to achieve function extends down to the nanoscale level of the individual, cable-like collagen fibrils. Using tendons from young adult bovine forelimbs, we performed stress-strain experiments on single collagen fibrils extracted from tendons with positional function, and tendons with energy storing function. Collagen fibrils from the two tendon types, which have known differences in intermolecular crosslinking, showed numerous differences in their responses to elongation. Unlike those from positional tendons, fibrils from energy storing tendons showed high strain stiffening and resistance to disruption in both molecular packing and conformation, helping to explain how these high stress tissues withstand millions of loading cycles with little reparative remodeling. Functional differences in load-bearing tissues are accompanied by important differences in nanoscale collagen fibril structure.

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.

Impact of Fiber Structure on the Material Stability and Rupture Mechanisms of Coronary Atherosclerotic Plaques

The rupture of an atherosclerotic plaque in the coronary circulation remains the main cause of heart attack. As a fiber-oriented structure, the fiber structure, in particular in the fibrous cap (FC), may affect both loading and material strength in the plaque. However, the role of fiber orientation and dispersion in plaque rupture is unclear. Local orientation and dispersion of fibers were calculated for the shoulder regions, mid FC, and regions with intimal thickening (IT) from histological images of 16 human coronary atherosclerotic lesions. Finite element analysis was performed to assess the effect of these properties on mechanical conditions. Fibers in shoulder regions had markedly reduced alignment (Median [interquartile range] 12.9° [6.6, 18.0], p < 0.05) compared with those in mid FC (6.1° [5.5, 9.0]) and IT regions (6.7° [5.1, 8.6]). Fiber dispersion was highest in shoulders (0.150 [0.121, 0.192]), intermediate in IT (0.119 [0.103, 0.144]), and lowest in mid FC regions (0.093 [0.081, 0.105], p < 0.05). When anisotropic properties were considered, stresses were significantly higher for the mid FC (p = 0.030) and IT regions (p = 0.002) and no difference was found for the shoulder or global regions. Shear (sliding) stress between fibers in each region and their proportion of maximum principal stress were: shoulder (25.8 kPa [17.1, 41.2], 12.4%), mid FC (13.9 kPa [5.8, 29.6], 13.8%), and IT (36.5 kPa [25.9, 47.3], 15.5%). Fiber structure within the FC has a marked effect on principal stresses, resulting in considerable shear stress between fibers. Fiber structure including orientation and dispersion may determine mechanical strength and thus rupture of atherosclerotic plaques.

A transversely isotropic coupled hyperelastic model for the mechanical behavior of tendons

Several constitutive models for fibrous soft tissues used in literature provide a completely isotropic response when fibers are compressed. However, recent experimental investigations confirm the expectation that tendons behave anisotropically during compression tests. Motivated by these facts, the present manuscript presents an appropriate choice of hyperelastic potentials able to predict the coupled mechanical behaviors of tendons under both tensile and compressive loads with a relatively small number of material parameters. The high stiffness of tendons under tensile tests is handled by a transversely isotropic model while the coupled compressive response is modeled by means of a Fung-type potential in terms of Seth-Hill's generalized strain tensors. In present study the logarithm strain measure is used instead of the usually employed Green-Lagrange strain. After a parameter identification procedure, the resulting model showed ability to satisfactorily reproduce the experimental data. Details on the analytical material tangent modulus are provided. Present results will then enhance further researches related to tendon dissipative effects and numerical multiscale investigations.

Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling

Characterizing the mechanical properties of white matter is important to understand and model brain development and injury. With embedded aligned axonal fibers, white matter is typically modeled as a transversely isotropic material. However, most studies characterize the white matter tissue using models with a single anisotropic invariant or in a small-strain regime. In this study, we combined a single experimental procedure - asymmetric indentation - with inverse finite element (FE) modeling to estimate the nearly incompressible transversely isotropic material parameters of white matter. A minimal form comprising three parameters was employed to simulate indentation responses in the large-strain regime. The parameters were estimated using a global optimization procedure based on a genetic algorithm (GA). Experimental data from two indentation configurations of porcine white matter, parallel and perpendicular to the axonal fiber direction, were utilized to estimate model parameters. Results in this study confirmed a strong mechanical anisotropy of white matter in large strain. Further, our results suggested that both indentation configurations are needed to estimate the parameters with sufficient accuracy, and that the indenter-sample friction is important. Finally, we also showed that the estimated parameters were consistent with those previously obtained via a trial-and-error forward FE method in the small-strain regime. These findings are useful in modeling and parameterization of white matter, especially under large deformation, and demonstrate the potential of the proposed asymmetric indentation technique to characterize other soft biological tissues with transversely isotropic properties.

A phase-field approach to model fracture of arterial walls: Theory and finite element analysis

This study uses a recently developed phase-field approach to model fracture of arterial walls with an emphasis on aortic tissues. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler-Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive model which is additively decomposed into an isotropic part for the ground matrix and an exponential anisotropic part for the two families of collagen fibers embedded in the ground matrix. In addition we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step (solved for the frozen crack phase-field parameter) and a crack evolution step (solved for the frozen deformation map); a history field governed by the failure criterion is successively updated. Subsequently, a conventional Galerkin procedure leads to the weak forms of the governing differential equations for the physical problem. Accordingly, we provide the discrete residual vectors and a corresponding linearization yields the element matrices for the two sub-problems. Finally, we demonstrate the numerical performance of the crack phase-field model by simulating uniaxial extension and simple shear fracture tests performed on specimens obtained from a human aneurysmatic thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.

A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method

Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight that intelligent numerical methods are powerful and accurate procedures to deal with the complex multiscale problem in the bone tissue with results in agreement with values found in literature for specific scale levels.

Bowstring Stretching and Quantitative Imaging of Single Collagen Fibrils via Atomic Force Microscopy

Collagen is the primary structural protein in animals. Serving as nanoscale biological ropes, collagen fibrils are responsible for providing strength to a variety of connective tissues such as tendon, skin, and bone. Understanding structure-function relationships in collagenous tissues requires the ability to conduct a variety of mechanical experiments on single collagen fibrils. Though significant advances have been made, certain tests are not possible using the techniques currently available. In this report we present a new atomic force microscopy (AFM) based method for tensile manipulation and subsequent nanoscale structural assessment of single collagen fibrils. While the method documented here cannot currently capture force data during loading, it offers the great advantage of allowing structural assessment after subrupture loading. To demonstrate the utility of this technique, we describe the results of 23 tensile experiments in which collagen fibrils were loaded to varying levels of strain and subsequently imaged in both the hydrated and dehydrated states. We show that following a dehydration-rehydration cycle (necessary for sample preparation), fibrils experience an increase in height and decrease in radial modulus in response to one loading-unloading cycle to strain <5%. This change is not altered by a second cycle to strain >5%. In fibril segments that ruptured during their second loading cycle, we show that the fibril structure is affected away from the rupture site in the form of discrete permanent deformations. By comparing the severity of select damage sites in both hydrated and dehydrated conditions, we demonstrate that dehydration masks damage features, leading to an underestimate of the degree of structural disruption. Overall, the method shows promise as a powerful tool for the investigation of structure-function relationships in nanoscale fibrous materials.

Tension tests on mammalian collagen fibrils

A brief overview of isolated collagen fibril mechanics testing is followed by presentation of the first results testing fibrils isolated from load-bearing mammalian tendons using a microelectromechanical systems platform. The in vitro modulus (326 ± 112 MPa) and fracture stress (71 ± 23 MPa) are shown to be lower than previously measured on fibrils extracted from sea cucumber dermis and tested with the same technique. Scanning electron microscope images show the fibrils can fail with a mechanism that involves circumferential rupture, whereas the core of the fibril stays at least partially intact.

Molecular and intermolecular effects in collagen fibril mechanics: a multiscale analytical model compared with atomistic and experimental studies

Both atomistic and experimental studies reveal the dependence of collagen fibril mechanics on biochemical and biophysical features such as, for instance, cross-link density, water content and protein sequence. In order to move toward a multiscale structural description of biological tissues, a novel analytical model for collagen fibril mechanics is herein presented. The model is based on a multiscale approach that incorporates and couples: thermal fluctuations in collagen molecules; the uncoiling of collagen triple helix; the stretching of molecular backbone; the straightening of the telopeptide in which covalent cross-links form; slip-pulse mechanisms due to the rupture of intermolecular weak bonds; molecular interstrand delamination due to the rupture of intramolecular weak bonds; the rupture of covalent bonds within molecular strands. The effectiveness of the proposed approach is verified by comparison with available atomistic results and experimental data, highlighting the importance of cross-link density in tuning collagen fibril mechanics. The typical three-region shape and hysteresis behavior of fibril constitutive response, as well as the transition from a yielding-like to a brittle-like behavior, are recovered with a special insight on the underlying nanoscale mechanisms. The model is based on parameters with a clear biophysical and biochemical meaning, resulting in a promising tool for analyzing the effect of pathological or pharmacological-induced histochemical alterations on the functional mechanical response of collagenous tissues.

Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.

Advanced glycation end-products reduce collagen molecular sliding to affect collagen fibril damage mechanisms but not stiffness

Advanced glycation end-products (AGE) contribute to age-related connective tissue damage and functional deficit. The documented association between AGE formation on collagens and the correlated progressive stiffening of tissues has widely been presumed causative, despite the lack of mechanistic understanding. The present study investigates precisely how AGEs affect mechanical function of the collagen fibril--the supramolecular functional load-bearing unit within most tissues. We employed synchrotron small-angle X-ray scattering (SAXS) and carefully controlled mechanical testing after introducing AGEs in explants of rat-tail tendon using the metabolite methylglyoxal (MGO). Mass spectrometry and collagen fluorescence verified substantial formation of AGEs by the treatment. Associated mechanical changes of the tissue (increased stiffness and failure strength, decreased stress relaxation) were consistent with reports from the literature. SAXS analysis revealed clear changes in molecular deformation within MGO treated fibrils. Underlying the associated increase in tissue strength, we infer from the data that MGO modified collagen fibrils supported higher loads to failure by maintaining an intact quarter-staggered conformation to nearly twice the level of fibril strain in controls. This apparent increase in fibril failure resistance was characterized by reduced side-by-side sliding of collagen molecules within fibrils, reflecting lateral molecular interconnectivity by AGEs. Surprisingly, no change in maximum fibril modulus (2.5 GPa) accompanied the changes in fibril failure behavior, strongly contradicting the widespread assumption that tissue stiffening in ageing and diabetes is directly related to AGE increased fibril stiffness. We conclude that AGEs can alter physiologically relevant failure behavior of collagen fibrils, but that tissue level changes in stiffness likely occur at higher levels of tissue architecture.

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

Despite current knowledge of tendon structure, the fundamental deformation mechanisms underlying tendon mechanics and failure are unknown. We recently showed that a shear lag model, which explicitly assumed plastic interfibrillar load transfer between discontinuous fibrils, could explain the multiscale fascicle mechanics, suggesting that fascicle yielding is due to plastic deformation of the interfibrillar matrix. However, it is unclear whether alternative physical mechanisms, such as elastic interfibrillar deformation or fibril yielding, also contribute to fascicle mechanical behavior. The objective of the current work was to determine if plasticity of the interfibrillar matrix is uniquely capable of explaining the multiscale mechanics of tendon fascicles including the tissue post-yield behavior. This was examined by comparing the predictions of a continuous fibril model and three separate shear lag models incorporating an elastic, plastic, or elastoplastic interfibrillar matrix with multiscale experimental data. The predicted effects of fibril yielding on each of these models were also considered. The results demonstrated that neither the continuous fibril model nor the elastic shear lag model can successfully predict the experimental data, even if fibril yielding is included. Only the plastic or elastoplastic shear lag models were capable of reproducing the multiscale tendon fascicle mechanics. Differences between these two models were small, although the elastoplastic model did improve the fit of the experimental data at low applied tissue strains. These findings suggest that while interfibrillar elasticity contributes to the initial stress response, plastic deformation of the interfibrillar matrix is responsible for tendon fascicle post-yield behavior. This information sheds light on the physical processes underlying tendon failure, which is essential to improve our understanding of tissue pathology and guide the development of successful repair.