Viscoelastic properties of isolated collagen fibrils

Collagen intrafibrillar mineralization as a result of the balance between osmotic equilibrium and electroneutrality

Mineralization of fibrillar collagen with biomimetic process-directing agents has enabled scientists to gain insight into the potential mechanisms involved in intrafibrillar mineralization. Here, by using polycation- and polyanion-directed intrafibrillar mineralization, we challenge the popular paradigm that electrostatic attraction is solely responsible for polyelectrolyte-directed intrafibrillar mineralization. As there is no difference when a polycationic or a polyanionic electrolyte is used to direct collagen mineralization, we argue that additional types of long-range non-electrostatic interaction are responsible for intrafibrillar mineralization. Molecular dynamics simulations of collagen structures in the presence of extrafibrillar polyelectrolytes show that the outward movement of ions and intrafibrillar water through the collagen surface occurs irrespective of the charges of polyelectrolytes, resulting in the experimentally verifiable contraction of the collagen structures. The need to balance electroneutrality and osmotic equilibrium simultaneously to establish Gibbs-Donnan equilibrium in a polyelectrolyte-directed mineralization system establishes a new model for collagen intrafibrillar mineralization that supplements existing collagen mineralization mechanisms.

Real-Time Assessment of Mechanical Tissue Trauma in Surgery

OBJECTIVE

This work presents a method to assess and prevent tissue trauma in real-time during surgery.

BACKGROUND

Tissue trauma occurs routinely during laparoscopic surgery with potentially severe consequences. As such, it is crucial that a surgeon is able to regulate the pressure exerted by surgical instruments. We propose a novel method to assess the onset of tissue trauma by considering the mechanical response of tissue as it is loaded in real-time.

METHODS

We conducted a parametric study using a lab-based grasping model and differing load conditions. Mechanical stress-time data were analyzed to characterize the tissue response to grasps. Qualitative and quantitative histological analyses were performed to inspect damage characteristics of the tissue under different load conditions. These were correlated against the mechanical measures to identify the nature of trauma onset with respect to our predictive metric.

RESULTS

Results showed increasing tissue trauma with load and a strong correlation with the mechanical response of the tissue. Load rate and load history also showed a clear effect on tissue response. The proposed method for trauma assessment was effective in identifying damage. The metric can be normalized with respect to loading rate and history, making it feasible in the unconstrained environment of intraoperative surgery.

SIGNIFICANCE

This work demonstrates that tissue trauma can be predicted using mechanical measures in real-time. Applying this technique to laparoscopic tools has the potential to reduce unnecessary tissue trauma and its associated complications by indicating through user feedback or actively regulating the mechanical impact of surgical instruments.

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.

Material properties of bovine intervertebral discs across strain rates

The intervertebral disc (IVD) is a complex structure responsible for distributing compressive loading to adjacent vertebrae and allowing the vertebral column to bend and twist. To study the mechanical behaviour of individual components of the IVD, it is common for specimens to be dissected away from their surrounding tissues for mechanical testing. However, disrupting the continuity of the IVD to obtain material properties of each component separately may result in erroneous values. In this study, an inverse finite element (FE) modelling optimisation algorithm has been used to obtain material properties of the IVD across strain rates, therefore bypassing the need to harvest individual samples of each component. Uniaxial compression was applied to ten fresh-frozen bovine intervertebral discs at strain rates of 10^-3-1/s. The experimental data were fed into the inverse FE optimisation algorithm and each experiment was simulated using the subject specific FE model of the respective specimen. A sensitivity analysis revealed that the IVD's response was most dependent upon the Young's modulus (YM) of the fibre bundles and therefore this was chosen to be the parameter to optimise. Based on the obtained YM values for each test corresponding to a different strain rate (ε̇), the following relationship was derived:YM=35.5lnε̇+527.5. These properties can be used in finite element models of the IVD that aim to simulate spinal biomechanics across loading rates.

Inferring spatial variations of microstructural properties from macroscopic mechanical response

Disease alters tissue microstructure, which in turn affects the macroscopic mechanical properties of tissue. In elasticity imaging, the macroscopic response is measured and is used to infer the spatial distribution of the elastic constitutive parameters. When an empirical constitutive model is used, these parameters cannot be linked to the microstructure. However, when the constitutive model is derived from a microstructural representation of the material, it allows for the possibility of inferring the local averages of the spatial distribution of the microstructural parameters. This idea forms the basis of this study. In particular, we first derive a constitutive model by homogenizing the mechanical response of a network of elastic, tortuous fibers. Thereafter, we use this model in an inverse problem to determine the spatial distribution of the microstructural parameters. We solve the inverse problem as a constrained minimization problem and develop efficient methods for solving it. We apply these methods to displacement fields obtained by deforming gelatin-agar co-gels and determine the spatial distribution of agar concentration and fiber tortuosity, thereby demonstrating that it is possible to image local averages of microstructural parameters from macroscopic measurements of deformation.

Method to extract minimally damaged collagen fibrils from tendon

A new method is presented to extract collagen fibrils from mammalian tendon tissue. Mammalian tendons are treated with a trypsin-based extraction medium and gently separated with tweezers in an aqueous solution. Collagen fibrils released in the solution are imaged using both dark-field light microscopy and scanning electron microscopy. The method successfully extracts isolated fibrils from rat tail and patellar tendons. To examine whether the method is likely to damage fibrils during extraction, sea cucumber dermis fibril lengths are compared against those obtained using only distilled water. The two methods produce fibrils of similar lengths. This is contrasted with fibrils being shortened when extracted using a tissue homogenizer. Scanning electron microscopy shows the new method preserves D-banding features on fibril surfaces and that fibril diameter does not vary substantially compared with water extracted fibrils.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

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.

Contribution of fluid in bone extravascular matrix to strain-rate dependent stiffening of bone tissue - A poroelastic study

Osteoporotic fractures represent an increasing cost to society, and its diagnosis methods based on bone density still lack accuracy in identifying risk of fracture. This is why a better understanding of mechanical behavior of bone tissue is of importance, especially when it comes to relating experimental observations to realistic physiological fall loading conditions. This study aims at exploring the stiffening effect of pore fluid in bone extravascular matrix subject to high strain rate loading that is more realistic to simulate a physiological fall. A computational approach is used, where bone tissue microstructure extracted from micro-CT images is modeled using finite elements. The solid phase of bone tissue is modeled as a poroelastic material, a porous matrix filled with fluid. When the extravascular matrix experiences certain volumetric deformation, the fluid in pores presents load carrying capacity, which consequently varies the apparent stiffness of bone tissue. It is shown that effects of fluid stiffening in bone can be significant, depending on the chosen material properties, the amount of volumetric strain in tissue and the loading rate with respect to hydraulic conductivity and drainage conditions. It is also shown that such stiffening effect is influenced by bone microstructure, and is more significant in cortical bone than in trabecular bone.

Breast cancer cells alter the dynamics of stromal fibronectin-collagen interactions

Breast cancer cells recruit surrounding stromal cells, such as cancer-associated fibroblasts (CAFs), to remodel their extracellular matrix (ECM) and promote invasive tumor growth. Two major ECM components, fibronectin (Fn) and collagen I (Col I), are known to interact with each other to regulate cellular behavior. In this study, we seek to understand how Fn and Col I interplay and promote a dysregulated signaling pathway to facilitate tumor progression. Specifically, we investigated the evolution of tumor-conditioned stromal ECM composition, structure, and relaxation. Furthermore, we assessed how evolving Fn-Col I interactions gradually affected pro-angiogenic signaling. Our data first indicate that CAFs initially assembled a strained, viscous, and unfolded Fn matrix. This early altered Fn matrix was later remodeled into a thick Col I-rich matrix that was characteristic of a dense tumor mass. Next, our results suggest that this ECM remodeling was primarily mediated by matrix metalloproteinases (MMPs). This MMP activity caused profound structural and mechanical changes in the developing ECM, which then modified vascular endothelial growth factor (VEGF) secretion by CAFs and matrix sequestration. Collectively, these findings enhance our understanding of the mechanisms by which Fn and Col I synergistically interplay in promoting a sustained altered signaling cascade to remodel the breast tumor stroma for invasive breast tumor growth.

Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations

Collagen fibril is a major component of connective tissues such as bone, tendon, blood vessels, and skin. The mechanical properties of this highly hierarchical structure are greatly influenced by the presence of covalent cross-links between individual collagen molecules. This study investigates the viscoelastic behavior of a collagen lysine-lysine cross-link based on creep simulations with applied forces in the range or 10 to 2000pN using steered molecular dynamics (SMD). The viscoelastic model of the cross-link was combined with a system composed by two segments of adjacent collagen molecules hence representing a reduced viscoelastic model for a simplified micro-fibril. It was found that the collagen micro-fibril assembly had a steady-state Young׳s modulus ranging from 2.24 to 3.27GPa, which is in agreement with reported experimental measurements. The propagation of longitudinal force wave along the molecule was implemented by adding a delay element to the model. The force wave speed was found to be correlated with the speed of one-dimensional elastic waves in rods. The presented reduced model with three degrees of freedom can serve as a building block for developing models of the next level of hierarchy, i.e., a collagen fibril.

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2s and 10-30s. Different finite time constants in the range of 1-7000s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000s, and to merge relaxation finite time constants in the 0.5-2s range into a single time content in the 1s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction.

STATEMENT OF SIGNIFICANCE

As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.

Characterization of Human Dental Pulp Tissue Under Oscillatory Shear and Compression

Availability of material as well as biological properties of native tissues is critical for biomaterial design and synthesis for regenerative engineering. Until recently, selection of biomaterials and biomolecule carriers for dental pulp regeneration has been done randomly or based on experience mainly due to the absence of benchmark data for dental pulp tissue. This study, for the first time, characterizes the linear viscoelastic material functions and compressive properties of human dental pulp tissue harvested from wisdom teeth, under oscillatory shear and compression. The results revealed a gel-like behavior of the pulp tissue over the frequency range of 0.1–100 rps. Uniaxial compression tests generated peak normal stress and compressive modulus values of 39.1±20.4 kPa and 5.5±2.8 kPa, respectively. Taken collectively, the linear viscoelastic and uniaxial compressive properties of the human dental pulp tissue reported here should enable the better tailoring of biomaterials or biomolecule carriers to be employed in dental pulp regeneration.

Structure-induced nonlinear viscoelasticity of non-woven fibrous matrices

Fibrous materials are widely utilized as tissue engineering scaffolds for tissue regeneration and other bioengineering applications. The structural as well as mechanical characteristics of the fibrous matrices under static and dynamic mechanical loading conditions influence the response of the cells. In this paper, we study the mechanical response of the non-woven fibrous matrices under oscillatory loading conditions and its dependence on the structural properties of fibrous matrix. We demonstrate that under oscillatory shear and elongation, the fibrous matrices demonstrate nonlinear viscoelasticity at all strain amplitudes. This is contrary to the behavior of other soft polymeric materials for which nonlinearity in the viscoelastic response vanishes for small strains. These observations suggest that despite their prevalence, the measures of linear viscoelasticity (e.g., storage and loss moduli) are inadequate for the general description of the viscoelastic nature of the fibrous materials. It was, however, found that linear viscoelastic nature of fibrous matrices for small amplitudes is restored when a pre-stretch is applied to the fibrous matrix along with oscillatory strains. Further, we also explored the influence of the structural properties of the fibrous matrices (fiber orientation, alignment and curvature) on their viscoelastic nature.

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.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Collagen network strengthening following cyclic tensile loading

The bulk mechanical properties of tissues are highly tuned to the physiological loads they experience and reflect the hierarchical structure and mechanical properties of their constituent parts. A thorough understanding of the processes involved in tissue adaptation is required to develop multi-scale computational models of tissue remodelling. While extracellular matrix (ECM) remodelling is partly due to the changing cellular metabolic activity, there may also be mechanically directed changes in ECM nano/microscale organization which lead to mechanical tuning. The thermal and enzymatic stability of collagen, which is the principal load-bearing biopolymer in vertebrates, have been shown to be enhanced by force suggesting that collagen has an active role in ECM mechanical properties. Here, we ask how changes in the mechanical properties of a collagen-based material are reflected by alterations in the micro/nanoscale collagen network following cyclic loading. Surprisingly, we observed significantly higher tensile stiffness and ultimate tensile strength, roughly analogous to the effect of work hardening, in the absence of network realignment and alterations to the fibril area fraction. The data suggest that mechanical loading induces stabilizing changes internal to the fibrils themselves or in the fibril–fibril interactions. If such a cell-independent strengthening effect is operational in vivo , then it would be an important consideration in any multiscale computational approach to ECM growth and remodelling.

Characteristics and Young's Modulus of Collagen Fibrils from Expanded Skin Using Anisotropic Controlled Rate Self-Inflating Tissue Expander

Mechanical properties of expanded skin tissue are different from normal skin, which is dependent mainly on the structural and functional integrity of dermal collagen fibrils. In the present study, mechanical properties and surface topography of both expanded and nonexpanded skin collagen fibrils were evaluated. Anisotropic controlled rate self-inflating tissue expanders were placed beneath the skin of sheep's forelimbs. The tissue expanders gradually increased in height and reached equilibrium in 2 weeks. They were left in situ for another 2 weeks before explantation. Expanded and normal skin samples were surgically harvested from the sheep (n = 5). Young's modulus and surface topography of collagen fibrils were measured using an atomic force microscope. A surface topographic scan showed organized hierarchical structural levels: collagen molecules, fibrils and fibers. No significant difference was detected for the D-banding pattern: 63.5 ± 2.6 nm (normal skin) and 63.7 ± 2.7 nm (expanded skin). Fibrils from expanded tissues consisted of loosely packed collagen fibrils and the width of the fibrils was significantly narrower compared to those from normal skin: 153.9 ± 25.3 and 106.7 ± 28.5 nm, respectively. Young's modulus of the collagen fibrils in the expanded and normal skin was not statistically significant: 46.5 ± 19.4 and 35.2 ± 27.0 MPa, respectively. In conclusion, the anisotropic controlled rate self-inflating tissue expander produced a loosely packed collagen network and the fibrils exhibited similar D-banding characteristics as the control group in a sheep model. However, the fibrils from the expanded skin were significantly narrower. The stiffness of the fibrils from the expanded skin was higher but it was not statistically different.

Measurement of Elastic Modulus of Collagen Type I Single Fiber

Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle/fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.

Characterization of irreversible physio-mechanical processes in stretched fetal membranes

We perform bulge tests on live fetal membrane (FM) tissues that simulate the mechanical conditions prior to contractions. Experimental results reveal an irreversible mechanical behavior that appears during loading and is significantly different than the mechanical behavior that appears during unloading or in subsequent loading cycles. The irreversible behavior results in a residual strain that does not recover upon unloading and remains the same for at least 1h after the FM is unloaded. Surprisingly, the irreversible behavior demonstrates a linear stress-strain relation. We introduce a new model for the mechanical response of collagen tissues, which accounts for the irreversible deformation and provides predictions in agreement with our experimental results. The basic assumption of the model is that the constitutive stress-strain relationship of individual elements that compose the collagen fibers has a plateau segment during which an irreversible transformation/deformation occurs. Fittings of calculated and measured stress-strain curves reveal a well-defined single-value property of collagenous tissues, which is related to the threshold strain εth for irreversible transformation. Further discussion of several physio-mechanical processes that can induce irreversible behavior indicate that the most probable process, which is in agreement with our results for εth, is a phase transformation of collagen molecules from an α-helix to a β-sheet structure. A phase transformation is a manifestation of a significant change in the molecular structure of the collagen tissues that can alter connections with surrounding molecules and may lead to critical biological changes, e.g., an initiation of labor.

STATEMENT OF SIGNIFICANCE

This study is driven by the hypothesis that pre-contraction mechanical stretch of the fetal membrane (FM) can lead to a change in the microstructure of the FM, which in turn induces a critical biological (hormonal) change that leads to the initiation of labor. We present mechanical characterizations of live FM tissues that reveal a significant irreversible process and a new model for the mechanical response of collagen tissues, which accounts for this process. Fittings of calculated and measured results reveal a well-defined single-value property of collagenous tissues, which is related to the threshold strain for irreversible transformation. Further discussion indicates that the irreversible deformation is induced by a phase transformation of collagen molecules that can lead to critical biological changes.

Effect of bimetallic iron:zinc nanoparticles on collagen stabilization

The ability of bimetallic iron:zinc nanoparticle to stabilize collagen for tissue engineering and leather tanning application has been studied.

Biomechanics of fibrous proteins of the extracellular matrix studied by Brillouin scattering

Brillouin light scattering (BLS) spectroscopy is a technique that is able to detect thermally excited phonons within a material. The speed of propagation of these phonons can be determined from the magnitude of the Brillouin frequency shift between incident and scattered light, thereby providing a measure of the mechanical properties of the material in the gigahertz range. The mechanical properties of the extracellular matrices of biological tissues and their constituent biopolymers are important for normal tissue function and disturbances in these properties are widely implicated in disease. BLS offers the prospect of measuring mechanical properties on a microscopic scale in living tissues, thereby providing insights into structure-function relationships under normal and pathological conditions. In this study, we investigated BLS in collagen and elastin-the fibrous proteins of the extracellular matrix (ECM). Measurements were made on type I collagen in rat tail tendon, type II collagen in articular cartilage and nuchal ligament elastin. The dependence of the BLS spectrum on fibre orientation was investigated in a backscattering geometry using a reflective substrate. Two peaks, a bulk mode arising from phonon propagation along a quasi-radial direction to the fibre axis and a mode parallel to the surface, depending on sample orientation relative to the fibre axis, could be distinguished. The latter peak was fitted to a model of wave propagation through a hexagonally symmetric elastic solid, and the five components of the elasticity tensor were combined to give axial and transverse Young's, shear and bulk moduli of the fibres. These were 10.2, 8.3, 3.2 and 10.9 GPa, and 6.1, 5.3, 1.9 and 8 GPa for dehydrated type I collagen and elastin, respectively. The former values are close to those previously reported. A microfocused BLS approach was also applied providing selection of single fibres. The moduli of collagen and elastin are much higher than those measured at lower frequency using macroscopic strains, and the difference between them is much less. We therefore believe, like previous investigators, that molecular-scale viscoelastic effects are responsible for the frequency dependence of the fibre biomechanics. Combining BLS with larger-scale mechanical testing methods therefore should, in the future, provide a means of following the evolution of mechanical properties in the formation of the complex structures found in the ECM.

Bio-fabrication and physiological self-release of tissue equivalents using smart peptide amphiphile templates

In this study we applied a smart biomaterial formed from a self-assembling, multi-functional synthetic peptide amphiphile (PA) to coat substrates with various surface chemistries. The combination of PA coating and alignment-inducing functionalised substrates provided a template to instruct human corneal stromal fibroblasts to adhere, become aligned and then bio-fabricate a highly-ordered, multi-layered, three-dimensional tissue by depositing an aligned, native-like extracellular matrix. The newly-formed corneal tissue equivalent was subsequently able to eliminate the adhesive properties of the template and govern its own complete release via the action of endogenous proteases. Tissues recovered through this method were structurally stable, easily handled, and carrier-free. Furthermore, topographical and mechanical analysis by atomic force microscopy showed that tissue equivalents formed on the alignment-inducing PA template had highly-ordered, compact collagen deposition, with a two-fold higher elastic modulus compared to the less compact tissues produced on the non-alignment template, the PA-coated glass. We suggest that this technology represents a new paradigm in tissue engineering and regenerative medicine, whereby all processes for the bio-fabrication and subsequent self-release of natural, bio-prosthetic human tissues depend solely on simple template-tissue feedback interactions.

Crack Propagation Versus Fiber Alignment in Collagen Gels: Experiments and Multiscale Simulation

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fisher's exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

Investigation of mechanisms of viscoelastic behavior of collagen molecule

Unique mechanical properties of collagen molecule make it one of the most important and abundant proteins in animals. Many tissues such as connective tissues rely on these properties to function properly. In the past decade, molecular dynamics (MD) simulations have been used extensively to study the mechanical behavior of molecules. For collagen, MD simulations were primarily used to determine its elastic properties. In this study, constant force steered MD simulations were used to perform creep tests on collagen molecule segments. The mechanical behavior of the segments, with lengths of approximately 20 (1X), 38 (2X), 74 (4X), and 290 nm (16X), was characterized using a quasi-linear model to describe the observed viscoelastic responses. To investigate the mechanisms of the viscoelastic behavior, hydrogen bonds (H-bonds) rupture/formation time history of the segments were analyzed and it was shown that the formation growth rate of H-bonds in the system is correlated with the creep growth rate of the segment (β=2.41βH). In addition, a linear relationship between H-bonds formation growth rate and the length of the segment was quantified. Based on these findings, a general viscoelastic model was developed and verified here, using the smallest segment as a building block, the viscoelastic properties of larger segments could be predicted. In addition, the effect of temperature control methods on the mechanical properties were studied, and it was shown that application of Langevin Dynamics had adverse effect on these properties while the Lowe-Anderson method was shown to be more appropriate for this application. This study provides information that is essential for multi-scale modeling of collagen fibrils using a bottom-up approach.

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

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

Multi-scale mechanical characterization of highly swollen photo-activated collagen hydrogels

Biological hydrogels have been increasingly sought after as wound dressings or scaffolds for regenerative medicine, owing to their inherent biofunctionality in biological environments. Especially in moist wound healing, the ideal material should absorb large amounts of wound exudate while remaining mechanically competent in situ. Despite their large hydration, however, current biological hydrogels still leave much to be desired in terms of mechanical properties in physiological conditions. To address this challenge, a multi-scale approach is presented for the synthetic design of cyto-compatible collagen hydrogels with tunable mechanical properties (from the nano- up to the macro-scale), uniquely high swelling ratios and retained (more than 70%) triple helical features. Type I collagen was covalently functionalized with three different monomers, i.e. 4-vinylbenzyl chloride, glycidyl methacrylate and methacrylic anhydride, respectively. Backbone rigidity, hydrogen-bonding capability and degree of functionalization (F: 16 ± 12–91 ± 7 mol%) of introduced moieties governed the structure–property relationships in resulting collagen networks, so that the swelling ratio (SR: 707 ± 51–1996 ± 182 wt%), bulk compressive modulus (E_c: 30 ± 7–168 ± 40 kPa) and atomic force microscopy elastic modulus (E_AFM: 16 ± 2–387 ± 66 kPa) were readily adjusted. Because of their remarkably high swelling and mechanical properties, these tunable collagen hydrogels may be further exploited for the design of advanced dressings for chronic wound care.

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

Background

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

Materials and Methods

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

Results and Conclusions

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

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.

Aggrecan nanoscale solid-fluid interactions are a primary determinant of cartilage dynamic mechanical properties

Poroelastic interactions between interstitial fluid and the extracellular matrix of connective tissues are critical to biological and pathophysiological functions involving solute transport, energy dissipation, self-stiffening and lubrication. However, the molecular origins of poroelasticity at the nanoscale are largely unknown. Here, the broad-spectrum dynamic nanomechanical behavior of cartilage aggrecan monolayer is revealed for the first time, including the equilibrium and instantaneous moduli and the peak in the phase angle of the complex modulus. By performing a length scale study and comparing the experimental results to theoretical predictions, we confirm that the mechanism underlying the observed dynamic nanomechanics is due to solid-fluid interactions (poroelasticity) at the molecular scale. Utilizing finite element modeling, the molecular-scale hydraulic permeability of the aggrecan assembly was quantified (kaggrecan = (4.8 ± 2.8) × 10(-15) m(4)/N·s) and found to be similar to the nanoscale hydraulic permeability of intact normal cartilage tissue but much lower than that of early diseased tissue. The mechanisms underlying aggrecan poroelasticity were further investigated by altering electrostatic interactions between the molecule's constituent glycosaminoglycan chains: electrostatic interactions dominated steric interactions in governing molecular behavior. While the hydraulic permeability of aggrecan layers does not change across species and age, aggrecan from adult human cartilage is stiffer than the aggrecan from newborn human tissue.

Efficient and optimized identification of generalized Maxwell viscoelastic relaxation spectra

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here an efficient algorithm that enables rapid identification of viscoelastic relaxation spectra. The algorithm was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen, revealing an extensive distribution of viscoelastic time constants.

Parametric imaging of viscoelasticity using optical coherence elastography

We demonstrate imaging of soft tissue viscoelasticity using optical coherence elastography. Viscoelastic creep deformation is induced in tissue using step-like compressive loading and the resulting time-varying deformation is measured using phase-sensitive optical coherence tomography. From a series of co-located B-scans, we estimate the local strain rate as a function of time, and parameterize it using a four-parameter Kelvin-Voigt model of viscoelastic creep. The estimated viscoelastic strain and time constant are used to visualize viscoelastic creep in 2D, dual-parameter viscoelastograms. We demonstrate our technique on six silicone tissue-simulating phantoms spanning a range of viscoelastic parameters. As an example in soft tissue, we report viscoelastic contrast between muscle and connective tissue in fresh, ex vivo rat gastrocnemius muscle and mouse abdominal transection. Imaging viscoelastic creep deformation has the potential to provide complementary contrast to existing imaging modalities, and may provide greater insight into disease pathology.

Deconstructing the Anterior Cruciate Ligament: What We Know and Do Not Know About Function, Material Properties, and Injury Mechanics

Anterior cruciate ligament (ACL) injury is a common and potentially catastrophic knee joint injury, afflicting a large number of males and particularly females annually. Apart from the obvious acute injury events, it also presents with significant long-term morbidities, in which osteoarthritis (OA) is a frequent and debilitative outcome. With these facts in mind, a vast amount of research has been undertaken over the past five decades geared toward characterizing the structural and mechanical behaviors of the native ACL tissue under various external load applications. While these efforts have afforded important insights, both in terms of understanding treating and rehabilitating ACL injuries; injury rates, their well-established sex-based disparity, and long-term sequelae have endured. In reviewing the expanse of literature conducted to date in this area, this paper identifies important knowledge gaps that contribute directly to this long-standing clinical dilemma. In particular, the following limitations remain. First, minimal data exist that accurately describe native ACL mechanics under the extreme loading rates synonymous with actual injury. Second, current ACL mechanical data are typically derived from isolated and oversimplified strain estimates that fail to adequately capture the true 3D mechanical response of this anatomically complex structure. Third, graft tissues commonly chosen to reconstruct the ruptured ACL are mechanically suboptimal, being overdesigned for stiffness compared to the native tissue. The net result is an increased risk of rerupture and a modified and potentially hazardous habitual joint contact profile. These major limitations appear to warrant explicit research attention moving forward in order to successfully maintain/restore optimal knee joint function and long-term life quality in a large number of otherwise healthy individuals.

Plumbagin caged silver nanoparticle stabilized collagen scaffold for wound dressing

Wound dressing material based on nano-biotechnological intervention by caging plumbagin on silver nanoparticle (PCSN) as a multi-site cross-linking agent of collagen scaffolds with potent anti-microbial and wound healing activity.

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.

Nanomechanical assessment of human and murine collagen fibrils via atomic force microscopy cantilever-based nanoindentation

The nanomechanical assessment of collagen fibrils via atomic force microscopy (AFM) is of increasing interest within the biomedical research community. In contrast to conventional nanoindentation there exists no common standard for conducting experiments and analysis of data. Currently used analysis approaches vary between studies and validation of quantitative results is usually not performed, which makes comparison of data from different studies difficult. Also there are no recommendations with regards to the maximum indentation depth that should not be exceeded to avoid substrate effects. Here we present a methodology and analysis approach for AFM cantilever-based nanoindentation experiments that allows efficient use of captured data and relying on a reference sample for determination of tip shape. Further we show experimental evidence that maximum indentation depth on collagen fibrils should be lower than 10-15% of the height of the fibril to avoid substrate effects and we show comparisons between our and other approaches used in previous works. While our analysis approach yields similar values for indentation modulus compared to the Oliver-Pharr method we found that Hertzian analysis yielded significantly lower values. Applying our approach we successfully and efficiently indented collagen fibrils from human bronchi, which were about 30 nm in size, considerably smaller compared to collagen fibrils obtained from murine tail-tendon. In addition, derived mechanical parameters of collagen fibrils are in agreement with data previously published. To establish a quantitative validation we compared indentation results from conventional and AFM cantilever-based nanoindentation on polymeric samples with known mechanical properties. Importantly we can show that our approach yields similar results when compared to conventional nanoindentation on polymer samples. Introducing an approach that is reliable, efficient and taking into account the AFM tip shape, we anticipate that the present work may act as a guideline for conducting AFM cantilever-based nanoindentation of collagen fibrils. This may aid understanding of collagen-related diseases such as asthma, lung fibrosis or bone disease with potential alterations of collagen fibril mechanics.

Heterogeneous micromechanical properties of the extracellular matrix in healthy and infarcted hearts

Infarcted hearts are macroscopically stiffer than healthy organs. Nevertheless, although cell behavior is mediated by the physical features of the cell niche, the intrinsic micromechanical properties of healthy and infarcted heart extracellular matrix (ECM) remain poorly characterized. Using atomic force microscopy, we studied ECM micromechanics of different histological regions of the left ventricle wall of healthy and infarcted mice. Hearts excised from healthy (n=8) and infarcted mice (n=8) were decellularized with sodium dodecyl sulfate and cut into 12 μm thick slices. Healthy ventricular ECM revealed marked mechanical heterogeneity across histological regions of the ventricular wall with the effective Young's modulus ranging from 30.2 ± 2.8 to 74.5 ± 8.7 kPa in collagen- and elastin-rich regions of the myocardium, respectively. Infarcted ECM showed a predominant collagen composition and was 3-fold stiffer than collagen-rich regions of the healthy myocardium. ECM of both healthy and infarcted hearts exhibited a solid-like viscoelastic behavior that conforms to two power-law rheology. Knowledge of intrinsic micromechanical properties of the ECM at the length scale at which cells sense their environment will provide further insight into the cell-scaffold interplay in healthy and infarcted hearts.

Interfibrillar shear stress is the loading mechanism of collagen fibrils in tendon

Despite the critical role tendons play in transmitting loads throughout the musculoskeletal system, little is known about the microstructural mechanisms underlying their mechanical function. Of particular interest is whether collagen fibrils in tendon fascicles bear load independently or if load is transferred between fibrils through interfibrillar shear forces. We conducted multiscale experimental testing and developed a microstructural shear lag model to explicitly test whether interfibrillar shear load transfer is indeed the fibrillar loading mechanism in tendon. Experimental correlations between fascicle macroscale mechanics and microscale interfibrillar sliding suggest that fibrils are discontinuous and share load. Moreover, for the first time, we demonstrate that a shear lag model can replicate the fascicle macroscale mechanics as well as predict the microscale fibrillar deformations. Since interfibrillar shear stress is the fundamental loading mechanism assumed in the model, this result provides strong evidence that load is transferred between fibrils in tendon and possibly other aligned collagenous tissues. Conclusively establishing this fibrillar loading mechanism and identifying the involved structural components should help develop repair strategies for tissue degeneration and guide the design of tissue engineered replacements.

The nano-scale mechanical properties of the extracellular matrix regulate dermal fibroblast function

Changes in the mechanical properties of dermis occur during skin aging or tissue remodeling and affect the activity of resident fibroblasts. With the aim to establish elastic culture substrates that reproduce the variable softness of dermis, we determined Young's elastic modulus E of human dermis at the cell perception level using atomic force microscopy. The E of dermis ranged from 0.1 to 10 kPa, varied depending on body area and dermal layer, and tended to increase with age in 26-55-year-old donors. The activation state of human dermal fibroblasts cultured on "skin-soft" E (5 kPa) silicone culture substrates was compared with stiff plastic culture (GPa), collagen gel cultures (0.1-9 kPa), and fresh human dermal tissue. Fibroblasts cultured on skin-soft silicones displayed low mRNA levels of fibrosis-associated genes and increased expression of the matrix metalloproteinases (MMPs) MMP-1 and MMP-3 as compared with collagen gel and plastic cultures. The activation profile exhibited by fibroblasts on "skin-soft" silicone culture substrates was most comparable with that of human dermis than any other tested culture condition. Hence, providing biomimetic mechanical conditions generates fibroblasts that are more suitable to investigate physiologically relevant cell processes than fibroblasts spontaneously activated by stiff conventional culture surfaces.

Nanointerfacial strength between non-collagenous protein and collagen fibrils in antler bone

Antler bone displays considerable toughness through the use of a complex nanofibrous structure of mineralized collagen fibrils (MCFs) bound together by non-collagenous proteins (NCPs). While the NCP regions represent a small volume fraction relative to the MCFs, significant surface area is evolved upon failure of the nanointerfaces formed at NCP-collagen fibril boundaries. The mechanical properties of nanointerfaces between the MCFs are investigated directly in this work using an in situ atomic force microscopy technique to pull out individual fibrils from the NCP. Results show that the NCP-fibril interfaces in antler bone are weak, which highlights the propensity for interface failure at the nanoscale in antler bone and extensive fibril pullout observed at antler fracture surfaces. The adhesion between fibrils and NCP is additionally suggested as being rate dependent, with increasing interfacial strength and fracture energy observed when pullout velocity decreases.

Modelling the mechanics of partially mineralized collagen fibrils, fibres and tissue

Progressive stiffening of collagen tissue by bioapatite mineral is important physiologically, but the details of this stiffening are uncertain. Unresolved questions about the details of the accommodation of bioapatite within and upon collagen's hierarchical structure have posed a central hurdle, but recent microscopy data resolve several major questions. These data suggest how collagen accommodates bioapatite at the lowest relevant hierarchical level (collagen fibrils), and suggest several possibilities for the progressive accommodation of bioapatite at higher hierarchical length scales (fibres and tissue). We developed approximations for the stiffening of collagen across spatial hierarchies based upon these data, and connected models across hierarchies levels to estimate mineralization-dependent tissue-level mechanics. In the five possible sequences of mineralization studied, percolation of the bioapatite phase proved to be an important determinant of the degree of stiffening by bioapatite. The models were applied to study one important instance of partially mineralized tissue, which occurs at the attachment of tendon to bone. All sequences of mineralization considered reproduced experimental observations of a region of tissue between tendon and bone that is more compliant than either tendon or bone, but the size and nature of this region depended strongly upon the sequence of mineralization. These models and observations have implications for engineered tissue scaffolds at the attachment of tendon to bone, bone development and graded biomimetic attachment of dissimilar hierarchical materials in general.

Biaxial deformation of collagen and elastin fibers in coronary adventitia

The microstructural deformation-mechanical loading relation of the blood vessel wall is essential for understanding the overall mechanical behavior of vascular tissue in health and disease. We employed simultaneous mechanical loading-imaging to quantify in situ deformation of individual collagen and elastin fibers on unstained fresh porcine coronary adventitia under a combination of vessel inflation and axial extension loading. Specifically, the specimens were imaged under biaxial loads to study microscopic deformation-loading behavior of fibers in conjunction with morphometric measurements at the zero-stress state. Collagen fibers largely orientate in the longitudinal direction, while elastin fibers have major orientation parallel to collagen, but with additional orientation angles in each sublayer of the adventitia. With an increase of biaxial load, collagen fibers were uniformly stretched to the loading direction, while elastin fibers gradually formed a network in sublayers, which strongly depended on the initial arrangement. The waviness of collagen decreased more rapidly at a circumferential stretch ratio of λθ = 1.0 than at λθ = 1.5, while most collagen became straightened at λθ = 1.8. These microscopic deformations imply that the longitudinally stiffer adventitia is a direct result of initial fiber alignment, and the overall mechanical behavior of the tissue is highly dependent on the corresponding microscopic deformation of fibers. The microstructural deformation-loading relation will serve as a foundation for micromechanical models of the vessel wall.

The emergence of an unusual stiffness profile in hierarchical biological tissues

Biological tissues usually exhibit complex multiscale structural architectures. In many of these, and particularly in mineralized tissues, the basic building block is a staggered array-a composite material made of soft matrix and stiff reinforcing elements. Here we study the stiffness of non-overlapping staggered arrays, a case that has not previously been considered in the literature, and introduce closed-form analytical expressions for its Young's modulus. These expressions are then used to estimate the stiffness of natural staggered biocomposites such as low-mineralized collagen fibril and mineralized tendon. We then consider a two-scale composite scheme for evaluating the modulus of a specific hierarchical structure, the compact bone tissue, which is made of mineralized collagen fibrils with weakly overlapping staggered architecture. It is found that small variations in the staggered structure induce significant differences in the macroscopic stiffness, and, in particular, provide a possible explanation for the as yet unexplained stiffening effects observed in medium-mineralized tissues.