A Three-Dimensional Computational Model of Collagen Network Mechanics

Extracellular matrix (ECM) strongly influences cellular behaviors, including cell proliferation, adhesion, and particularly migration. In cancer, the rigidity of the stromal collagen environment is thought to control tumor aggressiveness, and collagen alignment has been linked to tumor cell invasion. While the mechanical properties of collagen at both the single fiber scale and the bulk gel scale are quite well studied, how the fiber network responds to local stress or deformation, both structurally and mechanically, is poorly understood. This intermediate scale knowledge is important to understanding cell-ECM interactions and is the focus of this study. We have developed a three-dimensional elastic collagen fiber network model (bead-and-spring model) and studied fiber network behaviors for various biophysical conditions: collagen density, crosslinker strength, crosslinker density, and fiber orientation (random vs. prealigned). We found the best-fit crosslinker parameter values using shear simulation tests in a small strain region. Using this calibrated collagen model, we simulated both shear and tensile tests in a large linear strain region for different network geometry conditions. The results suggest that network geometry is a key determinant of the mechanical properties of the fiber network. We further demonstrated how the fiber network structure and mechanics evolves with a local formation, mimicking the effect of pulling by a pseudopod during cell migration. Our computational fiber network model is a step toward a full biomechanical model of cellular behaviors in various ECM conditions.     

Long-Range Force Transmission in Fibrous Matrices Enabled by Tension-Driven Alignment of Fibers

Cells can sense and respond to mechanical signals over relatively long distances across fibrous extracellular matrices. Recently proposed models suggest that long-range force transmission can be attributed to the nonlinear elasticity or fibrous nature of collagen matrices, yet the mechanism whereby fibers align remains unknown. Moreover, cell shape and anisotropy of cellular contraction are not considered in existing models, although recent experiments have shown that they play crucial roles. Here, we explore all of the key factors that influence long-range force transmission in cell-populated collagen matrices: alignment of collagen fibers, responses to applied force, strain stiffening properties of the aligned fibers, aspect ratios of the cells, and the polarization of cellular contraction. A constitutive law accounting for mechanically driven collagen fiber reorientation is proposed. We systematically investigate the range of collagen-fiber alignment using both finite-element simulations and analytical calculations. Our results show that tension-driven collagen-fiber alignment plays a crucial role in force transmission. Small critical stretch for fiber alignment, large fiber stiffness and fiber strain-hardening behavior enable long-range interaction. Furthermore, the range of collagen-fiber alignment for elliptical cells with polarized contraction is much larger than that for spherical cells with diagonal contraction. A phase diagram showing the range of force transmission as a function of cell shape and polarization and matrix properties is presented. Our results are in good agreement with recent experiments, and highlight the factors that influence long-range force transmission, in particular tension-driven alignment of fibers. Our work has important relevance to biological processes including development, cancer metastasis, and wound healing, suggesting conditions whereby cells communicate over long distances.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Relationship between cell stiffness and stress fiber amount,assessed by simultaneous atomic force microscopy and live-cell fluorescence imaging

Actomyosin stress fibers, one of the main components of the cell’s cytoskeleton, provide mechanical stability to adherent cells by applying and transmitting tensile forces onto the extracellular matrix (ECM) at the sites of cell–ECM adhesion. While it is widely accepted that changes in spatial and temporal distribution of stress fibers affect the cell’s mechanical properties, there is no quantitative knowledge on how stress fiber amount and organization directly modulate cell stiffness. We address this key open question by combining atomic force microscopy with simultaneous fluorescence imaging of living cells, and combine for the first time reliable quantitative parameters obtained from both techniques. We show that the amount of myosin and (to a lesser extent) actin assembled in stress fibers directly modulates cell stiffness in adherent mouse fibroblasts (NIH3T3). In addition, the spatial distribution of stress fibers has a second-order modulatory effect. In particular, the presence of either fibers located in the cell periphery, aligned fibers or thicker fibers gives rise to reinforced cell stiffness. Our results provide basic and significant information that will help design optimal protocols to regulate the mechanical properties of adherent cells via pharmacological interventions that alter stress fiber assembly or via micropatterning techniques that restrict stress fiber spatial organization.     

Effects of oxidative stress-induced changes in the actin cytoskeletal structure on myoblast damage under compressive stress: confocal-based cell-specific finite element analysis

Muscle cells are frequently subjected to both mechanical and oxidative stresses in various physiological and pathological situations. To explore the mechanical mechanism of muscle cell damage under loading and oxidative stresses, we experimentally studied the effects of extrinsic hydrogen peroxides on the actin cytoskeletal structure in C2C12 myoblasts and presented a finite element (FE) analysis of how such changes in the actin cytoskeletal structure affected a myoblast’s capability to resist damage under compression. A confocal-based cell-specific FE model was built to parametrically study the effects of stress fiber density, fiber cross-sectional area, fiber tensile prestrain, as well as the elastic moduli of the stress fibers, actin cortex, nucleus and cytoplasm. The results showed that a decrease in the elastic moduli of both the stress fibers and actin cortex could increase the average tensile strain on the actin cortex–membrane structure and reduce the apparent cell elastic modulus. Assuming the cell would die when a certain percentage of membrane elements were strained beyond a threshold, a lower elastic modulus of actin cytoskeleton would compromise the compressive resistance of a myoblast and lead to cell death more readily. This model was used with a Weibull distribution function to successfully describe the extent of myoblasts damaged in a monolayer under compression.     

A model of stress and strain in the interosseous ligament of the forearm based on fiber network theory

Fiber network theory was developed to describe cloth, a thin material with strength in the fiber directions. The interosseous ligament (IOL) of the forearm is a broad, thin ligament with highly aligned fibers. The objectives of this study were to develop a model of the stress and strain distributions in the IOL, based on fiber network theory, to compare the strains from the model with the experimentally measured strains, and to evaluate the force distribution across the ligament fibers from the model. The geometries of the radius, ulna, and IOL were reconstructed from CT scans. Position and orientation of IOL insertion sites and force in the IOL were measured during a forearm compression experiment in pronation, neutral rotation, and supination. An optical image-based technique was used to directly measure strain in two regions of the IOL in neutral rotation. For the network model, the IOL was represented as a parametric ruled three-dimensional surface, with rulings along local fiber directions. Fiber strains were calculated from the deformation field, and fiber stresses were calculated from the strains using average IOL tensile properties from a previous study. The in situ strain in the IOL was assumed uniform and was calculated so that the net force predicted by the network model in neutral rotation matched the experimental result. The net force in the IOL was comparable to experimental results in supination and pronation. The model predicted higher stress and strain in fibers near the elbow in neutral rotation, and higher stresses in fibers near the wrist in supination. Strains in neutral forearm rotation followed the same trends as those measured experimentally. In this study, a model of stress and strain in the IOL utilizing fiber network theory was successfully implemented. The model illustrates variations in the stress and strain distribution in the IOL. This model can be used to show surgeons how different fibers are taut in different forearm rotation positions-this information is important for understanding the biomechanical role of the IOL and for planning an IOL reconstruction.     

Influence of domain orientation on the mechanical properties of regenerated cellulose fibers

The determination of the crystal orientation of regenerated cellulose fibers produced under different drawing regimes is presented. Orientation is determined by using wide-angle X-ray diffraction from a synchrotron source and by measuring the azimuthal width of equatorial reflections. The orientation parameter theta is then determined to compare fiber samples. By using a 500 nm beam size, clear differences between the crystal orientations of the skin and the core of the fibers are reported for a range of differently processed fibers for the first time. These results are shown to have implications for the mechanical properties of regenerated cellulose fibers. By applying tensile deformation to fiber bundles it is shown that the most misoriented samples undergo rapid decreases in the orientation parameter, which is an indication of crystal reorientation. However, the more highly oriented fibers undergo little reorientation. An average shear modulus for these fibers is determined by placing the data on a master curve and fitting with a model equation. By using another model for the fibers of low orientation and the shear modulus from the master curve analysis, it is shown that the deformation of less oriented fibers is dominated by shear between crystals, whereas the more oriented filaments are likely to undergo more significant chain deformation. By using a new model for fibers of low orientation, a parameter ksigma is introduced that gives the proportion of the fiber stress that is due to crystal shear. Systematic differences between this parameter for fibers of increasing initial orientation are reported. Moreover it is shown that the fibers of initially lower average orientation are governed by uniform strain, in agreement with the new model, whereas more highly oriented fibers deform under uniform stress. Furthermore, the model that we propose for misoriented domains and the use of a new factor dictating the proportion of shear stress may have general applications in materials engineering.     

Stretch-Induced Stress Fiber Remodeling and the Activations of JNK and ERK Depend on Mechanical Strain Rate,but Not FAK

Background

Cells within tissues are subjected to mechanical forces caused by extracellular matrix deformation. Cells sense and dynamically respond to stretching of the matrix by reorienting their actin stress fibers and by activating intracellular signaling proteins, including focal adhesion kinase (FAK) and the mitogen-activated proteins kinases (MAPKs). Theoretical analyses predict that stress fibers can relax perturbations in tension depending on the rate of matrix strain. Thus, we hypothesized stress fiber organization and MAPK activities are altered to an extent dependent on stretch frequency.

Principal Findings

Bovine aortic endothelial cells and human osteosarcoma cells expressing GFP-actin were cultured on elastic membranes and subjected to various patterns of stretch. Cyclic stretching resulted in strain rate-dependent increases in stress fiber alignment, cell retraction, and the phosphorylation of the MAPKs JNK, ERK and p38. Transient step changes in strain rate caused proportional transient changes in the levels of JNK and ERK phosphorylations without affecting stress fiber organization. Disrupting stress fiber contractile function with cytochalasin D or Y27632 decreased the levels of JNK and ERK phosphorylation. Previous studies indicate that FAK is required for stretch-induced cell alignment and MAPK activations. However, cyclic uniaxial stretching induced stress fiber alignment and the phosphorylation of JNK, ERK and p38 to comparable levels in FAK-null and FAK-expressing mouse embryonic fibroblasts.

Conclusions

These results indicate that cyclic stretch-induced stress fiber alignment, cell retraction, and MAPK activations occur as a consequence of perturbations in fiber strain. These findings thus shed new light into the roles of stress fiber relaxation and reorganization in maintenance of tensional homeostasis in a dynamic mechanical environment.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Full field strain measurements of collagenous tissue by tracking fiber alignment through vector correlation

Full field strain measurements of biological tissue during loading are often limited to the quantification of fiduciary marker displacements on the tissue surface. These marker measurements can lack the necessary spatial resolution to characterize non-uniform deformation and may not represent the deformation of the load-bearing collagen microstructure. To overcome these potential limitations, a method was developed to track the deformation of the collagen fiber microstructure in ligament tissue. Using quantitative polarized light imaging, fiber alignment maps incorporating both direction and alignment strength at each pixel were generated during facet capsular ligament loading. A grid of virtual markers was superimposed over the tissue in the alignment maps, and the maximization of a vector correlation calculation between fiber alignment maps was used to track marker displacement. Tracking error was quantified through comparisons to the displacements of excised ligament tissue (n=3); separate studies applied uniaxial tension to isolated facet capsular ligament tissue (n=4) to evaluate tracking capabilities during large tissue deformations. The average difference between virtual marker and tissue displacements was 0.07±0.06 pixels. This error in marker location produced principal strain measurements of 1.2±1.6% when markers were spaced 4 pixels apart. During tensile tissue loading, substantial inhomogeneity was detected in the strain field using vector correlation tracking, and the location of maximum strain differed from that produced by standard tracking techniques using coarser meshes. These findings provide a method to directly measure fiber network strains using quantitative fiber alignment data, enabling a better understanding of structure–function relationships in tissues at different length scales.     

Foam-like compression behavior of fibrin networks

The rheological properties of fibrin networks have been of long-standing interest. As such there is a wealth of studies of their shear and tensile responses, but their compressive behavior remains unexplored. Here, by characterization of the network structure with synchronous measurement of the fibrin storage and loss moduli at increasing degrees of compression, we show that the compressive behavior of fibrin networks is similar to that of cellular solids. A nonlinear stress–strain response of fibrin consists of three regimes: (1) an initial linear regime, in which most fibers are straight, (2) a plateau regime, in which more and more fibers buckle and collapse, and (3) a markedly nonlinear regime, in which network densification occurs by bending of buckled fibers and inter-fiber contacts. Importantly, the spatially non-uniform network deformation included formation of a moving “compression front” along the axis of strain, which segregated the fibrin network into compartments with different fiber densities and structure. The Young’s modulus of the linear phase depends quadratically on the fibrin volume fraction while that in the densified phase depends cubically on it. The viscoelastic plateau regime corresponds to a mixture of these two phases in which the fractions of the two phases change during compression. We model this regime using a continuum theory of phase transitions and analytically predict the storage and loss moduli which are in good agreement with the experimental data. Our work shows that fibrin networks are a member of a broad class of natural cellular materials which includes cancellous bone, wood and cork.     

Contribution of the extracellular matrix to the viscoelastic behavior of the urinary bladder wall

We previously reported that when the stress relaxation response of urinary bladder wall (UBW) tissue was analyzed using a single continuous reduced relaxation function (RRF), we observed non-uniformly distributed, time-dependent residuals (Ann Biomed Eng 32(10):1409-1419, 2004). We concluded that the single relaxation spectrum was inadequate and that a new viscoelastic model for bladder wall was necessary. In the present study, we report a new approach composed of independent RRFs for smooth muscle and the extracellular matrix components (ECM), connected through a stress-dependent recruitment function. In order to determine the RRF for the ECM component, biaxial stress relaxation experiments were first performed on decellularized extracellular matrix network of the bladder obtained from normal and spinal cord injured rats. While it was assumed that smooth muscle followed a single spectrum RRF, modeling the UBW ECM required a dual-Gaussian spectrum. Experimental results revealed that the ECM stress relaxation response was insensitive to the initial stress level. Thus, the average ECM RRF parameters were determined by fitting the average stress relaxation data. The resulting stress relaxation behavior of whole bladder tissue was modeled by combining the ECM RRF with the RRF for the smooth muscle component using an exponential recruitment function representing the recruitment of collagen fibers at higher stress levels. In summary, the present study demonstrated, for the first time, that stress relaxation response of bladder tissue can be better modeled when divided into the contributions of the extracellular matrix and smooth muscle components. This modeling approach is suitable for prediction of mechanical behaviors of the urinary bladder and other organs that exhibit rapid tissue remodeling (i.e., smooth muscle hypertrophy and altered ECM synthesis) under various pathological conditions.     

Tissue engineering science: Consequences of cell traction force

Blood and tissue cells mechanically interact with soft tissues and tissue-equivalent reconstituted collagen gels in a variety of situations relevant to biomedicine and biotechnology. A key phenomenon in these interactions is the exertion of traction force by cells on local collagen fibers which typically constitute the solid network of these tissues and gels and impart gross mechanical integrity. Two important consequences of cells exerting traction on such collagen networks are first, when the cells co-ordinate their traction, resulting in cell migration, and second, when their traction is sufficient to deform the network. Such cell-collagen network interactions are coupled in a number of ways. Network deformation, for example, can result in net alignment of collagen fibers, eliciting contact guidance, wherein cells move with bidirectional bias along an axis of fiber alignment, potentially leading to a nonuniform cell distribution. This may govern cell accumulation in wounds and be exploited to control cell infiltration of bioartificial tissues and organs. Another consequence of cell traction is the resultant stress and strain in the network which modulate cell protein and DNA synthesis and differentiation. We summarize, here, relevant mathematical theories which we have used to describe the inherent coupling of cell dynamics and tissue mechanics in cell-populated collagen gels via traction. The development of appropriate models based on these theories, in an effort to understand how events in wound healing govern the rate and extent of wound contraction, and to measure cell traction forces in vitro, are described. Relevant observations and speculation from cell biology and medicine that motivate or serve to critique the assumptions made in the theories and models are also summarized.Abbreviations ECM Extracellular Matrix - FPCL Fibroblast-Populated Collagen Lattice - FPCM Fibroblast-Populated Collagen Microsphere     

On the computation of stress in affine versus nonaffine fibril kinematics within planar collagen network models

Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment.     

A multi-modular tensegrity model of an actin stress fiber

Stress fibers are contractile bundles in the cytoskeleton that stabilize cell structure by exerting traction forces on the extracellular matrix. Individual stress fibers are molecular bundles composed of parallel actin and myosin filaments linked by various actin-binding proteins, which are organized end-on-end in a sarcomere-like pattern within an elongated three-dimensional network. While measurements of single stress fibers in living cells show that they behave like tensed viscoelastic fibers, precisely how this mechanical behavior arises from this complex supramolecular arrangement of protein components remains unclear. Here we show that computationally modeling a stress fiber as a multi-modular tensegrity network can predict several key behaviors of stress fibers measured in living cells, including viscoelastic retraction, fiber splaying after severing, non-uniform contraction, and elliptical strain of a puncture wound within the fiber. The tensegrity model can also explain how they simultaneously experience passive tension and generate active contraction forces; in contrast, a tensed cable net model predicts some, but not all, of these properties. Thus, tensegrity models may provide a useful link between molecular and cellular scale mechanical behaviors and represent a new handle on multi-scale modeling of living materials.     

Interaction of stress and growth in a fibrous tissue

The influence of stress on the growth and remodeling of a soft biological tissue is considered. For this purpose, the soft tissue is idealized as a fiber network. The stress-free lengths of the fibers composing the network are not fixed as in an inert elastic solid, but are assumed to evolve as a result of growth and stress adaptation. Similarly, the topology of the fiber network may also evolve under the application of stress. A set of constitutive equations are proposed which relate the tissue stress to the deformation of the tissue as well as to its growth and microstructure. It is shown that distinctly different growth patterns which may arise during initial growth or wound healing can be modeled by the proposed mathematical analysis.     

Micromechanical models of helical superstructures in ligament and tendon fibers predict large Poisson's ratios

Experimental measurements of the Poisson's ratio in tendon and ligament tissue greatly exceed the isotropic limit of 0.5. This is indicative of volume loss during tensile loading. The microstructural origin of the large Poisson's ratios is unknown. It was hypothesized that a helical organization of fibrils within a fiber would result in a large Poisson's ratio in ligaments and tendons, and that this helical organization would be compatible with the crimped nature of these tissues, thus modeling their classic nonlinear stress–strain behavior. Micromechanical finite element models were constructed to represent crimped fibers with a super-helical organization, composed of fibrils embedded within a matrix material. A homogenization procedure was performed to determine both the effective Poisson's ratio and the Poisson function. The results showed that helical fibril organization within a crimped fiber was capable of simultaneously predicting large Poisson's ratios and the nonlinear stress–strain behavior seen experimentally. Parametric studies revealed that the predicted Poisson's ratio was strongly dependent on the helical pitch, crimp angle and the material coefficients. The results indicated that, for physiologically relevant parameters, the models were capable of predicting the large Poisson's ratios seen experimentally. It was concluded that helical organization within a crimped fiber can produce both the characteristic nonlinear stress–strain behavior and large Poisson's ratios, while fiber crimp alone could only account for the nonlinear stress–strain behavior.     

Analyis of structure/property relationships in silkworm (Bombyx mori) and spider dragline (Nephila edulis) silks using Raman spectroscopy

The molecular deformation of both silkworm (Bombyx mori) and spider dragline (Nephila edulis) silks has been studied using a combination of mechanical deformation and Raman spectroscopy. The stress/strain curves for both kinds of silk showed elastic behavior followed by plastic deformation. It was found that both materials have well-defined Raman spectra and that some of the bands in the spectra shift to lower frequency under the action of tensile stress or strain. The band shift was linearly dependent upon stress for both types of silk fiber. This observation provides a unique insight into the effect of tensile deformation upon molecular structure and the relationship between structure and mechanical properties. Two similar bands in the Raman spectra of both types of silk in the region of 1000-1300 cm(-1) had significant identical rates of Raman band shift of about 7 cm(-1)/GPa and 14 cm(-1)/GPa demonstrating the similarity between the silk fibers from two different animals.     

Glycosaminoglycans contribute to extracellular matrix fiber recruitment and arterial wall mechanics

Elastic and collagen fibers are well known to be the major load-bearing extracellular matrix (ECM) components of the arterial wall. Studies of the structural components and mechanics of arterial ECM generally focus on elastin and collagen fibers, and glycosaminoglycans (GAGs) are often neglected. Although GAGs represent only a small component of the vessel wall ECM, they are considerably important because of their diverse functionality and their role in pathological processes. The goal of this study was to study the mechanical and structural contributions of GAGs to the arterial wall. Biaxial tensile testing was paired with multiphoton microscopic imaging of elastic and collagen fibers in order to establish the structure–function relationships of porcine thoracic aorta before and after enzymatic GAG removal. Removal of GAGs results in an earlier transition point of the nonlinear stress–strain curves \((p<0.05)\). However, stiffness was not significantly different after GAG removal treatment, indicating earlier but not absolute stiffening. Multiphoton microscopy showed that when GAGs are removed, the adventitial collagen fibers are straighter, and both elastin and collagen fibers are recruited at lower levels of strain, in agreement with the mechanical change. The amount of stress relaxation also decreased in GAG-depleted arteries \((p<0.05)\). These findings suggest that the interaction between GAGs and other ECM constituents plays an important role in the mechanics of the arterial wall, and GAGs should be considered in addition to elastic and collagen fibers when studying arterial function.