Influence of fibril taper on the function of collagen to reinforce extracellular matrix

Collagen fibrils provide tensile reinforcement for extracellular matrix. In at least some tissues, the fibrils have a paraboloidal taper at their ends. The purpose of this paper is to determine the implications of this taper for the function of collagen fibrils. When a tissue is subjected to low mechanical forces, stress will be transferred to the fibrils elastically. This process was modelled using finite element analysis because there is no analytical theory for elastic stress transfer to a non-cylindrical fibril. When the tissue is subjected to higher mechanical forces, stress will be transferred plastically. This process was modelled analytically. For both elastic and plastic stress transfer, a paraboloidal taper leads to a more uniform distribution of axial tensile stress along the fibril than would be generated if it were cylindrical. The tapered fibril requires half the volume of collagen than a cylindrical fibril of the same length and the stress is shared more evenly along its length. It is also less likely to fracture than a cylindrical fibril of the same length in a tissue subjected to the same mechanical force.     

Bone stiffness explained by the liquid crystal model for the collagen fibril

A liquid crystal model for the structure of the collagen fibril explains how calcium phosphate crystals are capable of stiffening collagen fibrils in bone. Collagen fibrils consist of an oriented array of parallel rod-shaped collagen molecules. According to the liquid crystal model fibrils respond to tensile stress, applied in the axial direction, by some of the molecules tilting and changing their side-to-side arrangement. In bone the presence of crystals packed between the collagen molecules hinders the side-to-side rearrangement so that the response of the fibrils to stress is inhibited. Therefore the fibrils are stiffer in bone than in uncalcified tissue.     

Type V collagen controls the initiation of collagen fibril assembly

Vertebrate collagen fibrils are heterotypically composed of a quantitatively major and minor fibril collagen. In non-cartilaginous tissues, type I collagen accounts for the majority of the collagen mass, and collagen type V, the functions of which are poorly understood, is a minor component. Type V collagen has been implicated in the regulation of fibril diameter, and we reported recently preliminary evidence that type V collagen is required for collagen fibril nucleation (Wenstrup, R. J., Florer, J. B., Cole, W. G., Willing, M. C., and Birk, D. E. (2004) J. Cell. Biochem. 92, 113-124). The purpose of this study was to define the roles of type V collagen in the regulation of collagen fibrillogenesis and matrix assembly. Mouse embryos completely deficient in pro-alpha1(V) chains were created by homologous recombination. The col5a1-/- animals die in early embryogenesis, at approximately embryonic day 10. The type V collagen-deficient mice demonstrate a virtual lack of collagen fibril formation. In contrast, the col5a1+/- animals are viable. The reduced type V collagen content is associated with a 50% reduction in fibril number and dermal collagen content. In addition, relatively normal, cylindrical fibrils are assembled with a second population of large, structurally abnormal collagen fibrils. The structural properties of the abnormal matrix are decreased relative to the wild type control animals. These data indicate a central role for the evolutionary, ancient type V collagen in the regulation of fibrillogenesis. The complete dependence of fibril formation on type V collagen is indicative of the critical role of the latter in early fibril initiation. In addition, this fibril collagen is important in the determination of fibril structure and matrix organization.     

Effects of frozen storage temperature on the elasticity of tendons from a small murine model

The basic mechanism of reinforcement in tendons addresses the transfer of stress, generated by the deforming proteoglycan (PG)-rich matrix, to the collagen fibrils. Regulating this mechanism involves the interactions of PGs on the fibril with those in the surrounding matrix and between PGs on adjacent fibrils. This understanding is key to establishing new insights on the biomechanics of tendon in various research domains. However, the experimental designs in many studies often involved long sample preparation time. To minimise biological degradation the tendons are usually stored by freezing. Here, we have investigated the effects of commonly used frozen storage temperatures on the mechanical properties of tendons from the tail of a murine model (C57BL6 mouse). Fresh (unfrozen) and thawed samples, frozen at temperatures of -20°C and -80°C, respectively, were stretched to rupture. Freezing at -20°C revealed no effect on the maximum stress (σ), stiffness (E), the corresponding strain (ε) at σ and strain energy densities up to ε (u) and from ε until complete rupture (up). On the other hand, freezing at -80°C led to higher σ, E and u; ε and up were unaffected. The results implicate changes in the long-range order of radially packed collagen molecules in fibrils, resulting in fibril rupture at higher stresses, and changes to the composition of extrafibrillar matrix, resulting in an increase in the interaction energy between fibrils via collagen-bound PGs.     

Structure of type I and type III heterotypic collagen fibrils: an X-ray diffraction study

The molecular packing arrangement within collagen fibrils has a significant effect on the tensile properties of tissues. To date, most studies have focused on homotypic fibrils composed of type I collagen. This study investigates the packing of type I/III collagen molecules in heterotypic fibrils of colonic submucosa using a combination of X-ray diffraction data, molecular model building, and simulated X-ray diffraction fibre diagrams. A model comprising a 70-nm-diameter D- (approximately 65 nm) axial periodic structure containing type I and type III collagen chains was constructed from amino acid scattering factors organised in a liquid-like lateral packing arrangement simulated using a classical Lennard-Jones potential. The models that gave the most accurate correspondence with diffraction data revealed that the structure of the fibril involves liquid-like lateral packing combined with a constant helical inclination angle for molecules throughout the fibril. Combinations of type I:type III scattering factors in a ratio of 4:1 gave a reasonable correspondence with the meridional diffraction series. The attenuation of the meridional intensities may be explained by a blurring of the electron density profile of the D period caused by nonspecific or random interactions between collagen types I and III in the heterotypic fibril.     

Ageing changes in the tensile properties of tendons: influence of collagen fibril volume fraction

Connective tissues are biological composites comprising of collagen fibrils embedded in (and reinforcing) the hydrated proteoglycan-rich (PG) gel within the extracellular matrices (ECMs). Age-related changes to the mechanical properties of tissues are often associated with changes to the structure of the ECM, namely, fibril diameter. However, quantitative attempts to correlate fibril diameter to mechanical properties have yielded inconclusive evidence. Here, we described a novel approach that was based on the rule of mixtures for fiber composites to evaluate the dependence of age-related changes in tendon tensile strength (sigma) and stiffness (E) on the collagen fibril cross-sectional area fraction (rho), which is related to the fibril volume fraction. Tail tendons from C57BL6 mice from age groups 1.6-35.3 months old were stretched to failure to determine sigma and E. Parallel measurements of rho as a function of age were made using transmission electron microscopy. Mathematical models (rule of mixtures) of fibrils reinforcing a PG gel in tendons were used to investigate the influence of rho on ageing changes in sigma and E. The magnitudes of sigma, E, and rho increased rapidly from 1.6 months to 4.0 months (P-values <0.05) before reaching a constant (age independent) from 4.0 months to 29.0 months (P-values >0.05); this trend continued for E and rho (P-values >0.05) from 29.0 months to 35.3 months, but not for sigma, which decreased gradually (P-values <0.05). Linear regression analysis revealed that age-related changes in sigma and E correlated positively to rho (P-values <0.05). Collagen fibril cross-sectional area fraction rho is a significant predictor of ageing changes in sigma and E in the tail tendons of C57BL6 mice.     

Control of collagen fibril diameters in tissues.

It is proposed that radial growth of collagen fibrils, which takes place in all connective tissues to varying extents, according to the tensile stresses exerted on them, proceeds mainly by aggregation of protofibrils (approximately 10 nm) and existing fibrils. In young tissues, fibrils are prevented from making frequent intimate contacts which would lead to aggregation by abundant interfibrillar proteoglycan, that keeps the fibrils apart. Collagen fibrils are probably unable to fuse except when the molecules within them are packed in the same sense, i.e. fusing fibrils are parallel. The roughly equal numbers of parallel and antiparallel fibrils seen in several tissues must limit radial fibril growth in older tissues, where proteoglycan is usually less abundant. Possible origins of the balance of fibril polarities, which must be conserved after fibril nucleation on cell or non-cell templates, are analysed. The two controlling factors, ambient proteoglycan and fibril polarity, working against the tendency of fibrils to fuse, account for many features of the observed distributions of collagen fibril diameters in diverse tissues and at different ages.     

Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis

Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.     

Growth of Collagen Fibril Seeds from Embryonic Tendon: Fractured Fibril Ends Nucleate New Tip Growth

Collagen fibrils are the principal tensile element of vertebrate tissues where they occur in the extracellular matrix as spatially organised arrays. A major challenge is to understand how the mechanisms of nucleation, growth and remodelling yield fibrils of tissue-specific diameter and length. Here we have developed a seeding system whereby collagen fibrils were isolated from avian embryonic tendon and added to purified collagen solution, in order to characterise fibril surface nucleation and growth mechanisms. Fragmentation of tendon in liquid nitrogen followed by Dounce homogenisation generated fibril length fragments. Most (> 94%) of the fractured ends of fibrils, which show an abrupt square profile, were found to act as nucleation sites for further growth by molecular accretion. The mechanism of this nucleation and growth process was investigated by transmission electron microscopy, atomic force microscopy and scanning transmission electron microscopy mass mapping. Typically, a single growth spur occurred on the N-terminal end of seed fibrils whilst twin spurs frequently formed on the C-terminal end before merging into a single tip projection. The surface nucleation and growth process generated a smoothly tapered tip that achieved maximum diameter when the axial extension reached ∼ 13 μm. Lateral growth also occurred along the entire length of all seed fibrils that contained tip projections. The data support a model of collagen fibril growth in which the broken ends of fibrils are nucleation sites for propagation in opposite axial directions. The observed fibril growth behaviour has direct relevance to tendon matrix remodelling and repair processes that might involve rupture of collagen fibrils.     

Echinoderm collagen fibrils grow by surface-nucleation-and-propagation from both centers and ends

Collagen fibrils from sea cucumber (class Holothuroidea) dermis were previously found to grow by coordinated monomer addition at both centers and ends. This analysis of sea urchin (class Echinoidea) collagen fibrils was undertaken to compare the growth characteristics of fibrils from two classes of echinoderms, and to determine whether a single growth model could account for the main features of fibrils from these two taxa. Native collagen fibrils (37-431 micrometer long) from the spine ligaments of the sea urchin Eucidaris tribuloides were studied by scanning transmission electron microscopy and image analysis. The analyses revealed the mass per unit length, and hence the number of molecules in cross-section, along the entire length of each fibril. The fibrils were symmetrically spindle shaped. The maximum mass per unit length occurred in the center of each fibril, where the fibril contains anti-parallel molecules in equal numbers. The two pointed tips of each fibril showed similar linear axial mass distributions, indicating that the two tips retain shape and size similarity throughout growth. The linear axial mass distributions showed that the tips were paraboloidal, similar to those of vertebrate and sea cucumber fibrils. The computed maximum diameters of the fibrils increased linearly with fibril length. The overall shapes of the fibrils showed that they retain geometric similarity throughout growth. Computer modeling showed that the simplest self-assembly mechanism that can account for the features of these fibrils, and of the sea cucumber fibrils that have been described, is one in which the fibril tips produce independent axial growth, while lateral growth takes place through a surface nucleation and propagation mechanism. This mechanism produces coordinated growth in length and diameter as well as geometric similarity, characteristic features of echinoderm collagen fibrils.     

In situ atomic force microscopy of partially demineralized human dentin collagen fibrils

Dentin collagen fibrils were studied in situ by atomic force microscopy (AFM). New data on size distribution and the axial repeat distance of hydrated and dehydrated collagen type I fibrils are presented. Polished dentin disks from third molars were partially demineralized with citric acid, leaving proteins and the collagen matrix. At this stage collagen fibrils were not resolved by AFM, but after exposure to NaOCl(aq) for 100-240 s, and presumably due to the removal of noncollagenous proteins, individual collagen fibrils and the fibril network of dentin connected to the mineralized substrate were revealed. High-aspect-ratio silicon tips in tapping mode were used to image the soft fibril network. Hydrated fibrils showed three distinct groups of diameters: 100, 91, and 83 nm and a narrow distribution of the axial repeat distance at 67 nm. Dehydration resulted in a broad distribution of the fibril diameters between 75 and 105 nm and a division of the axial repeat distance into three groups at 67, 62, and 57 nm. Subfibrillar features (4 nm) were observed on hydrated and dehydrated fibrils. The gap depth between the thick and thin repeating segments of the fibrils varied from 3 to 7 nm. Phase mode revealed mineral particles on the transition from the gap to the overlap zone of the fibrils. This method appears to be a powerful tool for the analysis of fibrillar collagen structures in calcified tissues and may aid in understanding the differences in collagen affected by chemical treatments or by diseases.     

Three dimensional patient-specific collagen architecture modulates cartilage responses in the knee joint during gait

Site-specific variation of collagen fibril orientations can affect cartilage stresses in knee joints. However, this has not been confirmed by 3-D analyses. Therefore, we present a novel method for evaluation of the effect of patient-specific collagen architecture on time-dependent mechanical responses of knee joint cartilage during gait. 3-D finite element (FE) models of a human knee joint were created with the collagen architectures obtained from T₂ mapped MRI (patient-specific model) and from literature (literature model). The effect of accuracy of the implementation of collagen fibril architecture into the model was examined by using a submodel with denser FE mesh. Compared to the literature model, fibril strains and maximum principal stresses were reduced especially in the superficial/middle regions of medial tibial cartilage in the patient-specific model after the loading response of gait (up to ?413 and ?26%, respectively). Compared to the more coarsely meshed joint model, the patient-specific submodel demonstrated similar strain and stress distributions but increased values particularly in the superficial cartilage regions (especially stresses increased >60%). The results demonstrate that implementation of subject-specific collagen architecture of cartilage in 3-D modulates location- and time-dependent mechanical responses of human knee joint cartilage. Submodeling with more accurate implementation of collagen fibril architecture alters cartilage stresses particularly in the superficial/middle tissue.     

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

Tendon is a hydrated multi-level fibre composite, in which time-dependent behaviour is well established. Studies indicate significant stress relaxation, considered important for optimising tissue stiffness. However, whilst this behaviour is well documented, the mechanisms associated with the response are largely unknown. This study investigates the sub-structural mechanisms occurring during stress relaxation at both the macro (fibre) and nano (fibril) levels of the tendon hierarchy. Stress relaxation followed a two-stage exponential behaviour, during which structural changes were visible at the fibre and fibril levels. Fibril relaxation and fibre sliding showed a double exponential response, while fibre sliding was clearly the largest contributor to relaxation. The amount of stress relaxation and sub-structural reorganisation increased with increasing load increments, but fibre sliding was consistently the largest contributor to stress relaxation. A simple model of tendon viscoelasticity at the fibril and fibre levels has been developed, capturing this behaviour by serially coupling a Voigt element (collagen fibril), with two Maxwell elements (non-collagenous matrix between fibrils and fibres). This multi-level analysis provides a first step towards understanding how sub-structural interactions contribute to viscoelastic behaviour. It indicates that nano- and micro-scale shearing are significant dissipative mechanisms, and the kinetics of relaxation follows a two-stage exponential decay, well fitted by serially coupled viscoelastic elements.     

Tip-mediated fusion involving unipolar collagen fibrils accounts for rapid fibril elongation, the occurrence of fibrillar branched networks in skin and the paucity of collagen fibril ends in vertebrates.

Collagen fibrils are the principal source of mechanical strength of connective tissues such as tendon, skin, cornea, cartilage and bone. The ability of these tissues to withstand tensile forces is directly attributable to the length and diameter of the fibrils, and to interactions between individual fibrils. Although electron microscopy studies have provided information on fibril diameters, little is known about the length of fibrils in tissue and how fibrils interact with each other. The question of fibril length has been difficult to address because fibril ends are rarely observed in cross-sections of tissue. The paucity of fibril ends, or tips, has led to controversy about how long individual fibrils might be and how the fibrils grow in length and diameter. This review describes recent discoveries that are relevant to these questions. We now know that vertebrate collagen fibrils are synthesised as short (1-3 microm) early fibrils that fuse end-to-end in young tissues to generate very long fibrils. The diameter of the final fibril is determined by the diameter of the collagen early fibrils. During a late stage of tissue assembly fibril tips fuse to fibril shafts to generate branched networks. Of direct relevance to fibril fusion is the fact that collagen fibrils can be unipolar or bipolar, depending on the orientation of collagen molecules in the fibril. Fusion relies on: (1) specific molecular interactions at the carboxyl terminal ends of unipolar collagen fibrils; and (2) the insulator function of small proteoglycans to shield the surfaces of fibrils from inappropriate fusion reactions. The fusion of tips to shafts to produce branched networks of collagen fibrils is an elegant mechanism to increase the mechanical strength of tissues and provides an explanation for the paucity of fibril tips in older tissue.     

Position of single amino acid substitutions in the collagen triple helix determines their effect on structure of collagen fibrils

Collagen II fibrils are a critical structural component of the extracellular matrix of cartilage providing the tissue with its unique biomechanical properties. The self-assembly of collagen molecules into fibrils is a spontaneous process that depends on site-specific binding between specific domains belonging to interacting molecules. These interactions can be altered by mutations in the COL2A1 gene found in patients with a variety of heritable cartilage disorders known as chondrodysplasias. Employing recombinant procollagen II, we studied the effects of R75C or R789C mutations on fibril formation. We determined that both R75C and R789C mutants were incorporated into collagen assemblies. The effects of the R75C and R789C substitutions on fibril formation differed significantly. The R75C substitution located in the thermolabile region of collagen II had no major effect on the fibril formation process or the morphology of fibrils. In contrast, the R789C substitution located in the thermostable region of collagen II caused profound changes in the morphology of collagen assemblies. These results provide a basis for identifying pathways leading from single amino acid substitutions in collagen II to changes in the structure of individual fibrils and in the organization of collagenous matrices.     

Stress related collagen ultrastructure in human aortic valves--implications for tissue engineering

Understanding the response of tissue structures to mechanical stress is crucial for optimization of mechanical conditioning protocols in the field of heart valve tissue engineering. In heart valve tissue, it is unclear to what extent mechanical loading affects the collagen fibril morphology. To determine if local stress affects the collagen fibril morphology, in terms of fibril diameter, its distribution, and the fibril density, this was investigated in adult native human aortic valve leaflets. Transmission electron microscopy images of collagen fibrils were analyzed at three locations: the commissures, the belly, and the fixed edge of the leaflets. Subsequently, the mechanical behavior of human aortic valves was used in a computational model to predict the stress distribution in the valve leaflet during the diastolic phase of the cardiac cycle. The local stresses at the three locations were related to the collagen fibril morphology. The fibril diameter and density varied significantly between the measured locations, and appeared inversely related. The average fibril diameter increased from the fixed edge, to the belly, and to the commissures of the leaflets, while fibril density decreased. Interestingly, these differences corresponded well with the level of stress at the locations. The presented data showed that large tissue stress is associated with greater average fibril diameter, lower fibril density, and wider fibril size distribution compared with low stress locations in the leaflets. The findings here provide insight in the effect of mechanical loading on the collagen ultrastructure, and are valuable to improve conditioning protocols for tissue engineering.     

Modeling the effect of collagen fibril alignment on ligament mechanical behavior

Ligament mechanical behavior is primarily regulated by fibrous networks of type I collagen. Although these fibrous networks are typically highly aligned, healthy and injured ligament can also exhibit disorganized collagen architecture. The objective of this study was to determine whether variations in the collagen fibril network between neighboring ligaments can predict observed differences in mechanical behavior. Ligament specimens from two regions of bovine fetlock joints, which either exhibited highly aligned or disorganized collagen fibril networks, were mechanically tested in uniaxial tension. Confocal microscopy and FiberFit software were used to quantify the collagen fibril dispersion and mean fibril orientation in the mechanically tested specimens. These two structural parameters served as inputs into an established hyperelastic constitutive model that accounts for a continuous distribution of planar fibril orientations. The ability of the model to predict differences in the mechanical behavior between neighboring ligaments was tested by (1) curve fitting the model parameters to the stress response of the ligament with highly aligned fibrils and then (2) using this model to predict the stress response of the ligament with disorganized fibrils by only changing the parameter values for fibril dispersion and mean fibril orientation. This study found that when using parameter values for fibril dispersion and mean fibril orientation based on confocal imaging data, the model strongly predicted the average stress response of ligaments with disorganized fibrils (\(R^{2}=0.97\)); however, the model only successfully predicted the individual stress response of ligaments with disorganized fibrils in half the specimens tested. Model predictions became worse when parameters for fibril dispersion and mean fibril orientation were not based on confocal imaging data. These findings emphasize the importance of collagen fibril alignment in ligament mechanics and help advance a mechanistic understanding of fibrillar networks in healthy and injured ligament.     

Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model

Mineralized collagen fibrils are the basic building blocks of bone tissue at the supramolecular level. Several disease states, manipulation of the expression of specific proteins involved in biomineralization, and treatment with different agents alter the extent of mineralization as well as the morphology of mineral crystals which in turn affect the mechanical function of bone tissue. An experimental assessment of mineralized fibers' mechanical properties is challenged by their small size, leaving analytical and computational models as a viable alternative for investigation of the fibril-level mechanical properties. In the current study the variation of the elastic stiffness tensor of mineralized collagen fibrils with changing mineral volume fraction and mineral aspect ratios was predicted via a micromechanical model. The partitioning of applied stresses between mineral and collagen phases is also predicted for normal and shear loading of fibrils. Model predictions resulted in transversely isotropic collagen fibrils in which the modulus along the longer axis of the fibril was the greatest. All the elastic moduli increased with increasing mineral volume fraction whereas Poisson's ratios decreased with the exception of v12 (=v21). The partitioning of applied stresses were such that the stresses acting on mineral crystals were about 1.5, 15, and 3 times greater than collagen stresses when fibrils were loaded transversely, longitudinally, and in shear, respectively. In the overall the predictions were such that: (a) greatest modulus along longer axis; (b) the greatest mineral/collagen stress ratio along the longer axis of collagen fibers (i.e., greatest relief of stresses acting on collagen); and (c) minimal lateral contraction when fibers are loaded along the longer axis. Overall, the pattern of mineralization as put forth in this model predicts a superior mechanical function along the longer axis of collagen fibers, the direction which is more likely to experience greater stresses.     

Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure

The importance and priority of specific micro-structural and mechanical design parameters must be established to effectively engineer scaffolds (biomaterials) that mimic the extracellular matrix (ECM) environment of cells and have clinical applications as tissue substitutes. In this study, three-dimensional (3-D) matrices were prepared from type I collagen, the predominant compositional and structural component of connective tissue ECMs, and structural-mechanical relationships were studied. Polymerization conditions, including collagen concentration (0.3-3 mg/mL) and pH (6-9), were varied to obtain matrices of collagen fibrils with different microstructures. Confocal reflection microscopy was used to assess specific micro-structural features (e.g., diameter and length) and organization of component fibrils in 3-D. Microstructural analyses revealed that changes in collagen concentration affected fibril density while maintaining a relatively constant fibril diameter. On the other hand, both fibril length and diameter were affected by the pH of the polymerization reaction. Mechanically, all matrices exhibited a similar stress-strain curve with identifiable "toe," "linear," and "failure" regions. However the linear modulus and failure stress increased with collagen concentration and were correlated with an increase in fibril density. Additionally, both the linear modulus and failure stress showed an increase with pH, which was related to an increasedfibril length and a decreasedfibril diameter. The tensile mechanical properties of the collagen matrices also showed strain rate dependence. Such fundamental information regarding the 3-D microstructural-mechanical properties of the ECM and its component molecules are important to our overall understanding of cell-ECM interactions (e.g., mechanotransduction) and the development of novel strategies for tissue repair and replacement.     

A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels with application to the isotropic and passive properties of the infrarenal aorta

A fundamental understanding of the mechanical properties of the extracellular matrix (ECM) is critically important to quantify the amount of macroscopic stress and/or strain transmitted to the cellular level of vascular tissue. Structural constitutive models integrate histological and mechanical information, and hence, allocate stress and strain to the different microstructural components of the vascular wall. The present work proposes a novel multi-scale structural constitutive model of passive vascular tissue, where collagen fibers are assembled by proteoglycan (PG) cross-linked collagen fibrils and reinforce an otherwise isotropic matrix material. Multiplicative kinematics account for the straightening and stretching of collagen fibrils, and an orientation density function captures the spatial organization of collagen fibers in the tissue. Mechanical and structural assumptions at the collagen fibril level define a piece-wise analytical stress-stretch response of collagen fibers, which in turn is integrated over the unit sphere to constitute the tissue's macroscopic mechanical properties. The proposed model displays the salient macroscopic features of vascular tissue, and employs the material and structural parameters of clear physical meaning. Likewise, the constitutive concept renders a highly efficient multi-scale structural approach that allows for the numerical analysis at the organ level. Model parameters were estimated from isotropic mean-population data of the normal and aneurysmatic aortic wall and used to predict in-vivo stress states of patient-specific vascular geometries, thought to demonstrate the robustness of the particular Finite Element (FE) implementation. The collagen fibril level of the multi-scale constitutive formulation provided an interface to integrate vascular wall biology and to account for collagen turnover.