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.     

Magnetic alignment of collagen during self-assembly

Magnetically induced birefringence is used to monitor the thermally induced self-assembly of collagen fibrils from a solution of molecules. The magnetic torque alone can, at best, only orient the fibrils into planes normal to the field direction. Nevertheless, the gels formed have a high degree of uniaxial alignment, probably due to the additional ordering effects of surface interactions. Thus magnetic orientation is potentially useful in the study of fibrillogenesis and in the production of highly oriented collagen gels.     

The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet

We have recently demonstrated that the mitral valve anterior leaflet (MVAL) exhibited minimal hysteresis, no strain rate sensitivity, stress relaxation but not creep (Grashow et al., 2006, Ann Biomed Eng., 34(2), pp. 315-325; Grashow et al., 2006, Ann Biomed. Eng., 34(10), pp. 1509-1518). However, the underlying structural basis for this unique quasi-elastic mechanical behavior is presently unknown. As collagen is the major structural component of the MVAL, we investigated the relation between collagen fibril kinematics (rotation and stretch) and tissue-level mechanical properties in the MVAL under biaxial loading using small angle X-ray scattering. A novel device was developed and utilized to perform simultaneous measurements of tissue level forces and strain under a planar biaxial loading state. Collagen fibril D-period strain (epsilonD) and the fibrillar angular distribution were measured under equibiaxial tension, creep, and stress relaxation to a peak tension of 90 N/m. Results indicated that, under equibiaxial tension, collagen fibril straining did not initiate until the end of the nonlinear region of the tissue-level stress-strain curve. At higher tissue tension levels, epsilonD increased linearly with increasing tension. Changes in the angular distribution of the collagen fibrils mainly occurred in the tissue toe region. Using epsilonD, the tangent modulus of collagen fibrils was estimated to be 95.5+/-25.5 MPa, which was approximately 27 times higher than the tissue tensile tangent modulus of 3.58+/-1.83 MPa. In creep tests performed at 90 N/m equibiaxial tension for 60 min, both tissue strain and epsilonD remained constant with no observable changes over the test length. In contrast, in stress relaxation tests performed for 90 min epsilonD was found to rapidly decrease in the first 10 min followed by a slower decay rate for the remainder of the test. Using a single exponential model, the time constant for the reduction in collagen fibril strain was 8.3 min, which was smaller than the tissue-level stress relaxation time constants of 22.0 and 16.9 min in the circumferential and radial directions, respectively. Moreover, there was no change in the fibril angular distribution under both creep and stress relaxation over the test period. Our results suggest that (1) the MVAL collagen fibrils do not exhibit intrinsic viscoelastic behavior, (2) tissue relaxation results from the removal of stress from the fibrils, possibly by a slipping mechanism modulated by noncollagenous components (e.g. proteoglycans), and (3) the lack of creep but the occurrence of stress relaxation suggests a "load-locking" behavior under maintained loading conditions. These unique mechanical characteristics are likely necessary for normal valvular function.     

Molecular-scale topographic cues induce the orientation and directional movement of fibroblasts on two-dimensional collagen surfaces

Collagen fibres within the extracellular matrix lend tensile strength to tissues and form a functional scaffold for cells. Cells can move directionally along the axis of fibrous structures, in a process important in wound healing and cell migration. The precise nature of the structural cues within the collagen fibrils that can direct cell movement are not known. We have investigated the structural features of collagen that are required for directional motility of mouse dermal fibroblasts, by analysing cell movement on two-dimensional collagen surfaces. The surfaces were prepared with aligned fibrils of collagen type I, oriented in a predefined direction. These collagen-coated surfaces were generated with or without the characteristic 67 nm D-periodic banding. Quantitative analysis of cell morphodynamics showed a strong correlation of cell elongation and motional directionality with the orientation of D-periodic collagen microfibrils. Neither directed motility, nor cell body alignment, was observed on aligned collagen lacking D-periodicity, or on D-periodic collagen in the presence of peptide containing an RGD motif. The directional motility of fibroblast cells on aligned collagen type I fibrils cannot be attributed to contact guidance, but requires additional structural information. This allows us to postulate a physiological function for the 67 nm periodicity.     

Tension is required for fibripositor formation

Embryonic tendon cells (ETCs) have actin-rich fibripositors that accompany parallel bundles of collagen fibrils in the extracellular matrix. To study fibripositor function, we have developed a three-dimensional cell culture system that promotes and maintains fibripositors. We show that ETCs cultured in fixed-length fibrin gels replace the fibrin during ~6 days in culture with parallel bundles of narrow-diameter collagen fibrils that are uniaxially aligned with fibripositors, thereby generating a tendon-like construct. Fibripositors occurred simultaneously with onset of parallel collagen fibrils. Interestingly, the constructs have a tendon-like crimp. In initial experiments to study the effects of tension, we showed that cutting the constructs resulted in loss of tension, loss of fibripositors and the appearance of immature fibrils with no preferred orientation.     

Mechanical behavior of collagen-fibrin co-gels reflects transition from series to parallel interactions with increasing collagen content

Fibrin and collagen, biopolymers occurring naturally in the body, are biomaterials commonly-used as scaffolds for tissue engineering. How collagen and fibrin interact to confer macroscopic mechanical properties in collagen-fibrin composite systems remains poorly understood. In this study, we formulated collagen-fibrin co-gels at different collagen-to-fibrin ratios to observe changes in the overall mechanical behavior and microstructure. A modeling framework of a two-network system was developed by modifying our micro-scale model, considering two forms of interaction between the networks: (a) two interpenetrating but noninteracting networks ("parallel"), and (b) a single network consisting of randomly alternating collagen and fibrin fibrils ("series"). Mechanical testing of our gels show that collagen-fibrin co-gels exhibit intermediate properties (UTS, strain at failure, tangent modulus) compared to those of pure collagen and fibrin. The comparison with model predictions show that the parallel and series model cases provide upper and lower bounds, respectively, for the experimental data, suggesting that a combination of such interactions exists between the collagen and fibrin in co-gels. A transition from the series model to the parallel model occurs with increasing collagen content, with the series model best describing predominantly fibrin co-gels, and the parallel model best describing predominantly collagen co-gels.     

Collagen fiber alignment does not explain mechanical anisotropy in fibroblast populated collagen gels

Many load-bearing soft tissues exhibit mechanical anisotropy. In order to understand the behavior of natural tissues and to create tissue engineered replacements, quantitative relationships must be developed between the tissue structures and their mechanical behavior. We used a novel collagen gel system to test the hypothesis that collagen fiber alignment is the primary mechanism for the mechanical anisotropy we have reported in structurally anisotropic gels. Loading constraints applied during culture were used to control the structural organization of the collagen fibers of fibroblast populated collagen gels. Gels constrained uniaxially during culture developed fiber alignment and a high degree of mechanical anisotropy, while gels constrained biaxially remained isotropic with randomly distributed collagen fibers. We hypothesized that the mechanical anisotropy that developed in these gels was due primarily to collagen fiber orientation. We tested this hypothesis using two mathematical models that incorporated measured collagen fiber orientations: a structural continuum model that assumes affine fiber kinematics and a network model that allows for nonaffine fiber kinematics. Collagen fiber mechanical properties were determined by fitting biaxial mechanical test data from isotropic collagen gels. The fiber properties of each isotropic gel were then used to predict the biaxial mechanical behavior of paired anisotropic gels. Both models accurately described the isotropic collagen gel behavior. However, the structural continuum model dramatically underestimated the level of mechanical anisotropy in aligned collagen gels despite incorporation of measured fiber orientations; when estimated remodeling-induced changes in collagen fiber length were included, the continuum model slightly overestimated mechanical anisotropy. The network model provided the closest match to experimental data from aligned collagen gels, but still did not fully explain the observed mechanics. Two different modeling approaches showed that the level of collagen fiber alignment in our uniaxially constrained gels cannot explain the high degree of mechanical anisotropy observed in these gels. Our modeling results suggest that remodeling-induced redistribution of collagen fiber lengths, nonaffine fiber kinematics, or some combination of these effects must also be considered in order to explain the dramatic mechanical anisotropy observed in this collagen gel model system.     

Modeling of fibroblast-controlled strengthening and remodeling of uniaxially constrained collagen gels

A theoretical model for the remodeling of collagen gels is proposed. The collagen fabric is modeled as a network of collagen fibers, which in turn are composed of collagen fibrils. In the model, the strengthening of collagen fabric is accomplished by fibroblasts, which continuously recruit and attach more collagen fibrils to existing collagen fibers. The fibroblasts also accomplish a reorientation of collagen fibers. Fibroblasts are assumed to reorient collagen fibers toward the direction of maximum material stiffness. The proposed model is applied to experiments in which fibroblasts were inserted into a collagen gel. The model is able to predict the force-strain curves for the experimental collagen gels, and the final distribution of collagen fibers also agrees qualitatively with the experiments.     

Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior

The microstructure of tissues and tissue equivalents (TEs) plays a critical role in determining the mechanical properties thereof. One of the key challenges in constitutive modeling of TEs is incorporating the kinematics at both the macroscopic and the microscopic scale. Models of fibrous microstructure commonly assume fibrils to move homogeneously, that is affine with the macroscopic deformation. While intuitive for situations of fibril-matrix load transfer, the relevance of the affine assumption is less clear when primary load transfer is from fibril to fibril. The microstructure of TEs is a hydrated network of collagen fibrils, making its microstructural kinematics an open question. Numerical simulation of uniaxial extensile behavior in planar TE networks was performed with fibril kinematics dictated by the network model and by the affine model. The average fibril orientation evolved similarly with strain for both models. The individual fibril kinematics, however, were markedly different. There was no correlation between fibril strain and orientation in the network model, and fibril strains were contained by extensive reorientation. As a result, the macroscopic stress given by the network model was roughly threefold lower than the affine model. Also, the network model showed a toe region, where fibril reorientation precluded the development of significant fibril strain. We conclude that network fibril kinematics are not governed by affine principles, an important consideration in the understanding of tissue and TE mechanics, especially when load bearing is primarily by an interconnected fibril network.     

Extracellular matrix organization modulates fibroblast growth and growth factor responsiveness

To learn more about the relationship between extracellular matrix organization, cell shape, and cell growth control, we studied DNA synthesis by fibroblasts in collagen gels that were either attached to culture dishes or floating in culture medium during gel contraction. After 4 days of contraction, the collagen density (initially 1.5 mg/ml) reached 22 mg/ml in attached gels and 55 mg/ml in floating gels. After contraction, attached collagen gels were well organized; collagen fibrils were aligned in the plane of cell spreading; and fibroblasts had an elongated, bipolar morphology. Floating collagen gels, however, were unorganized; collagen fibrils were arranged randomly; and fibroblasts had a stellate morphology. DNA synthesis by fibroblasts in contracted collagen gels was suppressed if the gels were floating in medium but not if the gels were attached, and inhibition was independent of the extent of gel contraction. Therefore, growth of fibroblasts in contracted collagen gels could be regulated by differences in extracellular matrix organization and cell shape independently of extracellular matrix density. We also compared the responses of fibroblasts in contracted collagen gels and monolayer culture to peptide growth factors including fibroblast growth factor, platelet-derived growth factor, transforming growth factor-beta, and interleukin 1. Cells in floating collagen gels were generally unresponsive to any of the growth factors. Cells in attached collagen gels and monolayer culture were affected similarly by fibroblast growth factor but not by the others. Our results indicate that extracellular matrix organization influenced not only cell growth, but also fibroblast responsiveness to peptide growth factors.     

Fibrillogenesis in dense collagen solutions: a physicochemical study

Fibrillogenesis, the formation of collagen fibrils, is a key factor in connective tissue morphogenesis. To understand to what extent cells influence this process, we systematically studied the physicochemistry of the self-assembly of type I collagen molecules into fibrils in vitro. We report that fibrillogenesis in solutions of type I collagen, in a high concentration range close to that of living tissues (40-300 mg/ml), yields strong gels over wide pH and ionic strength ranges. Structures of gels were described by combining microscopic observations (transmission electron microscopy) with small- and wide-angle X-ray scattering analysis, and the influence of concentration, pH, and ionic strength on the fibril size and organization was evaluated. The typical cross-striated pattern and the corresponding small-angle X-ray scattering 67-nm diffraction peaks were visible in all conditions in the pH 6 to pH 12 range. In reference conditions (pH 7.4, ionic strength = 150 mM, 20 °C), collagen concentration greatly influences the overall macroscopic structure of the resultant fibrillar gels, as well as the morphology and structure of the fibrils themselves. At a given collagen concentration, increasing the ionic strength from 24 to 261 mM produces larger fibrils until the system becomes biphasic. We also show that fibrils can form in acidic medium (pH ∼ 2.5) at very high collagen concentrations, beyond 150 mg/ml, which suggests a possible cholesteric-to-smectic phase transition. This set of data demonstrates how simple physicochemical parameters determine the molecular organization of collagen. Such an in vitro model allows us to study the intricate process of fibrillogenesis in conditions of molecular packing close to that which occurs in biological tissue morphogenesis.     

Heparin modulates the organization of hydrated collagen gels and inhibits gel contraction by fibroblasts

We studied the effects of extracellular matrix components on fibroblast contraction of hydrated collagen gels. After 4-h incubations, heparin-containing collagen gels contracted only 10% compared with 50% contraction of control gels. Contraction was not affected by hyaluronic acid, dermatan sulfate, or fibronectin, implying that the activity of heparin was specific. The possibility that heparin inhibited attachment of the cells to the gels was ruled out. Also, addition of heparin to the incubation medium had no effect on contraction. Microscopic examination showed that control collagen gels were composed of a uniform network of interlocking fibrils of similar sizes. Heparin-containing gels, on the other hand, were highly variable with some collagen bundles containing 5-6 collagen fibrils and other regions containing amorphous material. Unlike the control gels, the fibrils of heparin-containing gels were not continuously interconnected. Based on the results, we propose that fibroblasts attach normally to the collagen fibrils of heparin-containing gels and attempt to contract the gels, but the mechanical forces exerted by fibroblasts on individual collagen fibrils cannot be propagated throughout the gels.     

Molecular packing in type I collagen fibrils. A model with neighbouring collagen molecules aligned in axial register

A detailed stereochemical analysis of intermolecular interactions of collagens made with molecular models and summarized experimental data resulted in a new three-dimensional structural model for collagen fibrils. In this model collagen molecules aligned in axial register form a bunch. The bunches are aligned head to tail and penetrate by 300 A into each other, forming microfibrils; these in turn assemble into fibrils. The new model differs from all the others in that its characteristic axial regularity, with a period of 670 A, results from staggering of the adjacent microfibrils formed by unstaggered molecules rather than from the axial staggering of neighbouring collagen molecules.     

The role of extracellular matrix in glioma invasion: a cellular Potts model approach

In this work, a cellular Potts model based on the differential adhesion hypothesis is employed to analyze the relative importance of select cell-cell and cell-extracellular matrix (ECM) contacts in glioma invasion. To perform these simulations, three types of cells and two ECM components are included. The inclusion of explicit ECM with an inhomogeneous fibrous component and a homogeneously dispersed afibrous component allows exploration of the importance of relative energies of cell-cell and cell-ECM contacts in a variety of environments relevant to in vitro and in vivo experimental investigations of glioma invasion. Simulations performed here focus chiefly on reproducing findings of in vitro experiments on glioma spheroids embedded in collagen I gels. For a given range and set ordering of energies associated with key cell-cell and cell-ECM interactions, our model qualitatively reproduces the dispersed glioma invasion patterns found for most glioma cell lines embedded as spheroids in collagen I gels of moderate concentration. In our model, we find that invasion is maximized at intermediate collagen concentrations, as occurs experimentally. This effect is seen more strongly in model gels composed of short collagen fibers than in those composed of long fibers, which retain significant connectivity even at low density. Additional simulations in aligned model matrices further elucidate how matrix structure dictates invasive patterns. Finally, simulations that allow invading cells to both dissolve and deposit ECM components demonstrate how Q-Potts models may be elaborated to allow active cell alteration of their surroundings. The model employed here provides a quantitative framework with which to bound the relative values of cell-cell and cell-ECM interactions and investigate how varying the magnitude and type of these interactions, as well as ECM structure, could potentially curtail glioma invasion.     

Remodelling of collagen fibre transition stretch and angular distribution in soft biological tissues and cell-seeded hydrogels

The extracellular matrix in many biological tissues is adapted to its mechanical environment. In this study, a phenomenological model for collagen remodelling is introduced that incorporates angular remodelling (fibre reorientation) and the adaptation of the so-called transition stretch. This is achieved by introducing a local stress-free configuration for the collagen network by a multiplicative decomposition of the deformation gradient and the appropriate definition of the anisotropic free Helmholtz energy potentials and structure tensors. The collagen network is either treated using discrete fibre directions or a continuous angular distribution. The first part of the study illustrates the influence of force- and displacement-controlled loading on either stress- or deformation-driven remodelling processes in tissues with various degrees of fibre reinforcement. The model is then applied to recent experimental studies of collagen remodelling, specifically periosteum adaptation (Foolen et?al. in J Biomech 43(16):3168–3176, 2010), collagen gel (Thomopoulos et?al. in J Biomech Eng 127(5):742–750, 2005) and fibrin cruciform (Sander et?al. in Ann Biomed Eng 1–16, 2010) compaction. The model is able to capture the basic effects of an adapting transition stretch over time in the periosteal simulations, as well as the compaction and the development of structural anisotropy in the collagen and fibrin gels. The model can potentially be applied to elucidate structure–function relationships, better interpret in vitro experiments involving collagen remodelling, and help investigate aspects of certain pathologies, such as connective tissue contracture.     

The development of structural and mechanical anisotropy in fibroblast populated collagen gels

An in vitro model system was developed to study structure-function relationships and the development of structural and mechanical anisotropy in collagenous tissues. Fibroblast-populated collagen gels were constrained either biaxially or uniaxially. Gel remodeling, biaxial mechanical properties, and collagen orientation were determined after 72 h of culture. Collagen gels contracted spontaneously in the unconstrained direction, uniaxial mechanical constraints produced structural anisotropy, and this structural anisotropy was associated with mechanical anisotropy. Cardiac and tendon fibroblasts were compared to test the hypothesis that tendon fibroblasts should generate greater anisotropy in vitro. However, no differences were seen in either structure or mechanics of collagen gels populated with these two cell types, or between fibroblast populated gels and acellular gels. This study demonstrates our ability to control and measure the development of structural and mechanical anisotropy due to imposed mechanical constraints in a fibroblast-populated collagen gel model system. While imposed constraints were required for the development of anisotropy in this system, active remodeling of the gel by fibroblasts was not. This model system will provide a basis for investigating structure-function relationships in engineered constructs and for studying mechanisms underlying the development of anisotropy in collagenous tissues.     

Collagen fibril formation in a wound healing model

Control of tissue composition and organization will be a key feature in the development of successful products through tissue engineering. However, the mechanism of collagen fibril formation, growth, and organization is not yet fully understood. In this study we have examined collagen fibril formation in a wound healing model in which the newly formed fibrils were kept distinct from preexisting tissue through use of a porous tubular biomaterial implant. Samples were examined after 4, 6, 14, and 28 days by light microscopy, in situ hybridization, and immunofluorescence microscopy. These showed a normal wound healing response, with significant collagen formation at 14 and 28 days. Individual collagen fibrils were isolated from these samples by gentle extraction in a gentamicin-containing buffer which allowed extraction of a large proportion of intact fibrils. Examination by transmission electron microscopy showed that approximately 80% of the intact fibrils showed a single polarity reversal, with both ends of each fibril comprising collagen amino-terminal domains; the remaining fibrils had no polarity reversal. All fibrils had similar diameters at both time points. Immunoelectron microscopy showed that all labeled fibrils contained both type I and III collagens. These data indicate that this wound healing model provides a system in which collagen fibril formation can be readily followed.     

Quantification of Collagen Ultrastructure after Penetrating Keratoplasty – Implications for Corneal Biomechanics

Purpose

To quantify long-term changes in stromal collagen ultrastructure following penetrating keratoplasty (PK), and evaluate their possible implications for corneal biomechanics.

Methods

A pair of 16 mm post-mortem corneo-scleral buttons was obtained from a patient receiving bilateral penetrating keratoplasty 12 (left)/28 (right) years previously. Small-angle x-ray scattering quantified collagen fibril spacing, diameter and spatial order at 0.5 mm or 0.25 mm intervals along linear scans across the graft margin. Corresponding control data was collected from two corneo-scleral buttons with no history of refractive surgery. Wide-angle x-ray scattering quantified collagen fibril orientation at 0.25 mm (horizontal)×0.25 mm (vertical) intervals across both PK specimens. Quantification of orientation changes in the graft margin were verified by equivalent analysis of data from a 13 year post-operative right PK specimen obtained from a second patient in a previous study, and comparison made with new and published data from normal corneas.

Results

Marked changes to normal fibril alignment, in favour of tangentially oriented collagen, were observed around the entire graft margin in all PK specimens. The total number of meridional fibrils in the wound margin was observed to decrease by up to 40%, with the number of tangentially oriented fibrils increasing by up to 46%. As a result, in some locations the number of fibrils aligned parallel to the wound outnumbered those spanning it by up to five times. Localised increases in fibril spacing and diameter, with an accompanying reduction in matrix order, were also evident.

Conclusions

Abnormal collagen fibril size and spatial order within the PK graft margin are indicative of incomplete stromal wound remodelling and the long term persistence of fibrotic scar tissue. Lasting changes in collagen fibril orientation in and around PK wounds may alter corneal biomechanics and compromise the integrity of the graft-host interface in the long term.     

Pericellular Conditions Regulate Extent of Cell-Mediated Compaction of Collagen Gels

Cell-mediated compaction of the extracellular matrix (ECM) plays a critical role in tissue engineering, wound healing, embryonic development, and many disease states. The ECM is compacted as a result of cellular traction forces. We hypothesize that a cell mechanically remodels the nearby ECM until some target conditions are obtained, and then the cell stops compacting. A key feature of this hypothesis is that ECM compaction primarily occurs in the pericellular region and the properties of the ECM in the pericellular region govern cellular force generation. We developed a mathematical model to describe the amount of macroscopic compaction of cell-populated collagen gels in terms of the initial cell and collagen densities, as well as the final conditions of the pericellular environment (defined as the pericellular volume where the collagen is compacted (V^∗) and the mass of collagen within this volume (m^∗)). This model qualitatively predicts the effects of varying initial cell and collagen concentrations on the extent of gel compaction, and by fitting V^∗ and m^∗, provides reasonable quantitative agreement with the extent of gel compaction observed in experiments with endothelial cells and fibroblasts. Microscopic analysis of compacted gels supports the assumption that collagen compaction occurs primarily in the pericellular environment.