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.     

A homogenization model of the annulus fibrosus

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli (E theta and E z) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus (G thetaz) was two orders of magnitude larger than directly measured values. The values of E theta and E z were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure-function relationships in disc degeneration and for functional tissue engineering.     

Scleral anisotropy and its effects on the mechanical response of the optic nerve head

This paper presents a computational modeling study of the effects of the collagen fiber structure on the mechanical response of the sclera and the adjacent optic nerve head (ONH). A specimen-specific inverse finite element method was developed to determine the material properties of two human sclera subjected to full-field inflation experiments. A distributed fiber model was applied to describe the anisotropic elastic behavior of the sclera. The model directly incorporated wide-angle X-ray scattering measurements of the anisotropic collagen structure. The converged solution of the inverse method was used in micromechanical studies of the mechanical anisotropy of the sclera at different scales. The effects of the scleral collagen fiber structure on the ONH deformation were evaluated by progressively filtering out local anisotropic features. It was found that the majority of the midposterior sclera could be described as isotropic without significantly affecting the mechanical response of the tissues of the ONH. In contrast, removing local anisotropic features in the peripapillary sclera produced significant changes in scleral canal expansion and lamina cribrosa deformation. Local variations in the collagen structure of the peripapillary sclera significantly influenced the mechanical response of the ONH.     

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.     

Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.     

Extra-fibrillar matrix mechanics of annulus fibrosus in tension and compression

The annulus fibrosus (AF) of the disk is a highly nonlinear and anisotropic material that undergoes a complex combination of loads in multiple orientations. The tensile mechanical behavior of AF in the lamellar plane is dominated by collagen fibers and has been accurately modeled using exponential functions. On the other hand, AF mechanics perpendicular to the lamella, in the radial direction, depend on the properties of the ground matrix with little to no fiber contribution. The ground matrix is mainly composed of proteoglycans (PG), which are negatively charged macromolecules that maintain the tissue hydration via osmotic pressure. The mechanical response of the ground matrix can be divided in the contribution of osmotic pressure and an elastic solid part known as extra-fibrillar matrix (EFM). Mechanical properties of the ground matrix have been measured using tensile and confined compression tests. However, EFM mechanics have not been measured directly. The objective of this study was to measure AF nonlinear mechanics of the EFM in tension and compression. To accomplish this, a combination of osmotic swelling and confined compression in disk radial direction, perpendicular to the lamella, was used. For this type of analysis, it was necessary to define a stress-free reference configuration. Thus, a brief analysis on residual stress in the disk and a procedure to estimate the reference configuration are presented. The proposed method was able to predict similar swelling deformations when using different loading protocols and models for the EFM, demonstrating its robustness. The stress-stretch curve of the EFM was linear in the range 0.9 < λ? < 1.3 with an aggregate modulus of 10.18±3.32 kPa; however, a significant nonlinearity was observed for compression below 0.8. The contribution of the EFM to the total aggregate modulus of the AF decreased from 70 to 30% for an applied compression of 50% of the initial thickness. The properties obtained in this study are essential for constitutive and finite element models of the AF and disk and can be applied to differentiate between functional degeneration effects such as PG loss and stiffening due to cross-linking.     

Micromechanical Modeling Study of Mechanical Inhibition of Enzymatic Degradation of Collagen Tissues

This study investigates how the collagen fiber structure influences the enzymatic degradation of collagen tissues. We developed a micromechanical model of a fibrous collagen tissue undergoing enzymatic degradation based on two central hypotheses. The collagen fibers are crimped in the undeformed configuration. Enzymatic degradation is an energy activated process and the activation energy is increased by the axial strain energy density of the fiber. We determined the intrinsic degradation rate and characteristic energy for mechanical inhibition from fibril-level degradation experiments and applied the parameters to predict the effect of the crimped fiber structure and fiber properties on the degradation of bovine cornea and pericardium tissues under controlled tension. We then applied the model to examine the effect of the tissue stress state on the rate of tissue degradation and the anisotropic fiber structures that developed from enzymatic degradation.     

Hyperelastic anisotropic microplane constitutive model for annulus fibrosus

In a recent paper, Peng et al. (2006, "An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis," ASME J. Appl. Mech., 73(5), pp. 815-824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, "A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis," J. Mech. Phys. Solids, 54(9), pp. 1952-1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, "Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue," ASME J. Biomech. Eng., 128(3), pp. 419-427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.     

Computational analyses of mechanically induced collagen fiber remodeling in the aortic heart valve

To optimize the mechanical properties and integrity of tissue-engineered aortic heart valves, it is necessary to gain insight into the effects of mechanical stimuli on the mechanical behavior of the tissue using mathematical models. In this study, a finite-element (FE) model is presented to relate changes in collagen fiber content and orientation to the mechanical loading condition within the engineered construct. We hypothesized that collagen fibers aligned with principal strain directions and that collagen content increased with the fiber stretch. The results indicate that the computed preferred fiber directions run from commissure to commissure and show a strong resemblance to experimental data from native aortic heart valves.     

Saturation-transfer electron paramagnetic resonance detection of anisotropic motion by sickle hemoglobin molecules in the polymer state

The motional behavior of spin-labeled deoxygenated sickle hemoglobin has been studied by using both 9- and 35-GHz saturation-transfer electron paramagnetic resonance (EPR). Using spectral subtraction techniques and saturation-transfer EPR parameter correlation plots, we find that the saturation-transfer EPR spectra for the sickle hemoglobin gel state at high temperature and high hemoglobin concentration cannot be described as a simple superposition of spectra from immobilized hemoglobin plus solution-state hemoglobin but instead suggest that the individual sickle hemoglobin molecules exhibit limited, anisotropic, rotational oscillation within the polymer fiber. The spectra also imply that the symmetry axis for sickle hemoglobin rotational oscillation is approximately coincident with the nitroxide z axis of the covalently attached spin-label. We suggest that this anisotropic rotational motion may be produced by one or two of the known intermolecular contact sites within the sickle hemoglobin fiber acting as strong intermolecular binding sites, and producing "motional alignment" within the fiber; determining the location of the strong binding site should be important in focusing the future development of antisickling agents.     

Three-dimensional simulation of anisotropic cell-driven collagen gel compaction

Tissue equivalents (TEs), formed by entrapping cells in a collagen gel, are an important model system for studying cell behavior. We have previously (Barocas and Tranquillo in J Biomech Eng 117:161–170, 1997a) developed an anisotropic biphasic theory of TE mechanics, which comprises five coupled partial differential equations describing interaction among cells and collagen fibers in the TE. The model equations, previously solved in one or two dimensions, were solved in three dimensions using an adaptive finite-element platform. The model was applied to three systems: a rectangular isometric cell traction assay, an otherwise- acellular gel containing two islands of cells, and an idealized tissue-engineered cardiac valve leaflet. In the first two cases, published experimental data were available for comparison, and the model results were consistent with the experimental observations. Fibers and cells aligned in the fixed direction in the isometric assay, and a region of strong fiber alignment arose between the two cell islands. For the valve problem, the alignment predicted by the model was generally similar to that observed experimentally, but an asymmetry in the experiment was not captured by the model.     

3D Mechanical properties of the layered esophagus: experiment and constitutive model

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.     

Characterizing local collagen fiber re-alignment and crimp behavior throughout mechanical testing in a mature mouse supraspinatus tendon model

BackgroundCollagen fiber re-alignment and uncrimping are two postulated mechanisms of tendon structural response to load. Recent studies have examined structural changes in response to mechanical testing in a postnatal development mouse supraspinatus tendon model (SST), however, those changes in the mature mouse have not been characterized. The objective of this study was to characterize collagen fiber re-alignment and crimp behavior throughout mechanical testing in a mature mouse SST.Method of approachA tensile mechanical testing set-up integrated with a polarized light system was utilized for alignment and mechanical analysis. Local collagen fiber crimp frequency was quantified immediately following the designated loading protocol using a traditional tensile set up and a flash-freezing method. The effect of number of preconditioning cycles on collagen fiber re-alignment, crimp frequency and mechanical properties in midsubstance and insertion site locations were examined.ResultsDecreases in collagen fiber crimp frequency were identified at the toe-region of the mechanical test at both locations. The insertion site re-aligned throughout the entire test, while the midsubstance re-aligned during preconditioning and the test's linear-region. The insertion site demonstrated a more disorganized collagen fiber distribution, lower mechanical properties and a higher cross-sectional area compared to the midsubstance location.ConclusionsLocal collagen fiber re-alignment, crimp behavior and mechanical properties were characterized in a mature mouse SST model. The insertion site and midsubstance respond differently to mechanical load and have different mechanisms of structural response. Additionally, results support that collagen fiber crimp is a physiologic phenomenon that may explain the mechanical test toe-region.     

Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II--A structural constitutive model

We have formulated the first constitutive model to describe the complete measured planar biaxial stress-strain relationship of the native and glutaraldehyde-treated aortic valve cusp using a structurally guided approach. When applied to native, zero-pressure fixed, and low-pressure fixed cusps, only three parameters were needed to simulate fully the highly anisotropic, and nonlinear in-plane biaxial mechanical behavior. Differences in the behavior of the native and zero- and low-pressure fixed cusps were found to be primarily due to changes in the effective fiber stress-strain behavior. Further, the model was able to account for the effects of small (< 10 deg) misalignments in the cuspal specimens with respect to the biaxial test axes that increased the accuracy of the model material parameters. Although based upon a simplified cuspal structure, the model underscored the role of the angular orientation of the fibers that completely accounted for extreme mechanical anisotropy and pronounced axial coupling. Knowledge of the mechanics of the aortic cusp derived from this model may aid in the understanding of fatigue damage in bioprosthetic heart valves and, potentially, lay the groundwork for the design of tissue-engineered scaffolds for replacement heart valves.     

An anisotropic multiphysics damage model with application to annulus fibrosus

An anisotropic multiphysics damage model is developed to characterize the couplings among multiple physical fields within soft tissues and the tissue damage based on thermodynamic principles. This anisotropic multiphysics damage model integrates the continuum mixture theory and a continuum damage model, and the anisotropic damage is considered by evolution of internal damage variables governing the anisotropic mechanical behaviors of tissues. The energy dissipation associated with the transport of fluid and ions is generally related to tissue damage. The anisotropic multiphysics damage model is applied to simulate a case of annulus fibrosus (AF) damage in an isolated intervertebral disc under compression, to understand the damage initiation and propagation. It is found that, for this case (with 1000 N/s of compression rate and neglected ground matrix damage), the damage initiated in the outer and middle posterior regions of AF at about 700 N of axial compression. The region-dependent yield stretch ratio predicted by this model is consistent with experimental findings. A sensitive study on the damage parameters is also presented. This study provides an additional insight into AF damage in the isolated disc under mechanical compression.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson's ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4+/-14.3 MPa versus 5.6+/-4.7 MPa, outer versus inner sites) and the Poisson's ratio v21 (0.67+/-0.22 versus 1.6+/-0.7, outer versus inner), but not in the axial modulus (0.8+/-0.9 MPa) or the Poisson's ratios V12 (1.8+/-1.4) or v13 (0.6+/-0.7). These properties were implemented in a linear an isotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for th     

Identification of regional mechanical anisotropy in soft tissue analogs

In a previous work (Raghupathy and Barocas, 2010, "Generalized Anisotropic Inverse Mechanics for Soft Tissues,"J. Biomech. Eng., 132(8), pp. 081006), a generalized anisotropic inverse mechanics method applicable to soft tissues was presented and tested against simulated data. Here we demonstrate the ability of the method to identify regional differences in anisotropy from full-field displacements and boundary forces obtained from biaxial extension tests on soft tissue analogs. Tissue heterogeneity was evaluated by partitioning the domain into homogeneous subdomains. Tests on elastomer samples demonstrated the performance of the method on isotropic materials with uniform and nonuniform properties. Tests on fibroblast-remodeled collagen cruciforms indicated a strong correlation between local structural anisotropy (measured by polarized light microscopy) and the evaluated local mechanical anisotropy. The results demonstrate the potential to quantify regional anisotropic material behavior on an intact tissue sample.