Remodeling of the collagen fiber architecture due to compaction in small vessels under tissue engineered conditions

Mechanical loading protocols in tissue engineering (TE) aim to improve the deposition of a properly organized collagen fiber network. In addition to collagen remodeling, these conditioning protocols can result in tissue compaction. Tissue compaction is beneficial to tissue collagen alignment, yet it may lead to a loss of functionality of the TE construct due to changes in geometry after culture. Here, a mathematical model is presented to relate the changes in collagen architecture to the local compaction within a TE small blood vessel, assuming that under static conditions, compaction is the main factor responsible for collagen fiber organization. An existing structurally based model is extended to incorporate volumetric tissue compaction. Subsequently, the model is applied to describe the collagen architecture of TE constructs under either strain based or stress based stimulus functions. Our computations indicate that stress based simulations result in a helical collagen fiber distribution along the vessel wall. The helix pitch angle increases from a circumferential direction in the inner wall, over about 45 deg in the middle vessel layer, to a longitudinal direction in the outer wall. These results are consistent with experimental data from TE small diameter blood vessels. In addition, our results suggest a stress dependent remodeling of the collagen, suggesting that cell traction is responsible for collagen orientation. These findings may be of value to design improved mechanical conditioning protocols to optimize the collagen architecture in engineered tissues.     

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.     

A computational model to describe the collagen orientation in statically cultured engineered tissues

Collagen provides cardiovascular tissues with the ability to withstand haemodynamic loads. A similar network is essential to obtain in tissue-engineered (TE) samples of the same nature. Yet, the mechanism of collagen orientation is not fully understood. Typically collagen remodelling is linked to mechanical loading. However, TE constructs also show an oriented collagen network when developed under static culture. Experiments under these conditions also indicate that the tissue gradually compacts due to contractile stresses developed in the α-actin fibres of the cells. Therefore, it is hypothesised that cellular contractile stresses are responsible for collagen orientation. A model describing the cellular α-actin turnover and the stresses developed by them is integrated in a structural constitutive model describing the mechanical behaviour of collagen fibres. Results show that the model can successfully capture the sample compaction, tissue stress generation and its heterogeneous collagen arrangement.     

Improved prediction of the collagen fiber architecture in the aortic heart valve

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.     

Biaxial tensile testing and constitutive modeling of human supraspinatus tendon

The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon's two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R(2) ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.     

Strain history and TGF-β1 induce urinary bladder wall smooth muscle remodeling and elastogenesis

Mechanical cues that trigger pathological remodeling in smooth muscle tissues remain largely unknown and are thought to be pivotal triggers for strain-induced remodeling. Thus, an understanding of the effects mechanical stimulation is important to elucidate underlying mechanisms of disease states and in the development of methods for smooth muscle tissue regeneration. For example, the urinary bladder wall (UBW) adaptation to spinal cord injury (SCI) includes extensive hypertrophy as well as increased collagen and elastin, all of which profoundly alter its mechanical response. In addition, the pro-fibrotic growth factor TGF-β1 is upregulated in pathologies of other smooth muscle tissues and may contribute to pathological remodeling outcomes. In the present study, we utilized an ex vivo organ culture system to investigate the response of UBW tissue under various strain-based mechanical stimuli and exogenous TGF-β1 to assess extracellular matrix (ECM) synthesis, mechanical responses, and bladder smooth muscle cell (BSMC) phenotype. Results indicated that a 0.5-Hz strain frequency triangular waveform stimulation at 15% strain resulted in fibrillar elastin production, collagen turnover, and a more compliant ECM. Further, this stretch regime induced changes in cell phenotype while the addition of TGF-β1 altered this phenotype. This phenotypic shift was further confirmed by passive strip biomechanical testing, whereby the bladder groups treated with TGF-β1 were more compliant than all other groups. TGF-β1 increased soluble collagen production in the cultured bladders. Overall, the 0.5-Hz strain-induced remodeling caused increased compliance due to elastogenesis, similar to that seen in early SCI bladders. Thus, organ culture of bladder strips can be used as an experimental model to examine ECM remodeling and cellular phenotypic shift and potentially elucidate BMSCs ability to produce fibrillar elastin using mechanical stretch either alone or in combination with growth factors.     

Local variations in the micromechanical properties of mouse femur: the involvement of collagen fiber orientation and mineralization

In this study we sought to understand the material level basis for local variations in the uniaxial micromechanical properties of mouse cortical bone. It was hypothesized that the opposing anterior and posterior quadrants will significantly differ in terms of their mechanical function, such that, the anterior portion will be stronger in tension whereas the posterior quadrant will be stronger in compression. Mechanical properties were assessed via microtensile and microcompressive tests of standardized coupon-shaped specimens from femurs of Swiss Webster mice (9 weeks). The mineralization and mineral quality was assessed via Raman spectroscopy and the overall collagen orientation was investigated with quantitative polarized imaging. Micromechanical tests demonstrated that the modulus, yield stress, maximum stress and fracture energy of the posterior quadrant was 66%, 53%, 42% and 31% of anterior quadrant; however, the compressive properties did not differ between the two quadrants. Raman microspectroscopic analysis indicated that the mineral matrix ratio, mineral crystallinity and carbonation did not vary between the quadrants. However, the collagen fibers in the anterior quadrant were significantly (p<0.05) more oriented along the longer axis of the diaphyseal shaft than the collagen fibers of the posterior quadrant. Therefore, we concluded that the orientation of collagen fibers with respect to the anatomical loading axis has a profound effect on the uniaxial mechanical function of murine bone. It will be a matter of further research to reveal the role of local variations in the mode of stress on this material level dichotomy in tissue organization and mechanical function.     

Collagen fiber organization is related to mechanical properties and remodeling in equine bone. A comparsion of two methods

We studied birefringence as an indicator of collagen fiber orientation in the diaphysis of the equine third metacarpal bone. We had previously shown that tissue from the lateral cortex of this bone is stronger monotonically, but less fatigue resistant, than tissue from the medial and dorsal regions. To learn whether collagen fiber orientation might play a role in this regional specialization, we tested three hypotheses using the same specimens: (1) collagen fiber orientation is regionally dependent; (2) remodeling changes collagen fiber orientation; (3) longitudinal collagen fibers correlate positively with modulus and monotonic bending strength and negatively with flexural fatigue life. Beams (N=36) cut parallel to the long axes of six pairs of bones had been tested to determine elastic modulus (N=36), and fatigue life (N=24) or monotonic strength (N=12) in four-point bending. Subsequently, histologic cross-sections were prepared, and porosity, active remodeling and past remodeling were quantified. Birefringence was measured as an indicator of transverse collagen orientation using plane-polarized light (PPL), and again using circularly polarized light (CPL). The CPL measurement was less variable than the PPL measurement. Both birefringence measures indicated that collagen was more longitudinally oriented in the lateral cortex than in the other two cortices. Longitudinally disposed collagen correlated with greater modulus and monotonic strength, but did not correlate with fatigue life. Remodeling was associated with more transverse collagen. Neither measure of birefringence was significantly correlated with porosity. It was concluded that, in the equine cannon bone, longitudinal collagen fiber orientation is regionally variable, contributes to increased modulus and strength but not fatigue life, and is reduced by osteonal remodeling.     

Disorganized collagen scaffold interferes with fibroblast mediated deposition of organized extracellular matrix in vitro

Many tissue engineering applications require the remodeling of a degradable scaffold either in vitro or in situ. Although inefficient remodeling or failure to fully remodel the temporary matrix can result in a poor clinical outcome, very few investigations have examined in detail, the interaction of regenerative cells with temporary scaffoldings. In a recent series of investigations, randomly oriented collagen gels were directly implanted into human corneal pockets and followed for 24 months. The resulting remodeling response exhibited a high degree of variability which likely reflects differing regenerative/synthetic capacity across patients. Given this variability, we hypothesize that a disorganized, degradable provisional scaffold could be disruptive to a uniform, organized reconstruction of stromal matrix. In this investigation, two established corneal stroma tissue engineering culture systems (collagen scaffold‐based and scaffold‐free) were compared to determine if the presence of the disorganized collagen gel influenced matrix production and organizational control exerted by primary human corneal fibroblast cells (PHCFCs). PHCFCs were cultured on thin disorganized reconstituted collagen substrate (RCS—five donors: average age 34.4) or on a bare polycarbonate membrane (five donors: average age 32.4 controls). The organization and morphology of the two culture systems were compared over the long‐term at 4, 8, and 11/12 weeks. Construct thickness and extracellular matrix organization/alignment was tracked optically with bright field and differential interference contrast (DIC) microscopy. The details of cell/matrix morphology and cell/matrix interaction were examined with standard transmission, cuprolinic blue and quick‐freeze/deep‐etch electron microscopy. Both the scaffold‐free and the collagen‐based scaffold cultures produced organized arrays of collagen fibrils. However, at all time points, the amount of organized cell‐derived matrix in the scaffold‐based constructs was significantly lower than that produced by scaffold‐free constructs (controls). We also observed significant variability in the remodeling of RCS scaffold by PHCFCs. PHCFCs which penetrated the RCS scaffold did exert robust local control over secreted collagen but did not appear to globally reorganize the scaffold effectively in the time period of the study. Consistent with our hypothesis, the results demonstrate that the presence of the scaffold appears to interfere with the global organization of the cell‐derived matrix. The production of highly organized local matrix by fibroblasts which penetrated the scaffold suggests that there is a mechanism which operates close to the cell membrane capable of controlling fibril organization. Nonetheless, the local control of the collagen alignment produced by cells within the scaffold was not continuous and did not result in overall global organization of the construct. Using a disorganized scaffold as a guide to produce highly organized tissue has the potential to delay the production of useful matrix or prevent uniform remodeling. The results of this study may shed light on the recent attempts to use disorganized collagenous matrix as a temporary corneal replacement in vivo which led to a variable remodeling response. Biotechnol. Bioeng. 2012; 109: 2683–2698. © 2012 Wiley Periodicals, Inc.     

A physically motivated constitutive model for cell-mediated compaction and collagen remodeling in soft tissues

Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.     

Imaging of Scleral Collagen Deformation Using Combined Confocal Raman Microspectroscopy and Polarized Light Microscopy Techniques

This work presents an optospectroscopic characterization technique for soft tissue microstructure using site-matched confocal Raman microspectroscopy and polarized light microscopy. Using the technique, the microstructure of soft tissue samples is directly observed by polarized light microscopy during loading while spatially correlated spectroscopic information is extracted from the same plane, verifying the orientation and arrangement of the collagen fibers. Results show the response and orientation of the collagen fiber arrangement in its native state as well as during tensile and compressive loadings in a porcine sclera model. An example is also given showing how the data can be used with a finite element program to estimate the strain in individual collagen fibers. The measurements demonstrate features that indicate microstructural reorganization and damage of the sclera’s collagen fiber arrangement under loading. The site-matched confocal Raman microspectroscopic characterization of the tissue provides a qualitative measure to relate the change in fibrillar arrangement with possible chemical damage to the collagen microstructure. Tests and analyses presented here can potentially be used to determine the stress-strain behavior, and fiber reorganization of the collagen microstructure in soft tissue during viscoelastic response.     

The Evolution of Collagen Fiber Orientation in Engineered Cardiovascular Tissues Visualized by Diffusion Tensor Imaging

The collagen architecture is the major determinant of the function and mechanical behavior of cardiovascular tissues. In order to engineer a functional and load-bearing cardiovascular tissue with a structure that mimics the native tissue to meet in vivo mechanical demands, a complete understanding of the collagen orientation mechanism is required. Several methods have been used to visualize collagen architecture in tissue-engineered (TE) constructs, but they either have a limited imaging depth or have a complicated set up. In this study, Diffusion Tensor Imaging (DTI) is explored as a fast and reliable method to visualize collagen arrangement, and Confocal Laser Scanning Microscopy (CLSM) was used as a validation technique. Uniaxially constrained TE strips were cultured for 2 days, 10 days, 3 and 6 weeks to investigate the evolution of the collagen orientation with time. Moreover, a comparison of the collagen orientation in high and low aspect ratio (length/width) TE constructs was made with both methods. Both methods showed similar fiber orientation in TE constructs. Collagen fibers in the high aspect ratio samples were mostly aligned in the constrained direction, while the collagen fibers in low aspect ratio strips were mainly oriented in the oblique direction. The orientation changed to the oblique direction by extending culture time and could also be visualized. DTI captured the collagen orientation differences between low and high aspect ratio samples and with time. Therefore, it can be used as a fast, non-destructive and reliable tool to study the evolution of the collagen orientation in TE constructs.     

Observations of multiscale, stress-induced changes of collagen orientation in tendon by polarized Raman spectroscopy

Collagen is a versatile structural molecule in nature and is used as a building block in many highly organized tissues, such as bone, skin, and cornea. The functionality and performance of these tissues are controlled by their hierarchical organization ranging from the molecular up to macroscopic length scales. In the present study, polarized Raman microspectroscopic and imaging analyses were used to elucidate collagen fibril orientation at various levels of structure in native rat tail tendon under mechanical load. In situ humidity-controlled uniaxial tensile tests have been performed concurrently with Raman confocal microscopy to evaluate strain-induced chemical and structural changes of collagen in tendon. The methodology is based on the sensitivity of specific Raman scattering bands (associated with distinct molecular vibrations, such as the amide I) to the orientation and the polarization direction of the incident laser light. Our results, based on the changing intensity of Raman lines as a function of orientation and polarization, support a model where the crimp and gap regions of collagen hierarchical structure are straightened at the tissue and molecular level, respectively. However, the lack of measurable changes in Raman peak positions throughout the whole range of strains investigated indicates that no significant changes of the collagen backbone occurs with tensing and suggests that deformation is rather redistributed through other levels of the hierarchical structure.     

Fibroblasts retain their tissue phenotype when grown in three-dimensional collagen gels

Fibroblasts are responsible for the synthesis, assembly, deposition, and organization of extracellular matrix molecules, and thus determine the morphology of connective tissues. Deposition of matrix molecules occurs in extracellular compartments, where the sequential stages are under cellular control. Cell orientation/polarity is important in determining how the cell orients these extracytoplasmic compartments and therefore how the matrix is assembled and oriented. However, the control of cell orientation is not understood. Fibroblasts from three tissues with different morphologies were studied to determine whether cells maintained their characteristic phenotype. Fibroblasts from cornea, which in vivo are oriented in orthogonal layers along with their matrix; from tendon, a uniaxial connective tissue, where cells orient parallel to each other; and from dermis, a connective tissue with no apparent cellular orientation, were used to study cell morphology and orientation in three-dimensional collagen gels. The different cells were grown for 3 and 7 days in identical three-dimensional collagen gels with a nonoriented matrix. Confocal fluorescence microscopy demonstrated that corneal fibroblasts oriented perpendicular to one another at 3 days, and after 7 days in hydrated gels these cells formed orthogonal sheets. Tendon fibroblasts were shown by the same methods to orient parallel to one another in bundles at both 3 and 7 days, throughout the depth of the gel. Dermal fibroblasts showed no apparent orientation throughout the hydrated gels at either time point examined. The organization of these different cell types was consistent with their tissue of origin as was the cell structure and polarity. These studies imply that cellular and tissue phenotype is innate to differentiated fibroblasts and that these cells will orient in a tissue-specific manner regardless of the extracellular matrix present.     

Understanding strain-induced collagen matrix development in engineered cardiovascular tissues from gene expression profiles

Mechanical conditioning is often used to enhance collagen synthesis, remodeling and maturation and, hence, the structural and mechanical properties of engineered cardiovascular tissues. Intermittent straining, i.e., alternating periods of cyclic and static strain, has previously been shown to result in more mature tissue compared with continuous cyclic straining. Nevertheless, the underlying mechanism is unknown. We have determined the short-term effects of continuous cyclic strain and of cyclic strain followed by static strain at the gene expression level to improve insight into the mechano-regulatory mechanism of intermittent conditioning on collagen synthesis, remodeling and maturation. Tissue-engineered constructs, consisting of human vascular-derived cells seeded onto rapidly degrading PGA/P4HB scaffolds, were conditioned with 4% strain at 1 Hz for 3 h in order to study the immediate effects of cyclic strain (n=18). Next, the constructs were either subjected to ongoing cyclic strain (4% at 1 Hz; n=9) or to static strain (n=9). Expression levels of genes involved in collagen synthesis, remodeling and maturation were studied at various time points up to 24 h within each straining protocol. The results indicate that a period of static strain following cyclic strain favors collagen synthesis and remodeling, whereas ongoing cyclic strain shifts this balance toward collagen remodeling and maturation. The data suggest that, with prolonged culture, the conditioning protocol should be changed from intermittent straining to continuous cyclic straining to improve collagen maturation after its synthesis and, hence, the tissue (mechanical) properties.     

Development of fibroblast-seeded collagen gels under planar biaxial mechanical constraints: a biomechanical study

Prior studies indicated that mechanical loading influences cell turnover and matrix remodeling in tissues, suggesting that mechanical stimuli can play an active role in engineering artificial tissues. While most tissue culture studies focus on influence of uniaxial loading or constraints, effects of multi-axial loading or constraints on tissue development are far from clear. In this study, we examined the biaxial mechanical properties of fibroblast-seeded collagen gels cultured under four different mechanical constraints for 6 days: free-floating, equibiaxial stretching (with three different stretch ratios), strip-biaxial stretching, and uniaxial stretching. Passive mechanical behavior of the cell-seeded gels was also examined after decellularization. A continuum-based two-dimensional Fung model was used to quantify the mechanical behavior of the gel. Based on the model, the value of stored strain energy and the ratio of stiffness in the stretching directions were calculated at prescribed strains for each gel, and statistical comparisons were made among the gels cultured under the various mechanical constraints. Results showed that gels cultured under the free-floating and equibiaxial stretching conditions exhibited a nearly isotropic mechanical behavior, while gels cultured under the strip-biaxial and uniaxial stretching conditions developed a significant degree of mechanical anisotropy. In particular, gels cultured under the equibiaxial stretching condition with a greater stretch ratio appeared to be stiffer than those with a smaller stretch ratio. Also, a decellularized gel was stiffer than its non-decellularized counterpart. Finally, the retained mechanical anisotropy in gels cultured under the strip-biaxial stretching and uniaxial stretching conditions after cell removal reflected an irreversible matrix remodeling.     

Reciprocal interactions between cells and extracellular matrix during remodeling of tissue constructs

Cells remodel extracellular matrix during tissue development and wound healing. Similar processes occur when cells compress and stiffen collagen gels. An important task for cell biologists, biophysicists, and tissue engineers is to guide these remodeling processes to produce tissue constructs that mimic the structure and mechanical properties of natural tissues. This requires an understanding of the mechanisms by which this remodeling occurs. Quantitative measurements of the contractile force developed by cells and the extent of compression and stiffening of the matrix describe the results of the remodeling processes. Not only do forces exerted by cells influence the structure of the matrix but also external forces exerted on the matrix can modulate the structure and orientation of the cells. The mechanisms of these processes remain largely unknown, but recent studies of the regulation of myosin-dependent contractile force and of cell protrusion driven by actin polymerization provide clues about the regulation of cellular functions during remodeling.     

A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.     

Modeling interlamellar interactions in angle-ply biologic laminates for annulus fibrosus tissue engineering

Mechanical function of the annulus fibrosus of the intervertebral disc is dictated by the composition and microstructure of its highly ordered extracellular matrix. Recent work on engineered angle-ply laminates formed from mesenchymal stem cell (MSC)-seeded nanofibrous scaffolds indicates that the organization of collagen fibers into planes of alternating alignment may play an important role in annulus fibrosus tissue function. Specifically, these engineered tissues can resist tensile deformation through shearing of the interlamellar matrix as layers of collagen differentially reorient under load. In the present work, a hyperelastic constitutive model was developed to describe the role of interlamellar shearing in reinforcing the tensile response of biologic laminates, and was applied to experimental results from engineered annulus constructs formed from MSC-seeded nanofibrous scaffolds. By applying the constitutive model to uniaxial tensile stress–strain data for bilayers with three different fiber orientations, material parameters were generated that characterize the contributions of extrafibrillar matrix, fibers, and interlamellar shearing interactions. By 10 weeks of in vitro culture, interlamellar shearing accounted for nearly 50% of the total stress associated with uniaxial extension in the anatomic range of ply angle. The model successfully captured changes in function with extracellular matrix deposition through variations in the magnitude of model parameters with culture duration. This work illustrates the value of engineered tissues as tools to further our understanding of structure–function relations in native tissues and as a test-bed for the development of constitutive models to describe them.