Structure-strength relations in mammalian tendon.

The stress-strain relations in mammalian tendon are analyzed in terms of the structure and mechanics of its constituents. The model considers the tensile and bending strength of the collagen fibers, the tensile strength of the elastin fibers, and the interaction between the matrix and the collagen fibers. The stress-strain relations are solved through variational considerations by assuming that the fibermaxtrix interactions can be modeled as beam on elastic foundation. The tissue thus modeled is a hyperelastic material. It is further shown that on the basis of the model, the dominant parameters to the tendon's behavior can be evaluated from simple tensile tests.     

Connecting incremental shear modulus and Poisson's ratio of lung tissue with morphology and rheology of microstructure

The width and curvature of the collagen and elastin fiber bundles in the human pulmonary interalveolar septa and alveolar mouths are measured. The data, together with the known mechanical properties of collagen and elastin fibers, are used to derive the incremental elastic moduli of the lung tissue. The constitutive equation for small incremental stress and strain superposed on a homeostatic inflated lung is linear and isotropic, and characterized by two material constants.     

The orthotropic viscoelastic behavior of aortic elastin

In this paper, we studied the viscoelastic behaviors of isolated aortic elastin using combined modeling and experimental approaches. Biaxial stress relaxation and creep experiments were performed to study the time-dependent behavior of elastin. Experimental results reveal that stress relaxation preconditioning is necessary in order to obtain repeatable stress relaxation responses. Elastin exhibits less stress relaxation than intact or decellularized aorta. The rate of stress relaxation of intact and decellularized aorta is linearly dependent on the initial stress levels. The rate of stress relaxation for elastin increases linearly at stress levels below about 60 kPa; however, the rate changes very slightly at higher initial stress levels. Experimental results also show that creep response is negligible for elastin, and the intact or decellularized aorta. A quasi-linear viscoelasticity model was incorporated into a statistical mechanics based eight-chain microstructural model at the fiber level to simulate the orthotropic viscoelastic behavior of elastin. A user material subroutine was developed for finite element analysis. Results demonstrate that this model is suitable to capture both the orthotropic hyperelasticity and viscoelasticity of elastin.     

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.     

Introducing mesoscopic information into constitutive equations for arterial walls

We propose a new elastic constitutive law for arterial tissue in which the limiting polymeric chain extensibility of both collagen and elastin fibres is accounted for. The elastic strain-energy function is separated additively into two parts: an isotropic contribution associated with the matrix (incorporating the elastin fibre network) and an anisotropic one associated with the collagen fibres. Information on the limiting extensibility in each case provides some mesoscopic input into the model. The (logarithm-based) model is compared with the Fung-Demiray exponential model and certain other recently proposed models. Some aspects of the elastic response under extension and inflation of a thin-walled circular cylindrical tube (the artery) are then examined and compared with the corresponding response of a rubber-like tube. We point out that our model, when both isotropic and anisotropic terms are included, can be developed to accommodate changing mechanical properties associated with degradation of the elastin and collagen by considering the material constants that define the limit of chain extensibility to evolve in time.     

Contributions of Glycosaminoglycans to Collagen Fiber Recruitment in Constitutive Modeling of Arterial Mechanics

The contribution of glycosaminoglycans (GAGs) to the biological and mechanical functions of biological tissue has emerged as an important area of research. GAGs provide structural basis for the organization and assembly of extracellular matrix (ECM). The mechanics of tissue with low GAG content can be indirectly affected by the interaction of GAGs with collagen fibers, which have long been known to be one of the primary contributors to soft tissue mechanics. Our earlier study showed that enzymatic GAG depletion results in straighter collagen fibers that are recruited at lower levels of stretch, and a corresponding shift in earlier arterial stiffening (Mattson et al., 2016). In this study, the effect of GAGs on collagen fiber recruitment was studied through a structure-based constitutive model. The model incorporates structural information, such as fiber orientation distribution, content, and recruitment of medial elastin, medial collagen, and adventitial collagen fibers. The model was first used to study planar biaxial tensile stress-stretch behavior of porcine descending thoracic aorta. Changes in elastin and collagen fiber orientation distribution, and collagen fiber recruitment were then incorporated into the model in order to predict the stress-stretch behavior of GAG depleted tissue. Our study shows that incorporating early collagen fiber recruitment into the model predicts the stress-stretch response of GAG depleted tissue reasonably well (rms = 0.141); considering further changes of fiber orientation distribution does not improve the predicting capability (rms = 0.149). Our study suggests an important role of GAGs in arterial mechanics that should be considered in developing constitutive models.     

Application of a microstructural constitutive model of the pulmonary artery to patient-specific studies: validation and effect of orthotropy

We applied a statistical mechanics based microstructural model of pulmonary artery mechanics, developed from our previous studies of rats with pulmonary arterial hypertension (PAH), to patient-specific clinical studies of children with PAH. Our previous animal studies provoked the hypothesis that increased cross-linking density of the molecular chains may be one biological remodeling mechanism by which the PA stiffens in PAH. This study appears to further confirm this hypothesis since varying molecular cross-linking density in the model allows us to simulate the changes in the P-D loops between normotensive and hypertensive conditions reasonably well. The model was combined with patient-specific three-dimensional vascular anatomy to obtain detailed information on the topography of stresses and strains within the proximal branches of the pulmonary vasculature. The effect of orthotropy on stressstrain within the main and branch PAs obtained from a patient was explored. This initial study also puts forward important questions that need to be considered before combining the microstructural model with complex patient-specific vascular geometries.     

Regional variations in the nonlinearity and anisotropy of bovine aortic elastin

Arterial walls have a regular and lamellar organization of elastin present as concentric fenestrated networks in the media. In contrast, elastin networks are longitudinally oriented in layers adjacent to the media. In a previous model exploring the biomechanics of arterial elastin, we had proposed a microstructurally motivated strain energy function modeled using orthotropic material symmetry. Using mechanical experiments, we showed that the neo-Hookean term had a dominant contribution to the overall form of the strain energy function. In contrast, invariants corresponding to the two fiber families had smaller contributions. To extend these investigations, we use biaxial force-controlled experiments to quantify regional variations in the anisotropy and nonlinearity of elastin isolated from bovine aortic tissues proximal and distal to the heart. Results from this study show that tissue nonlinearity significantly increases distal to the heart as compared to proximally located regions ( $p<0.05$ ). Distally located samples also have a trend for increased anisotropy ( $p=0.07$ ), with the circumferential direction stiffer than the longitudinal, as compared to an isotropic and relatively linear response for proximally located elastin samples. These results are consistent with the underlying tissue histology from proximally located samples that had higher optical density ( $p<0.05$ ), fiber thickness ( $p<0.05$ ), and trend for lower tortuosity ( $p<0.07$ ) in elastin fibers as compared to the thinner and highly undulating elastin fibers isolated from distally located samples. Our studies suggest that it is important to consider elastin fiber orientations in investigations that use microstructure-based models to describe the contributions of elastin and collagen to arterial mechanics.     

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

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

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

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

The Mechanobiology of Pulmonary Vascular Remodeling in the Congenital Absence of eNOS

Primary pulmonary hypertension is a rare but deadly disease. Lungs extracted from PPH patients are deficient in endothelial nitric oxide synthase (eNOS), making the eNOS-null mouse a potentially useful model of the disease. To better understand the progression of pulmonary vascular remodeling in the congenital absence of eNOS, we induced pulmonary hypertension in eNOS-null mice using hypobaric hypoxia, and then quantified large artery structure and function in contralateral vessels. In particular, to assess structure we quantified diameter, wall thickness, and collagen, elastin and smooth muscle cell content; to quantify function we performed pressure-diameter tests. After remodeling, the pulmonary arteries had increased wall, collagen and elastin thicknesses compared to controls (P<0.05). The remodeled pulmonary arteries also had increased elastic moduli at low and high strains compared to controls (P<0.05). The increases in moduli at low and high strain correlated with increases in elastin and collagen thickness, respectively (P<0.05). These results provide insight into the mechanobiology of pulmonary vascular remodeling in the congenital absence of eNOS, and the coupled nature of these changes.     

A Model of Bone Adaptation Using a Global Optimisation Criterion Based on the Trajectorial Theory of Wolff

Julius Wolff originally proposed that trabecular bone was influenced by mechanical stresses during the formative processes of growth and repair such that trabeculae were required to intersect at right angles. In this work, we have developed an analytical parametric microstructural model, which captures this restriction. Using homogenisation theory, a global material model was obtained. An optimal structure constructed of the homogenised material could then be found by optimising a cost function accounting for both the structural stiffness and the biological cost associated with metabolic maintenance of the bone tissue. The formulation was applied to an example problem of the proximal femur. Optimal densities and orientations were obtained for single load cases. The situation of multiple loads was also considered. In this case, we observe that the alignment of principal strains with the material orthotropy direction is, in general, not possible for all load cases. Thus less restrictive microstructures (nonorthotropic) will yield higher structural stiffnesses than strictly orthotropic microstructures.     

Multiphoton microscopy observations of 3D elastin and collagen fiber microstructure changes during pressurization in aortic media

Elastin and collagen fibers play important roles in the mechanical properties of aortic media. Because knowledge of local fiber structures is required for detailed analysis of blood vessel wall mechanics, we investigated 3D microstructures of elastin and collagen fibers in thoracic aortas and monitored changes during pressurization. Using multiphoton microscopy, autofluorescence images from elastin and second harmonic generation signals from collagen were acquired in media from rabbit thoracic aortas that were stretched biaxially to restore physiological dimensions. Both elastin and collagen fibers were observed in all longitudinal–circumferential plane images, whereas alternate bright and dark layers were observed along the radial direction and were recognized as elastic laminas (ELs) and smooth muscle-rich layers (SMLs), respectively. Elastin and collagen fibers are mainly oriented in the circumferential direction, and waviness of collagen fibers was significantly higher than that of elastin fibers. Collagen fibers were more undulated in longitudinal than in radial direction, whereas undulation of elastin fibers was equibiaxial. Changes in waviness of collagen fibers during pressurization were then evaluated using 2-dimensional fast Fourier transform in mouse aortas, and indices of waviness of collagen fibers decreased with increases in intraluminal pressure. These indices also showed that collagen fibers in SMLs became straight at lower intraluminal pressures than those in EL, indicating that SMLs stretched more than ELs. These results indicate that deformation of the aorta due to pressurization is complicated because of the heterogeneity of tissue layers and differences in elastic properties of ELs, SMLs, and surrounding collagen and elastin.     

Changes in the structure-function relationship of elastin and its impact on the proximal pulmonary arterial mechanics of hypertensive calves

Extracellular matrix remodeling has been proposed as one mechanism by which proximal pulmonary arteries stiffen during pulmonary arterial hypertension (PAH). Although some attention has been paid to the role of collagen and metallomatrix proteins in affecting vascular stiffness, much less work has been performed on changes in elastin structure-function relationships in PAH. Such work is warranted, given the importance of elastin as the structural protein primarily responsible for the passive elastic behavior of these conduit arteries. Here, we study structure-function relationships of fresh arterial tissue and purified arterial elastin from the main, left, and right pulmonary artery branches of normotensive and hypoxia-induced pulmonary hypertensive neonatal calves. PAH resulted in an average 81 and 72% increase in stiffness of fresh and digested tissue, respectively. Increase in stiffness appears most attributable to elevated elastic modulus, which increased 46 and 65%, respectively, for fresh and digested tissue. Comparison between fresh and digested tissues shows that, at 35% strain, a minimum of 48% of the arterial load is carried by elastin, and a minimum of 43% of the change in stiffness of arterial tissue is due to the change in elastin stiffness. Analysis of the stress-strain behavior revealed that PAH causes an increase in the strains associated with the physiological pressure range but had no effect on the strain of transition from elastin-dominant to collagen-dominant behavior. These results indicate that mechanobiological adaptations of the continuum and geometric properties of elastin, in response to PAH, significantly elevate the circumferential stiffness of proximal pulmonary arterial tissue.     

Genetically engineered chondrocytes overexpressing elastin improve cell retention and chondrogenesis in a three-dimensional GelMA culture system

Elastic cartilage possesses many elastic fibers and has a high degree of elasticity. However, insufficient elastic fiber production remains unsolved in elastic cartilage tissue engineering. Exogenous elastin is difficult to degrade and violates cell proliferation and migration during cartilage regeneration. Moreover, exogenous elastic fibers are difficult to assemble with endogenous extracellular matrix components. We produced genetically engineered chondrocytes overexpressing elastin to boost endogenous elastic fiber production. After identifying that genetic manipulation hardly impacted the cell viability and chondrogenesis of chondrocytes, we co-cultured genetically engineered chondrocytes with untreated chondrocytes in a three-dimensional gelatin methacryloyl (GelMA) system. In vitro study showed that the co-culture system produced more elastic fibers and increased cell retention, resulting in strengthened mechanics than the control system with untreated chondrocytes. Moreover, in vivo implantation revealed that the co-culture GelMA system greatly resisted host tissue invasion by promoting elastic fiber production and cartilage tissue regeneration compared with the control system. In summary, our study indicated that genetically engineered chondrocytes overexpressing elastin are efficient and safe for promoting elastic fiber production and cartilage regeneration in elastic cartilage tissue engineering.     

The layered structure of coronary adventitia under mechanical load

The mechanical loading-deformation relation of elastin and collagen fibril bundles is fundamental to understanding the microstructural properties of tissue. Here, we use multiphoton microscopy to obtain quantitative data of elastin and collagen fiber bundles under in situ loading of coronary adventitia. Simultaneous loading-imaging experiments on unstained fresh coronary adventitia allowed morphometric measurements of collagen and elastin fibril bundles and their individual deformation. Fiber data were analyzed at five different distension loading points (circumferential stretch ratio λ_θ = 1.0, 1.2, 1.4, 1.6, and 1.8) at a physiological axial stretch ratio of λ_axial = 1.3. Four fiber geometrical parameters were used to quantify the fibers: orientation angle, waviness, width, and area fraction. The results show that elastin and collagen fibers in inner adventitia form concentric densely packed fiber sheets, and the fiber orientation angle, width, and area fraction vary transmurally. The extent of fiber deformation depends on the initial orientation angle at no-distension state (λ_θ = 1.0 and λ_axial = 1.3). At higher distension loading, the orientation angle and waviness of fibers decrease linearly, but the width of collagen fiber is relatively constant at λ_θ = 1.0–1.4 and then decrease linearly for λ_θ ≥ 1.4. A decrease of the relative dispersion (SD/mean) of collagen fiber waviness suggests a heterogeneous mechanical response to loads. This study provides fundamental microstructural data for coronary artery biomechanics and we consider it seminal for structural models.     

A composite micromechanical model for connective tissues: Part I--Theory.

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].     

Elastic fiber production in cardiovascular tissue-equivalents.

Elastic fiber incorporation is critical to the success of tissue-engineered arteries and heart valves. Elastic fibers have not yet been observed in tissue-engineered replacements fabricated in vitro with smooth muscle cells. Here, rat smooth muscle cells (SMC) or human dermal fibroblasts (HDF) remodeled collagen or fibrin gels for 4 weeks as the basis for a completely biological cardiovascular tissue replacement. Immunolabeling, alkaline extraction and amino acid analysis identified and quantified elastin. Organized elastic fibers formed when neonatal SMC were cultured in fibrin gel. Fibrillin-1 deposition occurred but elastin was detected in regions without fibrillin-1, indicating that a microfibril template is not required for elastic fiber formation within fibrin. Collagen did not support substantial elastogenesis by SMC. The quantity of crosslinked elastic fibers was enhanced by treatment with TGF-beta1 and insulin, concomitant with increased collagen production. These additives overcame ascorbate's inhibition of elastogenesis in fibrin. The elastic fibers that formed in fibrin treated with TGF-beta1 and insulin contained crosslinks, as evidenced by the presence of desmosine and an altered elastin labeling pattern when beta-aminopropionitrile (BAPN) was added. These findings indicate that in vitro elastogenesis can be achieved in tissue engineering applications, and they suggest a physiologically relevant model system for the study of three-dimensional elastic structures.     

Age-dependent changes of airway and lung parenchyma in C57BL/6J mice.

In the current study, we hypothesize that senescent-dependent changes between airway and lung parenchymal tissues of C57BL/6J (B6) mice are not synchronized with respect to altered lung mechanics. Furthermore, aging modifications in elastin fiber and collagen content of the airways and lung parenchyma are remodeling events that differ with time. To test these hypotheses, we performed quasi-static pressure-volume (PV) curves and impedance measurements of the respiratory system in 2-, 20-, and 26-mo-old B6 mice. From the PV curves, the lung volume at 30 cmH(2)O pressure (V(30)) and respiratory system compliance (Crs) were significantly (P < 0.01) increased between 2 and 20 mo of age, representing about 80-84% of the total increase that occurred between 2 and 26 mo of age. Senescent-dependent changes in tissue damping and tissue elastance were analogous to changes in V(30) and Crs; that is, a majority of the parenchymal alterations in the lung mechanics occurred between 2 and 20 mo of age. In contrast, significant decreases in airway resistance (R) occurred between 20 and 26 mo of age; that is, the decrease in R between 2 and 20 mo of age represented only 29% (P > 0.05) of total decrease occurring through 26 mo. Morphometric analysis of the elastic fiber content in lung parenchyma was significantly (P < 0.01) decreased between 2 and 20 mo of age. To the contrary, increased collagen content was significantly delayed until 26 mo of age (P < 0.01, 2 vs. 26 mo). In conclusion, our data demonstrate that senescent-dependent changes in airway and lung tissue mechanics are not synchronized in B6 mice. Moreover, the reduction in elastic fiber content with age is an early lung remodeling event, and the increased collagen content in the lung parenchyma occurs later in senescence.