Strain transfer through the aortic valve

The complex structural organization of the aortic valve (AV) extracellular matrix (ECM) enables large and highly nonlinear tissue level deformations. The collagen and elastin (elastic) fibers within the ECM form an interconnected fibrous network (FN) and are known to be the main load-bearing elements of the AV matrix. The role of the FN in enabling deformation has been investigated and documented. However, there is little data on the correlation between tissue level and FN-level strains. Investigating this correlation will help establish the mode of strain transfer (affine or nonaffine) through the AV tissue as a key feature in microstructural modeling and will also help characterize the local FN deformation across the AV sample in response to applied tissue level strains. In this study, the correlation between applied strains at tissue level, macrostrains across the tissue surface, and local FN strains were investigated. Results showed that the FN strain distribution across AV samples was inhomogeneous and nonuniform, as well as anisotropic. There was no direct transfer of the deformation applied at tissue level to the fibrous network. Loading modes induced in the FN are different than those applied at the tissue as a result of different local strains in the valve layers. This nonuniformity of local strains induced internal shearing within the FN of the AV, possibly exposing the aortic valve interstitial cells (AVICs) to shear strains and stresses.     

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.     

Cellular stiffness response to external deformation: tensional homeostasis in a single fibroblast

Stiffness responses of fibroblasts were measured by scanning probe microscopy, following elongation or compression by deformation of an elastic substrate by 8%. The cellular stiffness, reflecting intracellular tension acting along stress fibers, decreased or increased instantly in response to the elongating or compressing stimuli, respectively. After this rapid change, the fibroblasts gradually recovered to their initial stiffness during the following 2 h, and then stabilized. The cells did not show conspicuous changes in shape after the 8% deformation during the SPM measurements. Fluorescence examination for GFP-actin demonstrated that the structure of the stress fibers was not altered noticeably by this small degree of deformation. Treatment with Y-27632, to inhibit myosin phosphorylation and abrogate cellular contractility, eliminated the change in stiffness after the mechanical elongation. These results indicate that fibroblasts possess a mechanism that regulates intracellular tension along stress fibers to maintain the cellular stiffness in a constant equilibrium state.     

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.     

Elastic Behavior and Platelet Retraction in Low- and High-Density Fibrin?Gels

Fibrin is a biopolymer that gives thrombi the mechanical strength to withstand the forces imparted on them by blood flow. Importantly, fibrin is highly extensible, but strain hardens at low deformation rates. The density of fibrin in clots, especially arterial clots, is higher than that in gels made at plasma concentrations of fibrinogen (3–10 mg/mL), where most rheology studies have been conducted. Our objective in this study was to measure and characterize the elastic regimes of low (3–10 mg/mL) and high (30–100 mg/mL) density fibrin gels using shear and extensional rheology. Confocal microscopy of the gels shows that fiber density increases with fibrinogen concentration. At low strains, fibrin gels act as thermal networks independent of fibrinogen concentration. Within the low-strain regime, one can predict the mesh size of fibrin gels by the elastic modulus using semiflexible polymer theory. Significantly, this provides a link between gel mechanics and interstitial fluid flow. At moderate strains, we find that low-density fibrin gels act as nonaffine mechanical networks and transition to affine mechanical networks with increasing strains within the moderate regime, whereas high-density fibrin gels only act as affine mechanical networks. At high strains, the backbone of individual fibrin fibers stretches for all fibrin gels. Platelets can retract low-density gels by >80% of their initial volumes, but retraction is attenuated in high-density fibrin gels and with decreasing platelet density. Taken together, these results show that the nature of fibrin deformation is a strong function of fibrin fiber density, which has ramifications for the growth, embolization, and lysis of thrombi.     

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r² = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.     

Microfibrils: a constitutive component of reticular fibers in the mouse lymph node

Summary Fibrous components other than collagen fibrils in the reticular fiber of mouse lymph node were studied by electron microscopy. Bundles of microfibrils not associated by elastin and single microfibrils dispersed among collagen fibrils were present. The diameter of the microfibrils was 13.29±2.43 nm (n=100). Elastin-associated microfibrils occurred at the periphery of the reticular fiber. Elastin was enclosed by microfibrils, thus forming the elastic fiber, which was clearly demonstrated by tannic acid-uranyl acetate staining. In the reticular fiber of lymph nodes, the elastic fiber consisted of many more microfibrils and a small amount of elastin. These microfibrils, together with the collagen fibrils, may contribut to the various functions of the reticular fibers.     

Mechanical properties of the tracheal mucosal membrane in the rabbit. II. Morphometric analysis.

Folding of the airway mucosal membrane provides a mechanical load that impedes airway smooth muscle contraction. Mechanical testing of rabbit tracheal mucosal membrane showed that the membrane is stiffer in the longitudinal than in the circumferential direction of the airway. To explain this difference in the mechanical properties, we studied the morphological structure of the rabbit tracheal mucosal membrane in both longitudinal and circumferential directions. The collagen fibers were found to form a random meshwork, which would not account for differences in stiffness in the longitudinal and circumferential directions. The volume fraction of the elastic fibers was measured using a point-counting technique. The orientation of the elastic fibers in the tissue samples was measured using a new method based on simple geometry and probability. The results showed that the volume fraction of the elastic fibers in the rabbit tracheal mucosal membrane was approximately 5% and that the elastic fibers were mainly oriented in the longitudinal direction. Age had no statistically significant effect on either the volume fraction or the orientation of the elastic fibers. Linear correlations were found between the steady-state stiffness and the quantity of the elastic fibers oriented in the direction of testing.     

A failure model for ligaments

We propose a failure model for ligament which assumes that sequential uncrimping and stretching of collagen fibers is responsible for the mechanical response of ligament. We further assume that the fibers rupture sequentially and in a brittle, strain-limited manner. The model was fit to stress strain curves obtained from medial collateral ligaments of New Zealand White rabbits from two age groups (4 and 7 months). The model indicated that collagen modulus values ranged from 300 to 680 MPa and that fiber failure strains ranged from 6 to 22%. The model provides a convenient means of describing the elastic and failure response of ligament using four structurally based parameters.     

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

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

Analysis of the tendinous structure in human masticatory muscles.

In the masticatory muscles, the development of bundles of the tendon was examined: they were composed of many collagen fibers and a few elastic fibers. In the masseter muscle, the property of the tendon differs in the distribution and size of collagen fibers and elastic fibers in comparison with those of other masticatory muscles. This difference is concerned with the kinetic force for the stress or the stretch of each tendon and muscle during jaw movement.     

Identification and characterisation of regional variations in the material properties of ureter according to microstructure

There are few previous studies on the elastic properties of ureter and most have been limited to essentially one-dimensional deformation measurements. The object of this study was, therefore, to identify regional variations in the multiaxial behaviour of rabbit ureter, subjected to in vitro inflation/extension testing under a physiological range of intraluminal pressures and longitudinal forces. A microstructure-motivated material model (via two- and four-fibre families in turn for elastin and collagen) was implemented and its capacity to mathematically characterise the experimental data contrasted favourably with that of the well-established phenomenological models, but it was compromised by parameter covariance. Extensive optimisation studies confirmed that the reduced model without contribution to the elastin and circumferential-fibre (collagen) families characterised the data equally well without over-parameterisation. In view of the fitted parameters, the ureteral tissue was stiffer longitudinally, justified by the preferential alignment of collagen along that axis and the lower ureter was stiffer than the upper ureter, justified by the histological observation of a thickest lamina propria, i.e. of highest collagen content, there. The lower ureter was less anisotropic than the upper ureter, possessing a comparatively larger amount of diagonally arranged collagen fibres in tunica mucosa, while having the usual amounts of longitudinally arranged fibres in tunica adventitia and of circumferentially arranged fibres in tunica muscularis. The present data may be used as inputs to mathematical models of the ureter, assessing regional and intramural stress distributions, through which it is hoped that an improved appreciation of ureteral function may be attained in both health and disease.     

Changes in protein secondary structure during gluten deformation studied by dynamic fourier transform infrared spectroscopy

Fourier transform infrared (FT-IR) spectroscopy was used to monitor changes in the secondary structure of wheat prolamins, the main components of gluten, during mechanical deformation in a series of cycles of extension and relaxation. A sample derived from protein bodies isolated from developing grain showed a buildup of persistent beta-sheet structure. In gluten, the ratio of beta-sheet to random and beta-turn structures changed on extension. After the applied force was released, the sample recovered some of its original shape and structure, but the material became stiffer in consecutive extension cycles. The relationship between gluten structure and mechanical properties is discussed in terms of a model in which conversion of beta-turn to beta-sheet structure is a response to extension and a means by which elastic energy is stored in the system.     

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.     

Durotaxis as an elastic stability phenomenon

It is well documented that directed motion of cells is influenced by substrate stiffness. When cells are cultured on a substrate of graded stiffness, they tend to move from softer to stiffer regions--a process known as durotaxis. In this study, we propose a mathematical model of durotaxis described as an elastic stability phenomenon. We model the cytoskeleton (CSK) as a planar system of prestressed elastic line elements representing actin stress fibers (SFs), which are anchored via focal adhesions (FAs) at their end points to an elastic substrate of variable stiffness. The prestress in the SFs exerts a pulling force on FAs reducing thereby their chemical potential. Using Maxwell's global stability criterion, we obtain that the model stability increases as it is moved from a softer towards a stiffer region of the substrate. Numerical simulations reveal that elastic stability of SFs has a predominantly stabilizing effect, greater than the stabilizing effect of decreasing chemical potential of FAs. This is a novel finding which indicates that elasticity of the CSK plays an important role in cell migration and mechanosensing in general.     

Prestress mediates force propagation into the nucleus

Several reports show that the nucleus is 10 times stiffer than the cytoplasm. Hence, it is not clear if intra-nuclear structures can be directly deformed by a load of physiologic magnitudes. If a physiologic load could not directly deform intra-nuclear structures, then signaling inside the nucleus would occur only via the mechanisms of diffusion or translocation. Using a synchronous detection approach, we quantified displacements of nucleolar structures in cultured airway smooth muscle cells in response to a localized physiologic load ( approximately 0.4 microm surface deformation) via integrin receptors. The nucleolus exhibited significant displacements. Nucleolar structures also exhibited significant deformation, with the dominant strain being the bulk strain. Increasing the pre-existing tensile stress (prestress) in the cytoskeleton significantly increased the stress propagation efficiency to the nucleolus (defined as nucleolus displacement per surface deformation) whereas decreasing the prestress significantly lowered the stress propagation efficiency to the nucleolus. Abolishing the stress fibers/actin bundles by plating the cells on poly-L-lysine-coated dishes dramatically inhibited stress propagation to the nucleolus. These results demonstrate that the prestress in the cytoskeleton is crucial in mediating stress propagation to the nucleolus, with implications for direct mechanical regulation of nuclear activities and functions.     

Determinants of Fluidlike Behavior and Effective Viscosity in Cross-Linked Actin Networks

The actin cortex has a well-documented ability to rapidly remodel and flow while maintaining long-range connectivity, but how this is achieved remains poorly understood. Here, we use computer simulations to explore how stress relaxation in cross-linked actin networks subjected to extensional stress depends on the interplay between network architecture and turnover. We characterize a regime in which a network response is nonaffine and stress relaxation is governed by the continuous dissipation of elastic energy via cyclic formation, elongation, and turnover of tension-bearing elements. Within this regime, for a wide range of network parameters, we observe a constant deformation (creep) rate that is linearly proportional to the rate of filament turnover, leading to a constant effective viscosity that is inversely proportional to turnover rate. Significantly, we observe a biphasic dependence of the creep rate on applied stress: below a critical stress threshold, the creep rate increases linearly with applied stress; above that threshold, the creep rate becomes independent of applied stress. We show that this biphasic stress dependence can be understood in terms of the nonlinear force-extension behavior of individual force-transmitting network elements. These results have important implications for understanding the origins and control of viscous flows both in the cortex of living cells and in other polymer networks.     

Determinants of Fluidlike Behavior and Effective Viscosity in Cross-Linked Actin Networks

The actin cortex has a well-documented ability to rapidly remodel and flow while maintaining long-range connectivity, but how this is achieved remains poorly understood. Here, we use computer simulations to explore how stress relaxation in cross-linked actin networks subjected to extensional stress depends on the interplay between network architecture and turnover. We characterize a regime in which a network response is nonaffine and stress relaxation is governed by the continuous dissipation of elastic energy via cyclic formation, elongation, and turnover of tension-bearing elements. Within this regime, for a wide range of network parameters, we observe a constant deformation (creep) rate that is linearly proportional to the rate of filament turnover, leading to a constant effective viscosity that is inversely proportional to turnover rate. Significantly, we observe a biphasic dependence of the creep rate on applied stress: below a critical stress threshold, the creep rate increases linearly with applied stress; above that threshold, the creep rate becomes independent of applied stress. We show that this biphasic stress dependence can be understood in terms of the nonlinear force-extension behavior of individual force-transmitting network elements. These results have important implications for understanding the origins and control of viscous flows both in the cortex of living cells and in other polymer networks.     

Mechanical implications of the domain structure of fiber-forming collagens: comparison of the molecular and fibrillar flexibilities of the alpha1-chains found in types I-III collagen

Fibrillar collagens store, transmit and dissipate elastic energy during tensile deformation. Results of previous studies suggest that the collagen molecule is made up of alternating rigid and flexible domains, and extension of the flexible domains is associated with elastic energy storage. In this study, we model the flexibility of the alpha1-chains found in types I-III collagen molecules and microfibrils in order to understand the molecular basis of elastic energy storage in collagen fibers by analysing the areas under conformational plots for dipeptide sequences. Results of stereochemical modeling suggest that the collagen triple helix is made up of rigid and flexible domains that alternate with periods that are multiples of three amino acid residues. The relative flexibility of dipeptide sequences found in the flexible regions is about a factor of five higher than that found for the flexibility of the rigid regions, and the flexibility of types II and III collagen molecules appears to be higher than that found for the type I collagen molecule. The different collagen alpha1-chains were compared by correlating the flexibilities. The results suggest that the flexibilities of the alpha1-chains of types I and III collagen are more closely related than the flexibilities of the alpha1-chains in types I and II and II and III collagen. The flexible domains found in the alpha1-chains of types I-III collagen were found to be conserved in the microfibril and had periods of about 15 amino acid residues and multiples thereof. The flexibility profiles of types I and II collagen microfibrils were found to be more highly correlated than those for types I and III and II and III. These results suggest that the domain structure of the alpha1-chains found in types I-III collagen is an efficient means for storage of elastic energy during stretching while preserving the triple helical structure of the overall molecule. It is proposed that all collagens that form fibers are designed to act as storage elements for elastic energy. The function of fibers rich in type I collagen is to store and then transmit this energy while fibers rich in types II and III collagen may store and then reflect elastic energy for dissipation through viscous fibrillar slippage. Impaired elastic energy storage by extracellular matrices may lead to cellular damage and changes in signaling by mechanochemical transduction at the extracellular matrix-cell interface.