Role of elastin anisotropy in structural strain energy functions of arterial tissue

The vascular wall exhibits nonlinear anisotropic mechanical properties. The identification of a strain energy function (SEF) is the preferred method to describe its complex nonlinear elastic properties. Earlier constituent-based SEF models, where elastin is modeled as an isotropic material, failed in describing accurately the tissue response to inflation–extension loading. We hypothesized that these shortcomings are partly due to unaccounted anisotropic properties of elastin. We performed inflation–extension tests on common carotid of rabbits before and after enzymatic degradation of elastin and applied constituent-based SEFs, with both an isotropic and an anisotropic elastin part, on the experimental data. We used transmission electron microscopy (TEM) and serial block-face scanning electron microscopy (SBFSEM) to provide direct structural evidence of the assumed anisotropy. In intact arteries, the SEF including anisotropic elastin with one family of fibers in the circumferential direction fitted better the inflation–extension data than the isotropic SEF. This was supported by TEM and SBFSEM imaging, which showed interlamellar elastin fibers in the circumferential direction. In elastin-degraded arteries, both SEFs succeeded equally well in predicting anisotropic wall behavior. In elastase-treated arteries fitted with the anisotropic SEF for elastin, collagen engaged later than in intact arteries. We conclude that constituent-based models with an anisotropic elastin part characterize more accurately the mechanical properties of the arterial wall when compared to models with simply an isotropic elastin. Microstructural imaging based on electron microscopy techniques provided evidence for elastin anisotropy. Finally, the model suggests a later and less abrupt collagen engagement after elastase treatment.     

A description of arterial wall mechanics using limiting chain extensibility constitutive models

Certain aspects of the mechanical response of arterial walls can be described using nonlinear elasticity theory. Uniaxial tests on vascular walls reveal nonlinear stress-strain behavior, with higher extensibility in the low stretch range and progressively lower extensibility with increasing stretch. This phenomenon is well known in the framework of rubber-like materials where it is called a strain-hardening or strain-stiffening effect. Constitutive models of incompressible hyperelasticity that take this into account include power-law models and limiting chain extensibility models. Our purpose in this paper is to bring to the attention of the biomechanics community some essential features of one such model of the latter type due to Gent. This model is compared with isotropic versions of biomechanical constitutive models by Takamizawa-Hayashi and Fung; the latter is a limiting version of a power-law material. Two particular problems are considered for which experimental data on arterial wall deformations are available. The first concerns small oscillations superposed on a large static stretch of a vertical string of arterial tissue. It is shown that the exponential model of Fung and the Gent model match well with the experimental data. The second problem is the extension of an internally pressurized circular cylindrical tube. It is shown that an inversion phenomenon observed experimentally for the human iliac artery can be described within a membrane theory by the Gent model whereas this cannot be described using the exponential model. The foregoing considerations are carried out for isotropic elastic materials in the absence of residual stress. Extensions to include anisotropy are also indicated.     

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.     

Ultrastructural visualization of elastic fibres with a tannate-metal salt method

Summary A modification of the tannic acid-metal salt method was applied as an ultrastructural stain for elastin. Thin sections of glutaraldehyde-fixed, embedded rat aorta and rabbit elastic cartilage, with and without osmication, were examined. Raising the pH of the tannic acid solution from 2.7 to 9.0 progressively increased the electron-density of elastic fibres and collagen fibrils in osmicated and unosmicated specimens. The maximum tannic acid staining of elastic fibres was observed in the pH range 7.0–9.0. Collagen staining, although less intense than that of elastic fibres, was also greatest in this pH range. Elastic fibres in osmicated specimens demonstrated the strongest tannic acid staining with a minimal increase in density of collagen and cell nuclei when compared to the unosmicated specimens. Sequential treatments of osmicated specimens with tannic acid pH 7.0–9.0, and uranyl acetate, pH 4.1, enhanced the density of the elastin intensely, increased collagen staining moderately, but hardly increased the density of nuclei and microfibrils. In elastase-digested osmicated specimens, all tannic acid (pH 7.0)-uranyl acetate-reactive elastin was selectively removed. These results demonstrate that all the neutral and alkaline tannic acid-uranyl acetate methods can be used as a postembedment stain for elastin specimens fixed in glutaraldehyde and osmium tetroxide.     

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.     

Effect of elastin degradation on carotid wall mechanics as assessed by a constituent-based biomechanical model

Arteries display a nonlinear anisotropic behavior dictated by the elastic properties and structural arrangement of its main constituents, elastin, collagen, and vascular smooth muscle. Elastin provides for structural integrity and for the compliance of the vessel at low pressure, whereas collagen gives the tensile resistance required at high pressures. Based on the model of Zulliger et al. (Zulliger MA, Rachev A, Stergiopulos N. Am J Physiol Heart Circ Physiol 287: H1335-H1343, 2004), which considers the contributions of elastin, collagen, and vascular smooth muscle cells (VSM) in an explicit form, we assessed the effects of enzymatic degradation of elastin on biomechanical properties of rabbit carotids. Pressure-diameter curves were obtained for controls and after elastin degradation, from which elastic and structural properties were derived. Data were fitted into the model of Zulliger et al. to assess elastic constants of elastin and collagen as well as the characteristics of the collagen engagement profile. The arterial segments were also prepared for histology to visualize and quantify elastin and collagen. Elastase treatment leads to a diameter enlargement, suggesting the existence of significant compressive prestresses within the wall. The elastic modulus was more ductile in treated arteries at low circumferential stretches and significantly greater at elevated circumferential stretches. Abrupt collagen fiber recruitment in elastase-treated arteries leads to a much stiffer vessel at high extensions. This change in collagen engagement properties results from structural alterations provoked by the degradation of elastin, suggesting a clear interaction between elastin and collagen, often neglected in previous constituent-based models of the arterial wall.     

In vivo estimation of the contribution of elastin and collagen to the mechanical properties in the human abdominal aorta: effect of age and sex

The mechanical properties of the aorta affect cardiac function and are related to cardiovascular morbidity/mortality. This study was designed to evaluate the isotropic (mainly elastin, elastin(iso)) and anisotropic (mainly collagen, collagen(ani)) material parameters within the human aorta in vivo. Thirty healthy men and women in three different age categories (23-30, 41-54, and 67-72 yr) were included. A novel mechanical model was used to identify the mechanical properties and the strain field with aid of simultaneously recorded pressure and radius in the abdominal aorta. The magnitudes of the material parameters relating to both the stiffness of elastin(iso) and collagen(ani) were in agreement with earlier in vitro studies. The load-bearing fraction attributed to collagen(ani) oscillated from 10 to 30% between diastolic and systolic pressures during the cardiac cycle. With age, stiffness of elastin(iso) increased in men, despite the decrease in elastin content that has been found due to elastolysis. Furthermore, an increase in stiffness of collagen(ani) at high physiological pressure was found. This might be due to increased glycation, as well as changed isoforms of collagen in the aortic wall with age. A marked sex difference was observed, with a much less age-related effect, both on elastin(iso) and collagen(ani) stiffness in women. Possible factors of importance could be the effect of sex hormones, as well as differing collagen isoforms, between the sexes.     

Structure and Development of the Notochord ‘Elastica Externa’ and Nearby Components of the Elastic Fibre System of Agnathans

Between 15 days and 3 months in age, the ‘elastica externa’ of the notochord sheath of larval lampreys develops from patches of moderately dense and amorphous material into a thick, continuous and electron-dense layer. In both lampreys and hagfish, this layer stains strongly with Verhoeff's elastic stain and aldehyde fuchsin and is penetrated by collagen fibrils on both its outer and inner boundaries. Peroxidase labelling using an antibody raised against human elastin specifically labels both the notochord ‘elastica externa’ and the elastic fibre system of lampreys. The diameters of the microfibrils (10–13 nm) of the oxytalan, elaunin and elastic fibres of lampreys and hagfish are the same as those of higher vertebrates. The connective tissue immediately dorsal and ventral to the notochord of lampreys contains mainly oxytalan fibres in very young ammocoetes, a combination of oxytalan, elaunin and elastic fibres in older ammocoetes, and predominantly elastic fibres in adult lampreys. While the region of the endomeninx at the base of the spinal cord contains almost exclusively oxytalan fibres in young ammocoetes, it also possesses numerous elastic fibres in adult lampreys. These findings indicate that, as in higher vertebrates, the elastic fibres of lampreys develop from oxytalan fibres via elaunin fibres.     

A new constitutive model for multi-layered collagenous tissues

Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.     

Adherence,proliferation and collagen turnover by human fibroblasts seeded into different types of collagen sponges

We describe an in vitro model that we have used to evaluate dermal substitutes and to obtain data on cell proliferation, the rate of degradation of the dermal equivalent, contractibility and de novo synthesis of collagen. We tested three classes of collagenous materials: (1) reconstituted non-crosslinked collagen, (2) reconstituted collagen that was chemically crosslinked with either glutaraldehyde, aluminium alginate or acetate, and (3) native collagen fibres, with or without other extracellular matrix molecules (elastin hydrolysate, hyaluronic acid or fibronectin). The non-crosslinked reconstituted collagen was degraded rapidly by human fibroblasts. Teh chemically crosslinked materials proved to be cytotoxic. Native collagen fibres were stable. In the absence of ascorbic acid, the addition of elastin hydrolysate to this type of matrix reduced the rate of collagen degradation. Both elastin hydrolysate and fibronectin partially prevented fibroblast-mediated contraction. Hyaluronic acid was only slightly effective in reducing the collagen degradation rate and more fibroblast-mediated contraction of the material was found than for the native collagen fibres with elastin hydrolysate and fibronectin. In the presence of ascorbate, collagen synthesis was enhanced in the native collagen matrix without additions and in the material containing elastin hydrolysate, but not in the material with hyaluronic acid. These results are indicative of the suitability of tissue substitutes for in vivo application.     

Occurrence of "elastic" fibres in the invertebrates

The connective tissues of a wide range of invertebrates have been investigated using a potassium permanganate/spirit blue staining technique. The method demonstrates fibres which are distinct from collagen, vertebrate elastic fibres, and reticular fibres. The fibres are variously associated with subepidermal collagen, muscles, basement membrances, the walls of blood vessels and the sheaths around nerve cords; the method also gives a positive reaction with the arborescent mesogloeal fibres of medusoid coelenterates. Their electron microscope appearance is distinctive and they exhibit a physical elasticity. Chemical tests indicate that following pretreatment with acidified potassium permanganate they show many, although not all, of the properties of vertebrate "elastin". It is concluded that they should be regarded as a special category of "elastic" fibre.     

STRUCTURAL BIOLOGY OF THE FIBRES OF THE COLLAGENOUS AND ELASTIC SYSTEMS

The different types of fibres of the collagenous and elastic systems can be demonstrated specifically in tissue sections by comparing the typical ultrastructural picture of each of the fibre types with studies using selective staining techniques for light microscopy. A practicalmodus operandi, which includes the recommended staining procedures and interpretation of the results, is presented. Micrographs and tables are provided to summarize the differential procedures. Reticulin fibres display a distinct argyrophilia when studied by means of silver impregnation techniques, and show up as a thin meshwork of weakly birefringent, greenish fibres when examined with the aid of the Picrosirius-polarization method. In addition, electron-microscopic studies showed that reticulin fibres are composed of a small number of thin collagen fibrils, contrasting with the very many thicker fibrils that could be localized ultrastructurally to the sites where non-argyrophilic, coarse collagen fibres had been characterized by the histochemical methods used. The three different fibre types of the elastic system belong to a continuous series: oxytalan—elaunin—elastic (all of the fibre types comprising collections of microfibrils with, in the given sequence, increasing amounts of elastin). The three distinct types of elastic system fibres have different staining characteristics and ultrastructural patterns. Ultrastructurally, a characteristic elastic fibre consists of two morphologically different components: a centrally located solid cylinder of amorphous and homogeneous elastin surrounded by tubular microfibrils. An oxytalan fibre is composed of a bundle of microfibrils, identical to the elastic fibre microfibrils, without amorphous material. In elaunin fibres, dispersed amorphous material (elastin) is intermingled among the microfibrils.     

Biomechanical and histological characteristics of passive esophagus: Experimental investigation and comparative constitutive modeling

Information on the passive biomechanical properties of two-layered esophagus is still limited, although this would enhance our understanding of its physiology/pathophysiology and help to address problems in surgery, medical-device applications, and for the optimal design of prostheses. In this study, rabbit esophagi were excised and dissected into mucosa–submucosa and muscle layers that were submitted to histological quantification of elastin and collagen content and orientation, as well as to inflation-extension testing and geometrical analysis, i.e. delineation of the zero-stress state serving as a reference configuration for biomechanical analysis. The pressure–radius data of both layers displayed a monotonically rising slope with inflating pressure, unlike the sigma shape characterizing elastin-rich tissues, for which biphasic constitutive models were initially postulated. Three phenomenological expressions of strain-energy function (SEF), commonly appearing in soft-tissue biomechanics literature, were used in an attempt to model the pseudoelastic response of esophageal tissue, namely the exponential Fung-type SEF, and the combined neo-Hookean (isotropic) or quadratic (anisotropic) and exponential Fung-type SEF. Accurate fits were attained for the pressure–radius–force data, spanning a wide range of longitudinal stretch ratios, when using the exponential form; the biphasic SEFs failed to generate improved fits, being also over-parameterized. According to the calculated material parameters, mucosa–submucosa was stiffer than muscle in both directions, justified by our histological observation of increased collagen content in that layer, and tissue was stiffer longitudinally, substantiated by the increased elastin and collagen contents and their preferential alignment towards that direction. Our results demonstrate that the passive response of esophagus is best modeled with an exponential Fung-type SEF.     

On the anisotropy and inhomogeneity of permeability in articular cartilage

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is "directed" by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.     

The characteristic three-banded birefringence of ligamentum nuchae elastic fibres indicates ordered micellar texture

The ultrastructural organization of the elastic fibres of bovine ligamentum nuchae is still controversial (Kádár 1979; Sandberg 1976; Sandberg et al. 1981; Quintarelli et al. 1973; Gosline 1976). Polarization microscopy demonstrated convincingly, contrary to a recent negative report (Aaron and Gosline 1980), an ordered birefringent micellar texture (Schmidt 1939; Romhányi 1965; Fischer 1979). The three-banded anisotropic pattern of the fibres can be explained by the optical interference of two micellar textures of opposite orientation, one arranged circularly in the surface layer and the other oriented longitudinally in the axial core of the fibres (Romhányi 1965). Analysis of the underlying molecular mechanism for the anisotropic staining reaction of these fibres with Congo red led to the conclusion that this is due to a definite structural order of specific cross-linking segments within the random network of elastin. The anisotropic staining reaction of the elastic fibres with Congo red is described as the most simple method to demonstrate the three-banded birefringent pattern of ligamentum nuchae elastic fibres even in histologic sections.     

Elasticity of passive blood vessels: a new concept

The mechanical properties of passive blood vessels are generally thought to depend on the parallel arrangement of elastin and collagen with linear elasticity and collagen recruitment depending on vessel strain [hook-on (HO) model]. We evaluated an alternative model [serial element (SE) model] consisting of the series arrangement of an infinite number of elements, each containing elastin with a constant elastic modulus and collagen that switches stepwise from slack (zero stress) to fully rigid (infinite stiffness) on ongoing element strain. Both models were implemented with Weibull distributions for collagen recruitment strain (HO model) and collagen tightening strain (SE model). The models were tested in experiments on rat mesenteric small arteries. Strain-tension relations were obtained before and after two rounds of digestion by collagenase. Both models fitted the data prior to digestion. However, for the HO model, this required unrealistically low estimates for collagen recruitment or elastic modulus and unrealistically high estimates for distension of collagen fibers. Furthermore, the data after digestion were far better predicted by the SE model compared with the HO model. Finally, the SE model required one parameter less (collagen elastic modulus). Therefore, the SE model provides a valuable starting point for the understanding of vascular mechanics and remodeling of vessels.     

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.     

Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments

Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.