Determination of strain energy function for arterial elastin: Experiments using histology and mechanical tests

The long-range reversible deformation of vertebrate arteries is primarily mediated by elastin networks that endure several million deformation cycles without appreciable fatigue. To determine how elastin contributes to the composite arterial properties, we studied the three-dimensional microstructure and biomechanics of isolated elastin. We initially estimated the sensitivity of these studies by comparing two elastin isolation protocols, autoclaving and alkali-extraction, and measured their effect on isolated elastin using uniaxial tests and histology. These studies show that autoclaved tissues have a trend for higher modulus (900.79+/-678.02 kPa) than alkali-extracted samples (417.74+/-162.23 kPa)albeit with higher collagen-proteoglycan impurities, and (2) greater optical density (78.6+/-9.1%) than alkali-extracted groups (46.2+/-5.9%), suggesting that autoclaving is superior to alkali-extraction for biomechanical tests on elastin. Using these data we show that an isotopic Mooney-Rivlin model cannot adequately represent arterial elastin. The neo-Hookean model, with coefficient 162.57 (+/-115.44) kPa for autoclaved and 76.94 (+/-27.76) kPa for alkali-extracted samples, fits the uniaxial data better. Autoclaved elastins also show linear stress-strain response and equal stiffness in circumferential and axial directions suggesting equal number of layers in these directions and that elastin may help distribute tensile stresses during vessel inflation. Histology of autoclaved and control porcine arteries reveals axial elastin fibers in intimal and adventitial layers but circumferential medial fibers. We propose an orthotropic material symmetry for arterial elastin with two orthogonally oriented and symmetrically placed mechanically equivalent fibers. An exact form of the constitutive equation will be obtained in a future study.     

Modelling the mechanical response of elastin for arterial tissue

We compare two constitutive models proposed to model the elastinous constituents of an artery. Holzapfel and Weizsäcker [1998. Biomechanical behavior of the arterial wall and its numerical characterization. Comput. Biol. Med. 28, 377–392] attribute a neo-Hookean response, i.e. $\Psi =c(I_1-3))$, to the elastin whilst Zulliger et al. [2004a. A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37, 989–1000] propose $\Psi =c(I_1-3{)}^{3/2}$. We analyse these constitutive models for two specific cases: (i) uniaxial extension of an elastinous sheet; (ii) inflation of a cylindrical elastinous membrane. For case (i) we illustrate the functional relationships between: (a) the Cauchy stress (CS) and the Green–Lagrange (GL) strain; (b) the tangent modulus (gradient of the CS–GL strain curve) and linearised strain. The predicted mechanical responses are compared with recent uniaxial extension tests on elastin [Gundiah, N., Ratcliffe, M.B., Pruitt, L.A., 2007. Determination of strain energy function for arterial elastin: experiments using histology and mechanical tests. J. Biomech. 40, 586–594; Lillie, M.A., Gosline, J.M., 2007a. Limits to the durability of arterial elastic tissue. Biomaterials 28, 2021–2031; 2007b. Mechanical properties of elastin along the thoracic aorta in the pig. J. Biomech. 40, 2214–2221]. The neo-Hookean model accurately predicts the mechanical response of a single elastin fibre. However, it is unable to accurately capture the mechanical response of arterial elastin, e.g. the initial toe region of arterial elastin (if it exists) or the gradual increase in modulus of arterial elastin that occurs as it is stretched. The alternative constitutive model ($n=\frac{3}{2}$) yields a nonlinear mechanical response that departs from recent uniaxial test data mentioned above, for the same stretch range. For case (ii) we illustrate the pressure–circumferential stretch relationships and the gradients of the pressure–circumferential stretch curves: significant qualitative differences are observed. For the neo-Hookean model, the gradient decreases rapidly to zero, however, for $n=\frac{3}{2}$, the gradient decreases more gradually to a constant value. We conclude that whilst the neo-Hookean model has limitations, it appears to capture more accurately the mechanical response of elastin.     

Mechanical and structural contributions of elastin and collagen fibers to interlamellar bonding in the arterial wall

Biomechanics and Modeling in Mechanobiology - The artery relies on interlamellar structural components, mainly elastin and collagen fibers, for maintaining its integrity and resisting dissection...     

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.     

Conformational energy calculations with averaged potential functions: Application to the repeat peptides of elastin

We present a method that can reduce conformational energy calculations for an arbitrary peptide consisting of n residues (n-peptide) to the complexity of a computation for (Gly)_n. This reduction, and the concomitant savings in computer time, is accomplished by replacing all side chains, as well as the backbone C^αH^α and C^αH₂^α groups, by “interaction centers.” The backbone CONH group is left intact in order to preserve its directional character. The interaction centers “see” each other, and the atoms of the CONH group via Boltzmann and space-averaged effective center-center and center-atom potentials, respectively. This averaged-interaction method is tested on the repeat tetra-, penta-, and hexapeptides of elastin, Val-Pro-Gly-Gly (VPGG), Val-Pro-Gly-Val-Gly (VPGVP), and Ala-Pro-Gly-Val-Gly-Val (APGVGV), using the stereoalphabet strategy for the energy calculations. The excellent qualitative and quantitative agreement we obtain with both full atom-atom calculations and extensive nmr data, coupled with the order-of-magnitude reduction in computer time, augurs well for the potential usefulness of the method.     

Orthogonal polynomials used as soft tissue energy density functions

A mathematical method is developed for computing the coefficients of soft tissue energy density polynomials, satisfying certain constraints. The polynomial coefficients are computed in the least squares sense. It is demonstrated that this method: (a) determines up to 30 polynomial coefficients whereas the unmodified least squares method based on Maclaurin power series determines up to nine coefficients; an (b) increases numerical stability and accuracy by several orders of magnitude. All computations are carried out in single precision on a LS1-11/23 laboratory minicomputer. The algorithm is particularly useful for on-line data analysis using small laboratory computers.     

Strain energy density function and uniform strain hypothesis for arterial mechanics

Stress distribution through the wall thickness of the canine carotid artery was analyzed on the basis of the uniform strain hypothesis in which the wall circumferential strain was assumed to be constant over the wall cross-section under physiological loading condition. A newly proposed logarithmic type of strain energy density function was used to describe the wall properties. In contrast with other studies, this hypothesis gave almost uniform distribution of wall stresses under the physiological condition and non-zero residual stresses when all external forces were removed.     

Physicochemical properties of arterial elastin and its associated glycoproteins

Microfibrillar glycoproteins are a significant component of vascular elastic tissue, but little is known about their contribution to vascular physiology and pathology. We have investigated some physicochemical properties of the glycoproteins that may be pertinent to these roles. Because of the difficulty in isolating intact glycoproteins in a form and quantity suitable for physicochemical examination, we based our analysis on a comparison of the properties of porcine thoracic aorta and pulmonary artery extracted with GuHCl and collagenase (preparation GC) and after further treatment with dithioerythritol to remove glycoproteins (preparation GC/DTE). Amino acid analysis showed that GC/DTE had the amino acid composition of pure elastin while GC contained a higher proportion of polar amino acids, particularly in the aortic preparation. GC stained with alcian blue, particularly in the intimal region, but GC/DTE did not. GC had a higher water content and a slower viscoelastic response and the circumferential elastic modulus was approximately 50% lower (whether expressed in terms of sample weight or elastin content). Clearly, therefore, the microfibrils do not stiffen the network and may prevent the alignment of elastin fibers in the circumferential direction. Their effect on hydration may arise either because they impose mechanical constraints on the geometry of the network or because they modify the inter‐ and intramolecular hydrophobic or electrostatic interactions that influence the tissue organization and hydration. Molecular probe measurements of the intrafibrillar pore structure using radiolabeled and fluorescent probes showed that removal of the microfibrils caused a slight decrease in the extrafibrillar water space and a larger decrease in the intrafibrillar water space. Sucrose, a small probe molecule, was able to penetrate most of the intrafibrillar water space when microfibrils were present but was virtually excluded when they were not. Potentiometric titration and radiotracer assays of ion binding both showed that the microfibrils contribute a considerable negative charge (−9 μmoles/g wet tissue in the aortic preparation and −16 μmoles/g wet weight in the pulmonary artery) and increase calcium binding by approximately 30%. © 1999 John Wiley & Sons, Inc. Biopoly 49: 255–265, 1999     

Progressive structural and biomechanical changes in elastin degraded aorta

Aortic aneurysm is an important clinical condition characterized by common structural changes such as the degradation of elastin, loss of smooth muscle cells, and increased deposition of fibrillary collagen. With the goal of investigating the relationship between the mechanical behavior and the structural/biochemical composition of an artery, this study used a simple chemical degradation model of aneurysm and investigated the progressive changes in mechanical properties. Porcine thoracic aortas were digested in a mild solution of purified elastase (5 U/mL) for 6, 12, 24, 48, and 96 h. Initial size measurements show that disruption of the elastin structure leads to increased artery dilation in the absence of periodic loading. The mechanical properties of the digested arteries, measured with a biaxial tensile testing device, progress through four distinct stages termed (1) initial-softening, (2) elastomer-like, (3) extensible-but-stiff, and (4) collagen-scaffold-like. While stages 1, 3, and 4 are expected as a result of elastin degradation, the S-shaped stress versus strain behavior of the aorta resulting from enzyme digestion has not been reported previously. Our results suggest that gradual changes in the structure of elastin in the artery can lead to a progression through different mechanical properties and thus reveal the potential existence of an important transition stage that could contribute to artery dilation during aneurysm formation.     

Cisplatin effects on rhythmic functions of mice: strain and tissue dependence

The competence to preserve the optimal timing relationships between rhythmic variables enables adaptation of mammals to alternate environmental conditions. The capability to re-entrain depends on genetic factors and the nature of imposed time cues. In the present study, the authors examined in rodent models, following a cancer chronochemotherapy, cisplatin (CP), the rhythm patterns of locomotor activity and of a few biochemical variables (alkaline phosphatase and creatinine phosphokinase in kidney tissue and plasma, kidney urea nitrogen, and white blood cell count). Males of two inbred mice strains, BALB/c and c57Bl/6J, received 10 consecutive daily intraperitoneal (i.p.) injections of either saline or CP at zeitgeber time 22 (ZT22). CP administration altered the rhythms of each examined function in both strains. The type and extent of the changes varied among variables, tissues/plasma, and mouse strain. Yet, the effect of CP was not detected on all parameters, but only in ～60% of them. In addition, in the majority of the studied parameters, BALB/c and c57Bl/6J mice differed in their response to CP. The temporal parameters of period and peak time were more affected by CP than were the level ones of mesor (time series mean) and amplitude of variation. This observation may indicate the involvement of independent pathways of action upon each of the rhythm parameter sets. As a result, the rhythm phenotype of each function was modified and novel timing relationships were shaped. The results show that the circadian systems of BALB/c and c57Bl/6J mice failed to re-entrain after cessation of CP injections (tested on the first day following the 10 d course of CP administration), pointing to a direct effect of the medication on the tissues. The findings imply that optimal chemotherapeutic protocols should be tailored individually, according to the current temporal order rather than administered at a fixed predetermined circadian time. Further studies are necessary to determine which variables and rhythmic parameters could be useful to determine the optimal timing of chronochemotherapy.     

Isotropy and anisotropy of the arterial wall

The passive biomechanical response of intact cylindrical rat carotid arteries is studied in vitro and compared with the mechanical response of rubber tubes. Using true stress and natural strain in the definition of the incremental modulus of elasticity, the tissue wall properties are analyzed over wide ranges of simultaneous circumferential and longitudinal deformations. The type of loading chosen is 'physiological' i.e. symmetric: the cylindrical segments are subjected to internal pressure and axial prestretch without torsion or shear. Several aspects pertaining to the choice of parameters characterizing the material are discussed and the analysis pertaining to the deformational behavior of a hypothetical compliant tube with Hookean wall material is presented. The experimental results show that while rubber response can be adequately represented as linearly elastic and isotropic, the overall response of vascular tissue is highly non-linear and anisotropic. However, for states of deformation that occur in vivo, the elasticity of arteries is quite similar to that of rubber tubes and as such the arterial wall may be viewed as incrementally isotropic for the range of deformations that occur in vivo.     

Pattern of accumulation of elastin and the level of mRNA for elastin in aortic tissue of growing chickens

Synthesis and accumulation of elastin in many elastic tissues begins in the last third of fetal development, reaches a maximum shortly after birth, and then declines rapidly. For the aorta of the chick and the pig and the ligamentum nuchae and lung of the sheep, it has been shown that increased levels of elastin production with fetal development are correlated with increased levels of elastin mRNA in the tissue, measured both by cell-free translation and by hybridization to cDNA probes. In this study we examine the relationship between insoluble elastin accumulation and message levels for tropoelastin in aortic tissue of chickens during posthatching development and growth. Whether evaluated by cell-free translation or by dot blot hybridization, steady state levels of tropoelastin message increase to a maximum at 2 weeks after hatching, and then fall rapidly with further development and growth. This pattern correlates well with production of insoluble elastin by the aorta, determined either by direct measurements of synthesis or by rate of accumulation of insoluble elastin. The data indicate that the major site of regulation of elastin production is pretranslational throughout the entire period of development and growth of the chicken aorta.     

Change in elastin structure in human aortic connective tissue diseases

Summary Biochemical pathogenesis of the aortic connective tissue diseases (such as, Marfan's syndrome, dissecting aneurysm or aortic aneurysm) was examined by estimating glycoprotein, collagen and elastin contents in the aorta and the intramolecular cross-linking component (isodesmosine) and the intermolecular cross-linking components (cystine, histidinoalanine) in comparison with the control samples obtained from subjects with aortic regurgitation. The elastin content in the aorta and isodesmosine content obtained from the extract of the aortic sample found to be decreased. Ratio of cysteine residues (Cys/Cys-Cys) in the elastin fraction in disease increased. Content of histidinoalanine was found to be decreased. It may be suggested that elastin is maintained in its native nature and shape by intra- and inter-molecular cross-linking bridges, and they are readily denatured by various disease conditions. After elastin was solubilized by elastase, immunoreactive elastin content in those aortic diseases was found to be increased in the human connective tissue. Serum elastase and elastase-like activities tend to increase more than those in the control. These findings may suggest that the change in the structure of elastin would make more susceptible to elastase and other proteolytic enzymes. The reasonable hypothesis may be that molecular defect of fibillin or other constitutional structural glycoproteins produce deficient and functionally incompetent elastin associated microfibrils, and the defect of microfibrils cause to insufficient intra- and inter-molecular cross-links in elastin.