A computational model for collagen fibre remodelling in the arterial wall

As the interaction between tissue adaptation and the mechanical condition within tissues is complex, mathematical models are desired to study this interrelation. In this study, a mathematical model is presented to investigate the interplay between collagen architecture and mechanical loading conditions in the arterial wall. It is assumed that the collagen fibres align along preferred directions, situated in between the principal stretch directions. The predicted fibre directions represent symmetrically arranged helices and agree qualitatively with morphometric data from literature. At the luminal side of the arterial wall, the fibres are oriented more circumferentially than at the outer side. The discrete transition of the fibre orientation at the media-adventitia interface can be explained by accounting for the different reference configurations of both layers. The predicted pressure-radius relations resemble experimentally measured sigma-shaped curves. As there is a strong coupling between the collagen architecture and the mechanical loading condition within the tissue, we expect that the presented model for collagen remodelling is useful to gain further insight into the processes involved in vascular adaptation, such as growth and smooth muscle tone adaptation.     

Improved arterial wall model by coculturing vascular endothelial and smooth muscle cells

We have constructed an in vitro arterial wall model by coculturing bovine arterial endothelial cells (ECs) and smooth muscle cells (SMCs). When ECs were seeded directly over SMCs and cocultured in an ordinary culture medium, ECs grew sparsely and did not form a confluent monolayer. Addition of ascorbic acid to the culture medium at concentrations greater than 50 μg/ml increased the production of type IV collagen by the SMCs, and ECs formed a confluent monolayer covering the entire surface of SMCs. Histological studies showed that the thickness of the cell layer composed of ECs and SMCs increased with increasing duration of coculture. This arterial wall model, prepared by our method, may serve as a simple and good in vitro model to study the effects of factors such as biological chemicals and shear stress on cell proliferation and other physiological functions of arterial walls.     

Dynamic effects on the formation and rupture of aneurysms

Dynamic analysis of an axially stretched arterial wall with collagen fibers distributed in two preferred directions under a suddenly applied constant internal pressure along with the possibility of the formation and rupture of aneurysm are examined within the framework of nonlinear dynamics. A two layer tube model with the fiber-reinforced composite-based incompressible anisotropic hyper-elastic material is employed to model the mechanical behavior of the arterial wall. The maximum amplitudes and the phase diagrams are given by numerical computation of the differential relation. It is shown that the arterial wall undergoes nonlinear periodic oscillation and no aneurysms are formed under the normal condition. However, an aneurysm may be formed under such abnormal conditions as the stiffness of the fibers is deduced or the direction of the fibers is oriented towards the axial direction. Furthermore, the possibility for the rupture of aneurysm is discussed with the distribution of stresses.     

An inelastic multi-mechanism constitutive equation for cerebral arterial tissue

Intracranial aneurysms (ICA) are abnormal saccular dilations of cerebral arteries, commonly found at apices of arterial bifurcations and outer walls of curved arterial segments. Histological evidence suggests the stages in ICA development include the deformation of a segment of arterial wall into a “bleb” with no identifiable neck region followed by the development of an aneurysm with a clear neck. Afterwards, the aneurysm may undergo further enlargement, possibly with significant biological response including calcification and thrombosis. Past studies of the biomechanics of cerebral aneurysm tissue have been directed at modeling elastic deformations of pre-existing aneurysms. Taking this approach, the aneurysm wall is treated as a different entity than the arterial tissue from which it developed. In the current work, a nonlinear, inelastic, dual-mechanism constitutive equation for cerebral arterial tissue is developed. It is the first to model the recruitment of collagen fibers and degradation of the internal elastic lamina, two important characteristics of early stage aneurysm formation.     

Determination of material parameters of the two-dimensional Holzapfel–Weizsäcker type model based on uniaxial extension data of arterial walls

Soft tissues are anisotropic materials yet a majority of mechanical property tests have been uniaxial, which often failed to recapitulate the tensile response in other directions. This paper aims to study the feasibility of determining material parameters of anisotropic tissues by uniaxial extension with a minimal loss of anisotropic information. We assumed that by preselecting a certain constitutive model, we could give the constitutive parameters based on uniaxial extension data from orthogonal strip samples. In our study, the Holzapfel–Weizsäcker type strain energy density function (H–W model) was used to determine the material parameters of arterial walls from two fresh donation bodies. The key points we applied were the relationships between strain components in uniaxial tensile tests and the methods of stochastic optimisation. Further numerical experiments were taken. The estimate–effect ratio, defined by the number of data with the precision of estimation less than 0.5% over whole size of data, was calculated to demonstrate the feasibility of our method. The material parameters for Chinese aorta and pulmonary artery were given with the maximum root mean square (RMS) errors 0.042, and the minimal estimate–effect ratio in numerical experiments was 90.79%. Our results suggest that the constitutive parameters of arterial walls can be determined from uniaxial extension data, given the passive mechanical behaviour governed by H–W model. This method may apply to other tissues using different constitutive models.     

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

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

Lamellar orientation in human cornea in relation to mechanical properties

We have applied wide-angle X-ray scattering to the human cornea in order to quantify the relative number of stromal collagen fibrils directed along the two preferred corneal lamellar directions: superior-inferior and nasal-temporal. The data suggest that, on average, the two directions are populated in equal proportion at the corneal centre. Here, approximately one-third of the fibrils throughout the stromal depth tend to lie within a 45 degrees sector of the superior-inferior meridian, and similarly for the nasal-temporal direction. However, in some eyes we have measured significant differences between the two preferential fibril populations, with some corneas exhibiting as much as 25% more collagen in one direction than the other. Based on these findings, a mechanical model of the normal cornea may be envisaged, whereby the fibril tension in the underlying "background" of isotropically arranged collagen helps to balance the intraocular pressure; while the extra preferentially aligned fibrils take up the additional tensile stress along the superior-inferior and nasal-temporal meridians exerted by the rectus muscles and the orbicularis. It is possible that, through a direct impact on the elastic modulus of the tissue, an imbalance of superior-inferior and nasal-temporal fibrils in some eyes might affect corneal shape.     

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.     

Junctions between microtubule walls.

We have studied lateral associations of microtubule walls by electron microscopy and image analysis. In negative stain they are observed as composite sheets having two or more domains usually facing in opposite directions. Thin sections show a variety of complex tubular arrays including structures resembling flagellar doublets and centriolar triplets. It appears that protofilaments can combine in two distinct modes, one leading to microtubule walls, the other forming junctions between walls. Both kinds of bonds seem to be inherent properties of tubulin and not of microtubule-associated protein.     

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.     

Impact of transmural heterogeneities on arterial adaptation

Recent experimental and computational studies have shown that transmurally heterogeneous material properties through the arterial wall are critical to understanding the heterogeneous expressions of constituent degrading molecules. Given that expression of such molecules is thought to be intimately linked to local magnitudes of stress, modelling the transmural stress distribution is critical to understanding arterial adaption during disease. The aim of this study was to develop an arterial growth and remodelling framework that can incorporate both transmurally heterogeneous constituent distributions and residual stresses, into a 3-D finite element model. As an illustrative example, we model the development of a fusiform aneurysm and investigate the effects of elastinous and collagenous heterogeneities on the stress distribution during evolution. It is observed that the adaptive processes of growth and remodelling exhibit transmural variations. For physiological heterogeneous constituent distributions, a stress peak appears in the media towards the intima, and a stress plateau occurs towards the adventitia. These features can be primarily attributed to the underlying heterogeneity of elastinous constituents. During arterial adaption, the collagen strain is regulated to remain in its homoeostatic level; consequently, the partial stress of collagen has less influence on the total stress than the elastin. However, following significant elastin degradation, collagen plays the dominant role for the transmural stress profile and a marked stress peak occurs towards the adventitia. We conclude that to improve our understanding of the arterial adaption and the aetiology of arterial disease, there is a need to: quantify transmural constituent distributions during histopathological examinations, understand and model the role of the evolving transmural stress distribution.     

Microplane constitutive model and computational framework for blood vessel tissue

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel's recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.     

Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization

We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils’ shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.     

The Caenorhabditis elegans rol-6 gene, which interacts with the sqt-1 collagen gene to determine organismal morphology, encodes a collagen.

The rol-6 gene is one of the more than 40 loci in Caenorhabditis elegans that primarily affect organismal morphology. Certain mutations in the rol-6 gene produce animals that have the right roller phenotype, i.e., they are twisted into a right-handed helix. The rol-6 gene interacts with another gene that affects morphology, sqt-1; a left roller allele of sqt-1 acts as a dominant suppressor of a right roller allele of rol-6. The sqt-1 gene has previously been shown to encode a collagen. We isolated and sequenced the rol-6 gene and found that it also encodes a collagen. The rol-6 gene was identified by physical mapping of overlapping chromosomal deficiencies that cover the gene and by identification of an allele-specific restriction site alteration. The amino acid sequence of the collagen encoded by rol-6 is more similar to that of the sqt-1 collagen than to any of the other ten C. elegans cuticle collagen sequences compared. The locations of cysteine residues flanking the Gly-X-Y repeat regions of rol-6 and sqt-1 are identical, but differ from those in the other collagens. The sequence similarities between rol-6 and sqt-1 indicate that they represent a new collagen subfamily in C. elegans. These findings suggest that these two collagens physically interact, possibly explaining the genetic interaction seen between the rol-6 and sqt-1 genes.     

Pulmonary arterial strain- and remodeling-induced stiffening are differentiated in a chronic model of pulmonary hypertension

Pulmonary hypertension (PH) is a debilitating vascular disease that leads to pulmonary artery (PA) stiffening, which is a predictor of patient mortality. During PH development, PA stiffening adversely affects right ventricular function. PA stiffening has been investigated through the arterial nonlinear elastic response during mechanical testing using a canine PH model. However, only circumferential properties were reported and in the absence of chronic PH-induced PA remodeling. Remodeling can alter arterial nonlinear elastic properties via chronic changes in extracellular matrix (ECM) content and geometry. Here, we used an established constitutive model to demonstrate and differentiate between strain-stiffening, which is due to nonlinear elasticity, and remodeling-induced stiffening, which is due to ECM and geometric changes, in a canine model of chronic thromboembolic PH (CTEPH). To do this, circumferential and axial tissue strips of large extralobar PAs from control and CTEPH tissues were tested in uniaxial tension, and data were fit to a phenomenological constitutive model. Strain-induced stiffening was evident from mechanical testing as nonlinear elasticity in both directions and computationally by a high correlation coefficient between the mechanical data and model (R² = 0.89). Remodeling-induced stiffening was evident from a significant increase in the constitutive model stress parameter, which correlated with increased PA collagen content and decreased PA elastin content as measured histologically. The ability to differentiate between strain- and remodeling-induced stiffening in vivo may lead to tailored clinical treatments for PA stiffening in PH patients.     

Heterogeneity in collagen biosynthesis by sprouting retinal endothelial cells

Bovine retinal microvascular endothelial cells can display two distinct and reversible morphologies in culture: ‘cobblestone’ and ‘sprouting’. The cobblestone morphology resembles the resting cells lining the lumen of mature vessels while the sprouting morphology resembles the angiogenic cells involved in the formation of new vessels. Retinal cells displayed some heterogeneity in the shape of the cells making up the cobblestone monolayer. In contrast, all cell lines displayed an identical sprouting morphology. We have investigated the synthesis of matrix macromolecules by retinal endothelial cells displaying either the cobblestone or the sprouting morphology. Type IV was the only collagen synthesised by eight different lines of early-passage (between one and six) cobblestone endothelial cells. Collagen types I and III were not detected in these cultures. In contrast, heterogeneity was observed in the types of collagen synthesised by four lines of early-passage cells displaying the sprouting morphology. That is, two lines synthesised collagen types I, III and IV, whereas two other lines continued to synthesise only type IV collagen. Both cobblestone and sprouting cells synthesised fibronectin and thrombospondin, although the relative amounts of these macromolecules varied with culture conditions. The pattern of collagen synthesis by cobblestone cells was also affected by in vitro ?ageing”?: 4/5 lines examined above passage eight synthesised collagen types I, III and IV. Our results indicate that there is heterogeneity in the sprouting phenotype displayed by retinal endothelial cells, and that this phenotype is not necessarily associated with the synthesis of type I collagen. We suggest that differences in the spectrum of matrix macromolecules synthesised by sprouting endothelial cells may play a role in the control of angiogenesis. © 1994 wiley-Liss, Inc.     

α-Actinin-4 Is Required for Amoeboid-type Invasiveness of Melanoma Cells

α-Actinin-4 (ACTN4), a key regulator of the actin cytoskeleton, is up-regulated in melanoma, though its role in melanoma remains speculative. We have discovered that in WM1158, a highly aggressive melanoma cell line, down-regulation of ACTN4 by shRNA induces a collagen I-dependent amoeboidal-to-mesenchymal transition. Re-expression of low levels of WT ACTN4 but not similar expression levels of ACTN1 successfully restores the amoeboidal morphology and limits collagen I gel compaction. A truncated ACTN4 mutant 1–890, which lacks the C-terminal tail, fails to rescue the amoeboidal morphology and to compact collagen I gel. Interestingly, in three-dimensional collagen I gels, ACTN4 KD cells are more polarized compared with cells in which scrambled shRNA is expressed. Surprisingly, ACTN4 KD cells migrate faster than the ones expressing the scrambled shRNA on a collagen I gel (two-dimensional) although these two cell lines migrate similarly on tissue culture. Most importantly, down-regulation of ACTN4 significantly reduced invasion of WM1158 cells into the three-dimensional collagen I gel, a representative of the dermis. Taken together, these findings suggest that ACTN4 plays an important role in maintaining the amoeboidal morphology of invasive melanoma and thus promoting dissemination through collagen-rich matrices.     

The effect of a thermal renal denervation cycle on the mechanical properties of the arterial wall

The aim of this study was to determine the effect that a thermal renal denervation cycle has on the mechanical properties of the arterial wall. Porcine arterial tissue specimens were tested in three groups: native tissue, decellularized tissue, decellularized with collagen digestion (e.g. elastin only). One arterial specimen was used as an unheated control specimen while another paired specimen was subjected to a thermal cycle of 70 °C for 120 s (n=10). The specimens were subjected to tensile loading and a shrinkage analysis. We observed two key results: The mechanical properties associated with the elastin extracellular matrix (ECM) were not affected by the thermal cycle. The effect of the thermal cycle on the collagen (ECM) was significant, in both the native and decellularized groups the thermal cycle caused a statistically significant decrease in stiffness, and failure strength, moreover the native tissue demonstrated a 27% reduction in lumen area post exposure to the thermal cycle. We have demonstrated that a renal denervation thermal cycle can significantly affect the mechanical properties of an arterial wall, and these changes in stiffness and failure strength were associated with alterations to the collagen rather than the elastin extracellular matrix component.     

A fiber-based constitutive model predicts changes in amount and organization of matrix proteins with development and disease in the mouse aorta

Decreased elastin in mice (Eln+/?) yields a functioning vascular system with elevated blood pressure and increased arterial stiffness that is morphologically distinct from wild-type mice (WT). Yet, function is retained enough that there is no appreciable effect on life span and some mechanical properties are maintained constant. It is not understood how the mouse modifies the normal developmental process to produce a functioning vascular system despite a deficiency in elastin. To quantify changes in mechanical properties, we have applied a fiber-based constitutive model to mechanical data from the ascending aorta during postnatal development of WT and Eln+/? mice. Results indicate that the fiber-based constitutive model is capable of distinguishing elastin amounts and identifying trends during development. We observe an increase in predicted circumferential stress contribution from elastin with age, which correlates with increased elastin amounts from protein quantification data. The model also predicts changes in the unloaded collagen fiber orientation with age, which must be verified in future work. In Eln+/? mice, elastin amounts are decreased at each age, along with the predicted circumferential stress contribution of elastin. Collagen amounts in Eln+/? aorta are comparable to WT, but the predicted circumferential stress contribution of collagen is increased. This may be due to altered organization or structure of the collagen fibers. Relating quantifiable changes in arterial mechanics with changes in extracellular matrix (ECM) protein amounts will help in understanding developmental remodeling and in producing treatments for human diseases affecting ECM proteins.