A strain energy function for arteries accounting for wall composition and structure

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.

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

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

Functional tissue-engineered valves from cell-remodeled fibrin with commissural alignment of cell-produced collagen

Heart valve replacements composed of living tissue that can adapt, repair, and grow with a patient would provide a more clinically beneficial option than current inert replacements. Bioartificial valves were produced by entrapping human dermal fibroblasts within a fibrin gel. Using a mold design that presents appropriate mechanical constraints to the cell-induced fibrin gel compaction, gross fiber alignment (commissure-to-commissure alignment in the leaflets and circumferential alignment in the root) and the basic geometry of a native aortic valve were obtained. After static incubation on the mold in complete medium supplemented with transforming growth factor beta 1, insulin, and ascorbate, collagen fibers produced by the entrapped cells were found to coalign with the fibrin based on histological analyses. The resultant tensile mechanical properties were anisotropic. Ultimate tensile strength and tensile modulus of the leaflets in the commissural direction were 0.53 and 2.34 MPa, respectively. The constructs were capable of withstanding backpressure commensurate with porcine aortic valves in regurgitation tests (330 mmHg) and opened and closed under physiological pressure swings of 10 and 20 mmHg, respectively. These data support proof of principle of using cell-remodeled fibrin gel to produce tissue-engineered valve replacements.

Three-part passive constitutive laws for the aorta in simple elongation

A variety of uniaxial constitutive laws have been proposed for the characterization of the aorta's nonlinear passive response, but a detailed comparison of them appears to be lacking. In this study, a systematic presentation of all available phenomenological formulations is undertaken and explicit formulae of constitutive laws are provided for simple elongation tests performed on healthy aortic strips. Common to all derived laws is the use of three analytical functions to approximate the low, physiologic, and high-stress parts of the aortic response, and the very close and essentially equally accurate fits that they give to the experimental data over the full range of stresses. Another feature of the three-part laws is their compatibility with the biphasic nature of the aortic tissue under passive conditions, allowing direct microstructural interpretation of their parameters. Importantly, although it is found that the aorta displays strain softening, i.e. its passive response is dependent on the highest previously experienced stress, the three-part character of the laws seems to be unaffected by the preconditioning procedure.

Computational predictions of the tensile properties of electrospun fibre meshes: effect of fibre diameter and fibre orientation

The mechanical properties of biomaterial scaffolds are crucial for their efficacy in tissue engineering and regenerative medicine. At the microscopic scale, the scaffold must be sufficiently rigid to support cell adhesion, spreading, and normal extracellular matrix deposition. Concurrently, at the macroscopic scale the scaffold must have mechanical properties that closely match those of the target tissue. The achievement of both goals may be possible by careful control of the scaffold architecture. Recently, electrospinning has emerged as an attractive means to form fused fibre scaffolds for tissue engineering. The diameter and relative orientation of fibres affect cell behaviour, but their impact on the tensile properties of the scaffolds has not been rigorously characterized. To examine the structure-property relationship, electrospun meshes were made from a polyurethane elastomer with different fibre diameters and orientations and mechanically tested to determine the dependence of the elastic modulus on the mesh architecture. Concurrently, a multiscale modelling strategy developed for type I collagen networks was employed to predict the mechanical behaviour of the polyurethane meshes. Experimentally, the measured elastic modulus of the meshes varied from 0.56 to 3.0 MPa depending on fibre diameter and the degree of fibre alignment. Model predictions for tensile loading parallel to fibre orientation agreed well with experimental measurements for a wide range of conditions when a fitted fibre modulus of 18 MPa was used. Although the model predictions were less accurate in transverse loading of anisotropic samples, these results indicate that computational modelling can assist in design of electrospun artificial tissue scaffolds.

A mathematical model of the mechanical deformation of the carotid artery wall and its application to clinical data

The study of arterial wall mechanics, including the study of stresses and strains experienced by the vascular wall, is pivotal in our understanding of arterial physiology. In this paper, a mathematical model is provided describing the deformation of the arterial wall in terms of 6 parameters. Actual deformation waveforms were also obtained from the analysis of B-mode ultrasound image sequences of the carotid artery using block-matching. The mathematical model was fitted to the clinical data using nonlinear least squares to determine the 6 parameters for 6 different locations along the posterior and 6 along the anterior walls, on the interface between the lumen and the intima-media complex (L-IM). On the posterior wall, 6 locations were also investigated at the interface between the intima-media complex and the adventitia (IM-A) as well as at the adventitia-surrounding tissue (A-T) boundary. The root mean square error was low for all locations indicating a good fit of the proposed model to the clinical data. The amplitude of the deformation, expressed through parameter alpha, was significantly lower in the A-T interface compared to the other two interfaces. The time when the systolic peak occurs, expressed through parameter t1, was significantly lower in the L-IM interface compared to the other two interfaces. Preliminary findings from a small group of diseased wall locations suggested that the parameters alpha, b and t1 were significantly different than healthy cases. This probably reflects alterations of arterial wall mechanics due to disease. This study showed that the proposed mathematical model is a satisfactory representation of the mechanical deformation of the carotid artery wall in the radial direction and can provide valuable information in the understanding of the mechanical behavior of the arterial wall.

Arterial remodeling in response to hypertension using a constituent-based model

Hypertension-induced arterial remodeling has been previously modeled using stress-driven remodeling rate equations in terms of global geometrical adaptation (Rachev A, Stergiopulos N, Meister JJ. Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J Biomech 29: 635–642, 1996) and was extended later to include adaptation of material properties (Rachev A, Stergiopulos N, Meister JJ. A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 120: 9–17, 1998). These models, however, used a phenomenological strain energy function (SEF), the parameters of which do not bear a clear physiological meaning. Here, we extend the work of Rachev et al. (1998) by applying similar remodeling rate equations to a constituent-based SEF. The new SEF includes a statistical description for collagen engagement, and remodeling now affects material properties only through changes in the collagen engagement probability density function. The model predicts asymptotic wall thickening and unchanged deformed inner radius as to conserve hoop stress and intimal shear stress, respectively, at the final adapted hypertensive state. Mechanical adaptation serves to restore arterial compliance to control levels. Average circumferential stress-strain curves show that the material at the final adapted hypertensive state is softer than its normotensive counterpart. These findings as well as the predicted pressure-diameter curves are in good qualitative agreement with experimental data. The novelty in our findings is that biomechanical adaptation leading to maintenance of compliance at the hypertensive state can be perfectly achieved by appropriate readjustment of the collagen engagement profile alone.

Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats

Arterial baroreceptors are essential for neurocirculatory control, providing rapid hemodynamic feedback to the central nervous system. The pressure-dependent discharge of carotid and aortic baroreceptor afferents has been extensively studied. A common assumption has been that circumferential deformation of the arterial wall is the predominant mechanical force affecting baroreceptor discharge. However, in vivo the arterial tree is under significant longitudinal tension, leading to the hypothesis that axially directed forces may contribute to baroreceptor function. To test this hypothesis, we utilized a combination of finite element modeling methods and an in vitro rat aortic arch preparation. Model formulation utilized traditional analytic constructs available in the literature followed by refinement of model material parameters through direct comparison of computationally and experimentally generated pressure-diameter curves. The numerical simulations strongly indicated a functional role for axial loading within the region of the baroreceptive nerve terminal. This prediction was confirmed through single-fiber recording of baroreceptor nerve discharge under conditions with and without longitudinal tension in the vessel preparation. The recordings (n = 5) demonstrated that longitudinal tension significantly (P < 0.02) lowered both the pressure threshold (P(th), mmHg) for baroreceptor discharge and sensitivity (S(th), Hz/mmHg). The effect was nearly instantaneous and sustained; i.e., under longitudinal tension average P(th) was 84 +/- 3 mmHg and S(th) was 0.71 +/- 0.15 Hz/mmHg, which immediately increased to a P(th) of 94 +/- 4 mmHg and a S(th) of 1.20 +/- 0.32 Hz/mmHg with loss of axial tension. Possible explanations of how an abrupt change in axial loading could result in a synchronized increase in afferent drive of the baroreceptor reflex, and the potentiating effect this could have on neurogenically mediated orthostatic intolerance are discussed.

Ageing of the conduit arteries

Conduit arteries become stiffer with age due to alterations in their morphology and the composition of the their major structural proteins, elastin and collagen. The elastic lamellae undergo fragmentation and thinning, leading to ectasia and a gradual transfer of mechanical load to collagen, which is 100-1000 times stiffer than elastin. Possible causes of this fragmentation are mechanical (fatigue failure) or enzymatic (driven by matrix metallo proteinases (MMP) activity), both of which may have genetic or environmental origins (fetal programming). Furthermore, the remaining elastin itself becomes stiffer, owing to calcification and the formation of cross-links due to advanced glycation end-products (AGEs), a process that affects collagen even more strongly. These changes are accelerated in the presence of disease such as hypertension, diabetes and uraemia and may be exacerbated locally by atherosclerosis. Raised MMP activity, calcification and impaired endothelial function are also associated with a high level of plasma homocysteine, which itself increases with age. Impaired endothelial function leads to increased resting vascular smooth muscle tone and further increases in vascular stiffness and mean and/or pulse pressure. The effect of increased stiffness, whatever its underlying causes, is to reduce the reservoir/buffering function of the conduit arteries near the heart and to increase pulse wave velocity, both of which increase systolic and pulse pressure. These determine the peak load on the heart and the vascular system as a whole, the breakdown of which, like that of any machine, depends more on the maximum loads they must bear than on their average. Reversing or stabilising the increased arterial stiffness associated with age and disease by targeting any or all of its causes provides a number of promising new approaches to the treatment of systolic hypertension and its sequelae, the main causes of mortality and morbidity in the developed world.

Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls

Passive elastic behavior of arterial wall remains difficult to model. Although phenomenological and structural models exist, the question of how the three-dimensional network structure of the collagen in the artery determines its mechanical properties is still open. A model is presented that incorporates a collagen network as well as the noncollagenous material that comprise the artery. The collagen architecture is represented as a network of interconnected fibers, and a neo-Hookean constitutive equation is used to describe the contribution of the noncollagenous matrix. The model is multiscale in that volume-averaging theory is applied to the collagen network, and it is structural in that parameters of the microstructure of the collagen network were considered instead of a macroscopic constitutive law. The computational results provided a good fit to published experimental data for decellularized porcine carotid arteries. The model predicted increased circumferential compliance for increased axial stretch, consistent with previously published reports, and a relatively small sensitivity to open angle. Even at large extensions, the model predicted that the noncollagenous matrix would be in compression, preventing collapse of the collagen network. The incorporation of fiber-fiber interactions led to an accurate model of artery wall behavior with relatively few parameters. The counterintuitive result that the noncollagenous component is in compression during extension and inflation of the tissue suggests that the collagen is important even at small strains, with the noncollagenous components supporting the network, but not resisting the load directly. More accurate representation of the microstructure of the artery wall is needed to explore this issue further.

Stress-modulated collagen fiber remodeling in a human carotid bifurcation

This work concerns with the implementation of a new stress-driven remodeling model for simulating the overall structure and mechanical behavior of a human carotid bifurcation. By means of an iterative finite element based procedure collagen fiber direction and maximal principal stresses are computed. We find that the predicted fibers' architecture at the cylindrical branches and at the apex of the bifurcation correlates well with histological observations. Some insights about the mechanical response of the sinus bulb and the bifurcation apex are revealed and discussed. The results are compared with other, isotropic and orthotropic, models available in the literature.

Structural strain energy function applied to the ageing of the human aorta

Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch (lambda(z)) and residual strain (opening angle) in the biomechanical analysis. Both lambda(z) and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure-diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.

3D Mechanical properties of the layered esophagus: experiment and constitutive model

The identification of a three dimensional constitutive model is useful for describing the complex mechanical behavior of a nonlinear and anisotropic biological tissue such as the esophagus. The inflation tests at the fixed axial extension of 1, 1.125, and 1.25 were conducted on the muscle and mucosa layer of a porcine esophagus separately and the pressure-radius-axial force was recorded. The experimental data were fitted with the constitutive model to obtain the structure-related parameters, including the collagen amount and fiber orientation. Results showed that a bilinear strain energy function (SEF) with four parameters could fit the inflation data at an individual extension very well while a six-parameter model had to be used to capture the inflation behaviors at all three extensions simultaneously. It was found that the collagen distribution was axial preferred in both layers and the mucosa contained more collagen, which were in agreement with the findings through a pair of uniaxial tensile test in our previous study. The model was expected to be used for the prediction of stress distribution within the esophageal wall under the physiological state and provide some useful information in the clinical studies of the esophageal diseases.

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.

Mechanical properties of elastin along the thoracic aorta in the pig

Understanding the mechanical environment of each component within the arterial wall is fundamental for understanding vascular growth and remodelling and for engineering artificial vascular conduits. We have investigated the mechanical status of arterial elastin by measuring the circumferential mechanical properties of purified elastin as function of position along the descending thoracic aorta of the pig. The tensile circumferential secant modulus, E(sec), measured in uniaxial mechanical tests, increased 30% (P<0.001), from a value of 0.88 MPa in the proximal tissue near the aortic arch to 1.14 MPa in the distal tissue near the diaphragm, indicating the stiffness of the elastin sample increased with position. Breaking stress was 54% higher in the distal tissue compared to the proximal (P<0.001), but the breaking stretch ratio did not change. E(sec) correlated with the ratio of radius to wall thickness measured in the no load state, r(nl)/h(nl), suggesting that the rise in stiffness was linked to ring morphology. The higher stiffness and strength of the distal tissue might be explained by a higher proportion of circumferentially oriented fibres in the distal tissue, which would indicate that the elastin meshwork in the thoracic aorta may become progressively anisotropic with distance from the heart. The ratio r(nl)/(h(nl)E (sec))rose only 7%, which suggests that the in vivo circumferential strain on the elastin may be constant along the pig thoracic aorta. The positional variation in elastin's properties should be taken into account in mechanical studies on purified elastin and in mathematical models of aorta mechanics.

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.

Stress-driven collagen fiber remodeling in arterial walls

A stress-driven model for the relation between the collagen morphology and the loading conditions in arterial walls is proposed. We assume that the two families of collagen fibers in arterial walls are aligned along preferred directions, located between the directions of the two maximal principal stresses. For the determination of these directions an iterative finite element based procedure is developed. As an example the remodeling of a section of a human common carotid artery is simulated. We find that the predicted fiber morphology correlates well with experimental observations. Interesting outcomes of the model including local shear minimization and the possibility of axial compressions due to high blood pressure are revealed and discussed.

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress-strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379-4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1-48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.

Directional, regional, and layer variations of mechanical properties of esophageal tissue and its interpretation using a structure-based constitutive model

The esophagus, like other soft tissues, exhibits nonlinear and anisotropic mechanical properties. As a composite structure, the properties of the outer muscle and inner mucosal layer are different. It is expected that the complex mechanical properties will induce nonhomogeneous stress distributions in the wall and nonuniform tissue remodeling. Both are important factors which influence the function of mechanosensitive receptor located in various layers of the wall. Hence, the characterization of the mechanical properties is essential to understand the neuromuscular motion of the esophagus. In this study, the uniaxial tensile tests were conducted along two mutually orthogonal directions of porcine esophageal tissue to identify the directional (circumferential and axial), regional (abdominal, thoracic, and cervical), and layer (muscle and mucosa) variations of the mechanical properties. A structure-based constitutive model, which took the architectures of the tissue's microstructures into account, was applied to describe the mechanical behavior of the esophagus. Results showed that the constitutive model successfully described the mechanical behavior and provided robust estimates of the material parameters. In conclusion, the model was demonstrated to be a good descriptor of the mechanical properties of the esophagus and it was able to facilitate the directional, layer, and regional comparisons of the mechanical properties in terms of the associated material parameters.

Modeling cell and matrix anisotropy in fibroblast populated collagen vessels

Microstructurally based models for bio-artificial tissues are needed to predict in vivo mechanical behavior and to validate assumptions for models of biologic tissues. We develop a microstructural model, based on on Zahalak et al. (2000) [Biophys 79(5):2369-2381], to describe matrix and tissue anisotropy observed in recent biaxial tests of fibroblast populated collagen vessels (FPCVs) with different cell orientations (Wagenseil et al. in Ann Biomed Eng 32(5):720-731 2004). The model includes pseudo-elastic cell behavior and pseudo-elastic, non-linear matrix behavior with recruitment of initially buckled collagen fibers. We obtained estimates of collagen matrix parameters from measurements of FPCVs treated with 2x 10(-6) M Cytochalasin D and used these estimates to determine cell parameters in FPCVs activated with 5% fetal calf serum. The estimated stiffness of individual fibroblasts was 41-1,165 kPa. Parameter estimates for both cell and matrix were influenced by the non-linearity of the biaxial test data, making it difficult to obtain unique parameter values for some experiments. Additional microstructural measurements of the collagen matrix may help to more precisely determine the relative contributions of cells and matrix.

Mechanical Characterization of Anisotropic Planar Biological Soft Tissues Using Large Indentation: A Computational Feasibility Study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.

Effects of elastin haploinsufficiency on the mechanical behavior of mouse arteries

Supravalvular aortic stenosis (SVAS) is associated with decreased elastin and altered arterial mechanics. Mice with a single deletion in the elastin gene (ELN+/−) are models for SVAS. Previous studies have shown that elastin haploinsufficiency in these mice causes hypertension, decreased arterial compliance, and changes in arterial wall structure. Despite these differences, ELN+/− mice have a normal life span, suggesting that the arteries remodel and adapt to the decreased amount of elastin. To test this hypothesis, we performed in vitro mechanical tests on abdominal aorta, ascending aorta, and left common carotid artery from ELN+/− and wild-type (C57BL/6J) mice. We compared the circumferential and longitudinal stress-stretch relationships and residual strains. The circumferential stress-stretch relationship is similar between genotypes and changes <3% with longitudinal stretch at lengths within 10% of the in vivo value. At mean arterial pressure, the circumferential stress in the ascending aorta is higher in ELN+/− than in wild type. Although arterial pressures are higher, the increased number of elastic lamellae in ELN+/− arteries results in similar tension/lamellae compared with wild type. The longitudinal stress-stretch relationship is similar between genotypes for most arteries. Compared with wild type, the in vivo longitudinal stretch is lower in ELN+/− abdominal and carotid arteries and the circumferential residual strain is higher in ELN+/− ascending aorta. The increased circumferential residual strain brings the transmural strain distribution in ELN+/− ascending aorta close to wild-type values. The mechanical behavior of ELN+/− arteries is likely due to the reduced elastin content combined with adaptive remodeling during vascular development.

Contribution of vasoconstriction to the origin of atherosclerosis: a conceptual study

Research during the past century has clearly shown that endothelial injury (EI) and/or endothelial dysfunction (ED) are among the major events determining the onset of atherosclerosis. Included in the events that may elicit endothelial damage, vasoconstriction (VC) has received relatively little attention. This conceptual review attempts to show that in elastic and conduit arteries, VC is not only capable of producing EI/ED, but is also closely associated with many recognized proatherogenic stimuli. Of related interest is the observation that a number of suspected antiatherogenic stimuli oppose VC by their vasodilatory effects, lending further support to this relationship. In addition, recent developments in the knowledge of the molecular basis of VC (including the role of specific inhibitors) are discussed, and their potential for preventing lesion formation and thus becoming novel therapeutic alternatives against the onset of atherosclerosis are highlighted.

A Structural Constitutive Model For Collagenous Cardiovascular Tissues Incorporating the Angular Fiber Distribution

Accurate constitutive models are required to gain further insight into the mechanical behavior of cardiovascular tissues. In this study, a structural constitutive framework for cardiovascular tissues is introduced that accounts for the angular distribution of collagen fibers. To demonstrate its capabilities, the model is applied to study the biaxial behavior of the arterial wall and the aortic valve. The pressure–radius relationships of the arterial wall accurately describe experimentally observed sigma-shaped curves. In addition, the nonlinear and anisotropic mechanical properties of the aortic valve can be analyzed with the proposed model. We expect that the current model offers strong possibilities to further investigate the complex mechanical behavior of cardiovascular tissues, including their response to mechanical stimuli.

A constitutive formulation of arterial mechanics including vascular smooth muscle tone

A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load bearing is modulated by the contraction. This novel pseudo-SEF models not only arterial mechanics at maximal VSM contraction but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified with experimentally obtained pressure-radius curves and zero-stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The pressure-radius curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well ( r2> 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone, suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.