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.     

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.     

Arterial remodeling in response to increased blood flow using a constituent-based model

Previous theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the arterial wall remain unchanged during the remodeling process. According to experimental findings, however, remodeling due to increased flow is accompanied by alteration in the structural properties of elastin, which results in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling hypothesizing that the variation in mechanical properties of elastin is initiated and driven by the deviation of the intimal shear stress from its baseline value. Geometrical remodeling restores the wall stress distribution as it was under normal flow conditions. A constrained mixture approach is followed. Artery is modeled as a thick-walled cylindrical tube made of non-linear, elastic, anisotropic and incompressible material. Data for a rabbit thoracic aorta have been employed. At the final adapted state, the model predicts a non-monotonic dependence of arterial compliance on the magnitude of flow. This result is in agreement with available experimental data in the literature.     

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

Identification of a Strain Energy Function (SEF) is used when describing the complex mechanical properties of soft biological tissues such as the arterial wall. Classic SEFs, such as the one proposed by Chuong and Fung (J. Biomech. Eng. 105(3) (1983) 268), have been mostly phenomenological and neglect the particularities of the wall structure. A more structural model was proposed by Holzapfel et al. (J. Elasticity 61 (2000) 1-48.) when they included the characteristic angle at which the collagen fibers are helically wrapped, resulting in an excellent SEF for applications such as finite element modeling. We have expanded upon the idea of structural SEFs by including not only the wavy nature of the collagen but also the fraction of both elastin and collagen contained in the media, which can be determined by histology. The waviness of the collagen is assumed to be distributed log-logistically. In order to evaluate this novel SEF, we have used it to fit experimental data from inflation-extension tests performed on rat carotids. We have compared the results of the fit to the SEFs of Choung and Fung and Holzapfel et al. The novel SEF is found to behave similarly to that of Holzapfel et al., both succeed in describing the typical S-shaped pressure-radius curves with comparable quality of fit. The parameters of the novel SEF obtained from the fitting, bearing the physical meaning of the elastic modulus of collagen, the elastic modulus of elastin, the collagen waviness, and the collagen fiber angle, were compared to experimental data and discussed.     

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 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.     

Theoretical study on the effects of pressure-induced remodeling on geometry and mechanical non-homogeneity of conduit arteries

A structure-based mathematical model for the remodeling of arteries in response to sustained hypertension is proposed. The model is based on the concepts of volumetric growth and constitutive modeling of the arterial tissue within the framework of the constrained mixture theory. The major novel result of this study is that remodeling is associated with a local change in the mass fractions of the wall constituents that ultimately leads to mechanical non-homogeneity of the arterial wall. In the new homeostatic state that develops after a sustained increase in arterial pressure, the mass fraction of elastin decreases from the intimal side to the adventitial side of arteries, while the collagen fraction manifests an opposite trend. The results obtained are supported by some experimental observations reported in the literature.     

Geometrical,functional, and histomorphometric adaptation of rat carotid artery in induced hypertension

Acute and long-term (up to 56 days) evolution of geometry, structural properties, vascular smooth muscle (VSM) tone and histomorphometric properties of the rat common carotid arteries under induced hypertension were investigated. Hypertension was induced in 8-week old male Wistar rats by total ligation of the aorta between the two kidneys. Rats were sacrificed 2, 4, 8 and 56 days postsurgery. The arterial wall layers thicken non-uniformly during the adaptation process, the inner layers thicken more in the acute phase of hypertension, whereas the outer layers of the wall are thicker than the inner layers at the end of the adaptation phase. Collagen content in the wall media exhibits a non-linear evolution, with a rapid increase in the acute hypertension phase followed by a slower increase at long-term. The elastin content increase is slight and steady, whereas VSM shows a steady but considerable increase which outdoes the collagen increase in long-term phase. VSM tone increases rapidly in the acute phase of remodelling (0-8 days) and this increase in tone contributes to a considerable increase in arterial compliance in the operating pressure range. At long-term (56 days) VSM tone returns to near control level, but compliance is even further increased, which suggests that at long-term the compliance increase is attributed primarily to structural remodelling.     

Remodelling of collagen fibre transition stretch and angular distribution in soft biological tissues and cell-seeded hydrogels

The extracellular matrix in many biological tissues is adapted to its mechanical environment. In this study, a phenomenological model for collagen remodelling is introduced that incorporates angular remodelling (fibre reorientation) and the adaptation of the so-called transition stretch. This is achieved by introducing a local stress-free configuration for the collagen network by a multiplicative decomposition of the deformation gradient and the appropriate definition of the anisotropic free Helmholtz energy potentials and structure tensors. The collagen network is either treated using discrete fibre directions or a continuous angular distribution. The first part of the study illustrates the influence of force- and displacement-controlled loading on either stress- or deformation-driven remodelling processes in tissues with various degrees of fibre reinforcement. The model is then applied to recent experimental studies of collagen remodelling, specifically periosteum adaptation (Foolen et?al. in J Biomech 43(16):3168–3176, 2010), collagen gel (Thomopoulos et?al. in J Biomech Eng 127(5):742–750, 2005) and fibrin cruciform (Sander et?al. in Ann Biomed Eng 1–16, 2010) compaction. The model is able to capture the basic effects of an adapting transition stretch over time in the periosteal simulations, as well as the compaction and the development of structural anisotropy in the collagen and fibrin gels. The model can potentially be applied to elucidate structure–function relationships, better interpret in vitro experiments involving collagen remodelling, and help investigate aspects of certain pathologies, such as connective tissue contracture.     

Bortezomib,a Proteasome Inhibitor,Attenuates Angiotensin II-Induced Hypertension and Aortic Remodeling in Rats

Background

Hypertension is a highly prevalent disorder and a major risk factor for cardiovascular diseases. Hypertensive vascular remodeling is the pathological mal-adaption of blood vessels to the hypertensive condition that contributes to further development of high blood pressure and end-organ damage. Hypertensive remodeling involves, at least in part, changes in protein turnover. The ubiquitin proteasome system (UPS) is a major protein quality and quantity control system. This study tested the hypothesis that the proteasome inhibitor, bortezomib, would attenuate AngII-induced hypertension and its sequelae such as aortic remodeling in rats.

Methodology/Principal Findings

Male Sprague Dawley rats were subjected to AngII infusion for two weeks in the absence or presence of bortezomib. Mean arterial pressure was measured in conscious rats. Aortic tissue was collected for estimation of wall area, collagen deposition and expression of tissue inhibitors of matrix metalloproteases (TIMP), Ki67 (a marker of proliferation), reactive oxygen species (ROS) and VCAM-1 (a marker of inflammation). AngII infusion increased arterial pressure significantly (160±4 mmHg vs. vehicle treatment 133±2 mmHg). This hypertensive response was attenuated by bortezomib (138±5 mmHg). AngII hypertension was associated with significant increases in aortic wall to lumen ratio (∼29%), collagen deposition (∼14%) and expression of TIMP1 and TIMP2. AngII also increased MMP2 activity, proteasomal chymotrypsin-like activity, Ki67 staining, ROS generation and VCAM-1 immunoreactivity. Co-treatment of AngII-infused rats with bortezomib attenuated these AngII-induced responses.

Conclusions

Collectively, these data support the idea that proteasome activity contributes to AngII-induced hypertension and hypertensive aortic vascular remodeling at least in part by modulating TIMP1/2 and MMP2 function. Preliminary observations are consistent with a role for ROS, inflammatory and proliferative mechanisms in this effect. Further understanding of the mechanisms by which the proteasome is involved in hypertension and vascular structural remodeling may reveal novel targets for pharmacological treatment of hypertension, hypertensive remodeling or both.     

Evolving mechanical properties of a model of abdominal aortic aneurysm

The novel three-dimensional (3D) mathematical model for the development of abdominal aortic aneurysm (AAA) of Watton et al. Biomech Model Mechanobiol 3(2): 98–113, (2004) describes how changes in the micro-structure of the arterial wall lead to the development of AAA, during which collagen remodels to compensate for loss of elastin. In this paper, we examine the influence of several of the model’s material and remodelling parameters on growth rates of the AAA and compare with clinical data. Furthermore, we calculate the dynamic properties of the AAA at different stages in its development and examine the evolution of clinically measurable mechanical properties. The model predicts that the maximum diameter of the aneurysm increases exponentially and that the ratio of systolic to diastolic diameter decreases from 1.13 to 1.02 as the aneurysm develops; these predictions are consistent with physiological observations of Vardulaki et al. Br J Surg 85:1674–1680 (1998) and Lanne et al. Eur J Vasc Surg 6:178–184 (1992), respectively. We conclude that mathematical models of aneurysm growth have the potential to be useful, noninvasive diagnostic tools and thus merit further development.     

Validation of a pressure diameter method for determining modulus and strain of collagen engagement for long branches of bovine pulmonary arteries

Recent studies have shown that capacitance measurements of large arteries provide better prognosis and diagnosis than tests of resistance alone in pulmonary hypertension (Mahapatra et al., 2006, "Relationship of Pulmonary Arterial Capacitance and Mortality in Idiopathic Pulmonary Arterial Hypertension," J. Am. Coll. Cardiol., 47(4), pp. 799-803; Reuben, 1971, "Compliance of the Human Pulmonary Arterial System in Disease," Circ. Res., 29, pp. 40-50]. Decreased arterial capacitance causes increased load to the heart and is the direct result of increased stiffness and elastic modulus of the arterial wall. Here, we validate a pressure-diameter (PD) method for comparing the elastic modulus and collagen engagement for post-hilar pulmonary arteries with a large range of arterial diameter. The tissue mechanics of the post-hilar arteries are not well-characterized in pulmonary hypertension. It is believed that future studies with this method will provide useful insight into the role of passive tissue mechanics of these arteries in the pathophysiology of pulmonary hypertension, eventually improving clinical diagnosis, prognosis, and treatment. Post-hilar pulmonary arteries, excised from healthy and hypertensive calves and healthy cows, were inflated over a range of 0 [mm Hg] to 110 [mm Hg] in an isolated tissue bath. Internal pressure was recorded with an electric pressure catheter. Artery diameter and longitudinal stretch were recorded photographically. Stress-strain data curves were extracted using Lame's law of thick-walled tubes. Radial strips were removed from each section and tested in a uniaxial (MTS) tester for validation. Both the elastic modulus and collagen engagement strain were similar to results obtained by more traditional means. The average difference between measured values of the two methods for collagen engagement strain was 3.3% of the average value of the engagement strain. The average difference between the measured values of the two methods for modulus of elasticity was 7.4% of the average value of the modulus. The maximum, theoretical, relative error for the stress determined with the PD method was calculated at 20.3%. The PD method proved to be a suitable replacement for uniaxial strain tests in comparing collagen engagement strains. The method allowed faster testing of tissues of multiple diameters, while removing the effect of end conditions. The PD method will be of further utility in continued study of tissue mechanics in pulmonary hypertension studies.     

Time-course of venous wall biomechanical adaptation in pressure and flow-overload: Assessment by a microstructure-based material model

Arteriovenous fistulae have been previously created by our group, through implantation of e-PTFE grafts between the carotid artery and jugular vein in healthy pigs, to gather comprehensive data on the time-course of the adapted geometry, composition, and biomechanical properties of the venous wall exposed to chronic increases in pressure and flow. The aim of this study was to mathematically assess the biomechanical adaptation of venous wall, by characterizing our previous in vitro inflation/extension testing data obtained 2, 4, and 12 weeks post-fistula, using a microstructure-based material model. Our choice for such a model considered a quadratic function for elastin with a four-fiber family term for collagen, and permitted realistic data characterization for both overloaded and control veins. As structural validation to the hemodynamically-driven differences in the material response, computerized histology was employed to quantitate the composition and orientation of collagen and elastin-fiber networks. The parameter values optimized showed marked differences among the overloaded and control veins, namely decrease in the quadratic function parameters and increase in the four-fiber family parameters. Differences among the two vein types were highlighted with respect to the underlying microstructure, namely the reduced elastin and increased collagen contents induced by pressure and flow-overload. Explicit correlations were found of the material parameters with the two basic scleroprotein contents, substantiating the material model used and the characterization findings presented. Our results are expected to improve the current understanding of the dynamics of venous adaptation under sustained pressure- and flow-overload conditions, for which data are largely unavailable and contradictory.     

Three-section transmission-line arterial model for noninvasive assessment of vascular remodeling in primary hypertension

High central arterial blood pressure can be sustained by the capacity of living arteries to respond to hemodynamic stimuli by changing their structural and/or functional characteristics. These adaptations are considered to occur in a time-dependency, in which different patterns of vascular geometry are identified at all stages. This paper proposes a three-section transmission-line model of the brachial-radial arterial segment and a rational procedure to analyze its transfer function that can be used to interpret the longitudinal remodeling process of medium-sized arteries. The three sections of the model correspond to different arterial segments of the forearm. The model processed pressure signals collected noninvasively from normotensive and hypertensive volunteers at brachial and radial arteries. Aiming to explain possible hypertrophic inward remodeling, geometrical model parameters obtained from normotensive individuals were modified in order to generate high-pressure pulses observed in the hypertensive subjects. The resulting transfer functions for the hypertrophy adaptation exhibit properties related to the pathophysiology of the remodeling process, mainly the reduced amplification of the higher harmonics of the pulse waveform. The results suggest the model can be used to assess noninvasively the hypertension-induced adaptations related to geometrical characteristics of the medium-size arteries.     

The collagen fibril architecture in the lamina cribrosa and peripapillary sclera predicted by a computational remodeling approach

The biomechanics of the optic nerve head is assumed to play an important role in ganglion cell loss in glaucoma. Organized collagen fibrils form complex networks that introduce strong anisotropic and nonlinear attributes into the constitutive response of the peripapillary sclera (PPS) and lamina cribrosa (LC) dominating the biomechanics of the optic nerve head. The recently presented computational remodeling approach (Grytz and Meschke in Biomech Model Mechanobiol 9:225–235, 2010) was used to predict the micro-architecture in the LC and PPS, and to investigate its impact on intraocular pressure–related deformations. The mechanical properties of the LC and PPS were derived from a microstructure-oriented constitutive model that included the stretch-dependent stiffening and the statistically distributed orientations of the collagen fibrils. Biomechanically induced adaptation of the local micro-architecture was captured by allowing collagen fibrils to be reoriented in response to the intraocular pressure–related loading conditions. In agreement with experimental observations, the remodeling algorithm predicted the existence of an annulus of fibrils around the scleral canal in the PPS, and a predominant radial orientation of fibrils in the periphery of the LC. The peripapillary annulus significantly reduced the intraocular pressure–related expansion of the scleral canal and shielded the LC from high tensile stresses. The radial oriented fibrils in the LC periphery reinforced the LC against transversal shear stresses and reduced LC bending deformations. The numerical approach presents a novel and reasonable biomechanical explanation of the spatial orientation of fibrillar collagen in the optic nerve head.     

In spontaneously hypertensive rats alterations in aortic wall properties precede development of hypertension

In hypertension arterial wall properties do not necessarily depend on increased blood pressure alone. The present study investigates the relationship between the development of hypertension and thoracic aortic wall properties in 1.5-, 3-, and 6-mo-old spontaneously hypertensive rats (SHR); Wistar-Kyoto rats (WKY) served as controls. During ketamine-xylazine anesthesia, compliance and distensibility were assessed by means of a noninvasive ultrasound technique combined with invasive blood pressure measurements. Morphometric measurements provided in vivo media cross-sectional area and thickness, allowing the calculation of the incremental elastic modulus. Extracellular matrix protein contents were determined as well. Blood pressure was not significantly different in 1.5-mo-old SHR and WKY, but compliance and distensibility were significantly lower in SHR. Incremental elastic modulus was not significantly different between SHR and WKY at this age. Media thickness and media cross-sectional area were significantly larger in SHR than in WKY, but there was no consistent difference in collagen density and content between the strains. Blood pressure was significantly higher in 3- and 6-mo-old SHR than in WKY, and compliance was significantly lower in SHR. The findings in this study show that in SHR, in which hypertension develops over weeks, alterations in functional aortic wall properties precede the development of hypertension. The decrease in compliance and distensibility at a young age most likely results from media hypertrophy rather than a change in intrinsic elastic properties.     

Haemodynamics and wall remodelling of a growing cerebral aneurysm: a computational model

We have developed a computational simulation model for investigating an often postulated hypothesis connected with aneurysm growth. This hypothesis involves a combination of two parallel and interconnected mechanisms: according to the first mechanism, an endothelium-originating and wall shear stress-driven apoptotic behavior of smooth muscle cells, leading to loss of vascular tone is believed to be important to the aneurysm behavior. Vascular tone refers to the degree of constriction experienced by a blood vessel relative to its maximally dilated state. All resistance and capacitance vessels under basal conditions exhibit some degree of smooth muscle contraction that determines the diameter, and hence tone, of the vessel. The second mechanism is connected to the arterial wall remodeling. Remodeling of the arterial wall under constant tension is a biomechanical process of rupture, degradation and reconstruction of the medial elastin and collagen fibers. In order to investigate these two mechanisms within a computationally tractable framework, we devise mechanical analogues that involve three-dimensional haemodynamics, yielding estimates of the wall shear stress and pressure fields and a quasi-steady approach for the apoptosis and remodeling of the wall. These analogues are guided by experimental information for the connection of stimuli to responses at a cellular level, properly averaged over volumes or surfaces. The model predicts aneurysm growth and can attribute specific roles to the two mechanisms involved: the smooth muscle cell-related loss of tone is important to the initiation of aneurysm growth, but cannot account alone for the formation of fully grown sacks; the fiber-related remodeling is pivotal for the latter.     

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.