Quantification of the mechanical behavior of carotid arteries from wild-type, dystrophin-deficient, and sarcoglycan-delta knockout mice

Vascular Remodeling During Late-Gestation Pregnancy: An In-Vitro Assessment of the Murine Ascending Thoracic Aorta

Maternal mortality due to cardiovascular disease is a rising concern in the U.S. Pregnancy triggers changes in the circulatory system, potentially influencing the structure of the central vasculature. Evidence suggests a link between a woman's pregnancy history and future cardiovascular health, but our understanding remains limited. To fill this gap, we examined the passive mechanics of the murine ascending thoracic aorta during late gestation. By performing biaxial mechanical testing on the ascending aorta, we were able to characterize the mechanical properties of both control and late-gestation tissues. By examining mechanical, structural, and geometric properties, we confirmed that remodeling of the aortic wall occurred. Morphological and mechanical properties of the tissue indicated an outward expansion of the tissue, as reflected in changes in wall thickness (∼12% increase) and luminal diameter (∼6% increase) at its physiologically loaded state in the pregnant group. With these geometric adaptations and despite increased hemodynamic loads, pregnancy did not induce significant changes in the tensile wall stress at the similar physiological pressure levels of the pregnant and control tissues. The alterations also included reduced intrinsic stiffness in the circumferential direction (∼18%) and reduced structural stiffness (∼26%) in the pregnant group. The observed vascular remodeling maintained the elastic stored energy of the aortic wall under systolic loads, indicating preservation of vascular function. Data from our study of pregnancy-related vascular remodeling will provide valuable insights for future investigations of maternal cardiovascular health.

A biochemomechanical model of collagen turnover in arterial adaptations to hemodynamic loading

The production, removal, and remodeling of fibrillar collagen is fundamental to mechanical homeostasis in arteries, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have proven able to predict salient features of the progression of certain vascular adaptations as well as disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically within the range of 10-70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Constituent-based quasi-linear viscoelasticity: a revised quasi-linear modelling framework to capture nonlinear viscoelasticity in arteries

Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.

A Biochemomechanical Model of Collagen Turnover in Arterial Adaptations to Hemodynamic Loading

The production, removal, and remodeling of fibrillar collagen is fundamental to arterial homeostasis, including dynamic morphological and microstructural changes that occur in response to sustained changes in blood flow and pressure under physiological conditions. These dynamic processes involve complex, coupled biological, chemical, and mechanical mechanisms that are not completely understood. Nevertheless, recent simulations using constrained mixture models with phenomenologically motivated constitutive relations have demonstrated a capability to predict salient features of the progression of certain vascular adaptations and disease processes. Collagen turnover is modeled, in part, via stress-dependent changes in collagen half-life, typically taken within the range of 10â€"70 days. By contrast, in this work we introduce a biochemomechanical approach to model the cellular synthesis of procollagen as well as its transition from an intermediate state of assembled microfibrils to mature cross-linked fibers, with mechano-regulated removal. The resulting model can simulate temporal changes in geometry, composition, and stress during early vascular adaptation (weeks to months) for modest changes in blood flow or pressure. It is shown that these simulations capture salient features from data presented in the literature from different animal models.

Biaxial biomechanical properties of the nonpregnant murine cervix and uterus

From a biomechanical perspective, female reproductive health is an understudied area of research. There is an incomplete understanding of the complex function and interaction between the cervix and uterus. This, in part, is due to the limited research into multiaxial biomechanical functions and geometry of these organs. Knowledge of the biomechanical function and interaction between these organs may elucidate etiologies of conditions such as preterm birth. Therefore, the objective of this study was to quantify the multiaxial biomechanical properties of the murine cervix and uterus using a biaxial testing set-up. To accomplish this, an inflation-extension testing protocol (n = 15) was leveraged to quantify biaxial biomechanical properties while preserving native matrix interactions and geometry. Ultrasound imaging and histology (n = 10) were performed to evaluate regional geometry and microstructure, respectively. Histological analysis identified a statistically significant greater collagen content and significantly smaller smooth muscle content in the cervix as compared to the uterus. No statistically significant differences in elastic fibers were identified. Analysis of bilinear fits revealed a significantly stiffer response from the circumferentially orientated ECM fibers compared to axially orientated fibers in both organs. Bilinear fits and a two-fiber family constitutive model showed that the cervix was significantly less distensible than the uterus. We submit that the regional biaxial information reported in this study aids in establishing an appropriate reference configuration for mathematical models of the uterine-cervical complex. Thus, may aid future work to elucidate the biomechanical mechanisms leading to cervical or uterine conditions.

Effects of elastase digestion on the murine vaginal wall biaxial mechanical response

Although the underlying mechanisms of pelvic organ prolapse (POP) remain unknown, disruption of elastic fiber metabolism within the vaginal wall extracellular matrix has been highly implicated. It has been hypothesized that elastic fiber fragmentation correlates to decreased structural integrity and increased risk of prolapse; however, the mechanisms by which elastic fiber damage may contribute to prolapse are poorly understood. Further, the role of elastic fibers in normal vaginal wall mechanics has not been fully ascertained. Therefore, the objective of this study is to investigate the contribution of elastic fibers to murine vaginal wall mechanics. Vaginal tissue from C57BL/6 female mice were mechanically tested using biaxial extension-inflation protocols before and after intraluminal exposure to elastase. Elastase digestion induced marked changes in the vaginal geometry, and biaxial mechanical properties, suggesting that elastic fibers may play an important role in vaginal wall mechanical function. Additionally, a constitutive model that considered two diagonal families of collagen fibers with a slight preference towards the circumferential direction described the data reasonably well before and after digestion. The present findings may be important to determine the underlying structural and mechanical mechanisms of POP, and aid in the development of growth and remodeling models for improved assessment and prediction of changes in structure-function relationships with prolapse development. Keywords: vaginal wall, women's health, mechanical testing, pelvic floor disorders, elastic fibers Disclosures: none.

Central Arterial Function Measured by Non-invasive Pulse Wave Analysis is Abnormal in Patients with Duchenne Muscular Dystrophy

Duchenne muscular dystrophy (DMD) is an X-linked recessive disorder caused by mutation of dystrophin. Cardiovascular involvement includes dilated cardiomyopathy. Non-invasive assessment of vascular function has not been evaluated in DMD. We hypothesize arterial wave reflection is abnormal in patients with DMD. Pulse wave analysis was performed on DMD patients with a SphygmoCor SCOR-PVx System to determine central blood pressure and augmentation index (AIx) as an assessment of arterial wave reflection. Results were compared to a control group. A total of 43 patients with DMD were enrolled, and compared to 43 normal controls. Central systolic blood pressure was lower, while both AIx-75 (7.8 ± 9.6% vs. 2.1 ± 10.4%, p 0.01, DMD vs. normal) and AIx-not corrected (16.8 ± 10.1% vs. -3.6 ± 10.9, p < 0.001, DMD vs. normal) were higher in the DMD compared to control. Using multivariable linear regression model, the variables found to have a significant effect on AIx-not corrected included diagnosis of DMD, height, and heart rate (r ² = 0.257). The current data suggest that, despite lower central systolic blood pressure, patients with DMD have higher wave reflection when compared to normal controls, which may represent increased arterial stiffness. Overall there appears to be no effect on ventricular systolic function, however the long-term consequence in this group is unknown. Further study is required to determine the mechanism of these differences, which may be related to the effects of systemic steroids or the role of dystrophin in vascular function.

Effect of ovariectomy and Sideritis euboea extract administration on large artery mechanics, morphology, and structure in middle-aged rats

BACKGROUND

Arterial function is regulated by estrogen, but no consistent pattern of arterial mechanical remodeling in response to depleted estrogen levels is available.

OBJECTIVE

To examine long-term effects of ovariectomy (OVX) on the mechanical properties, morphology, and histological structure of the carotid artery in middle-aged rats and a potentially protective effect of Sideritis euboea extract (SID), commonly consumed as "mountain tea".

METHODS

10-month-old female Wistar rats were allocated into control (sham-operated), OVX, OVX+SID, and OVX+MALT (maltodextrin; excipient used for dilution of SID) groups. They were sacrificed after 6 months and their carotid arteries were submitted to inflation/extension tests and to dimensional and histological evaluation.

RESULTS

Remodeling in OVX rats was characterized by a decreased in situ axial extension ratio, along with increased opening angle, thickness, and area of the vessel wall and of its medial layer, but unchanged lumen diameter. Compositional changes involved increased elastin/collagen densities. Characterization by the "four-fiber" microstructure-motivated model revealed similar in situ biaxial response of carotid arteries in OVX and control rats.

CONCLUSIONS

Carotid artery remodeling in OVX rats was largely consistent with hypertensive remodeling, despite the minor arterial pressure changes found, and was not altered by administration of SID, despite previous evidence of its osteo-protective effect.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the 'computational dissection' of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

Loss of Elastic Fiber Integrity Compromises Common Carotid Artery Function: Implications for Vascular Aging

Competent elastic fibers endow central arteries with the compliance and resilience that are fundamental to their primary mechanical function in vertebrates. That is, by enabling elastic energy to be stored in the arterial wall during systole and then to be used to work on the blood during diastole, elastic fibers decrease ventricular workload and augment blood flow in pulsatile systems. Indeed, because elastic fibers are formed during development and stretched during somatic growth, their continual tendency to recoil contributes to the undulation of the stiffer collagen fibers, which facilitates further the overall compliance of the wall under physiologic pressures while allowing the collagen to limit over-distension during acute increases in blood pressure. In this paper, we use consistent methods of measurement and quantification to compare the biaxial material stiffness, structural stiffness, and energy storage capacity of murine common carotid arteries having graded degrees of elastic fiber integrity - normal, elastin-deficient, fibrillin-1 deficient, fibulin-5 null, and elastase-treated. The finding that the intrinsic material stiffness tends to be maintained nearly constant suggests that intramural cells seek to maintain a favorable micromechanical environment in which to function. Nevertheless, a loss of elastic energy storage capability due to the loss of elastic fiber integrity severely compromises the primary function of these central arteries.

Decreased elastic energy storage, not increased material stiffness, characterizes central artery dysfunction in fibulin-5 deficiency independent of sex

Central artery stiffness has emerged over the past 15 years as a clinically significant indicator of cardiovascular function and initiator of disease. Loss of elastic fiber integrity is one of the primary contributors to increased arterial stiffening in aging, hypertension, and related conditions. Elastic fibers consist of an elastin core and multiple glycoproteins; hence defects in any of these constituents can adversely affect arterial wall mechanics. In this paper, we focus on mechanical consequences of the loss of fibulin-5, an elastin-associated glycoprotein involved in elastogenesis. Specifically, we compared the biaxial mechanical properties of five central arteries-the ascending thoracic aorta, descending thoracic aorta, suprarenal abdominal aorta, infrarenal abdominal aorta, and common carotid artery-from male and female wild-type and fibulin-5 deficient mice. Results revealed that, independent of sex, all five regions in the fibulin-5 deficient mice manifested a marked increase in structural stiffness but also a marked decrease in elastic energy storage and typically an increase in energy dissipation, with all differences being most dramatic in the ascending and abdominal aortas. Given that the primary function of large arteries is to store elastic energy during systole and to use this energy during diastole to work on the blood, fibulin-5 deficiency results in a widespread diminishment of central artery function that can have significant effects on hemodynamics and cardiac function.

Critical buckling pressure in mouse carotid arteries with altered elastic fibers

Arteries can buckle axially under applied critical buckling pressure due to a mechanical instability. Buckling can cause arterial tortuosity leading to flow irregularities and stroke. Genetic mutations in elastic fiber proteins are associated with arterial tortuosity in humans and mice, and may be the result of alterations in critical buckling pressure. Hence, the objective of this study is to investigate how genetic defects in elastic fibers affect buckling pressure. We use mouse models of human disease with reduced amounts of elastin (Eln+/-) and with defects in elastic fiber assembly due to the absence of fibulin-5 (Fbln5-/-). We find that Eln+/- arteries have reduced buckling pressure compared to their wild-type controls. Fbln5-/- arteries have similar buckling pressure to wild-type at low axial stretch, but increased buckling pressure at high stretch. We fit material parameters to mechanical test data for Eln+/-, Fbln5-/- and wild-type arteries using Fung and four-fiber strain energy functions. Fitted parameters are used to predict theoretical buckling pressure based on equilibrium of an inflated, buckled, thick-walled cylinder. In general, the theoretical predictions underestimate the buckling pressure at low axial stretch and overestimate the buckling pressure at high stretch. The theoretical predictions with both models replicate the increased buckling pressure at high stretch for Fbln5-/- arteries, but the four-fiber model predictions best match the experimental trends in buckling pressure changes with axial stretch. This study provides experimental and theoretical methods for further investigating the influence of genetic mutations in elastic fibers on buckling behavior and the development of arterial tortuosity.

Effects of age on the physiological and mechanical characteristics of human femoropopliteal arteries

Surgical and interventional therapies for peripheral artery disease (PAD) are notorious for high rates of failure. Interactions between the artery and repair materials play an important role, but comprehensive data describing the physiological and mechanical characteristics of human femoropopliteal arteries are not available. Fresh femoropopliteal arteries were obtained from 70 human subjects (13-79 years old), and in situ vs. excised arterial lengths were measured. Circumferential and longitudinal opening angles were determined for proximal superficial femoral, proximal popliteal and distal popliteal arteries. Mechanical properties were assessed by multi-ratio planar biaxial extension, and experimental data were used to calculate physiological stresses and stretches, in situ axial force and anisotropy. Verhoeff-Van Gieson-stained axial and transverse arterial sections were used for histological analysis. Most specimens demonstrated nonlinear deformations and were more compliant longitudinally than circumferentially. In situ axial pre-stretch decreased 0.088 per decade of life. In situ axial force and axial stress also decreased with age, but circumferential physiological stress remained constant. Physiological circumferential stretch decreased 55-75% after 45 years of age. Histology demonstrated a thickened external elastic lamina with longitudinally oriented elastin that was denser in smaller, younger arteries. Axial elastin likely regulates axial pre-stretch to help accommodate the complex deformations required of the artery wall during locomotion. Degradation and fragmentation of elastin as a consequence of age, cyclic mechanical stress and atherosclerotic arterial disease may contribute to decreased in situ axial pre-stretch, predisposing to more severe kinking of the artery during limb flexion and loss of energy-efficient arterial function.

Bio-Chemo-Mechanical Models of Vascular Mechanics

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.

Aging impairs smooth muscle-mediated regulation of aortic stiffness: a defect in shock absorption function?

Increased aortic stiffness is an early and independent biomarker of cardiovascular disease. Here we tested the hypothesis that vascular smooth muscle cells (VSMCs) contribute significantly to aortic stiffness and investigated the mechanisms involved. The relative contributions of VSMCs, focal adhesions (FAs), and matrix to stiffness in mouse aorta preparations at optimal length and with confirmed VSMC viability were separated by the use of small-molecule inhibitors and activators. Using biomechanical methods designed for minimal perturbation of cellular function, we directly quantified changes with aging in aortic material stiffness. An alpha adrenoceptor agonist, in the presence of N(G)-nitro-l-arginine methyl ester (l-NAME) to remove interference of endothelial nitric oxide, increases stiffness by 90-200% from baseline in both young and old mice. Interestingly, increases are robustly suppressed by the Src kinase inhibitor PP2 in young but not old mice. Phosphotyrosine screening revealed, with aging, a biochemical signature of markedly impaired agonist-induced FA remodeling previously associated with Src signaling. Protein expression measurement confirmed a decrease in Src expression with aging. Thus we report here an additive model for the in vitro biomechanical components of the mouse aortic wall in which 1) VSMCs are a surprisingly large component of aortic stiffness at physiological lengths and 2) regulation of the VSMC component through FA signaling and hence plasticity is impaired with aging, diminishing the aorta's normal shock absorption function in response to stressors.

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress-strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753-756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.

Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries

Surgical and interventional therapies for atherosclerotic lesions of the infrainguinal arteries are notorious for high rates of failure. Frequently, this leads to expensive reinterventions, return of disabling symptoms or limb loss. Interaction between the artery and repair material likely plays an important role in reconstruction failure, but data describing the mechanical properties and functional characteristics of human femoropopliteal and tibial arteries are currently not available. Diseased superficial femoral (SFA, n = 10), popliteal (PA, n = 8) and tibial arteries (TA, n = 3) from 10 patients with critical limb ischemia were tested to determine passive mechanical properties using planar biaxial extension. All specimens exhibited large nonlinear deformations and anisotropy. Under equibiaxial loading, all arteries were stiffer in the circumferential direction than in the longitudinal direction. Anisotropy and longitudinal compliance decreased distally, but circumferential compliance increased, possibly to maintain a homeostatic multiaxial stress state. Constitutive parameters for a four-fiber family invariant-based model were determined for all tissues to calculate in vivo axial pre-stretch that allows the artery to function in the most energy efficient manner while also preventing buckling during extremity flexion. Calculated axial pre-stretch was found to decrease with age, disease severity and more distal arterial location. Histological analysis of the femoropopliteal artery demonstrated a distinct sub-adventitial layer of longitudinal elastin fibers that appeared thicker in healthier arteries. The femoropopliteal artery characteristics and properties determined in this study may assist in devising better diagnostic and treatment modalities for patients with peripheral arterial disease.

Effects of mechanical properties and atherosclerotic artery size on biomechanical plaque disruption - mouse vs. human

Mouse models of atherosclerosis are extensively being used to study the mechanisms of atherosclerotic plaque development and the results are frequently extrapolated to humans. However, major differences have been described between murine and human atherosclerotic lesions and the determination of similarities and differences between these species has been largely addressed recently. This study takes over and extends previous studies performed by our group and related to the biomechanical characterization of both mouse and human atherosclerotic lesions. Its main objective was to determine the distribution and amplitude of mechanical stresses including peak cap stress (PCS) in aortic vessels from atherosclerotic apoE(-/-) mice, in order to evaluate whether such biomechanical data would be in accordance with the previously suggested lack of plaque rupture in this model. Successful finite element analysis was performed from the zero-stress configuration of aortic arch sections and mainly indicated (1) the modest role of atherosclerotic lesions in the observed increase in residual parietal stresses in apoE(-/-) mouse vessels and (2) the low amplitude of murine PCS as compared to humans. Overall, the results from the present study support the hypothesis that murine biomechanical properties and artery size confer less propensity to rupture for mouse lesions in comparison with those of humans.

Disparate Changes in the Mechanical Properties of Murine Carotid Arteries and Aorta in Response to Chronic Infusion of Angiotensin-II

Chronic infusion of angiotensin-II has proved useful for generating dissecting aortic aneurysms in atheroprone mice. These lesions preferentially form in the suprarenal abdominal aorta and sometimes in the ascending aorta, but reasons for such localization remain unknown. This study focused on why these lesions do not form in other large (central) arteries. Toward this end, we quantified and compared the geometry, composition, and biaxial material behavior (using a nonlinear constitutive relation) of common carotid arteries from three groups of mice: non-treated controls as well as mice receiving a subcutaneous infusion of angiotensin-II for 28 days that either did or did not lead to the development of a dissecting aortic aneurysm. Consistent with the mild hypertension induced by the angiotensin-II, the carotid wall thickened as expected and remodeled modestly. There was no evidence, however, of a marked loss of elastic fibers or smooth muscle cells, each of which appear to be initiating events for the development of aneurysms, and there was no evidence of intramural discontinuities that might give rise to dissections.

Beyond burst pressure: initial evaluation of the natural history of the biaxial mechanical properties of tissue-engineered vascular grafts in the venous circulation using a murine model

We previously developed and validated a murine model for investigating neotissue formation in tissue-engineered vascular grafts (TEVGs). Herein, we present the first longitudinal assessment of both the microstructural composition and the mechanical properties of a TEVG through the process of neovessel formation (total scaffold degradation). We show that when (poly)glycolic acid-based biodegradable scaffolds were used as inferior vena cava interposition grafts in mice, the evolving neovessel developed biaxial properties that approached those of the native vein within 24 weeks of implantation. Further, we found that these changes in biaxial properties related temporally to extracellular matrix production and remodeling, including deposition of collagen (types I and III), elastic fibers (elastin and fibrillin-1), and glycosaminoglycans in addition to changes in matrix metalloproteinase (MMP)-2 and -9 activity. Improving our understanding of the mechanobiological principles underlying vascular neotissue formation in TEVGs holds great promise for improving the design of TEVGs and enabling us to continue the translation of this technology from the bench to the clinic.

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.

Biaxial mechanical properties of the inferior vena cava in C57BL/6 and CB-17 SCID/bg mice

Multiple murine models have proven useful in studying the natural history of neovessel development in the tissue engineering of vascular grafts. Nevertheless, to better understand longitudinal changes in the biomechanics of such neovessels, we must first quantify native tissue structure and properties. In this paper, we present the first biaxial mechanical data for, and nonlinear constitutive modeling of, &QJ;the inferior vena cava from two models used in tissue engineering: wild-type C57BL/6 and immunodeficient CB-17 SCID/bg mice. Results show that inferior vena cava from the latter are significantly stiffer in the circumferential direction, both materially (as assessed by a stored energy function) and structurally (as assessed by the compliance), despite a lower intramural content of fibrillar collagen and similar wall thickness. Quantifying the natural history of neovessel development in different hosts could lead to increased insight into the mechanisms by which cells fashion and maintain extracellular matrix in order to match best the host stiffness while ensuring sufficient vascular integrity.

Biomechanical phenotyping of central arteries in health and disease: advantages of and methods for murine models

The stiffness and structural integrity of the arterial wall depends primarily on the organization of the extracellular matrix and the cells that fashion and maintain this matrix. Fundamental to the latter is a delicate balance in the continuous production and removal of structural constituents and the mechanical state in which such turnover occurs. Perturbations in this balance due to genetic mutations, altered hemodynamics, or pathological processes result in diverse vascular phenotypes, many of which have yet to be well characterized biomechanically. In this paper, we emphasize the particular need to understand regional variations in the biaxial biomechanical properties of central arteries in health and disease and, in addition, the need for standardization in the associated biaxial testing and quantification. As an example of possible experimental methods, we summarize testing protocols that have evolved in our laboratory over the past 8 years. Moreover, we note advantages of a four fiber family stress-stretch relation for quantifying passive biaxial behaviors, the use of stored energy as a convenient scalar metric of the associated material stiffness, and the utility of appropriate linearizations of the nonlinear, anisotropic relations both for purposes of comparison across laboratories and to inform computational fluid-solid-interaction models. We conclude that, notwithstanding prior advances, there remain many opportunities to advance our understanding of arterial mechanics and mechanobiology, particularly via the diverse genetic, pharmacological, and surgical models that are, or soon will be, available in the mouse.

Dysfunction in elastic fiber formation in fibulin-5 null mice abrogates the evolution in mechanical response of carotid arteries during maturation

Elastin fragmentation is a common characteristic of vascular diseases, such as abdominal aortic aneurysms, peripheral arterial disease, and aortic dissection. Examining growth and remodeling in the presence of dysfunctional elastic fibers provides insight into the adaptive or maladaptive changes that tissues undergo in compensating for structural deficiencies. This study used the maturation of fibulin-5 knockout (KO) and wild-type mice to study the effects of fragmented elastic fibers on the growth and remodeling of carotid arteries. The microstructural content and organization and the biaxial mechanical behavior of common carotid arteries were measured, and parameter estimation performed from KO and WT mice aged 3, 4, 8, and 13 wk. Gross measurements and biaxial tests revealed significant differences in pressure-diameter behavior, in vivo axial stretch, opening angle, compliance, and wall stresses during maturation of wild-type arteries, but little change in these values in KO mice. Multiphoton microscopy used to image collagen fibers across the vessel wall in pressurized and stretched arteries suggests that there is little variation in fiber angles between different ages. Parameter estimation revealed significant differences in material parameters between genotypes and age groups. This study suggests that neonatal formation and cross-linking of functional elastic fibers, followed by increases in artery size due to growth with little remodeling of the elastic fibers, endow arteries with large distensibility and contribute to the evolution of mechanical behavior of arteries during maturation. Dysfunction in neonatal formation of elastic fibers abrogates many of the changes in mechanical response that take place during the maturation.

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.

Constitutive modeling of mouse carotid arteries using experimentally measured microstructural parameters

Changes in the local mechanical environment and tissue mechanical properties affect the biological activity of cells and play a key role in a variety of diseases, such as cancer, arthritis, nephropathy, and cardiovascular disease. Constitutive relations have long been used to predict the local mechanical environment within biological tissues and to investigate the relationship between biological responses and mechanical stimuli. Recent constitutive relations for soft tissues consider both material and structural properties by incorporating parameters that describe microstructural organization, such as fiber distributions, fiber angles, fiber crimping, and constituent volume fractions. The recently developed technique of imaging the microstructure of a single artery as it undergoes multiple deformations provides quantitative structural data that can reduce the number of estimated parameters by using parameters that are truly experimentally intractable. Here, we employed nonlinear multiphoton microscopy to quantify collagen fiber organization in mouse carotid arteries and incorporated measured fiber distribution data into structurally motivated constitutive relations. Microscopy results demonstrate that collagen fibers deform in an affine manner over physiologically relevant deformations. The incorporation of measured fiber angle distributions into constitutive relations improves the model's predictive accuracy and does not significantly reduce the goodness of fit. The use of measured structural parameters rather than estimated structural parameters promises to improve the predictive capabilities of the local mechanical environment, and to extend the utility of intravital imaging methods for estimating the mechanical behavior of tissues using in situ structural information.

Experimental investigation and constitutive modeling of the 3D histomechanical properties of vein tissue

Numerous studies have provided material models of arterial walls, but limited information is available on the pseudo-elastic response of vein walls and their underlying microstructure, and only few constitutive formulations have been proposed heretofore. Accordingly, we identified the histomechanics of healthy porcine jugular veins by applying an integrated approach of inflation/extension tests and histomorphometric evaluation. Several alternate phenomenological and microstructure-based strain-energy functions (SEF) were attempted to mimic the material response. Evaluation of their descriptive/predictive capacities showed that the exponential Fung-type SEF alone or in tandem with the neo-Hookean term did not capture the deformational response at high pressures. This problem was solved to a degree with the neo-Hookean and two-fiber (diagonally arranged) family SEF, but altogether the least reliable fit was generated. Fitting precision was much improved with the four-fiber (diagonally, circumferentially, longitudinally arranged) family model, as the inability of neo-Hookean function with force data was alleviated by use of the longitudinal-fiber family. Implementation of a quadratic term as a descriptor of low-pressure anisotropy facilitated the simulation of low-pressure and force data, and the four-fiber families simulated more faithfully than the two-fiber families the physiologic and high-pressure response. Importantly, this SEF was consistent with vein angioarchitecture, namely the occurrence of extensive elastin fibers along the longitudinal axis and few orthogonal fibers attached to them and of three collagen sets with circumferential, longitudinal, and diagonal arrangement, respectively. Our findings help to establish the relationship between vein microstructure and its biomechanical response, yet additional observations are obligatory prior to endeavoring generalizations to other veins.

Active axial stress in mouse aorta

The study verifies the development of active axial stress in the wall of mouse aorta over a range of physiological loads when the smooth muscle cells are stimulated to contract. The results obtained show that the active axial stress is virtually independent of the magnitude of pressure, but depends predominately on the longitudinal stretch ratio. The dependence is non-monotonic and is similar to the active stress-stretch dependence in the circumferential direction reported in the literature. The expression for the active axial stress fitted to the experimental data shows that the maximum active stress is developed at longitudinal stretch ratio 1.81, and 1.56 is the longitudinal stretch ratio below which the stimulation does not generate active stress. The study shows that the magnitude of active axial stress is smaller than the active circumferential stress. There is need for more experimental investigations on the active response of different types of arteries from different species and pathological conditions. The results of these studies can promote building of refined constrictive models in vascular rheology.

Extracellular matrix and the mechanics of large artery development

The large, elastic arteries, as their name suggests, provide elastic distention and recoil during the cardiac cycle in vertebrate animals. The arteries are distended from the pressure of ejecting blood during the active contraction of the left ventricle (LV) during systole and recoil to their original dimensions during relaxation of the LV during diastole. The cyclic distension occurs with minimal energy loss, due to the elastic properties of one of the major structural extracellular matrix (ECM) components, elastin. The maximum distension is limited to prevent damage to the artery by another major ECM component, collagen. The mix of ECM components in the wall largely determines the passive mechanical behavior of the arteries and the subsequent load on the heart during systole. While much research has focused on initial artery formation, there has been less attention on the continuing development of the artery to produce the mature composite wall complete with endothelial cells (ECs), smooth muscle cells (SMCs), and the necessary mix of ECM components for proper cardiovascular function. This review focuses on the physiology of large artery development, including SMC differentiation and ECM production. The effects of hemodynamic forces and ECM deposition on the evolving arterial structure and function are discussed. Human diseases and mouse models with genetic mutations in ECM proteins that affect large artery development are summarized. A review of constitutive models and growth and remodeling theories is presented, along with future directions to improve understanding of ECM and the mechanics of large artery development.

Acute mechanical effects of elastase on the infrarenal mouse aorta: implications for models of aneurysms

Intraluminal exposure of the infrarenal aorta to porcine pancreatic elastase represents one of the most commonly used experimental models of the development and progression of abdominal aortic aneurysms. Morphological and histological effects of elastase on the aortic wall have been well documented in multiple rodent models, but there has been little attention to the associated effects on mechanical properties. In this paper, we present the first biaxial mechanical data on, and associated nonlinear constitutive descriptors of, the effects of elastase on the infrarenal aorta in mice. Quantification of the dramatic, acute effects of elastase on wall behavior in vitro is an essential first step toward understanding the growth and remodeling of aneurysms in vivo, which depends on both the initial changes in the mechanics and the subsequent inflammation-mediated turnover of cells and extracellular matrix that contributes to the evolving mechanics.

Mechanical assessment of elastin integrity in fibrillin-1-deficient carotid arteries: implications for Marfan syndrome

AIMS

Elastin is the primary component of elastic fibres in arteries, which contribute significantly to the structural integrity of the wall. Fibrillin-1 is a microfibrillar glycoprotein that appears to stabilize elastic fibres mechanically and thereby to delay a fatigue-induced loss of function due to long-term repetitive loading. Whereas prior studies have addressed some aspects of ageing-related changes in the overall mechanical properties of arteries in mouse models of Marfan syndrome, we sought to assess for the first time the load-carrying capability of the elastic fibres early in maturity, prior to the development of ageing-related effects, dilatation, or dissection.

METHODS AND RESULTS

We used elastase to degrade elastin in common carotid arteries excised, at 7-9 weeks of age, from a mouse model (mgR/mgR) of Marfan syndrome that expresses fibrillin-1 at 15-25% of normal levels. In vitro biaxial mechanical tests performed before and after exposure to elastase suggested that the elastic fibres exhibited a nearly normal load-bearing capability. Observations from nonlinear optical microscopy suggested further that competent elastic fibres not only contribute to load-bearing, they also increase the undulation of collagen fibres, which endows the normal arterial wall with a more compliant response to pressurization.

CONCLUSION

These findings support the hypothesis that it is an accelerated fatigue-induced damage to or protease-related degradation of initially competent elastic fibres that render arteries in Marfan syndrome increasingly susceptible to dilatation, dissection, and rupture.

Evolving biaxial mechanical properties of mouse carotid arteries in hypertension

Quantifying the time course of load-induced changes in arterial wall geometry, microstructure, and properties is fundamental to developing mathematical models of growth and remodeling. Arteries adapt to altered pressure and flow by modifying wall thickness, inner diameter, and axial length via marked cell and matrix turnover. To estimate particular biomaterial implications of such adaptations, we used a 4-fiber family constitutive relation to quantify passive biaxial mechanical behaviors of mouse carotid arteries 0 (control), 7-10, 10-14, or 35-56 days after an aortic arch banding surgery that increased pulse pressure and pulsatile flow in the right carotid artery. In vivo circumferential and axial stretches at mean arterial pressure were, for example, 11% and 26% lower, respectively, in hypertensive carotids 35-56 days after banding than in normotensive controls; this finding is consistent with observations that hypertension decreases distensibility. Interestingly, the strain energy W stored in the carotids at individual in vivo conditions was also less in hypertensive compared with normotensive carotids. For example, at 35-56 days after banding, W was 24%, 39%, and 47% of normal values at diastolic, mean, and systolic pressures, respectively. The energy stored during the cardiac cycle, W(sys)-W(dias), also tended to be less, but this reduction did not reach significance. When computed at normal in vivo values of biaxial stretch, however, W was well above normal for the hypertensive carotids. This net increase resulted from an overall increase in the collagen-related anisotropic contribution to W despite a decrease in the elastin-related isotropic contribution. The latter was consistent with observed decreases in the mass fraction of elastin.

Mechanical properties of suprarenal and infrarenal abdominal aorta: implications for mouse models of aneurysms

Multiple mouse models have been developed to increase our understanding of the natural history of abdominal aortic aneurysms. An advantage of such models is that one can quantify the time course of changes in geometry, histology, cell biology, and mechanics as a lesion develops. One of the most commonly used mouse models yields lesions in the suprarenal abdominal aorta whereas most other models target the infrarenal abdominal aorta, consistent with the clinical observation that nearly all abdominal aneurysms in humans occur in the infrarenal aorta. Understanding reasons for similarities and differences between diverse mouse models and human lesions may provide increased insight that would not be possible studying a single situation alone. Toward this end, however, we must first compare directly the native structure and properties of these two portions of the abdominal aorta in the mouse. In this paper, we present the first biaxial mechanical data and nonlinear constitutive descriptors for the suprarenal and infrarenal aorta in mice, which reveals only subtle mechanical differences despite marked morphological and histological differences. Such data promise to increase our ability to understand and model the natural history of these deadly lesions.

Adaptation of a planar microbiaxial optomechanical device for the tubular biaxial microstructural and macroscopic characterization of small vascular tissues

Murine models of disease are a powerful tool for researchers to gain insight into disease formation, progression, and therapies. The biomechanical indicators of diseased tissue provide a unique insight into some of these murine models, since the biomechanical properties in scenarios such as aneurysm and Marfan syndrome can dictate tissue failure and mortality. Understanding the properties of the tissue on the macroscopic scale has been shown to be important, as one can then understand the tissue's ability to withstand the high stresses seen in the cardiac pulsatile cycle. Alterations in the biomechanical response can foreshadow prospective mechanical failure of the tissue. These alterations are often seen on the microstructural level, and obtaining detailed information on such changes can offer a better understanding of the phenomena seen on the macroscopic level. Unfortunately, mouse models present problems due to the size and delicate features in the mechanical testing of such tissues. In addition, some smaller arteries in large-animal studies (e.g., coronary and cerebral arteries) can present the same issues, and are sometimes unsuitable for planar biaxial testing. The purpose of this paper is to present a robust method for the investigation of the mechanical properties of small arteries and the classification of the microstructural orientation and degree of fiber alignment. This occurs through the cost-efficient modification of a planar biaxial tester that works in conjunction with a two-photon nonlinear microscope. This system provides a means to further investigate how microstructure and mechanical properties are modified in diseased transgenic animals where the tissue is in small tube form. Several other hard-to-test tubular specimens such as cerebral aneurysm arteries and atherosclerotic coronary arteries can also be tested using the described modular device.

Novel optical system for in vitro quantification of full surface strain fields in small arteries: II. Correction for refraction and illustrative results

In a companion paper, we described a theoretical foundation for and initial experimental implementation of a novel stereo-digital image correlation (DIC) method for quantifying the size, shape and deformation of small cylindrical specimens along their full length and around their entire circumference. In this paper, we further show that this panoramic-DIC method can be used to study mouse carotid arteries without affecting their native mechanical properties and show the advantage of the approach in studying more complex mouse aorta. In particular, we first resolve the ubiquitous issue of refraction in non-contacting optical measurements of strain while tissues are immersed in physiologic saline and we show that surface preparation for DIC does not affect the inferred mechanical properties either qualitatively or quantitatively, the latter via the use of a four-fibre family hyperelastic constitutive relation and associated estimation of material parameters using nonlinear regression. We thus submit that panoramic-DIC-based strain measurement has significant potential to increase our understanding of arterial mechanics in genetic models of arterial health and disease by allowing investigators to exploit advances in transgenic mice.

Novel optical system for in vitro quantification of full surface strain fields in small arteries: I. Theory and design

Recent advances in vascular biology and pathophysiology have revealed the need to understand better the genetic basis of arterial stiffness, disease progression and responses to clinical intervention. Towards this end, in vitro experiments on arteries from genetically modified mice promise to provide significantly increased insight into both health and disease. The need to test small arteries, often of complex shape, necessitates new methods for experimental arterial mechanics, however, ones that can provide information on local changes in geometry and strain. In this paper, we present a theoretical framework for a new panoramic digital image correlation-based method sufficient to collect such information and we demonstrate the utility of this approach via validation studies on phantoms having dimensions on the order of 500-1000 μm, similar to those of large mouse arteries. In particular, we show that placing the specimen within a conical mirror and imaging the specimen via a gimbal-mounted mirror using a single camera yields stereo information sufficient to quantify the size, shape and deformation along the full length and around the entire circumference of small arteries. In a companion paper, we show further that this approach can be implemented effectively while testing arteries within a physiological solution that maintains native biomechanical properties.

Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy

The selection of a mathematical descriptor for the passive arterial mechanical behavior has been long debated in the literature and customarily constrained by lack of pertinent data on the underlying microstructure. Our objective was to analyze the response of carotid artery subjected to inflation/extension with phenomenological and microstructure-based candidate strain-energy functions (SEFs), according to species (rabbit vs. pig) and region (proximal vs. distal). Histological variations among segments were examined, aiming to explicitly relate them with the differential material response. The Fung-type model could not capture the biphasic response alone. Combining a neo-Hookean with a two-fiber family term alleviated this restraint, but force data were poorly captured, while consideration of low-stress anisotropy via a quadratic term allowed improved simulation of both pressure and force data. The best fitting was achieved with the quadratic and Fung-type or four-fiber family SEF. The latter simulated more closely than the two-fiber family the high-stress response, being structurally justified for all artery types, whereas the quadratic term was justified for transitional and muscular arteries exhibiting notable elastin anisotropy. Diagonally arranged fibers were associated with pericellular medial collagen, and circumferentially and longitudinally arranged fibers with medial and adventitial collagen bundles, evidenced by the significant correlations of SEF parameters with quantitative histology.

Deformation measurements and material property estimation of mouse carotid artery using a microstructure-based constitutive model

A series of pressurization and tensile loading experiments on mouse carotid arteries is performed with deformation measurements acquired during each experiment using three-dimensional digital image correlation. Using a combination of finite element analysis and a microstructure-based constitutive model to describe the response of biological tissue, the measured surface strains during pressurization, and the average axial strains during tensile loading, an inverse procedure is used to identify the optimal constitutive parameters for the mouse carotid artery. The results demonstrate that surface strain measurements can be combined with computational methods to identify material properties in a vascular tissue. Additional computational studies using the optimal material parameters for the mouse carotid artery are discussed with emphasis on the significance of the qualitative trends observed.

A structural constitutive model considering angular dispersion and waviness of collagen fibres of rabbit facial veins

Background

Structural constitutive models of vascular wall integrate information on composition and structural arrangements of tissue. In blood vessels, collagen fibres are arranged in coiled and wavy bundles and the individual collagen fibres have a deviation from their mean orientation. A complete structural constitutive model for vascular wall should incorporate both waviness and orientational distribution of fibres. We have previously developed a model, for passive properties of vascular wall, which considers the waviness of collagen fibres. However, to our knowledge there is no structural model of vascular wall which integrates both these features.

Methods

In this study, we have suggested a structural strain energy function that incorporates not only the waviness but also the angular dispersion of fibres. We studied the effect of parameters related to the orientational distribution on macro-mechanical behaviour of tissue during inflation-extension tests. The model was further applied on experimental data from rabbit facial veins.

Results

Our parametric study showed that the model is less sensitive to the orientational dispersion when fibres are mainly oriented circumferentially. The macro-mechanical response is less sensitive to changes in the mean orientation when fibres are more dispersed. The model accurately fitted the experimental data of veins, while not improving the quality of the fit compared to the model without dispersion. Our results showed that the orientational dispersion of collagen fibres could be compensated by a less abrupt and shifted to higher strain collagen engagement pattern. This should be considered when the model is fitted to experimental data and model parameters are used to study structural modifications of collagen fibre network in physiology and disease.

Conclusions

The presented model incorporates structural features related to waviness and orientational distribution of collagen fibres and thus offers possibilities to better understand the relation between structure and function in the vascular wall. Also, the model can be used to further study mechanically induced collagen remodelling in vascular tissue in health and disease.

Modelling carotid artery adaptations to dynamic alterations in pressure and flow over the cardiac cycle

Motivated by recent clinical and laboratory findings of important effects of pulsatile pressure and flow on arterial adaptations, we employ and extend an established constrained mixture framework of growth (change in mass) and remodelling (change in structure) to include such dynamical effects. New descriptors of cell and tissue behavior (constitutive relations) are postulated and refined based on new experimental data from a transverse aortic arch banding model in the mouse that increases pulsatile pressure and flow in one carotid artery. In particular, it is shown that there was a need to refine constitutive relations for the active stress generated by smooth muscle, to include both stress- and stress rate-mediated control of the turnover of cells and matrix and to account for a cyclic stress-mediated loss of elastic fibre integrity and decrease in collagen stiffness in order to capture the reported evolution, over 8 weeks, of luminal radius, wall thickness, axial force and in vivo axial stretch of the hypertensive mouse carotid artery. We submit, therefore, that complex aspects of adaptation by elastic arteries can be predicted by constrained mixture models wherein individual constituents are produced or removed at individual rates and to individual extents depending on changes in both stress and stress rate from normal values.

Characterization of the mechanical properties of the coronary sinus for percutaneous transvenous mitral annuloplasty

The coronary sinus (CS) vessel serves as a conduit for the deployment of percutaneous transvenous mitral annuloplasty (PTMA) devices for the treatment of functional mitral regurgitation. Characterization of the mechanical response of the CS is an important step towards an understanding of tissue-device interaction in PTMA intervention. The purpose of this study was to investigate the mechanical properties of the porcine CS using the pressure-inflation test and constitutively model the wall behavior using a four fiber family strain energy function (SEF). The results showed that the CS exhibited an S-shaped pressure-radius response and could be dilated up to 88% at a pressure of 80mmHg. Excellent results from model fitting indicated that the four fiber family SEF could capture the experimental data well and could be used in future numerical simulations of tissue-device interaction. In addition, a histological study was performed to identify the micro-structure of the CS wall. We found a high content of striated myocardial fibers (SMFs) surrounding the CS wall, which was also mainly composed of SMFs, while the content of smooth muscle cells was very low. Elastin and collagen fibers were highly concentrated in the luminal and outer layers and sparsely distributed in the medial layer of the CS wall. These structural and mechanical properties of the CS should be taken into consideration in future PTMA device designs.

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.

Constitutive modelling of arteries

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

Microstructurally motivated constitutive modeling of mouse arteries cultured under altered axial stretch

Good predictions of the local mechanical environment of the tissue with known geometry and applied loads are fundamental to quantifying the biological response of tissues to mechanical stimuli. Whereas mean stresses in cylindrical sections of blood vessels may be calculated directly from measured loads and vessel geometry (e.g., Laplace's law), predicting how these stresses are distributed across the wall requires knowledge of the constitutive behavior of the tissue. Previously, we reported biaxial biomechanical data for mouse carotid arteries before and after exposure to altered axial extension in organ culture. Here we considered phenomenological and microstructurally motivated constitutive models and identified material parameters for each via nonlinear regression. Specifically, we considered the model of Chuong and Fung, a four fiber-family model, and several new variants of a rule-of-mixtures model; in the latter, we modeled the artery as a mixture of collagen, elastin, muscle, and water. We found that the four fiber-family model fitted data significantly better than the model of Chuong and Fung. When identifying parameters for the rule-of-mixtures models, we imposed penalties that required each constituent to be structurally significant; e.g., elastin contributing significantly to the overall response over low loads and collagen dominating the response over high loads. Such constraints ascribe additional microstructural "meaning" to the constitutive model. Although imposing such penalties necessarily reduces the goodness of fit of model predictions to experimental data compared to regression without such penalties, the modest reduction in the goodness of fit observed in our results was off-set by the improved structural interpretation such models provide. Such microstructurally motivated models will be useful in characterizing vascular growth and remodeling in terms of the evolution of microstructural metrics that may be quantified experimentally.