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

Microstructure and Mechanical Property of Glutaraldehyde-Treated Porcine Pulmonary Ligament

There is a significant need for fixed biological tissues with desired structural and material constituents for tissue engineering applications. Here, we introduce the lung ligament as a fixed biological material that may have clinical utility for tissue engineering. To characterize the lung tissue for potential clinical applications, we studied glutaraldehyde-treated porcine pulmonary ligament (n = 11) with multiphoton microscopy (MPM) and conducted biaxial planar experiments to characterize the mechanical property of the tissue. The MPM imaging revealed that there are generally two families of collagen fibers distributed in two distinct layers: The first family largely aligns along the longitudinal direction with a mean angle of θ = 10.7 ± 9.3 deg, while the second one exhibits a random distribution with a mean θ = 36.6 ± 27.4. Elastin fibers appear in some intermediate sublayers with a random orientation distribution with a mean θ = 39.6 ± 23 deg. Based on the microstructural observation, a microstructure-based constitutive law was proposed to model the elastic property of the tissue. The material parameters were identified by fitting the model to the biaxial stress-strain data of specimens, and good fitting quality was achieved. The parameter e0 (which denotes the strain beyond which the collagen can withstand tension) of glutaraldehyde-treated tissues demonstrated low variability implying a relatively consistent collagen undulation in different samples, while the stiffness parameters for elastin and collagen fibers showed relatively greater variability. The fixed tissues presented a smaller e0 than that of fresh specimen, confirming that glutaraldehyde crosslinking increases the mechanical strength of collagen-based biomaterials. The present study sheds light on the biomechanics of glutaraldehyde-treated porcine pulmonary ligament that may be a candidate for tissue engineering.

Quantification of the passive and active biaxial mechanical behaviour and microstructural organization of rat thoracic ducts

Mechanical loading conditions are likely to play a key role in passive and active (contractile) behaviour of lymphatic vessels. The development of a microstructurally motivated model of lymphatic tissue is necessary for quantification of mechanically mediated maladaptive remodelling in the lymphatic vasculature. Towards this end, we performed cylindrical biaxial testing of Sprague-Dawley rat thoracic ducts (n = 6) and constitutive modelling to characterize their mechanical behaviour. Spontaneous contraction was quantified at transmural pressures of 3, 6 and 9 cmH2O. Cyclic inflation in calcium-free saline was performed at fixed axial stretches between 1.30 and 1.60, while recording pressure, outer diameter and axial force. A microstructurally motivated four-fibre family constitutive model originally proposed by Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1-48. (doi:10.1023/A:1010835316564)) was used to quantify the passive mechanical response, and the model of Rachev and Hayashi was used to quantify the active (contractile) mechanical response. The average error between data and theory was 8.9 ± 0.8% for passive data and 6.6 ± 2.6% and 6.8 ± 3.4% for the systolic and basal conditions, respectively, for active data. Multi-photon microscopy was performed to quantify vessel wall thickness (32.2 ± 1.60 µm) and elastin and collagen organization for three loading conditions. Elastin exhibited structural 'fibre families' oriented nearly circumferentially and axially. Sample-to-sample variation was observed in collagen fibre distributions, which were often non-axisymmetric, suggesting material asymmetry. In closure, this paper presents a microstructurally motivated model that accurately captures the biaxial active and passive mechanical behaviour in lymphatics and offers potential for future research to identify parameters contributing to mechanically mediated disease development.

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

BACKGROUND

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall's anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example.

METHOD

Porcine common carotid arteries (n=10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF.

RESULTS

Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (κ1,2,3=[13.5,0.0,25.2] and κ1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data.

CONCLUSIONS

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.

STATEMENT OF SIGNIFICANCE

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial and uniaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, an effective orientation density that accounts for cross-links between the main collagen fibers has been porposed. The model provides a good approximation to the experimental data.

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

The skin tissue has been shown to behave like a nonlinear anisotropic material. This study was aimed to employ a constitutive fiber family equation to characterize the nonlinear anisotropic mechanical behavior of the rat and mice skin tissues in different anatomical locations, including the abdomen and back, using histostructural and uniaxial data. The rat and mice skin tissues were excised from the animals' body and then the histological analyses were performed on each skin type to determine the mean fiber orientation angle. Afterward, the preconditioned skin tissues were subjected to a series of quasi-static axial and circumferential loads until the incidence of failure. The crucial role of fiber orientation was explicitly added into a proposed strain energy density function. The material coefficients were determined using the constrained nonlinear optimization method based on the axial and circumferential extension data of the rat and mice samples at different anatomical locations. The material coefficients of the skins were given with R(2) ≥ 0.998. The results revealed a significant load-bearing capacity and stiffness of the rat abdomen compared to the rat back tissues. In addition, the mice abdomen showed a higher stiffness in the axial direction in comparison with circumferential one, while the mice back displayed its highest stiffness in the circumferential direction. The material coefficients of the rat and mice skin tissues were determined and well compared to the experimental data. The optimized fiber angles were also compared to the experimental histological data, and in all cases less than 11.85% differences were observed in both the skin tissues.

Arterial mechanics considering the structural and mechanical contributions of ECM constituents

Considering the organization and engagement behavior of different extracellular matrix (ECM) constituents in the medial and adventitial layer of the arterial wall, in this study, we proposed a new constitutive model of ECM mechanics that considers the distinct structural and mechanical contributions of medial elastin, medial collagen, and adventitial collagen, to incorporate the constituent-specific fiber orientation and the sequential fiber engagement in arterial mechanics. Planar biaxial tensile testing method was used to characterize the orthotropic and hyperelastic behavior of porcine thoracic aorta. Fiber distribution functions of medial elastin, medial collagen, and adventitial collagen were incorporated into the constitutive model. Considering the sequential engagement of ECM constituents in arterial mechanics, a recruitment density function was incorporated into the model to capture the delayed engagement of adventitial collagen. A freely jointed chain model was used to capture the mechanical behavior of elastin and collagen at the fiber level. The tissue-level ECM mechanics was obtained by incorporating fiber distribution, engagement, and elastin and collagen content. The multi-scale constitutive model considering the structural and mechanical contributions of the three major ECM constituents allows us to directly incorporate information obtained from quantitative multi-photon imaging and analysis, and biochemical assay for the prediction of tissue-level mechanical response. Moreover, the model shows promises in fitting and predicting with a small set of material parameters, which has physical meanings and can be related to the structure of the ECM.

Validation of an arterial constitutive model accounting for collagen content and crosslinking

During the progression of pulmonary hypertension (PH), proximal pulmonary arteries (PAs) increase in both thickness and stiffness. Collagen, a component of the extracellular matrix, is mainly responsible for these changes via increased collagen fiber amount (or content) and crosslinking. We sought to differentiate the effects of collagen content and cross-linking on mouse PA mechanical changes using a constitutive model with parameters derived from experiments in which collagen content and cross-linking were decoupled during hypoxic pulmonary hypertension (HPH). We employed an eight-chain orthotropic element model to characterize collagen's mechanical behavior and an isotropic neo-Hookean form to represent elastin. Our results showed a strong correlation between the material parameter related to collagen content and measured collagen content (R(2)=0.82, P<0.0001) and a moderate correlation between the material parameter related to collagen crosslinking and measured crosslinking (R(2)=0.24, P=0.06). There was no significant change in either the material parameter related to elastin or the measured elastin content from histology. The model-predicted pressure at which collagen begins to engage was ∼25mmHg, which is consistent with experimental observations. We conclude that this model may allow us to predict changes in the arterial extracellular matrix from measured mechanical behavior in PH patients, which may provide insight into prognoses and the effects of therapy.

STATEMENT OF SIGNIFICANCE

The literature has proposed several constitutive models to describe the mechanical effects of arterial collagen but none separates collagen content from crosslinking. Given that both are critical to arterial mechanics, the novel model described here does so. Furthermore, our novel model is well tested by experimental data; model parameters were reasonably correlated with measured collagen content and crosslinking and the model-predicted collagen transition stretch was consistent with that obtained experimentally. Given that arterial collagen structural changes and collagen engagement are critical to arterial stiffening in several disease states, this model, by linking mechanical and biological properties, may allow us to predict important biological changes during disease progression from measured mechanical behavior.

Piecewise Pulse Wave Imaging (pPWI) for Detection and Monitoring of Focal Vascular Disease in Murine Aortas and Carotids In Vivo

Atherosclerosis and Abdominal Aortic Aneurysms (AAAs) are two common vascular diseases associated with mechanical changes in the arterial wall. Pulse Wave Imaging (PWI), a technique developed by our group to assess and quantify the mechanical properties of the aortic wall in vivo, may provide valuable diagnostic information. This work implements piecewise PWI (pPWI), an enhanced version of PWI designed for focal vascular diseases. Localized, sub-regional PWVs and PWI moduli ( EPWI ) were estimated within 2-4 mm wall segments of murine normal, atherosclerotic and aneurysmal arteries. Overall, stiffness was found to increase in the atherosclerotic cases. The mean sub-regional PWV was found to be 2.57±0.18 m/s for the normal aortas (n = 7) with a corresponding mean EPWI of 43.82±5.86 kPa. A significant increase ( (p ≤ 0.001)) in the group means of the sub-regional PWVs was found between the normal aortas and the aortas of mice on high-fat diet for 20 ( 3.30±0.36 m/s) and 30 weeks ( 3.56±0.29 m/s). The mean of the sub-regional PWVs ( 1.57±0.78 m/s) and EPWI values ( 19.23±15.47 kPa) decreased significantly in the aneurysmal aortas (p ≤ 0.05) . Furthermore, the mean coefficient of determination (r(2)) of the normal aortas was significantly higher (p ≤ 0.05) than those of the aneurysmal and atherosclerotic cases. These findings demonstrated that pPWI may be able to provide useful biomarkers for monitoring focal vascular diseases.

Vascular Mechanics in Decellularized Aortas and Coronary Resistance Microvessels in Type 2 Diabetic db/db Mice

We previously reported differences in stiffness between macro- and micro-vessels in type 2 diabetes (T2DM). The aim of this study was to define the mechanical properties of the ECM independent of vascular cells in coronary resistance micro-vessels (CRMs) and macro-vessels (aorta) in control Db/db and T2DM db/db mice. Passive vascular remodeling and mechanics were measured in both intact and decellularized CRMs and aortas from 0 to 125 mmHg. We observed no differences in intact control and diabetic aortic diameters, wall thicknesses, or stiffnesses (p > 0.05). Aortic decellularization caused a significant increase in internal and external diameters and incremental modulus over a range of pressures that occurred to a similar degree in T2DM. Differences in aortic diameters due to decellularization occurred at lower pressures (0-75 mmHg) and converged with intact aortas at higher, physiological pressures (100-125 mmHg). In contrast, CRM decellularization caused increased internal diameter and incremental modulus only in the db/db mice, but unlike the aorta, the intact and decellularized CRM curves were more parallel. These data suggest that (1) micro-vessels may be more sensitive to early adverse consequences of diabetes than macro-vessels and (2) the ECM is a structural limit in aortas, but not CRMs.

Hyperelastic models for hydration of cellular tissue

In this paper we present hyperelastic models for swelling elastic shells, due to pressurization of the internal cavity. These shells serve as model systems for cells having cell walls, as can be found in bacteria, plants and fungi. The pressurized internal cavity represents the cell vacuole with intact membrane at a certain turgor pressure, and the elastic shell represents the hydrated cell wall. At pressurization the elastic shell undergoes inhomogeneous deformation. Its deformation is governed by a strain energy function. Using the scaling law of Cloizeaux for the osmotic pressure, we obtain approximate analytical expressions of the cell volume versus turgor pressure - which are quite comparable to numerical solutions of the problem. Subsequently, we have simulated the swelling of shells - where the cell wall material is embedded with microfibrils, leading to strain hardening and anisotropic cell expansion. The purpose of our investigations is to elucidate the contribution of cell membrane integrity and turgor to the water holding capacity (hydration) of plant foods. We conclude with a discussion of the impact of this work on the hydration of food material, and other fields like plant science and the soft matter physics of responsive gels.

Mechanical factors direct mouse aortic remodelling during early maturation

Numerous diseases have been linked to genetic mutations that lead to reduced amounts or disorganization of arterial elastic fibres. Previous work has shown that mice with reduced amounts of elastin (Eln+/-) are able to live a normal lifespan through cardiovascular adaptations, including changes in haemodynamic stresses, arterial geometry and arterial wall mechanics. It is not known if the timeline and presence of these adaptations are consistent in other mouse models of elastic fibre disease, such as those caused by the absence of fibulin-5 expression (Fbln5-/-). Adult Fbln5-/- mice have disorganized elastic fibres, decreased arterial compliance and high blood pressure. We examined mechanical behaviour of the aorta in Fbln5-/- mice through early maturation when the elastic fibres are being assembled. We found that the physiologic circumferential stretch, stress and modulus of Fbln5-/- aorta are maintained near wild-type levels. Constitutive modelling suggests that elastin contributions to the total stress are decreased, whereas collagen contributions are increased. Understanding how collagen fibre structure and mechanics compensate for defective elastic fibres to meet the mechanical requirements of the maturing aorta may help to better understand arterial remodelling in human elastinopathies.

A mechanical argument for the differential performance of coronary artery grafts

Coronary artery bypass grafting (CABG) acutely disturbs the homeostatic state of the transplanted vessel making retention of graft patency dependent on chronic remodeling processes. The time course and extent to which remodeling restores vessel homeostasis will depend, in part, on the nature and magnitude of the mechanical disturbances induced upon transplantation. In this investigation, biaxial mechanical testing and histology were performed on the porcine left anterior descending artery (LAD) and analogs of common autografts, including the internal thoracic artery (ITA), radial artery (RA), great saphenous vein (GSV) and lateral saphenous vein (LSV). Experimental data were used to quantify the parameters of a structure-based constitutive model enabling prediction of the acute vessel mechanical response pre-transplantation and under coronary loading conditions. A novel metric Ξ was developed to quantify mechanical differences between each graft vessel in situ and the LAD in situ, while a second metric Ω compares the graft vessels in situ to their state under coronary loading. The relative values of these metrics among candidate autograft sources are consistent with vessel-specific variations in CABG clinical success rates with the ITA as the superior and GSV the inferior graft choices based on mechanical performance. This approach can be used to evaluate other candidate tissues for grafting or to aid in the development of synthetic and tissue engineered alternatives.

On the effect of preload and pre-stretch on hemodynamic simulations: an integrative approach

In this work, we address the simulation of three-dimensional arterial blood flow and its effect on the stress state of arterial walls. The novel contribution is the unprecedented combination of several modeling techniques to account for (1) the fact that known configurations for the arterial wall are in a preloaded state, (2) the compliance of the vessel segments, (3) proper boundary data over the non-physical interfaces resulting from the isolation of an arterial district from the rest of the arterial tree, (4) the presence of surrounding tissues in which the vessel is embedded and (5) residual stress state due to pre-stretch. Firstly, we formulate both the forward mechanical problem when the reference (zero-load) configuration is assumed to be known and, the preload problem arising when the known domain is a configuration at equilibrium with a certain load state (typically due to internal pressure and tethering forces). Then, two additional complexities are faced: the fluid-structure interaction problem that follows when the compliant vessels are coupled with the blood flow, and the introduction of non-physical boundaries coming from the artificial isolation of the arterial district from the original vessel. This, in turn, posses the problem of coupling dimensionally heterogeneous models to incorporate the effect of upstream and downstream systemic impedances. Additionally, a viscoelastic support on the external surface of the vessel is also incorporated. Two examples are presented to quantify in a physiologically consistent scenario the differences in simulation results when either considering or not the preload state of arterial walls. These computational simulations shed light on the validity of simplifying hypotheses in most hemodynamic models.

Numerical Study of Turbulent Pulsatile Blood Flow through Stenosed Artery Using Fluid-Solid Interaction

The turbulent pulsatile blood flow through stenosed arteries considering the elastic property of the wall is investigated numerically. During the numerical model validation both standard k-ε model and RNG K-ε model are used. Compared with the RNG K-ε model, the standard K-ε model shows better agreement with previous experimental results and is better able to show the reverse flow region. Also, compared with experimental data, the results show that, up to 70% stenosis, the flow is laminar and for 80% stenosis the flow becomes turbulent. Assuming laminar or turbulent flow and also rigid or elastic walls, the results are compared with each other. The investigation of time-averaged shear stress and the oscillatory shear index for 80% stenosis show that assuming laminar flow will cause more error than assuming a rigid wall. The results also show that, in turbulent flow compared with laminar flow, the importance of assuming a flexible artery wall is more than assuming a rigid artery wall.

Investigation of the optimal collagen fibre orientation in human iliac arteries

The distribution of collagen fibres plays a significant role in the mechanical behaviour of artery walls. Experimental data show that in most artery wall layers there are two (or more) in-plane symmetrically disposed families of fibres. However, a recent investigation revealed that some artery wall layers have only one preferred fibre direction, notably in the medial layer of human common iliac arteries. This paper aims to provide a possible explanation for this intriguing phenomenon. An invariant-based constitutive model is utilized to characterize the mechanical behaviour of tissues. We then use three different hypotheses to determine the 'optimal fibre angle' in an iliac artery model. All three hypotheses lead to the same result that the optimal fibre angle in the medial layer of the iliac artery is close to the circumferential direction. The axial pre-stretch, in particular, is found to play an essential role in determining the optimal fibre angle.

DIFFERENCES BETWEEN PULMONARY ARTERIAL AND AORTIC MATERIAL PROPERTIES

To investigate the differences of mechanical responses between pulmonary artery and aorta to different biaxial loading conditions, we simulated the process of human pulmonary artery and aorta subjected to biaxial loading based on four-family fiber strain density function model determined from uniaxial extension data of arterial walls. It was shown that different stress–strain curves of pulmonary artery and aorta under biaxial loading conditions: different loading ratios between the loads in two perpendicular directions and displacement-controlled equibiaxial stretch. Tissue stiffness, defined as the first derivative of the stress–strain response at a strain point, of human pulmonary artery and aorta were obtained when they were subjected to biaxial loads (systemic pressure). The two-dimensional mechanical response of artery can be acquired by determination of the four-family fiber strain density function model of the tissue based on uniaxial extensile data. There are differences between material properties of pulmonary artery and aorta: aorta is stiffer circumferentially than longitudinally, and pulmonary artery is more compliant circumferentially than longitudinally.

Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.

A constitutive modeling interpretation of the relationship among carotid artery stiffness, blood pressure, and age in hypertensive subjects

Aging has a profound influence on arterial wall structure and function. We have previously reported the relationship among pulse wave velocity, age, and blood pressure in hypertensive subjects. In the present study, we aimed for a quantitative interpretation of the observed changes in wall behavior with age using a constitutive modeling approach. We implemented a model of arterial wall biomechanics and fitted this to the group-averaged pressure-area ( P-A) relationship of the “young” subgroup of our study population. Using this model as our take-off point, we assessed which parameters had to be changed to let the model describe the “old” subgroup’s P-A relationship. We allowed elastin stiffness and collagen recruitment parameters to vary and adjusted residual stress parameters according to published age-related changes. We required wall stress to be homogeneously distributed over the arterial wall and assumed wall stress normalization with age by keeping average “old” wall stress at the “young” level. Additionally, we required axial force to remain constant over the cardiac cycle. Our simulations showed an age-related shift in pressure-load bearing from elastin to collagen, caused by a decrease in elastin stiffness and a considerable increase in collagen recruitment. Correspondingly, simulated diameter and wall thickness increased by about 20 and 17%, respectively. The latter compared well with a measured thickness increase of 21%. We conclude that the physiologically realistic changes in constitutive properties we found under physiological constraints with respect to wall stress could well explain the influence of aging in the stiffness-pressure-age pattern observed.

Modeling of human artery tissue with probabilistic approach

Accurate modeling of biological soft tissue properties is vital for realistic medical simulation. Mechanical response of biological soft tissue always exhibits a strong variability due to the complex microstructure and different loading conditions. The inhomogeneity in human artery tissue is modeled with a computational probabilistic approach by assuming that the instantaneous stress at a specific strain varies according to normal distribution. Material parameters of the artery tissue which are modeled with a combined logarithmic and polynomial energy equation are represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters are determined using genetic algorithm (GA) and inverse mean-value first-order second-moment (IMVFOSM) method, respectively. This nondeterministic approach was verified using computer simulation based on the Monte-Carlo (MC) method. Cumulative distribution function (CDF) of the MC simulation corresponds well with that of the experimental stress-strain data and the probabilistic approach is further validated using data from other studies. By taking into account the inhomogeneous mechanical properties of human biological tissue, the proposed method is suitable for realistic virtual simulation as well as an accurate computational approach for medical device validation.

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.

Contribution of collagen fiber undulation to regional biomechanical properties along porcine thoracic aorta

As major extracellular matrix components, elastin, and collagen play crucial roles in regulating the mechanical properties of the aortic wall and, thus, the normal cardiovascular function. The mechanical properties of aorta, known to vary with age and multitude of diseases as well as the proximity to the heart, have been attributed to the variations in the content and architecture of wall constituents. This study is focused on the role of layer-specific collagen undulation in the variation of mechanical properties along the porcine descending thoracic aorta. Planar biaxial tensile tests are performed to characterize the hyperelastic anisotropic mechanical behavior of tissues dissected from four locations along the thoracic aorta. Multiphoton microscopy is used to image the associated regional microstructure. Exponential-based and recruitment-based constitutive models are used to account for the observed mechanical behavior while considering the aortic wall as a composite of two layers with independent properties. An elevated stiffness is observed in distal regions compared to proximal regions of thoracic aorta, consistent with sharper and earlier collagen recruitment estimated for medial and adventitial layers in the models. Multiphoton images further support our prediction that higher stiffness in distal regions is associated with less undulation in collagen fibers. Recruitment-based models further reveal that regardless of the location, collagen in the media is recruited from the onset of stretching, whereas adventitial collagen starts to engage with a delay. A parameter sensitivity analysis is performed to discriminate between the models in terms of the confidence in the estimated model parameters.

A combination of histological analyses and uniaxial tensile tests to determine the material coefficients of the healthy and atherosclerotic human coronary arteries

Atherosclerosis is considered as the most severe form of cardiovascular diseases as it alters the structure of the elastin and collagen and, consequently, the mechanical properties of the artery wall. The role of collagen fibers orientations in the mechanical properties of the healthy and atherosclerotic human coronary arteries so far has not been well determined. In this study, a fiber family based constitutive equation was employed to address the mechanical behavior of healthy and atherosclerotic human coronary arteries using the combination of histostructural and uniaxial data. A group of six healthy and atherosclerotic human coronary arteries was excised at autopsy and histological analyses were performed on each artery to determine the mean angle of collagen fibers. The preconditioned arterial tissues were then subjected to a series of quasi-static axial and circumferential loadings. The key role of fiber orientation was explicitly added into a proposed strain energy density function. The constrained nonlinear optimization method was used to determine the material coefficients based on the axial and circumferential extension data of the arteries. The material coefficients of coronary arteries were given with R(2)≥0.991. The results regardless of loading direction revealed a significant load-bearing capacity and stiffness of atherosclerotic arteries compared to the healthy ones (p<0.005). The optimized fiber angles were in good agreement with the experimental histological data as only 2.52% and 10.10% differences were observed for the healthy and atherosclerotic arteries, respectively. The stored energy function of the healthy arteries was found to be higher than that of atherosclerotic ones. These findings help us to understand the directional mechanical properties of coronary arteries which may have implications for different types of interventions and surgeries, including bypass, stenting, and balloon-angioplasty.

Evaluation of Biaxial Mechanical Properties of Aortic Media Based on the Lamellar Microstructure

Evaluation of the mechanical properties of arterial wall components is necessary for establishing a precise mechanical model applicable in various physiological and pathological conditions, such as remodeling. In this contribution, a new approach for the evaluation of the mechanical properties of aortic media accounting for the lamellar structure is proposed. We assumed aortic media to be composed of two sets of concentric layers, namely sheets of elastin (Layer I) and interstitial layers composed of mostly collagen bundles, fine elastic fibers and smooth muscle cells (Layer II). Biaxial mechanical tests were carried out on human thoracic aortic samples, and histological staining was performed to distinguish wall lamellae for determining the dimensions of the layers. A neo-Hookean strain energy function (SEF) for Layer I and a four-parameter exponential SEF for Layer II were allocated. Nonlinear regression was used to find the material parameters of the proposed microstructural model based on experimental data. The non-linear behavior of media layers confirmed the higher contribution of elastic tissue in lower strains and the gradual engagement of collagen fibers. The resulting model determines the nonlinear anisotropic behavior of aortic media through the lamellar microstructure and can be assistive in the study of wall remodeling due to alterations in lamellar structure during pathological conditions and aging.

Insights into regional adaptations in the growing pulmonary artery using a meso-scale structural model: effects of ascending aorta impingement

As the next step in our investigations into the structural adaptations of the main pulmonary artery (PA) during postnatal growth, we utilized the extensive experimental measurements of the growing ovine PA from our previous study (Fata et al., 2013, "Estimated in vivo Postnatal Surface Growth Patterns of the Ovine Main Pulmonary Artery and Ascending Aorta," J. Biomech. Eng., 135(7), pp. 71010-71012). to develop a structural constitutive model for the PA wall tissue. Novel to the present approach was the treatment of the elastin network as a distributed fiber network rather than a continuum phase. We then utilized this model to delineate structure-function differences in the PA wall at the juvenile and adult stages. Overall, the predicted elastin moduli exhibited minor differences remained largely unchanged with age and region (in the range of 150 to 200 kPa). Similarly, the predicted collagen moduli ranged from ∼1,600 to 2700 kPa in the four regions studied in the juvenile state. Interestingly, we found for the medial region that the elastin and collagen fiber splay underwent opposite changes (collagen standard deviation juvenile = 17 deg to adult = 28 deg, elastin standard deviation juvenile = 35 deg to adult = 27 deg), along with a trend towards more rapid collagen fiber strain recruitment with age, along with a drop in collagen fiber moduli, which went from 2700 kPa for the juvenile stage to 746 kPa in the adult. These changes were likely due to the previously observed impingement of the relatively stiff ascending aorta on the growing PA medial region. Intuitively, the effects of the local impingement would be to lower the local wall stress, consistent with the observed parallel decrease in collagen modulus. These results suggest that during the postnatal somatic growth period local stresses can substantially modulate regional tissue microstructure and mechanical behaviors in the PA. We further underscore that our previous studies indicated an increase in effective PA wall stress with postnatal maturation. When taken together with the fact that the observed changes in mechanical behavior and structure in the growing PA wall were modest in the other three regions studied, our collective results suggest that the majority of the growing PA wall is subjected to increasing stress levels with age without undergoing major structural adaptations. This observation is contrary to the accepted theory of maintenance of homeostatic stress levels in the regulation of vascular function, and suggests alternative mechanisms might regulate postnatal somatic growth. Understanding the underlying mechanisms will help to improve our understanding of congenital defects of the PA and lay the basis for functional duplication in their repair and replacement.

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.

Structural and mechanical characterisation of bridging veins: A review

Bridging veins drain the venous blood from the cerebral cortex into the superior sagittal sinus (SSS) and doing so they bridge the subdural space. Despite their importance in head impact biomechanics, little is known about their properties with respect to histology, morphology and mechanical behaviour. Knowledge of these characteristics is essential for creating a biofidelic finite element model to study the biomechanics of head impact, ultimately leading to the improved design of protective devices by setting up tolerance criteria. This paper presents a comprehensive review of the state-of-the-art knowledge on bridging veins. Tolerance criteria to prevent head injury through impact have been set by a number of research groups, either directly through impact experiments or by means of finite element (FE) simulations. Current state-of-the-art FE head models still lack a biofidelic representation of the bridging veins. To achieve this, a thorough insight into their nature and behaviour is required. Therefore, an overview of the general morphology and histology is provided here, showing the clearly heterogeneous nature of the bridging vein complex, with its three different layers and distinct morphological and histological changes at the region of outflow into the superior sagittal sinus. Apart from a complex morphology, bridging veins also exhibit complex mechanical behaviour, being nonlinear, viscoelastic and prone to damage. Existing material models capable of capturing these properties, as well as methods for experimental characterisation, are discussed. Future work required in bridging vein research is firstly to achieve consensus on aspects regarding morphology and histology, especially in the outflow cuff segment. Secondly, the advised material models need to be populated with realistic parameters through biaxial mechanical experiments adapted to the dimensions of the bridging vein samples. Finally, updating the existing finite element head models with these parameters will render them truly biofidelic, allowing the establishment of accurate tolerance criteria and, ultimately, better head protection devices.

Modelling the influence of endothelial heterogeneity on the progression of arterial disease: application to abdominal aortic aneurysm evolution

We sophisticate a fluid-solid growth computational framework for modelling aneurysm evolution. A realistic structural model of the arterial wall is integrated into a patient-specific geometry of the vasculature. This enables physiologically representative distributions of haemodynamic stimuli, obtained from a rigid-wall computational fluid dynamics analysis, to be linked to growth and remodelling algorithms. Additionally, a quasistatic structural analysis quantifies the cyclic deformation of the arterial wall so that collagen growth and remodelling can be explicitly linked to the cyclic deformation of vascular cells. To simulate aneurysm evolution, degradation of elastin is driven by reductions in wall shear stress (WSS) below homeostatic thresholds. Given that the endothelium exhibits spatial and temporal heterogeneity, we propose a novel approach to define the homeostatic WSS thresholds: We allow them to be spatially and temporally heterogeneous. We illustrate the application of this novel fluid-solid growth framework to model abdominal aortic aneurysm (AAA) evolution and to examine how the influence of the definition of the WSS homeostatic threshold influences AAA progression. We conclude that improved understanding and modelling of the endothelial heterogeneity is important for modelling aneurysm evolution and, more generally, other vascular diseases where haemodynamic stimuli play an important role.

The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization

Physical cues play a fundamental role in a wide range of biological processes, such as embryogenesis, wound healing, tumour invasion and connective tissue morphogenesis. Although it is well known that during these processes, cells continuously interact with the local extracellular matrix (ECM) through cell traction forces, the role of these mechanical interactions on large scale cellular and matrix organization remains largely unknown. In this study, we use a simple theoretical model to investigate cellular and matrix organization as a result of mechanical feedback signals between cells and the surrounding ECM. The model includes bi-directional coupling through cellular traction forces to deform the ECM and through matrix deformation to trigger cellular migration. In addition, we incorporate the mechanical contribution of matrix fibres and their reorganization by the cells. We show that a group of contractile cells will self-polarize at a large scale, even in homogeneous environments. In addition, our simulations mimic the experimentally observed alignment of cells in the direction of maximum stiffness and the building up of tension as a consequence of cell and fibre reorganization. Moreover, we demonstrate that cellular organization is tightly linked to the mechanical feedback loop between cells and matrix. Cells with a preference for stiff environments have a tendency to form chains, while cells with a tendency for soft environments tend to form clusters. The model presented here illustrates the potential of simple physical cues and their impact on cellular self-organization. It can be used in applications where cell-matrix interactions play a key role, such as in the design of tissue engineering scaffolds and to gain a basic understanding of pattern formation in organogenesis or tissue regeneration.

Non-linear micromechanics of soft tissues

Microstructure-based constitutive models have been adopted in recent studies of non-linear mechanical properties of biological soft tissues. These models provide more accurate predictions of the overall mechanical responses of tissues than phenomenological approaches. Based on standard approximations in non-linear mechanics, we classified the microstructural models into three categories: (1) uniform-field models with solid-like matrix, (2) uniform-field models with fluid-like matrix, and (3) second-order estimate models. The first two categories assume affine deformation field where the deformation of microstructure is the same as that of the tissue, regardless of material heterogeneities; i.e., they represent the upper bounds of the exact effective strain energy and stress of soft tissues. In addition, the first type is not purely structurally motivated and hence cannot accurately predict the microscopic mechanical behaviors of soft tissues. The third category considers realistic geometrical features, material properties of microstructure and interactions among them and allows for flexible deformation in each constituent. The uniform-field model with fluid-like matrix and the second-order estimate model are microstructure-based, and can be applied to different tissues based on micro-structural features.

Biaxial deformation of collagen and elastin fibers in coronary adventitia

The microstructural deformation-mechanical loading relation of the blood vessel wall is essential for understanding the overall mechanical behavior of vascular tissue in health and disease. We employed simultaneous mechanical loading-imaging to quantify in situ deformation of individual collagen and elastin fibers on unstained fresh porcine coronary adventitia under a combination of vessel inflation and axial extension loading. Specifically, the specimens were imaged under biaxial loads to study microscopic deformation-loading behavior of fibers in conjunction with morphometric measurements at the zero-stress state. Collagen fibers largely orientate in the longitudinal direction, while elastin fibers have major orientation parallel to collagen, but with additional orientation angles in each sublayer of the adventitia. With an increase of biaxial load, collagen fibers were uniformly stretched to the loading direction, while elastin fibers gradually formed a network in sublayers, which strongly depended on the initial arrangement. The waviness of collagen decreased more rapidly at a circumferential stretch ratio of λθ = 1.0 than at λθ = 1.5, while most collagen became straightened at λθ = 1.8. These microscopic deformations imply that the longitudinally stiffer adventitia is a direct result of initial fiber alignment, and the overall mechanical behavior of the tissue is highly dependent on the corresponding microscopic deformation of fibers. The microstructural deformation-loading relation will serve as a foundation for micromechanical models of the vessel wall.

Review: the role of biomechanical modeling in the rupture risk assessment for abdominal aortic aneurysms

AAA disease is a serious condition and a multidisciplinary approach including biomechanics is needed to better understand and more effectively treat this disease. A rupture risk assessment is central to the management of AAA patients, and biomechanical simulation is a powerful tool to assist clinical decisions. Central to such a simulation approach is a need for robust and physiologically relevant models. Vascular tissue senses and responds actively to changes in its mechanical environment, a crucial tissue property that might also improve the biomechanical AAA rupture risk assessment. Specifically, constitutive modeling should not only focus on the (passive) interaction of structural components within the vascular wall, but also how cells dynamically maintain such a structure. In this article, after specifying the objectives of an AAA rupture risk assessment, the histology and mechanical properties of AAA tissue, with emphasis on the wall, are reviewed. Then a histomechanical constitutive description of the AAA wall is introduced that specifically accounts for collagen turnover. A test case simulation clearly emphasizes the need for constitutive descriptions that remodels with respect to the mechanical loading state. Finally, remarks regarding modeling of realistic clinical problems and possible future trends conclude the article.

Application of speckle-tracking in the evaluation of carotid artery function in subjects with hypertension and diabetes

BACKGROUND

Speckle-tracking enables direct tracking of carotid arterial wall motion. Timing intervals determined with carotid speckle-tracking and slopes calculated from carotid artery area versus cardiac cycle curves may provide further information on arterial function and stiffness. The proposed arterial stiffness parameters were examined in healthy controls (n = 20), nondiabetic patients with hypertension (n = 20), and patients with type 2 diabetes (n = 21).

METHODS

Bilateral electrocardiographically gated ultrasonograms of the distal common carotid artery were acquired using a 12-MHz vascular probe. Four timing intervals were derived from speckle-tracked carotid arterial strain curves: (1) carotid predistension period, (2) peak carotid arterial strain time, (3) arterial distension period, and (4) arterial diastolic time. In addition, carotid artery area curves were recorded over the cardiac cycle and subdivided into four segments, S1 to S4, relating to arterial distention and contraction periods.

RESULTS

Mean far wall predistension period and peak carotid arterial strain time were more delayed in patients with diabetes and hypertension than in controls. Global mean arterial distension period was prolonged and arterial diastolic time was shorter in patients with hypertension and diabetes than in controls. Slopes of segments S2 and S4 were markedly steeper in the combined group of patients with hypertension and diabetes compared with healthy controls (P = .03 and P = .02, respectively).

CONCLUSIONS

Speckle-tracking-based measures of arterial stiffness may provide potential additive value in assessing vascular function in patients at risk for cardiovascular disease.

Elastin and collagen fibre microstructure of the human aorta in ageing and disease: a review

Aortic disease is a significant cause of death in developed countries. The most common forms of aortic disease are aneurysm, dissection, atherosclerotic occlusion and ageing-induced stiffening. The microstructure of the aortic tissue has been studied with great interest, because alteration of the quantity and/or architecture of the connective fibres (elastin and collagen) within the aortic wall, which directly imparts elasticity and strength, can lead to the mechanical and functional changes associated with these conditions. This review article summarizes the state of the art with respect to characterization of connective fibre microstructure in the wall of the human aorta in ageing and disease, with emphasis on the ascending thoracic aorta and abdominal aorta where the most common forms of aortic disease tend to occur.

A new multiscale model for the mechanical behavior of vein walls

The purpose of the present work is to propose a new multiscale model for the prediction of the mechanical behavior of vein walls. This model is based on one of our previous works which considered scale transitions applied to undulated collagen fibers. In the present work, the scale below was added to take the anisotropy of collagen fibrils into account. One scale above was also added, modeling the global reorientation of collagen fibers inside the vessel wall. The model was verified on experimental data from the literature, leading to a satisfactory agreement. The proposed multiscale approach also allows the extraction of local stresses and strains at each scale. This approach is presented here in the case of vein walls, but can easily be extended to other tissues which contain similar constituents.

Characterization of biaxial mechanical behavior of porcine aorta under gradual elastin degradation

Arteries are composed of multiple constituents that endow the wall with proper structure and function. Many vascular diseases are associated with prominent mechanical and biological alterations in the wall constituents. In this study, planar biaxial tensile test data of elastase-treated porcine aortic tissue (Chow et al. in Biomech Model Mechanobiol 2013) is re-examined to characterize the altered mechanical behavior at multiple stages of digestion through constitutive modeling. Exponential-based as well as recruitment-based strain energy functions are employed and the associated constitutive parameters for individual digestion stages are identified using nonlinear parameter estimation. It is shown that when the major portion of elastin is degraded from a cut-open artery in the load-free state, the embedded collagen fibers are recruited at lower stretch levels under biaxial loads, leading to a rapid stiffening behavior of the tissue. Multiphoton microscopy illustrates that the collagen waviness decreases significantly with the degradation time, resulting in a rapid recruitment when the tissue is loaded. It is concluded that even when residual stresses are released, there exists an intrinsic mechanical interaction between arterial elastin and collagen that determines the mechanics of arteries and carries important implications to vascular mechanobiology.

Passive pressure-diameter relationship and structural composition of rat mesenteric lymphangions

BACKGROUND

Lymph flow depends on both the rate of lymph production by tissues and the extent of passive and active pumping. Here we aim to characterize the passive mechanical properties of a lymphangion in both mid-lymphangion and valve segments to assess regional differences along a lymphangion, as well as evaluating its structural composition.

METHODS AND RESULTS

Mesenteric lymphatic vessels were isolated and cannulated in a microchamber for pressure-diameter (P-D) testing. Vessels were inflated from 0 to 20 cmH(2)O at a rate of 4 cmH(2)O/min, and vessel diameter was continuously tracked, using an inverted microscope, video camera, and custom LabVIEW program, at both mid-lymphangion and valve segments. Isolated lymphatic vessels were also pressure-fixed at 2 and 7 cmH(2)O and imaged using a nonlinear optical microscope (NLOM) to obtain collagen and elastin structural information. We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O), which was modeled using a three-parameter constitutive equation. No significant difference in the passive P-D response was observed between mid-lymphangion and valve regions. NLOM imaging revealed an inner elastin layer and outer collagen layer at all locations. Lymphatic valve leaflets were predominantly elastin with thick axially oriented collagen bands at the insertion points.

CONCLUSIONS

We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O) and developed the first constitutive equation to describe the passive P-D response for a lymphangion. The passive P-D response did not vary among regions, in agreement with the composition of elastin and collagen in the lymphatic wall.

A simple constitutive model for the Scapholunate ligament

A simple constitutive equation is presented to describe the non-linear load-displacement behavior of the Scapholunate ligament. The model is based on an elastic large strain probabilistic constitutive equation and has been formulated offering three characteristic constants. Experimental data from five human cadaveric Scapholunate ligaments were used to corroborate the accuracy of the model. Good correlation (r(2)=0.90-0.98) was found with the experimental data. Representative characteristic constants for the human Scapholunate ligament based on the model were determined.

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.

The layered structure of coronary adventitia under mechanical load

The mechanical loading-deformation relation of elastin and collagen fibril bundles is fundamental to understanding the microstructural properties of tissue. Here, we use multiphoton microscopy to obtain quantitative data of elastin and collagen fiber bundles under in situ loading of coronary adventitia. Simultaneous loading-imaging experiments on unstained fresh coronary adventitia allowed morphometric measurements of collagen and elastin fibril bundles and their individual deformation. Fiber data were analyzed at five different distension loading points (circumferential stretch ratio λ(θ) = 1.0, 1.2, 1.4, 1.6, and 1.8) at a physiological axial stretch ratio of λ(axial) = 1.3. Four fiber geometrical parameters were used to quantify the fibers: orientation angle, waviness, width, and area fraction. The results show that elastin and collagen fibers in inner adventitia form concentric densely packed fiber sheets, and the fiber orientation angle, width, and area fraction vary transmurally. The extent of fiber deformation depends on the initial orientation angle at no-distension state (λ(θ) = 1.0 and λ(axial) = 1.3). At higher distension loading, the orientation angle and waviness of fibers decrease linearly, but the width of collagen fiber is relatively constant at λ(θ) = 1.0-1.4 and then decrease linearly for λ(θ) ≥ 1.4. A decrease of the relative dispersion (SD/mean) of collagen fiber waviness suggests a heterogeneous mechanical response to loads. This study provides fundamental microstructural data for coronary artery biomechanics and we consider it seminal for structural models.

A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.