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

Traction-separation law parameters for the description of age-related changes in the delamination strength of the human descending thoracic aorta

Aortic dissection is a life-threatening disease that consists in the development of a tear in the wall of the aorta. The initial tear propagates as a discontinuity leading to separation within the aortic wall, which can result in the creation of a so-called false lumen. A fatal threat occurs if the rupture extends through the whole thickness of the aortic wall, as blood may then leak. It is generally accepted that the dissection, which can sometime extend along the entire length of the aorta, propagates via a delamination mechanism. The aim of the present paper is to provide experimentally validated parameters of a mathematical model for the description of the wall's cohesion. A model of the peeling experiment was built in Abaqus. The delamination interface was described by a piecewise linear traction-separation law. The bulk behavior of the aorta was assumed to be nonlinearly elastic, anisotropic, and incompressible. Our simulations resulted in estimates of the material parameters for the traction-separation law of the human descending thoracic aorta, which were obtained by minimizing the differences between the FEM predictions and the delamination force given by the regression of the peeling experiments. The results show that the stress at damage initiation, Tc, should be understood as an age-dependent quantity, and under the assumptions of our model this dependence can be expressed by linear regression as Tc =  - 13.03·10-4·Age + 0.2485 if the crack front advances in the axial direction, and Tc =  - 7.58·10-4·Age + 0.1897 if the crack front advances in the direction of the aortic circumference (Tc [MPa], Age [years]). Other model parameters were the stiffness K and the separation at failure, δf-δc (K = 0.5 MPa/mm, δf-δc = 0.1 mm). The material parameters provided by our study can be used in numerical simulations of the biomechanics of dissection propagation through the aorta especially when age-associated phenomena are studied.

Multimodal experimental studies of the passive mechanical behavior of human aortas: Current approaches and future directions

Cardiovascular diseases are the leading cause of death worldwide and include, among others, critical conditions of the aortic wall. Importantly, such critical conditions require effective diagnosis and treatment, which are not yet accurate enough. However, they could be significantly strengthened with predictive material models of the aortic wall. In particular, such predictive models could support surgical decisions, preoperative planning, and estimation of postoperative tissue remodeling. However, developing a predictive model requires experimental data showing both structural parameters and mechanical behavior. Such experimental data can be obtained using multimodal experiments. This review therefore discusses the current approaches to multimodal experiments. Importantly, the strength of the aortic wall is determined primarily by its passive components, i.e., mainly collagen, elastin, and proteoglycans. Therefore, this review focuses on multimodal experiments that relate the passive mechanical behavior of the human aortic wall to the structure and organization of its passive components. In particular, the multimodal experiments are classified according to the expected results. Multiple examples are provided for each experimental class and summarized with highlighted advantages and disadvantages of the method. Finally, future directions of multimodal experiments are envisioned and evaluated. STATEMENT OF SIGNIFICANCE: Multimodal experiments are innovative approaches that have gained interest very quickly, but also recently. This review presents therefore a first clear summary of groundbreaking research in the field of multimodal experiments. The benefits and limitations of various types of multimodal experiments are thoroughly discussed, and a comprehensive overview of possible results is provided. Although this review focuses on multimodal experiments performed on human aortic tissues, the methods used and described are not limited to human aortic tissues but can be extended to other soft materials.

Who bears the load? IOP-induced collagen fiber recruitment over the corneoscleral shell

Collagen is the main load-bearing component of cornea and sclera. When stretched, both of these tissues exhibit a behavior known as collagen fiber recruitment. In recruitment, as the tissues stretch the constitutive collagen fibers lose their natural waviness, progressively straightening. Recruited, straight, fibers bear substantially more mechanical load than non-recruited, wavy, fibers. As such, the process of recruitment underlies the well-established nonlinear macroscopic behavior of the corneoscleral shell. Recruitment has an interesting implication: when recruitment is incomplete, only a fraction of the collagen fibers is actually contributing to bear the loads, with the rest remaining "in reserve". In other words, at a given intraocular pressure (IOP), it is possible that not all the collagen fibers of the cornea and sclera are actually contributing to bear the loads. To the best of our knowledge, the fraction of corneoscleral shell fibers recruited and contributing to bear the load of IOP has not been reported. Our goal was to obtain regionally-resolved estimates of the fraction of corneoscleral collagen fibers recruited and in reserve. We developed a fiber-based microstructural constitutive model that could account for collagen fiber undulations or crimp via their tortuosity. We used experimentally-measured collagen fiber crimp tortuosity distributions in human eyes to derive region-specific nonlinear hyperelastic mechanical properties. We then built a three-dimensional axisymmetric model of the globe, assigning region-specific mechanical properties and regional anisotropy. The model was used to simulate the IOP-induced shell deformation. The model-predicted tissue stretch was then used to quantify collagen recruitment within each shell region. The calculations showed that, at low IOPs, collagen fibers in the posterior equator were recruited the fastest, such that at a physiologic IOP of 15 mmHg, over 90% of fibers were recruited, compared with only a third in the cornea and the peripapillary sclera. The differences in recruitment between regions, in turn, mean that at a physiologic IOP the posterior equator had a fiber reserve of only 10%, whereas the cornea and peripapillary sclera had two thirds. At an elevated IOP of 50 mmHg, collagen fibers in the limbus and the anterior/posterior equator were almost fully recruited, compared with 90% in the cornea and the posterior sclera, and 70% in the peripapillary sclera and the equator. That even at such an elevated IOP not all the fibers were recruited suggests that there are likely other conditions that challenge the corneoscleral tissues even more than IOP. The fraction of fibers recruited may have other potential implications. For example, fibers that are not bearing loads may be more susceptible to enzymatic digestion or remodeling. Similarly, it may be possible to control tissue stiffness through the fraction of recruited fibers without the need to add or remove collagen.

Changes in the microstructure of the human aortic adventitia under biaxial loading investigated by multi-photon microscopy

Among the three layers of the aortic wall, the media is primarily responsible for its mechanical properties, but the adventitia prevents the aorta from overstretching and rupturing. The role of the adventitia is therefore crucial with regard to aortic wall failure, and understanding the load-induced changes in tissue microstructure is of high importance. Specifically, the focus of this study is on the changes in collagen and elastin microstructure in response to macroscopic equibiaxial loading applied to the aortic adventitia. To observe these changes, multi-photon microscopy imaging and biaxial extension tests were performed simultaneously. In particular, microscopy images were recorded at 0.02 stretch intervals. The microstructural changes of collagen fiber bundles and elastin fibers were quantified with the parameters of orientation, dispersion, diameter, and waviness. The results showed that the adventitial collagen was divided from one into two fiber families under equibiaxial loading conditions. The almost diagonal orientation of the adventitial collagen fiber bundles remained unchanged, but the dispersion was substantially reduced. No clear orientation of the adventitial elastin fibers was observed at any stretch level. The waviness of the adventitial collagen fiber bundles decreased under stretch, but the adventitial elastin fibers showed no change. These original findings highlight differences between the medial and adventitial layers and provide insight into the stretching process of the aortic wall. STATEMENT OF SIGNIFICANCE: To provide accurate and reliable material models, it is essential to understand the mechanical behavior of the material and its microstructure. Such understanding can be enhanced with tracking of the microstructural changes caused by mechanical loading of the tissue. This study provides therefore a unique dataset of structural parameters of the human aortic adventitia obtained under equibiaxial loading. The structural parameters describe orientation, dispersion, diameter, and waviness of collagen fiber bundles and elastin fibers. Eventually, the microstructural changes in the human aortic adventitia are compared with the microstructural changes in the human aortic media from a previous study. This comparison reveals the cutting-edge findings on the differences in the response to the loading between these two human aortic layers.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

Changes in the microstructure of the human aortic medial layer under biaxial loading investigated by multi-photon microscopy

Understanding the correlation between tissue architecture, health status, and mechanical properties is essential for improving material models and developing tissue engineering scaffolds. Since structural-based material models are state of the art, there is an urgent need for experimentally obtained structural parameters. For this purpose, the medial layer of nine human abdominal aortas was simultaneously subjected to equibiaxial loading and multi-photon microscopy. At each loading interval of 0.02, collagen and elastin fibers were imaged based on their second-harmonic generation signal and two-photon excited autofluorescence, respectively. The structural alterations in the fibers were quantified using the parameters of orientation, diameter, and waviness. The results of the mechanical tests divided the sample cohort into the ruptured and non-ruptured, and stiff and non-stiff groups, which were covered by the findings from histological investigations. The alterations in structural parameters provided an explanation for the observed mechanical behavior. In addition, the waviness parameters of both collagen and elastin fibers showed the potential to serve as indicators of tissue strength. The data provided address deficiencies in current material models and bridge multiscale mechanisms in the aortic media. STATEMENT OF SIGNIFICANCE: Available material models can reproduce, but cannot predict, the mechanical behavior of human aortas. This deficiency could be overcome with the help of experimentally validated structural parameters as provided in this study. Simultaneous multi-photon microscopy and biaxial extension testing revealed the microstructure of human aortic media at different stretch levels. Changes in the arrangement of collagen and elastin fibers were quantified using structural parameters such as orientation, diameter and waviness. For the first time, structural parameters of human aortic tissue under continuous loading conditions have been obtained. In particular, the waviness parameters at the reference configuration have been associated with tissue stiffness, brittleness, and the onset of atherosclerosis.

Predicting and understanding arterial elasticity from key microstructural features by bidirectional deep learning

Microstructural features and mechanical properties are closely related in all soft biological tissues. Both yet exhibit considerable inter-individual differences and are affected by factors such as aging and disease and its progression. Histological analysis, modern in situ imaging, and biomechanical testing have deepened our understanding of these complex interrelations, yet two key questions remain: (1) Given the specific microstructure, can one predict the macroscopic mechanical properties without mechanical testing? (2) Can one quantify individual contributions of the different microstructural features to the macroscopic mechanical properties in an automated, systematic and largely unbiased way? Here we propose a bidirectional deep learning architecture to address these two questions. Our architecture uses data from standard histological analyses, two-photon microscopy and biaxial biomechanical testing. Its capabilities are demonstrated by predicting with high accuracy (R²=0.92) the evolving mechanical properties of the murine aorta during maturation and aging. Moreover, our architecture reveals that the extracellular matrix composition and organization are the most prominent factors governing the macroscopic mechanical properties of the tissues studied herein. STATEMENT OF SIGNIFICANCE:  .

Differences in Collagen Fiber Diameter and Waviness between Healthy and Aneurysmal Abdominal Aortas

Collagen plays a key role in the strength of aortic walls, so studying micro-structural changes during disease development is critical to better understand collagen reorganization. Second-harmonic generation microscopy is used to obtain images of human aortic collagen in both healthy and diseased states. Methods are being developed in order to efficiently determine the waviness, that is, tortuosity and amplitude, as well as the diameter, orientation, and dispersion of collagen fibers, and bundles in healthy and aneurysmal tissues. The results show layer-specific differences in the collagen of healthy tissues, which decrease in samples of aneurysmal aortic walls. In healthy tissues, the thick collagen bundles of the adventitia are characterized by greater waviness, both in the tortuosity and in the amplitude, compared to the relatively thin and straighter collagen fibers of the media. In contrast, most aneurysmal tissues tend to have a more uniform structure of the aortic wall with no significant difference in collagen diameter between the luminal and abluminal layers. An increase in collagen tortuosity compared to the healthy media is also observed in the aneurysmal luminal layer. The data set provided can help improve related material and multiscale models of aortic walls and aneurysm formation.

Biomechanical characterization and constitutive modeling of the layer-dissected residual strains and mechanical properties of abdominal porcine aorta

We analyze the residual stresses and mechanical properties of layer-dissected infrarenal abdominal aorta (IAA). We measured the axial pre-stretch and opening angle and performed uniaxial tests to study and compare the mechanical behavior of both intact and layer-dissected porcine IAA samples under physiological loads. Finally, some of the most popular anisotropic hyperelastic constitutive models (GOH and microfiber models) were proposed to estimate the mechanical properties of the abdominal aorta by least-square fitting of the recorded in-vitro uniaxial test results. The results show that the residual stresses are layer dependent. In all cases, we found that the OA in the media layer is lower than in the whole artery, the intima and the adventitia. For the axial pre-stretch, we found that the adventitia and the media were slightly stretched in the environment of the intact arterial strip, whereas the intima appears to be compressed. Regarding the mechanical properties, the media seems to be the softest layer over the whole deformation domain showing high anisotropy, while the intima and adventitia exhibit considerable stiffness and a lower anisotropy response. Finally, all the hyperelastic anisotropic models considered in this study provided a reasonable approximation of the experimental data. The GOH model showed the best fitting.

Spatial lay-out of various smooth muscles

The characteristic mechanical activities of the smooth muscles found in all organs of the body are highly variable and depend mainly on the spatial arrangement of the muscle cells and the stroma: mass, orientation, relationships, links, constraints, which are deployed in various configurations. These structural features are examined here for their mechanical relevance, in light and electron microscopic views of several muscles of viscera and blood vessels, in a selection of mammalian species. Smooth muscles are incompressible and therefore maintain constant volume. They do not have available space and any movement of a part requires displacement of another part. Most of them have no terminations or points of attachment, and in hollow organs such as intestines, blood vessels and uro-genital tract they usually form structures closed onto themselves, such as rings or bag-like containers In these situations, changes in the size of the lumen is achieved very efficiently by a concentric inward enlargement that accompanies muscle contraction. The longitudinal arrangement of collagen blocks an elongation of small blood vessels upon contraction, further enhancing the efficiency of lumen reduction. In other muscles, links between layers and special arrangements of the stroma allow both shortening and elongation of a tubular organ to occur. The mechanics of smooth muscles has many characteristic features (some unique, some shared with those of hydrostats, some at variance with other muscles) and histological data are a contribution to our understanding of these properties.

Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average

We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress-strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.

Constitutive modeling using structural information on collagen fiber direction and dispersion in human superficial femoral artery specimens of different ages

Arterial mechanics plays an important role in vascular pathophysiology and repair, and advanced imaging can inform constitutive models of vascular behavior. We have measured the mechanical properties of 14 human superficial femoral arteries (SFAs) (age 12-70, mean 48±19 years) using planar biaxial extension, and determined the preferred collagen fiber direction and dispersion using multiphoton microscopy. The collagen fiber direction and dispersion were evaluated using second-harmonic generation imaging and modeled using bivariate von Mises distributions. The microstructures of elastin and collagen were assessed using two-photon fluorescence imaging and conventional bidirectional histology. The mechanical and structural data were used to describe the SFA mechanical behavior using two- and four-fiber family invariant-based constitutive models. Older SFAs were stiffer and mechanically more nonlinear than younger specimens. In the adventitia, collagen fibers were undulated and diagonally-oriented, while in the media, they were straight and circumferentially-oriented. The media was rich in collagen that surrounded the circumferentially-oriented smooth muscle cells, and the elastin was present primarily in the internal and external elastic laminae. Older SFAs had a more circumferential collagen fiber alignment, a decreased circumferential-radial fiber dispersion, but the same circumferential-longitudinal fiber dispersion as younger specimens. Both the two- and the four-fiber family constitutive models were able to capture the experimental data, and the fits were better for the four-fiber family formulation. Our data provide additional details on the SFA intramural structure and inform structurally-based constitutive models.

Quantification of the regional bioarchitecture in the human aorta

Regional variance in human aortic bioarchitecture responsible for the elasticity of the vessel is poorly understood. The current study quantifies the elements responsible for aortic compliance, namely, elastin, collagen and smooth muscle cells, using histological and stereological techniques on human tissue with a focus on regional heterogeneity. Using donated cadaveric tissue, a series of samples were excised between the proximal ascending aorta and the distal abdominal aorta, for five cadavers, each of which underwent various staining procedures to enhance specific constituents of the wall. Using polarised light microscopy techniques, the orientation of collagen fibres was studied for each location and each tunical layer of the aorta. Significant transmural and longitudinal heterogeneity in collagen fibre orientations were uncovered throughout the vessel. It is shown that a von Mises mixture model is required accurately to fit the complex collagen fibre distributions that exist along the aorta. Additionally, collagen and smooth muscle cell density was observed to increase with increasing distance from the heart, whereas elastin density decreased. Evidence clearly demonstrates that the aorta is a highly heterogeneous vessel which cannot be simplistically represented by a single compliance value. The quantification and fitting of the regional aortic bioarchitectural data, although not without its limitations, including mean cohort age of 77.6 years, facilitates the development of next-generation finite element models that can potentially simulate the influence of regional aortic composition and microstructure on vessel biomechanics.

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

A multiscale active structural model of the arterial wall accounting for smooth muscle dynamics

Arterial wall dynamics arise from the synergy of passive mechano-elastic properties of the vascular tissue and the active contractile behaviour of smooth muscle cells (SMCs) that form the media layer of vessels. We have developed a computational framework that incorporates both these components to account for vascular responses to mechanical and pharmacological stimuli. To validate the proposed framework and demonstrate its potential for testing hypotheses on the pathogenesis of vascular disease, we have employed a number of pharmacological probes that modulate the arterial wall contractile machinery by selectively inhibiting a range of intracellular signalling pathways. Experimental probes used on ring segments from the rabbit central ear artery are: phenylephrine, a selective α1-adrenergic receptor agonist that induces vasoconstriction; cyclopiazonic acid (CPA), a specific inhibitor of sarcoplasmic/endoplasmic reticulum Ca²⁺-ATPase; and ryanodine, a diterpenoid that modulates Ca²⁺ release from the sarcoplasmic reticulum. These interventions were able to delineate the role of membrane versus intracellular signalling, previously identified as main factors in smooth muscle contraction and the generation of vessel tone. Each SMC was modelled by a system of nonlinear differential equations that account for intracellular ionic signalling, and in particular Ca²⁺ dynamics. Cytosolic Ca²⁺ concentrations formed the catalytic input to a cross-bridge kinetics model. Contractile output from these cellular components forms the input to the finite-element model of the arterial rings under isometric conditions that reproduces the experimental conditions. The model does not account for the role of the endothelium, as the nitric oxide production was suppressed by the action of L-NAME, and also due to the absence of shear stress on the arterial ring, as the experimental set-up did not involve flow. Simulations generated by the integrated model closely matched experimental observations qualitatively, as well as quantitatively within a range of physiological parametric values. The model also illustrated how increased intercellular coupling led to smooth muscle coordination and the genesis of vascular tone.

Molecular-level collagen damage explains softening and failure of arterial tissues: A quantitative interpretation of CHP data with a novel elasto-damage model

The present experimental-modelling study provides a quantitative interpretation of mechanical data and damage measurements obtained from collagen hybridizing peptide (CHP) techniques on overstretched sheep cerebral arterial tissues. To this aim, a structurally-motivated constitutive model is developed in the framework of continuum damage mechanics. The model includes two internal variables for describing the effects of collagen triple-helical unfolding via interstrand delamination: one governs plastic mechanisms in collagen fibers, leading to a stress softening response of the tissue at the macroscale; the other one describes the loss of fiber structural integrity, leading to tissue final failure. The proposed model is calibrated using the obtained mechanical experimental data, showing excellent fitting capabilities. The predicted evolution of internal variables agree well with independent measurements of molecular-level CHP-based damage data, obtaining an independent a posteriori validation of damage predictions. Moreover, available data on inelastic tissue elongation following supraphysiological loads are successfully reproduced. These outcomes further the hypothesis that the accumulation of interstrand delamination is a primary cause for the evolution of inelastic mechanisms in tissues, and in particular of stress softening up to failure.

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

Clinical assessment of arterial stiffness relies on noninvasive measurements of regional pulse wave velocity or local distensibility. However, arterial stiffness measures do not discriminate underlying changes in arterial wall constituent properties (e.g., in collagen, elastin, or smooth muscle), which is highly relevant for development and monitoring of treatment. In arterial stiffness in recent clinical-epidemiological studies, we systematically review clinical-epidemiological studies (2012–) that interpreted arterial stiffness changes in terms of changes in arterial wall constituent properties (63 studies included of 514 studies found). Most studies that did so were association studies (52 of 63 studies) providing limited causal evidence. Intervention studies (11 of 63 studies) addressed changes in arterial stiffness through the modulation of extracellular matrix integrity (5 of 11 studies) or smooth muscle tone (6 of 11 studies). A handful of studies (3 of 63 studies) used mathematical modeling to discriminate between extracellular matrix components. Overall, there exists a notable gap in the mechanistic interpretation of stiffness findings. In constitutive model-based interpretation, we first introduce constitutive-based modeling and use it to illustrate the relationship between constituent properties and stiffness measurements (“forward” approach). We then review all literature on modeling approaches for the constitutive interpretation of clinical arterial stiffness data (“inverse” approach), which are aimed at estimation of constitutive properties from arterial stiffness measurements to benefit treatment development and monitoring. Importantly, any modeling approach requires a tradeoff between model complexity and measurable data. Therefore, the feasibility of changing in vivo the biaxial mechanics and/or vascular smooth muscle tone should be explored. The effectiveness of modeling approaches should be confirmed using uncertainty quantification and sensitivity analysis. Taken together, constitutive modeling can significantly improve clinical interpretation of arterial stiffness findings.

Contributions of Glycosaminoglycans to Collagen Fiber Recruitment in Constitutive Modeling of Arterial Mechanics

The contribution of glycosaminoglycans (GAGs) to the biological and mechanical functions of biological tissue has emerged as an important area of research. GAGs provide structural basis for the organization and assembly of extracellular matrix (ECM). The mechanics of tissue with low GAG content can be indirectly affected by the interaction of GAGs with collagen fibers, which have long been known to be one of the primary contributors to soft tissue mechanics. Our earlier study showed that enzymatic GAG depletion results in straighter collagen fibers that are recruited at lower levels of stretch, and a corresponding shift in earlier arterial stiffening (Mattson et al., 2016). In this study, the effect of GAGs on collagen fiber recruitment was studied through a structure-based constitutive model. The model incorporates structural information, such as fiber orientation distribution, content, and recruitment of medial elastin, medial collagen, and adventitial collagen fibers. The model was first used to study planar biaxial tensile stress-stretch behavior of porcine descending thoracic aorta. Changes in elastin and collagen fiber orientation distribution, and collagen fiber recruitment were then incorporated into the model in order to predict the stress-stretch behavior of GAG depleted tissue. Our study shows that incorporating early collagen fiber recruitment into the model predicts the stress-stretch response of GAG depleted tissue reasonably well (rms = 0.141); considering further changes of fiber orientation distribution does not improve the predicting capability (rms = 0.149). Our study suggests an important role of GAGs in arterial mechanics that should be considered in developing constitutive models.

Assessing Collagen and Elastin Pressure-dependent Microarchitectures in Live, Human Resistance Arteries by Label-free Fluorescence Microscopy

The pathogenic contribution of resistance artery remodeling is documented in essential hypertension, diabetes and the metabolic syndrome. Investigations and development of microstructurally motivated mathematical models for understanding the mechanical properties of human resistance arteries in health and disease have the potential to aid understanding how disease and medical treatments affect the human microcirculation. To develop these mathematical models, it is essential to decipher the relationship between the mechanical and microarchitectural properties of the microvascular wall. In this work, we describe an ex vivo method for passive mechanical testing and simultaneous label-free three-dimensional imaging of the microarchitecture of elastin and collagen in the arterial wall of isolated human resistance arteries. The imaging protocol can be applied to resistance arteries of any species of interest. Image analyses are described for quantifying i) pressure-induced changes in internal elastic lamina branching angles and adventitial collagen straightness using Fiji and ii) collagen and elastin volume densities determined using Ilastik software. Preferably all mechanical and imaging measurements are performed on live, perfused arteries, however, an alternative approach using standard video-microscopy pressure myography in combination with post-fixation imaging of re-pressurized vessels is discussed. This alternative method provides users with different options for analysis approaches. The inclusion of the mechanical and imaging data in mathematical models of the arterial wall mechanics is discussed, and future development and additions to the protocol are proposed.

Structural and Functional Differences Between Porcine Aorta and Vena Cava

Elastin and collagen fibers are the major load-bearing extracellular matrix (ECM) constituents of the vascular wall. Arteries function differently than veins in the circulatory system; however as a result from several treatment options, veins are subjected to sudden elevated arterial pressure. It is thus important to recognize the fundamental structure and function differences between a vein and an artery. Our research compared the relationship between biaxial mechanical function and ECM structure of porcine thoracic aorta and inferior vena cava. Our study suggests that aorta contains slightly more elastin than collagen due to the cyclical extensibility, but vena cava contains almost four times more collagen than elastin to maintain integrity. Furthermore, multiphoton imaging of vena cava showed longitudinally oriented elastin and circumferentially oriented collagen that is recruited at supraphysiologic stress, but low levels of strain. However in aorta, elastin is distributed uniformly, and the primarily circumferentially oriented collagen is recruited at higher levels of strain than vena cava. These structural observations support the functional finding that vena cava is highly anisotropic with the longitude being more compliant and the circumference stiffening substantially at low levels of strain. Overall, our research demonstrates that fiber distributions and recruitment should be considered in addition to relative collagen and elastin contents. Also, the importance of accounting for the structural and functional differences between arteries and veins should be taken into account when considering disease treatment options.

Evaluation of microstructurally motivated constitutive models to describe age-dependent tendon healing

Tendon injuries are common to all ages. Injured tendons typically do not recover full functionality. The amount and organization of tendon constituents dictate their mechanical properties. The impact of changes in these constituents during (patho)physiologic processes (e.g., aging and healing) are not fully understood. Toward this end, microstructurally motivated strain energy functions (SEFs) offer insight into underlying mechanisms of age-dependent healing. Several SEFs have been adapted for tendon; however, most are phenomenological. Therefore, the aims of this study are: (1) evaluate the descriptive capability of SEFs in age-dependent murine patellar tendon healing and (2) identify a SEF for implementation in a growth and remodeling (G&R) model. To accomplish these aims, models were fitted to patellar tendon tensile data from multiple age groups and post-injury timepoints. Model sensitivity to parameters and the determinability of the parameters were assessed. A two-way analysis of variance was used to identify changes in parameters and the feasibility of implementing each model into a G&R model is discussed. The evaluated SEFs exhibited adequate descriptive capability. Parameter determinability and sensitivity analysis, however, highlighted the need for additional data to inform and validate the models to increase physiologic relevance and enable G&R model formulation to determine underlying mechanisms of age-dependent healing. This work, as a first, evaluated changes in tendon mechanical properties both as functions of age and injury in an age-dependent manner using microstructurally motivated models, highlights inherent dependencies between parameters of widely used hyperelastic models, and identified unique post-injury behavior by the aging group compared to the mature and aged groups.

Constitutive modeling of the passive inflation-extension behavior of the swine colon

In the present work, we propose the first structural constitutive model of the passive mechanical behavior of the swine colon that is validated against physiological inflation-extension tests, and accounts for residual strains. Sections from the spiral colon and the descending colon were considered to investigate potential regional variability. We found that the proposed constitutive model accurately captures the passive inflation-extension behavior of both regions of the swine colon (coefficient of determination R²=0.94±0.02). The model revealed that the circumferential muscle layer does not provide significant mechanical support under passive conditions and the circumferential load is actually carried by the submucosa layer. The stress analysis permitted by the model showed that the colon tissue can distend up to 30% radially without significant increase in the wall stresses suggesting a highly compliant behavior of the tissue. This is in-line with the requirement for the tissue to easily accommodate variable quantities of fecal matter. The analysis also showed that the descending colon is significantly more compliant than the spiral colon, which is relevant to the storage function of the descending colon. Histological analysis showed that the swine colon possesses a four-layer structure similar to the human colon, where the longitudinal muscle layer is organized into bands called taeniae, a typical feature of the human colon. The model and the estimated parameters can be used in a Finite Element framework to conduct simulations with realistic geometry of the swine colon. The resulting computational model will provide a foundation for virtual assessment of safe and effective devices for the treatment of colonic diseases.

Imaging and modeling of acute pressure-induced changes of collagen and elastin microarchitectures in pig and human resistance arteries

The impact of disease-related changes in the extracellular matrix (ECM) on the mechanical properties of human resistance arteries largely remains to be established. Resistance arteries from both pig and human parietal pericardium (PRA) display a different ECM microarchitecture compared with frequently used rodent mesenteric arteries. We hypothesized that the biaxial mechanics of PRA mirror pressure-induced changes in the ECM microarchitecture. This was tested using isolated pig PRA as a model system, integrating vital imaging, pressure myography, and mathematical modeling. Collagenase and elastase digestions were applied to evaluate the load-bearing roles of collagen and elastin, respectively. The incremental elastic modulus linearly related to the straightness of adventitial collagen fibers circumferentially and longitudinally (both R2 ≥ 0.99), whereas there was a nonlinear relationship to the internal elastic lamina elastin fiber branching angles. Mathematical modeling suggested a collagen recruitment strain (means ± SE) of 1.1 ± 0.2 circumferentially and 0.20 ± 0.01 longitudinally, corresponding to a pressure of ~40 mmHg, a finding supported by the vital imaging. The integrated method was tested on human PRA to confirm its validity. These showed limited circumferential distensibility and elongation and a collagen recruitment strain of 0.8 ± 0.1 circumferentially and 0.06 ± 0.02 longitudinally, reached at a distending pressure below 20 mmHg. This was confirmed by vital imaging showing negligible microarchitectural changes of elastin and collagen upon pressurization. In conclusion, we show here, for the first time in resistance arteries, a quantitative relationship between pressure-induced changes in the extracellular matrix and the arterial wall mechanics. The strength of the integrated methods invites for future detailed studies of microvascular pathologies.

NEW & NOTEWORTHY This is the first study to quantitatively relate pressure-induced microstructural changes in resistance arteries to the mechanics of their wall. Principal findings using a pig model system were confirmed in human arteries. The combined methods provide a strong tool for future hypothesis-driven studies of microvascular pathologies.

Fetal Growth Restriction Induces Heterogeneous Effects on Vascular Biomechanical and Functional Properties in Guinea Pigs (Cavia porcellus)

Aim: Fetal growth restriction (FGR) is associated with a variety of cardiometabolic diseases in adulthood which could involve remodeling processes of the vascular walls that could start in the fetal period. However, there is no consensus whether this remodeling affects in a similar way the whole vascular system. We aimed to determine the effects of FGR on the vasoactive and biomechanical properties of umbilical and systemic vessels in fetal guinea pigs.

Methods: FGR was induced by implanting ameroid occluders at mid-gestation in uterine arteries of pregnant guinea pigs, whilst the control group was exposed to simulated surgery. At the term of gestation, systemic arteries (aorta, carotid and femoral) and umbilical vessels were isolated to determine ex vivo contractile and biomechanical responses (stretch-stress until rupture) on a wire myograph, as well as opening angle and residual stresses. Histological characteristics in tissue samples were measured by van Gieson staining.

Results: Aorta and femoral arteries from FGR showed an increased in biomechanical markers of stiffness (p < 0.01), contractile capacity (p < 0.05) and relative media thickness (p < 0.01), but a reduced internal diameter (p < 0.001), compared with controls. There were no differences in the biomechanical properties of carotid and umbilical from control and FGR fetuses, but FGR umbilical arteries had a decreased contractile response to KCl (p < 0.05) along with a reduced relative media thickness (p < 0.05).

Conclusion: Altogether, these changes in functional, mechanical and morphological properties suggest that FGR is associated with a heterogeneous pro-constrictive vascular remodeling affecting mainly the lower body fetal arteries. These effects would be set during a pathologic pregnancy in order to sustain the fetal blood redistribution in the FGR and may persist up to adulthood increasing the risk of a cardiovascular disease.

A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment

Incorporation of collagen structural information into the study of biomechanical behavior of ascending thoracic aortic (ATA) wall tissue should provide better insight into the pathophysiology of ATA. Structurally motivated constitutive models that include fiber dispersion and recruitment can successfully capture overall mechanical response of the arterial wall tissue. However, these models cannot examine local microarchitectural features of the collagen network, such as the effect of fiber disruptions and interaction between fibrous and non-fibrous components, which may influence emergent biomechanical properties of the tissue. Motivated by this need, we developed a finite element based three-dimensional structural model of the lamellar units of the ATA media that directly incorporates the collagen fiber microarchitecture. The fiber architecture was computer generated utilizing network features, namely fiber orientation distribution, intersection density and areal concentration, obtained from image analysis of multiphoton microscopy images taken from human aneurysmal ascending thoracic aortic media specimens with bicuspid aortic valve (BAV) phenotype. Our model reproduces the typical J-shaped constitutive response of the aortic wall tissue. We found that the stress state in the non-fibrous matrix was homogeneous until the collagen fibers were recruited, but became highly heterogeneous after that event. The degree of heterogeneity was dependent upon local network architecture with high stresses observed near disrupted fibers. The magnitude of non-fibrous matrix stress at higher stretch levels was negatively correlated with local fiber density. The localized stress concentrations, elucidated by this model, may be a factor in the degenerative changes in aneurysmal ATA tissue.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.

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.