Origin of axial prestretch and residual stress in arteries

Experimental characterization of residual deformations in human descending thoracic aortas

The effect of residual stresses on the deformation of human aortas under pulsatile pressure is relevant. Experimental measurements of residual deformations are necessary to characterize residual stresses in human aortas. For this reason, an experimental study is carried out. In the present study, longitudinal and circumferential strips from descending thoracic aortas obtained from 21 donors, harvested during organ donation explant, underwent residual deformation measurements. The intact wall and the three separated layers were tested in both directions, resulting in 8 tests per donor, which gives a relevant set of experimental data for further studies. Results show significant residual deformations both in circumferential and longitudinal directions, which are compatible with a significantly compressed intima in the unloaded aorta. In particular, the measured mean effective curvature was -0.193 ± 0.064 (1/mm) for the circumferential strips and -0.076 ± 0.030 (1/mm) for longitudinal strips of the full wall. The effects of age and gender were also investigated.

Structural and Mechanical Properties of Human Superficial Femoral and Popliteal Arteries

The femoropopliteal artery (FPA) is the main artery in the lower limb. It supplies blood to the leg muscles and undergoes complex deformations during limb flexion. Atherosclerotic disease of the FPA (peripheral arterial disease, PAD) is a major public health burden, and despite advances in surgical and interventional therapies, the clinical outcomes of PAD repairs continue to be suboptimal, particularly in challenging calcified lesions and biomechanically active locations. A better understanding of human FPA mechanical and structural characteristics in relation to age, risk factors, and the severity of vascular disease can help develop more effective and longer-lasting treatments through computational modeling and device optimization. This review aims to summarize recent research on the main biomechanical and structural properties of human superficial femoral and popliteal arteries that comprise the FPA and describe their anatomy, composition, and mechanical behavior under different conditions.

Renal denervation restores biomechanics of carotid arteries in a rat model of hypertension

The prevalence of hypertension increases with aging and is associated with increased arterial stiffness. Resistant hypertension is presented when drug treatments fail to regulate a sustained increased blood pressure. Given that the mechanisms between the sympathetic nervous system and the kidney play an important role in blood regulation, renal denervation (RDN) has emerged as a therapeutic potential in resistant hypertension. In this study, we investigated the effects of RDN on the biomechanical response and microstructure of elastic arteries. Common carotid arteries (CCA) excised from 3-month, 8-month, and 8-month denervated rats were subjected to biaxial extension-inflation test. Our results showed that hypertension developed in the 8-month-old rats. The sustained elevated blood pressure resulted in arterial remodeling which was manifested as a significant stress increase in both axial and circumferential directions after 8 months. RDN had a favorable impact on CCAs with a restoration of stresses in values similar to control arteries at 3 months. After biomechanical testing, arteries were imaged under a multi-photon microscope to identify microstructural changes in extracellular matrix (ECM). Quantification of multi-photon images showed no significant alterations of the main ECM components, elastic and collagen fibers, indicating that arteries remained intact after RDN. Regardless of the experimental group, our microstructural analysis of the multi-photon images revealed that reorientation of the collagen fibers might be the main microstructural mechanism taking place during pressurization with their straightening happening during axial stretching.

Compromised homeostasis in aged carotid arteries revealed by microstructural studies of elastic lamellae

Healthy arteries are continuously subjected to diverse mechanical stimuli and adapt in order to maintain a mechanical homeostasis which is characterized by a uniform distribution of wall stresses. However, aging may compromise the homeostatic microenvironment within arteries. Structural heterogeneity has been suggested as a potential microstructural mechanism that could lead to homogeneous stress distribution across the arterial wall. Our previous study on the unfolding and stretching of the elastic lamellae revealed the underlying microstructural mechanism for equalizing the circumferential stresses through wall; inner elastic layers are wavier and unfold more than the outer layers which helps to evenly distribute lamellar stretching (Yu et al., 2018). In this study, we investigated the effect of aging on lamellar deformation and its implications for tissue homeostasis. Common carotid arteries from aged mice were imaged under a multi-photon microscope while subjected to biaxial extension and inflation at five different pressures ranging from 0 up to 120 mmHg. Lamellar unfolding during pressurization was then determined from the reconstructed cross-sectional images of elastic lamellae. Tissue-level circumferential stretch was combined with the lamellar unfolding to calculate lamellar stretching. Our results revealed that the straightness gradient of aged elastic lamellae is similar to the young ones. However, during pressurization, the inner elastic lamella of the aged mice unfolded significantly more than the inner layer in young arteries. An important finding of our study is the uneven increase in inter-lamellar space which contributed to a nonuniform stretching of the elastic lamellae of aged mice arteries, elevated stress gradient, and a shifting of the load-bearing component to adventitia. Our results shed light into the complex microstructural mechanisms that take place in aging and adversely affect arterial mechanical behavior and homeostasis.

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences

INTRODUCTION

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments.

MATERIALS AND METHODS

This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated.

RESULTS AND CONCLUSION

Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

A two-scale numerical study on the mechanobiology of abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) are a serious condition whose pathophysiology is related to phenomena occurring at different length scales. To gain a better understanding of the disease, this work presents a multi-scale computational study that correlates AAA progression with microstructural and mechanical alterations in the tissue. Macro-scale geometries of a healthy aorta and idealized aneurysms with increasing diameter are developed on the basis of existing experimental data and subjected to physiological boundary conditions. Subsequently, microscopic representative volume elements of the abluminal side of each macro-model are employed to analyse the local kinematics at the cellular scale. The results suggest that the formation of the aneurysm disrupts the micromechanics of healthy tissue, which could trigger collagen growth and remodelling by mechanosensing cells. The resulting changes to the macro-mechanics and microstructure of the tissue seem to establish a new homeostatic state at the cellular scale, at least for the diameter range investigated.

Glycosaminoglycans modulate compressive stiffness and circumferential residual stress in the porcine thoracic aorta

The mechanical properties of the aorta are influenced by the extracellular matrix, a network mainly comprised of fibers and glycosaminoglycans (GAG). In this work, we demonstrate that GAG contribute to the opening angle (a marker of circumferential residual stresses) in intact and glycated aortic tissue. Enzymatic GAG depletion was associated with a decrease in the opening angle, by approximately 25% (p = 0.009) in the ascending (AS) region, 32% (p = 0.003) in the aortic arch (AR), and 42% (p = 0.001) in the lower descending thoracic (LDT) region. A similar effect of GAG depletion on aortic ring opening angle was also observed in previously glycated tissues. Using indentation testing, we found that the radial compressive stiffness significantly increased in the AS region following GAG depletion, compared to fresh (p = 0.006) and control samples (p = 0.021), and that the compressive properties are heterogeneous along the aortic tree. A small loss of water content was also detected after GAG depletion, which was most prominent under hypotonic conditions. Finally, the AS region was also associated with a significant loss of compressive deformation (circumferential stretch that is < 1) in the inner layer of the aorta following GAG depletion, suggesting that GAG interact with ECM fibers in their effect on aortic mechanics. The importance of this work lies in its identification of the role of GAG in modulating the mechanical properties of the aorta, namely the circumferential residual stresses and the radial compressive stiffness, as well as contributing to the swelling state and the level of circumferential prestretch in the tissue. STATEMENT OF SIGNIFICANCE: The mechanical properties of the aorta are influenced by the composition and organization of its extracellular matrix (ECM) and are highly relevant to medical conditions affecting the structural integrity of the aorta. The extent of contribution of glycosaminoglycans (GAG), a relatively minor ECM component, to the mechanical properties of the aorta, remains poorly characterized. This works shows that GAG contribute on average 30% to the opening angle (an indicator of circumferential residual stresses) of porcine aortas, and that GAG-depletion is associated with an increased radial compressive stiffness of the aorta. GAG-depletion was also associated with a loss of water content and compressive deformation in the inner layers of the aortic wall providing insight into potential mechanisms for their biomechanical role.

Renal denervation restores biomechanics of carotid arteries in a rat model of hypertension

The prevalence of hypertension increases with aging and is associated with increased arterial stiffness. Resistant hypertension is presented when drug treatments fail to regulate a sustained increased blood pressure. Given that the mechanisms between the sympathetic nervous system and the kidney play an important role in blood regulation, renal denervation (RDN) has emerged as a therapeutic potential in resistant hypertension. In this study, we investigated the effects of RDN on the biomechanical response and microstructure of elastic arteries. Common carotid arteries (CCA) were excised from 3-, 8- and 8-month-old denervated rats, and subjected to biaxial extension-inflation test. Our results showed that hypertension developed in the 8-month-old rats. The sustained elevated blood pressure resulted in arterial remodeling which was manifested as a significant stress increase in both axial and circumferential directions after 8 months. RDN had a favorable impact on CCAs with a restoration of stresses in values similar to control arteries at 3 months. After biomechanical testing, arteries were imaged under a multi-photon microscope to identify microstructural changes in extracellular matrix (ECM). Quantification of multi-photon images showed no significant alterations of the main ECM components, elastic and collagen fibers, indicating that arteries remained intact after RDN. Regardless of the experimental group, our microstructural analysis of the multi-photon images revealed that reorientation of the collagen fibers might be the main microstructural mechanism taking place during pressurization with their straightening happening during axial stretching.

A novel constitutive model considering the role of elastic lamellae' structural heterogeneity in homogenizing transmural stress distribution in arteries

Understanding how the homeostatic stress state can be reached in arterial tissues can provide new insights into vascular physiology. Even though the function of maintaining homeostasis is often linked to the concentric layers of medial elastic lamellae, how the lamellae are capable of evenly distributing the stress transmurally remains to be understood. The recent microstructural study by Yu et al. (2018 J. R. Soc. Interface 15, 20180492) revealed that, circumferentially, lamellar layers closer to the lumen are wavier than the ones further away from it and, thus, experience more unfolding when subjected to blood pressure. Motivated by this peculiar finding, the current study, for the first time, proposes a novel approach to model elastic lamellae and such structural heterogeneity using the extensible worm-like chain model. When implemented into the material description of the conventional two-layer artery model, in which adventitial collagen is modelled using the inextensible worm-like chain model, it is demonstrated that structural heterogeneity in elastic lamellae plays an important role in dictating transmural stress distribution and, therefore, the homeostasis of the arterial wall.

New Computational Approach to Shunt Design in Congenital Heart Palliation

Shunts are commonly used to redirect blood to pulmonary arteries in procedures that palliate congenital cardiovascular defects. Previous clinical studies and hemodynamic simulations reveal a critical role of shunt diameter in balancing flow to pulmonary versus systemic vessels, but the biomechanical process of creating the requisite anastomosis between the shunt and host vessel has received little attention. Here, we report a new Lagrange multiplier-based finite element approach that represents the shunt and host vessels as individual structures and predicts the anastomosis geometry and attachment force that result when the shunt is sutured at an incision in the host, followed by pressurization. Simulations suggest that anastomosis orifice opening increases markedly with increasing length of the host incision and moderately with increasing blood pressure. The host artery is further predicted to conform to common stiff synthetic shunts, whereas more compliant umbilical vessel shunts should conform to the host, with orifice area transitioning between these two extremes via a Hill-type function of shunt stiffness. Moreover, a direct relationship is expected between attachment forces and shunt stiffness. This new computational approach promises to aid in surgical planning for diverse vascular shunts by predicting in vivo pressurized geometries.

Fitting mechanical properties of the aortic wall and individual layers to experimental tensile tests including residual stresses

The authors have observed that a stress-strain curve for uniaxial tension of an aortic intact wall cannot be simply obtained by combining the strain energy functions of the three individual aortic layers - intima, media and adventitia - even taking into account the interaction among the three layers; the strain energy functions of the three layers are obtained fitting tensile tests on strips from the individual layers. Due to the layer separation, the residual stresses are released and thus they do not affect the stress-strain curves of the individual layers. The present study shows that it is instead possible to fit the intact wall experimental curves with the combination of the strain energy functions of the three individual layers if residual strains are added. The residual strains are used as optimization parameters with specific constraints and allowing for the buckling (wrinkling) of the intima under unpressurized condition of the aortic wall, as experimentally observed. By varying these parameters in the experimentally observed range of values, it is possible to find a solution with the combined responses of the individual layers matching the experimental stress-strain curves of the intact wall.

Computational modelling of multi-temporal ventricular-vascular interactions during the progression of pulmonary arterial hypertension

A computational framework is developed to consider the concurrent growth and remodelling (G&R) processes occurring in the large pulmonary artery (PA) and right ventricle (RV), as well as ventricular-vascular interactions during the progression of pulmonary arterial hypertension (PAH). This computational framework couples the RV and the proximal PA in a closed-loop circulatory system that operates in a short timescale of a cardiac cycle, and evolves over a long timescale due to G&R processes in the PA and RV. The framework predicts changes in haemodynamics (e.g. 68.2% increase in mean PA pressure), RV geometry (e.g. 38% increase in RV end-diastolic volume) and PA tissue microstructure (e.g. 90% increase in collagen mass) that are consistent with clinical and experimental measurements of PAH. The framework also predicts that a reduction in RV contractility is associated with long-term RV chamber dilation, a common biomarker observed in the late-stage PAH. Sensitivity analyses on the G&R rate constants show that large PA stiffening (both short and long term) is affected by RV remodelling more than the reverse. This framework can serve as a foundation for the future development of a more predictive and comprehensive cardiovascular G&R model with realistic heart and vascular geometries.

Linking the region-specific tissue microstructure to the biaxial mechanical properties of the porcine left anterior descending artery

Coronary atherosclerosis is the main cause of death worldwide. Advancing the understanding of coronary microstructure-based mechanics is fundamental for the development of therapeutic tools and surgical procedures. Although the passive biaxial properties of the coronary arteries have been extensively explored, their regional differences and the relationship between tissue microstructure and mechanics have not been fully characterized. In this study, we characterized the passive biaxial mechanical properties and microstructural properties of the proximal, medial, and distal regions of the porcine left anterior descending artery (LADA). We also attempted to relate the biaxial stress-stretch response of the LADA and its respective birefringent responses to the polarized light for obtaining information about the load-dependent microstructural variations. We found that the LADA extensibility is reduced in the proximal-to-distal direction and that the medial region exhibits more heterogeneous mechanical behavior than the other two regions. We have also observed highly dynamic microstructural behavior where fiber families realign themselves depending on loading. In addition, we found that the microstructure of the distal region exhibited highly aligned fibers along the longitudinal axis of the artery. To verify this microstructural feature, we imaged the LADA specimens with multi-photon microscopy and observed that the adventitia microstructure transitioned from a random fiber network in the proximal region to highly aligned fibers in the distal region. Our findings could offer new perspectives for understanding coronary mechanics and aid in the development of tissue-engineered vascular grafts, which are currently limited due to their mismatch with native tissue in terms of mechanical properties and microstructural features. STATEMENT OF SIGNIFICANCE: The tissue biomechanics of coronary arteries is fundamental for the development of revascularization techniques such as coronary artery bypass. These therapeutics require a deep understanding of arterial mechanics, microstructure, and mechanobiology to prevent graft failure and reoperation. The present study characterizes the unique regional mechanical and microstructural properties of the porcine left anterior descending artery using biaxial testing, polarized-light imaging, and confocal microscopy. This comprehensive characterization provides an improved understanding of the collagen/elastin architecture in response to mechanical loads using a region-specific approach. The unique tissue properties obtained from this study will provide guidance for the selection of anastomotic sites in coronary artery bypass grafting and for the design of tissue-engineered vascular grafts.

Computational analysis of the role of mechanosensitive Notch signaling in arterial adaptation to hypertension

Arteries grow and remodel in response to mechanical stimuli. Hypertension, for example, results in arterial wall thickening. Cell-cell Notch signaling between vascular smooth muscle cells (VSMCs) is known to be involved in this process, but the underlying mechanisms are still unclear. Here, we investigated whether Notch mechanosensitivity to strain may regulate arterial thickening in hypertension. We developed a multiscale computational framework by coupling a finite element model of arterial mechanics, including residual stress, to an agent-based model of mechanosensitive Notch signaling, to predict VSMC phenotypes as an indicator of growth and remodeling. Our simulations revealed that the sensitivity of Notch to strain at mean blood pressure may be a key mediator of arterial thickening in hypertensive arteries. Further simulations showed that loss of residual stress can have synergistic effects with hypertension, and that changes in the expression of Notch receptors, but not Jagged ligands, may be used to control arterial growth and remodeling and to intensify or counteract hypertensive thickening. Overall, we identify Notch mechanosensitivity as a potential mediator of vascular adaptation, and we present a computational framework that can facilitate the testing of new therapeutic and regenerative strategies.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

The effects of viscoelasticity on residual strain in aortic soft tissues

Residual stress is thought to play a critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in the intact state. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art structural tensor model for arterial tissues from Holzapfel and Ogden for fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e. more elastically). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as the one illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues. STATEMENT OF SIGNIFICANCE: Residual stress plays a crucial role in achieving a homeostatic stress environment in soft biological tissues. However, the analysis of residual stress typically focuses on hyperelastic material models despite evidence of viscoelastic behavior. This work is the first attempt at analyzing the effects of viscoelasticity on residual stress. The application of viscoelasticity was crucial for producing realistic opening dynamics in arteries. The overall residual stresses were estimated to be 50% less than those from using hyperelastic material models, while the opening angles were projected to be 25% more than those measured after 16 hours, suggesting underestimated residual strain. This study highlights the importance viscoelasticity in the analysis of residual stress even in weakly dissipative materials like the human aorta.

Intramural Distributions of GAGs and Collagen vs. Opening Angle of the Intact Porcine Aortic Wall

The heterogeneity and contribution of collagen and elastin to residual stresses have been thoroughly studied, but more recently, glycosaminoglycans (GAGs) also emerged as potential regulators. In this study, the opening angle of aortic rings (an indicator of circumferential residual stresses) and the mural distributions of sulfated GAGs (sGAG), collagen, and elastin were quantified in the ascending, aortic arch and descending thoracic regions of 5- to 6-month-old pigs. The opening angle correlated positively with the aortic ring's mean radius and thickness, with good and moderate correlations respectively. The correlations between the sGAG, collagen, elastin, and collagen:sGAG ratio and the opening angle were evaluated to identify aortic compositional factors that could play roles in regulating circumferential residual stresses. The total collagen:sGAG ratio displayed the strongest correlation with the opening angle (r = - 0.715, p < 0.001), followed by the total sGAG content which demonstrated a good correlation (r = 0.623, p < 0.001). Additionally, the intramural gradients of collagen, sGAG and collagen:sGAG correlated moderately with the opening angle. We propose that, in addition to the individual role sGAG play through their content and intramural gradient, the interaction between collagen and sGAG should be considered when evaluating circumferential residual stresses in the aorta.

Progressive Microstructural Deterioration Dictates Evolving Biomechanical Dysfunction in the Marfan Aorta

Medial deterioration leading to thoracic aortic aneurysms arises from multiple causes, chief among them mutations to the gene that encodes fibrillin-1 and leads to Marfan syndrome. Fibrillin-1 microfibrils associate with elastin to form elastic fibers, which are essential structural, functional, and instructional components of the normal aortic wall. Compromised elastic fibers adversely impact overall structural integrity and alter smooth muscle cell phenotype. Despite significant progress in characterizing clinical, histopathological, and mechanical aspects of fibrillin-1 related aortopathies, a direct correlation between the progression of microstructural defects and the associated mechanical properties that dictate aortic functionality remains wanting. In this paper, age-matched wild-type, Fbn1 ^C1041G/+, and Fbn1 ^mgR/mgR mouse models were selected to represent three stages of increasing severity of the Marfan aortic phenotype. Ex vivo multiphoton imaging and biaxial mechanical testing of the ascending and descending thoracic aorta under physiological loading conditions demonstrated that elastic fiber defects, collagen fiber remodeling, and cell reorganization increase with increasing dilatation. Three-dimensional microstructural characterization further revealed radial patterns of medial degeneration that become more uniform with increasing dilatation while correlating strongly with increased circumferential material stiffness and decreased elastic energy storage, both of which comprise aortic functionality.

Considerations for analysis of endothelial shear stress and strain in FSI models of atherosclerosis

Atherosclerosis is a lipid driven chronic inflammatory disease that is characterized by the formation of plaques at predilection sites. These predilection sites (side branches, curved segments, and bifurcations) have often been associated with disturbed shear stress profiles. However, in addition to shear stress, endothelial cells also experience artery wall strain that could contribute to atherosclerosis progression. Herein, we describe a method to accurately obtain these shear stress and strain profiles. We developed a fluid-structure interaction (FSI) framework for modelling arteries within a commercially available package (Abaqus, version 6.14) that included known prestresses (circumferential, axial and pressure associated). In addition, we co-registered 3D histology to a micro-CT-derived 3D reconstruction of an atherosclerotic carotid artery from a cholesterol-fed ApoE^-/- mouse to include the spatial distribution of lipids within a subject-specific model. The FSI model also incorporated a nonlinear hyperelastic material model with regionally-varying properties that distinguished between healthy vessel wall and plaque. FSI predicted a lower shear stress than CFD (~-12%), but further decreases in plaque regions with softer properties (~-24%) were dependent on the approach used to implement the prestresses in the artery wall. When implemented with our new hybrid approach (zero prestresses in regions of lipid deposition), there was significant heterogeneity in endothelial shear stress in the atherosclerotic artery due to variations in stiffness and, in turn, wall strain. In conclusion, when obtaining endothelial shear stress and strain in diseased arteries, a careful consideration of prestresses is necessary. This paper offers a way to implement them.

A novel framework for quantifying the subject-specific three-dimensional residual stress field in the aortic wall

BACKGROUND

Quantification of subject-specific residual stress field remains a challenge that prohibits accurate stress analysis and refined understanding of the biomechanical behavior of the aortic wall.

METHOD

This study presents a framework combining experiments, constitutive modeling, and computer simulation to quantify the subject-specific three-dimensional residual stress field of the aortic wall. The material properties and residual deformations were acquired from the same porcine aortic sample, so that the subject-specific residual stress field was quantified analytically. Consequently, a novel stress-driven tissue growth model was developed and incorporated in a finite element aortic model to recover the subject-specific residual stress with the help of analytical solution. We then evaluated the framework's efficacy by simulating the residual stress distribution in the aortic dissection (AD).

RESULT

Subject-specific residual stress field of the aortic sample was quantified analytically. No appreciable discrepancy was observed between the numerically simulated and analytically derived residual stress distributions, indicating the effectiveness of the tissue growth model. Errors arising from the numerically simulated circumferential opening angle and axial bending angle were within 5% relative to experimental results, highlighting that the framework was accurate in terms of subject-specific residual stress estimation. Finally, numerical simulations recovered the buckling behavior of the intimal flap of the dissected aorta and revealed the expansion of the false lumen and compression of the true lumen as the tear propagates circumferentially.

CONCLUSION

The proposed framework is effective in quantifying the three-dimensional subject-specific residual stress field and it is potentially applicable in more sophisticated scenarios involving residual stress.

Mechano-regulated cell-cell signaling in the context of cardiovascular tissue engineering

Cardiovascular tissue engineering (CVTE) aims to create living tissues, with the ability to grow and remodel, as replacements for diseased blood vessels and heart valves. Despite promising results, the (long-term) functionality of these engineered tissues still needs improvement to reach broad clinical application. The functionality of native tissues is ensured by their specific mechanical properties directly arising from tissue organization. We therefore hypothesize that establishing a native-like tissue organization is vital to overcome the limitations of current CVTE approaches. To achieve this aim, a better understanding of the growth and remodeling (G&R) mechanisms of cardiovascular tissues is necessary. Cells are the main mediators of tissue G&R, and their behavior is strongly influenced by both mechanical stimuli and cell-cell signaling. An increasing number of signaling pathways has also been identified as mechanosensitive. As such, they may have a key underlying role in regulating the G&R of tissues in response to mechanical stimuli. A more detailed understanding of mechano-regulated cell-cell signaling may thus be crucial to advance CVTE, as it could inspire new methods to control tissue G&R and improve the organization and functionality of engineered tissues, thereby accelerating clinical translation. In this review, we discuss the organization and biomechanics of native cardiovascular tissues; recent CVTE studies emphasizing the obtained engineered tissue organization; and the interplay between mechanical stimuli, cell behavior, and cell-cell signaling. In addition, we review past contributions of computational models in understanding and predicting mechano-regulated tissue G&R and cell-cell signaling to highlight their potential role in future CVTE strategies.

Constrained Mixture Models of Soft Tissue Growth and Remodeling - Twenty Years After

Soft biological tissues compromise diverse cell types and extracellular matrix constituents, each of which can possess individual natural configurations, material properties, and rates of turnover. For this reason, mixture-based models of growth (changes in mass) and remodeling (change in microstructure) are well-suited for studying tissue adaptations, disease progression, and responses to injury or clinical intervention. Such approaches also can be used to design improved tissue engineered constructs to repair, replace, or regenerate tissues. Focusing on blood vessels as archetypes of soft tissues, this paper reviews a constrained mixture theory introduced twenty years ago and explores its usage since by contrasting simulations of diverse vascular conditions. The discussion is framed within the concept of mechanical homeostasis, with consideration of solid-fluid interactions, inflammation, and cell signaling highlighting both past accomplishments and future opportunities as we seek to understand better the evolving composition, geometry, and material behaviors of soft tissues under complex conditions.

The Contribution of Glycosaminoglycans/Proteoglycans to Aortic Mechanics in Health and Disease: A Critical Review

While elastin and collagen have received a lot of attention as major contributors to aortic biomechanics, glycosaminoglycans (GAGs) and proteoglycans (PGs) recently emerged as additional key players whose roles must be better elucidated if one hopes to predict aortic ruptures caused by aneurysms and dissections more reliably. GAGs are highly negatively charged polysaccharide molecules that exist in the extracellular matrix (ECM) of the arterial wall. In this critical review, we summarize the current understanding of the contributions of GAGs/PGs to the biomechanics of the normal aortic wall, as well as in the case of aortic diseases such as aneurysms and dissections. Specifically, we describe the fundamental swelling behavior of GAGs/PGs and discuss their contributions to residual stresses and aortic stiffness, thereby highlighting the importance of taking these polyanionic molecules into account in mathematical and numerical models of the aorta. We suggest specific lines of investigation to further the acquisition of experimental data to complement simulations and solidify our current understanding. We underscore different potential roles of GAGs/PGs in thoracic aortic aneurysm (TAAD) and abdominal aortic aneurysm (AAA). Namely, we report findings according to which the accumulation of GAGs/PGs in TAAD causes stress concentrations which may be sufficient to initiate and propagate delamination. On the other hand, there seems to be no clear indication of a relationship between the marked reduction in GAG/PG content and the stiffening and weakening of the aortic wall in AAA.

A Parametric Study on Factors Influencing the Onset and Propagation of Aortic Dissection Using the Extended Finite Element Method

OBJECTIVE

Aortic dissection is a life-threatening event which starts most of the time with an intimal tear propagating along the aortic wall, while blood enters the medial layer and delaminates the medial lamellar units. Studies investigating the mechanisms underlying the initiation sequence of aortic dissection are rare in the literature, the majority of studies being focused on the propagation event. Numerical models can provide a deeper understanding of the phenomena involved during the initiation and the propagation of the initial tear, and how geometrical and mechanical parameters affect this event. In the present paper, we investigated the primary factors contributing to aortic dissection.

METHODS

A two-layer arterial model with an initial tear was developed, representing three different possible configurations depending on the initial direction of the tear. Anisotropic damage initiation criteria were developed based on uniaxial and shear experiments from the literature to predict the onset and the direction of crack propagation. We used the XFEM-based cohesive segment method to model the initiation and the early propagation of the tear along the aorta. A design of experiment was used to quantify the influence of 7 parameters reflecting crack geometry and mechanics of the wall on the critical pressure triggering the dissection and the directions of propagation of the tear.

RESULTS

The results showed that the obtained critical pressures (mean range from 206 to 251 mmHg) are in line with measurement from the literature. The medial tensile strength was found to be the most influential factor, suggesting that a medial degeneration is needed to reach a physiological critical pressure and to propagate a tear in an aortic dissection. The geometry of the tear and its location inside the aortic wall were also found to have an important role not only in the triggering of tear propagation, but also in the evolution of the tear into either aortic rupture or aortic dissection. A larger and deeper initial tear increases the risk of aortic dissection.

CONCLUSION

The numerical model was able to reproduce the behaviour of the aorta during the initiation and propagation of an aortic dissection. In addition to confirm multiple results from the literature, different types of tears were compared and the influence of several geometrical and mechanical parameters on the critical pressure and direction of propagation was evaluated with a parametric study for each tear configuration.

SIGNIFICANCE

Although these results should be experimentally validated, they allow a better understanding of the phenomena behind aortic dissection and can help in improving the diagnosis and treatment of this disease.

Comparison of morphometric, structural, mechanical, and physiologic characteristics of human superficial femoral and popliteal arteries

Peripheral arterial disease differentially affects the superficial femoral (SFA) and the popliteal (PA) arteries, but their morphometric, structural, mechanical, and physiologic differences are poorly understood. SFAs and PAs from 125 human subjects (age 13-92, average 52±17 years) were compared in terms of radii, wall thickness, and opening angles. Structure and vascular disease were quantified using histology, mechanical properties were determined with planar biaxial extension, and constitutive modeling was used to calculate the physiologic stress-stretch state, elastic energy, and the circumferential physiologic stiffness. SFAs had larger radii than PAs, and both segments widened with age. Young SFAs were 5% thicker, but in old subjects the PAs were thicker. Circumferential (SFA: 96→193°, PA: 105→139°) and longitudinal (SFA: 139→306°, PA: 133→320°) opening angles increased with age in both segments. PAs were more diseased than SFAs and had 11% thicker intima. With age, intimal thickness increased 8.5-fold, but medial thickness remained unchanged (620μm) in both arteries. SFAs had 30% more elastin than the PAs, and its density decreased ~50% with age. SFAs were more compliant than PAs circumferentially, but there was no difference longitudinally. Physiologic circumferential stress and stiffness were 21% and 11% higher in the SFA than in the PA across all ages. The stored elastic energy decreased with age (SFA: 1.4→0.4kPa, PA: 2.5→0.3kPa). While the SFA and PA demonstrate appreciable differences, most of them are due to vascular disease. When pathology is the same, so are the mechanical properties, but not the physiologic characteristics that remain distinct due to geometrical differences.

An integrated set-up for ex vivo characterisation of biaxial murine artery biomechanics under pulsatile conditions

Ex vivo characterisation of arterial biomechanics enables detailed discrimination of the various cellular and extracellular contributions to arterial stiffness. However, ex vivo biomechanical studies are commonly performed under quasi-static conditions, whereas dynamic biomechanical behaviour (as relevant in vivo) may differ substantially. Hence, we aim to (1) develop an integrated set-up for quasi-static and dynamic biaxial biomechanical testing, (2) quantify set-up reproducibility, and (3) illustrate the differences in measured arterial stiffness between quasi-static and dynamic conditions. Twenty-two mouse carotid arteries were mounted between glass micropipettes and kept fully vasodilated. While recording pressure, axial force (F), and inner diameter, arteries were exposed to (1) quasi-static pressure inflation from 0 to 200 mmHg; (2) 300 bpm dynamic pressure inflation (peaking at 80/120/160 mmHg); and (3) axial stretch (λ_z) variation at constant pressures of 10/60/100/140/200 mmHg. Measurements were performed in duplicate. Single-point pulse wave velocities (PWV; Bramwell-Hill) and axial stiffness coefficients (c_ax = dF/dλ_z) were calculated at the in vivo value of λ_z. Within-subject coefficients of variation were ~ 20%. Dynamic PWVs were consistently higher than quasi-static PWVs (p < 0.001); c_ax increased with increasing pressure. We demonstrated the feasibility of ex vivo biomechanical characterisation of biaxially-loaded murine carotid arteries under pulsatile conditions, and quantified reproducibility allowing for well-powered future study design.

Analysis of the passive biomechanical behavior of a sheep-specific aortic artery in pulsatile flow conditions

In this work, a novel numerical-experimental procedure is proposed, through the use of the Cardiac Simulation Test (CST), device that allows the exposure of the arterial tissue to in-vitro conditions, mimicking cardiac cycles generated by the heart. The main goal is to describe mechanical response of the arterial wall under physiological conditions, when it is subjected to a variable pressure wave over time, which causes a stress state affecting the biomechanical behavior of the artery wall. In order to get information related to stress and strain states, numerical simulation via finite element method, is performed under a condition of systolic and diastolic pressure. The description of this methodological procedure is performed with a sample corresponding to a sheep aorta without cardiovascular pathologies. There are two major findings: the evaluation of the mechanical properties of the sheep aorta through the above-mentioned tests and, the numerical simulation of the mechanical response under the conditions present in the CST. The results state that differences between numerical and experimental circumferential stretch in diastole and systole to distinct zones studied do not exceed 1%. However, greater discrepancies can be seen in the distensibility and incremental modulus, two main indicators, which are in the order of 30%. In addition, numerical results determine an increase of the principal maximum stress and strain between the case of systolic and diastolic pressure, corresponding to 31.1% and 14.9% for the stress and strain measurement respectively; where maximum values of these variables are located in the zone of the ascending aorta and the aortic arch.

From Transcript to Tissue: Multiscale Modeling from Cell Signaling to Matrix Remodeling

Tissue-level biomechanical properties and function derive from underlying cell signaling, which regulates mass deposition, organization, and removal. Here, we couple two existing modeling frameworks to capture associated multiscale interactions-one for vessel-level growth and remodeling and one for cell-level signaling-and illustrate utility by simulating aortic remodeling. At the vessel level, we employ a constrained mixture model describing turnover of individual wall constituents (elastin, intramural cells, and collagen), which has proven useful in predicting diverse adaptations as well as disease progression using phenomenological constitutive relations. Nevertheless, we now seek an improved mechanistic understanding of these processes; we replace phenomenological relations in the mixture model with a logic-based signaling model, which yields a system of ordinary differential equations predicting changes in collagen synthesis, matrix metalloproteinases, and cell proliferation in response to altered intramural stress, wall shear stress, and exogenous angiotensin II. This coupled approach promises improved understanding of the role of cell signaling in achieving tissue homeostasis and allows us to model feedback between vessel mechanics and cell signaling. We verify our model predictions against data from the hypertensive murine infrarenal abdominal aorta as well as results from validated phenomenological models, and consider effects of noisy signaling and heterogeneous cell populations.

Assessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures From In Vivo DENSE Magnetic Resonance Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions

The establishment of in vivo, noninvasive patient-specific, and regionally resolved techniques to quantify aortic properties is key to improving clinical risk assessment and scientific understanding of vascular growth and remodeling. A promising and novel technique to reach this goal is an inverse finite element method (FEM) approach that utilizes magnetic resonance imaging (MRI)-derived displacement fields from displacement encoding with stimulated echoes (DENSE). Previous studies using DENSE MRI suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously during the cardiac cycle. We hypothesize that this heterogeneity is driven in healthy aortas by regional adventitial tethering and interaction with perivascular tissues, which can be modeled with elastic foundation boundary conditions (EFBCs) using a collection of radially oriented springs with varying stiffness with circumferential distribution. Nine healthy IAAs were modeled using previously acquired patient-specific imaging and displacement fields from steady-state free procession (SSFP) and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse FEM. In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived heterogeneous strain distribution. Estimated aortic wall properties were in reasonable agreement with previously reported experimental biaxial testing data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features, suggesting that EFBC could be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for clinical research and future incorporation into cardiovascular fluid-structure analyses.

Geometrically nonlinear modelling of pre-stressed viscoelastic fibre-reinforced composites with application to arteries

Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.

Transient swelling behavior of the bovine caudal disc

The intervertebral disc is an avascular composite structure, comprised of the nucleus pulposus (NP) and the annulus fibrosus (AF). Previous tissue-level experiments either examined relative differences in swelling capacity of the two disc regions at a single time point or tested explant structures that did not replicate in situ boundary conditions. Previous joint-level studies that investigated time-dependent fluid flow into the disc provided limited information about swelling-induced intradiscal strains with respect to time and boundary constraints. Therefore, the objective of this study was to investigate time-dependent swelling behavior of the intervertebral disc ex situ. The first study investigated time-dependent free-swelling response of the whole disc and the disc's subcomponents separately (i.e., NP and AF). Findings from this study showed that the swelling rate and swelling capacity of NP explants under free-swelling conditions were greater than AF explants. The second study evaluated the effect of boundary conditions on in-plane strain distributions of intact discs and AF rings. Swelling-induced strain was highly heterogeneous in AF rings, where negative circumferential strains were observed in the inner AF and tensile circumferential strains were observed in the outer AF. Radial strains in AF rings were an order of magnitude greater than circumferential strains. Restricting fluid flow only to the outer AF periphery reduced the swelling of the inner AF. Swelling of intact discs affected both NP and AF swelling behaviors, where NP hydration decreased by 60%. Furthermore, the presence of the NP reduced peak radial strains in the AF and resulted in uniform strain distribution throughout the AF. In conclusion, these studies highlight that tissue hydration and swelling-induced strains largely depend on regional biochemical composition and geometric boundary constraints.

Wrinkling instabilities for biologically relevant fiber-reinforced composite materials with a case study of Neo-Hookean/Ogden-Gasser-Holzapfel bilayer

Wrinkling is a ubiquitous surface phenomenon in many biological tissues and is believed to play an important role in arterial health. As arteries are highly nonlinear, anisotropic, multilayered composite systems, it is necessary to investigate wrinkling incorporating these material characteristics. Several studies have examined surface wrinkling mechanisms with nonlinear isotropic material relationships. Nevertheless, wrinkling associated with anisotropic constitutive models such as Ogden-Gasser-Holzapfel (OGH), which is suitable for soft biological tissues, and in particular arteries, still requires investigation. Here, the effects of OGH parameters such as fibers' orientation, stiffness, and dispersion on the onset of wrinkling, wrinkle wavelength and amplitude are elucidated through analysis of a bilayer system composed of a thin, stiff neo-Hookean membrane and a soft OGH substrate subjected to compression. Critical contractile strain at which wrinkles occur is predicted using both finite element analysis and analytical linear perturbation approach. Results suggest that besides stiffness mismatch, anisotropic features associated with fiber stiffness and distribution might be used in natural layered systems to adjust wrinkling and subsequent folding behaviors. Further analysis of a bilayer system with fibers in the (x-y) plane subjected to compression in the x direction shows a complex dependence of wrinkling strain and wavelength on fiber angle, stiffness, and dispersion. This behavior is captured by an approximation utilizing the linearized anisotropic properties derived from OGH model. Such understanding of wrinkling in this artery wall-like system will help identify the role of wrinkling mechanisms in biological artery in addition to the design of its synthetic counterparts.

Anisotropic residual stresses in arteries

The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7, 787-799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35, 530-545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries-intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12, 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13, 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.

Particle-based computational modelling of arterial disease

Accumulated glycosaminoglycans (GAGs) can sequester water and induce swelling within the intra-lamellar spaces of the medial layer of an artery. It is increasingly believed that stress concentrations caused by focal swelling can trigger the damage and delamination that is often seen in thoracic aortic disease. Here, we present computational simulations using an extended smoothed particle hydrodynamics approach to examine potential roles of pooled GAGs in initiating and propagating intra-lamellar delaminations. Using baseline models of the murine descending thoracic aorta, we first calculate stress distributions in a healthy vessel. Next, we examine increases in mechanical stress in regions surrounding GAG pools. The simulations show that smooth muscle activation can partially protect the wall from swelling-associated damage, consistent with experimental observations, but the wall can yet delaminate particularly in cases of smooth muscle dysfunction or absence. Moreover, pools of GAGs located at different but nearby locations can extend and coalesce, thus propagating a delamination. These findings, combined with a sensitivity study on the input parameters of the model, suggest that localized swelling can alter aortic mechanics in ways that eventually can cause catastrophic damage within the wall. There is, therefore, an increased need to consider roles of GAGs in aortic pathology.

Variation of Axial Residual Strains Along the Course and Circumference of Human Aorta Considering Age and Gender

Our understanding of aortic biomechanics is customarily limited by lack of information on the axial residual stretches of the vessel in both humans and experimental animals that would facilitate the identification of its actual zero-stress state. The aim of this study was thus to acquire hitherto unreported quantitative knowledge of axial opening angle and residual stretches in different segments and quadrants of the human aorta according to age and gender. Twenty-three aortas were harvested during autopsy from the aortic root to the iliac bifurcation and were divided into ≥12 segments and 4 quadrants. Morphometric measurements were taken in the excised/curled configuration of rectangular strips considered to be under zero-stress using image-analysis software to study the axial/circumferential variation of axial opening angle, internal/external residual stretch, and thickness of the aortic wall. The measured data demonstrated: (1) an axial opening angle peak at the arch branches, decreasing toward the ascending and to a near-constant value in the descending thoracic aorta, and increasing in the abdominal aorta; (2) the variation of residual stretches resembled that of opening angle, but axial differences in external residual stretch were more prominent; (3) wall thickness showed a progressive diminution along the vessel; (4) the highest opening angle/residual stretches were found in the inner quadrant and the lowest in the outer quadrant; (5) the anterior was the thinnest quadrant throughout the aorta; (6) age caused thickening but greatly reduced axial opening angle/residual stretches, without differences between males and females.

A computational model to predict cell traction-mediated prestretch in the mitral valve

Prestretch is observed in many soft biological tissues, directly influencing the mechanical behavior of the tissue in question. The development of this prestretch occurs through complex growth and remodeling phenomena, which yet remain to be elucidated. In the present study it was investigated whether local cell-mediated traction forces can explain the development of global anisotropic tissue prestretch in the mitral valve. Towards this end, a model predicting actin stress fiber-generated traction forces was implemented in a finite element framework of the mitral valve. The overall predicted magnitude of prestretch induced valvular contraction after release of in vivo boundary constraints was in good agreement with data reported on valvular retraction after excision from the heart. Next, by using a systematic variation of model parameters and structural properties, a more anisotropic prestretch development in the valve could be obtained, which was also similar to physiological values. In conclusion, this study shows that cell-generated traction forces could explain prestretch magnitude and anisotropy in the mitral valve.

Multi-sector approximation method for arteries: the residual stresses of circumferential rings with non-trivial openings

The opening angle method is a popular choice in biomechanics to estimate residual stresses in arteries. Experimentally, it means that an artery is cut into rings; then the rings are cut axially or radially allowing them to open into sectors; finally, the corresponding opening angles are measured to give residual stress levels by solving an inverse problem. However, for many tissues, for example in pathological tissues, the ring does not open according to the theory into a neat single circular sector, but rather creates an asymmetric geometry, often with abruptly changing curvature(s). This phenomenon may be due to a number of reasons including variation in thickness, microstructure, mechanical properties, etc. As a result, these samples are often eliminated from studies relying on the opening angle method, which limits progress in understanding and evaluating residual stresses in real arteries. With this work, we propose an effective approach to deal with these non-trivial openings of rings. First, we digitize pictures of opened rings to split them into multiple, connected circular sectors. Then we measure the corresponding opening angles for each sub-sector. Subsequently, we can determine the residual stresses for individual sectors in a closed-ring configuration and, thus, approximate the circumferential residual bending effects.

Mechanical stresses associated with flattening of human femoropopliteal artery specimens during planar biaxial testing and their effects on the calculated physiologic stress-stretch state

Planar biaxial testing is commonly used to characterize the mechanical properties of arteries, but stresses associated with specimen flattening during this test are unknown. We quantified flattening effects in human femoropopliteal arteries (FPAs) of different ages and determined how they affect the calculated arterial physiologic stress-stretch state. Human FPAs from 472 tissue donors (age 12-82 years, mean 53 ± 16 years) were tested using planar biaxial extension, and morphometric and mechanical characteristics were used to assess the flattening effects. Constitutive parameters for the invariant-based model were adjusted to account for specimen flattening and used to calculate the physiologic stresses, stretches, axial force, circumferential stiffness, and stored energy for the FPAs in seven age groups. Flattened specimens were overall 12 ± 4% stiffer longitudinally and 19 ± 11% stiffer circumferentially when biaxially tested. Differences between the stress-stretch curves adjusted and non-adjusted for the effects of flattening were relatively constant across all age groups longitudinally, but increased with age circumferentially. In all age groups, these differences were smaller than the intersubject variability. Physiologic stresses, stretches, axial force, circumferential stiffness, and stored energy were all qualitatively and quantitatively similar when calculated with and without the flattening effects. Stresses, stretches, axial force, and stored energy reduced with age, but circumferential stiffness remained relatively constant between 25 and 65 years of age suggesting a homeostatic target of 0.75 ± 0.02 MPa. Flattening effects associated with planar biaxial testing are smaller than the intersubject variability and have little influence on the calculated physiologic stress-stretch state of human FPAs.

Increased Cell Traction-Induced Prestress in Dynamically Cultured Microtissues

Prestress is a phenomenon present in many cardiovascular tissues and has profound implications on their in vivo functionality. For instance, the in vivo mechanical properties are altered by the presence of prestress, and prestress also influences tissue growth and remodeling processes. The development of tissue prestress typically originates from complex growth and remodeling phenomena which yet remain to be elucidated. One particularly interesting mechanism in which prestress develops is by active traction forces generated by cells embedded in the tissue by means of their actin stress fibers. In order to understand how these traction forces influence tissue prestress, many have used microfabricated, high-throughput, micrometer scale setups to culture microtissues which actively generate prestress to specially designed cantilevers. By measuring the displacement of these cantilevers, the prestress response to all kinds of perturbations can be monitored. In the present study, such a microfabricated tissue gauge platform was combined with the commercially available Flexcell system to facilitate dynamic cyclic stretching of microtissues. First, the setup was validated to quantify the dynamic microtissue stretch applied during the experiments. Next, the microtissues were subjected to a dynamic loading regime for 24 h. After this interval, the prestress increased to levels over twice as high compared to static controls. The prestress in these tissues was completely abated when a ROCK-inhibitor was added, showing that the development of this prestress can be completely attributed to the cell-generated traction forces. Finally, after switching the microtissues back to static loading conditions, or when removing the ROCK-inhibitor, prestress magnitudes were restored to original values. These findings show that intrinsic cell-generated prestress is a highly controlled parameter, where the actin stress fibers serve as a mechanostat to regulate this prestress. Since almost all cardiovascular tissues are exposed to a dynamic loading regime, these findings have important implications for the mechanical testing of these tissues, or when designing cardiovascular tissue engineering therapies.

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.

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

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

Evaluating residual strain throughout the murine female reproductive system

Mounting evidence suggests that cells within soft tissues seek to maintain a preferred biomechanical state. Residual stress is defined as the stress that remains in a tissue when all external loads are removed and contributes to tissue mechanohomeostasis by decreasing the transmural gradient of wall stress. Current computational models of pelvic floor mechanics, however, often do not consider residual stress. Residual strain, a result of residual stress can be quantitatively measured through opening angle experiments. Therefore, the objective of this study is to quantify the regional variations in opening angles along the murine female reproductive system at estrus and diestrus, to quantify residual strain in the maintenance state of sexually mature females. Further, evidence suggests that hydrophilic glycosaminoglycan/proteoglycans are integral to cervical remodeling. Thus, variations in opening angles following hypo-osmotic loading are evaluated. Opening angle experiments were performed along the murine reproductive system in estrus (n = 8) and diestrus (n = 8) and placed in hypo-osmotic solution. Measurements of thickness and volume were also obtained for each group. Differences (p < 0.05) in opening angle were observed with respect to region and loading, however, differences with respect to estrous stage were not significant. Thickness values were significant (p < 0.05) with respect to region only. The effects of both estrous cycle and region resulted in significant differences (p < 0.05) in observed volume. The observed regional differences indicate variation in the stress-free state among the reproductive system which may have implications for future computational models to advance women's reproductive health.

Comparative Analysis of Porcine and Human Thoracic Aortic Stiffness

OBJECTIVES

To compare porcine and human thoracic aortic stiffness using the available literature.

METHODS

The available literature was searched for studies reporting data on porcine or human thoracic aortic mechanical behaviour. A four fibre constitutive model was used to transform the data from included studies. Thus, equi-biaxial stress stretch curves were generated to calculate circumferential and longitudinal aortic stiffness. Analysis was performed separately for the ascending and descending thoracic aorta. Data on human aortic stiffness were divided by age <60 or ≥60 years. Porcine and human aortic stiffness were compared.

RESULTS

Eleven studies were included, six reported on young porcine aortas, four on human aortas of various ages, and one reported on both. In the ascending aorta, circumferential and longitudinal stiffness were 0.42±0.08 MPa and 0.37±0.06 MPa for porcine aortas (4-9 months) versus 0.55±0.15 MPa and 0.45±0.08 MPa for humans <60 years, and 1.02±0.59 MPa and 1.03±0.54 MPa for humans ≥60 years. In the descending aorta, circumferential and longitudinal stiffness were 0.46±0.03 MPa and 0.44±0.01 MPa for porcine aortas (4-10 months) versus 1.04±0.70 MPa and 1.24±0.76 MPa for humans <60 years, and 3.15±3.31 MPa and 1.17±0.31 MPa for humans ≥60 years.

CONCLUSIONS

The stiffness of young porcine aortic tissue shows good correspondence with human tissue aged <60 years, especially in the ascending aorta. Young porcine aortic tissue is less stiff than human aortic tissue aged ≥60 years.

Mechanical characterization of arteries affected by fetal growth restriction in guinea pigs (Cavia porcellus)

Fetal growth restriction (FGR) is a perinatal condition associated with a low birth weight that results mainly from maternal and placental constrains. Newborns affected by this condition are more likely to develop in the long term cardiovascular diseases whose origins would be in an altered vascular structure and function defined during fetal development. Thus, this study presents the modeling and numerical simulation of systemic vessels from guinea pig fetuses affected by FGR. We aimed to characterize the biomechanical properties of the arterial wall of FGR-derived the aorta, carotid, and femoral arteries by performing ring tensile and ring opening tests and, based on these data, to simulate the biomechanical behavior of FGR vessels under physiological conditions. The material parameters were first obtained from the experimental data of the ring tensile test. Then, the residual stresses were determined from the ring opening test and taken as initial stresses in the simulation of the ring tensile test. These two coupled steps are iteratively considered in a nonlinear least-squares algorithm to obtain the final material parameters. Then, the stress distribution changes along the arterial wall under physiological pressure were quantified using the adjusted material parameters. Overall, the obtained results provide a realistic approximation of the residual stresses and the changes in the mechanical behavior under physiological conditions.