Prefailure and failure mechanics of the porcine ascending thoracic aorta: experiments and a multiscale model

Mechanical Models of Collagen Networks for Understanding Changes in the Failure Properties of Aging Skin

Skin undergoes mechanical alterations due to changes in the composition and structure of the collagenous dermis with aging. Previous studies have conflicting findings, with both increased and decreased stiffness reported for aging skin. The underlying structure-function relationships that drive age-related changes are complex and difficult to study individually. One potential contributor to these variations is the accumulation of nonenzymatic crosslinks within collagen fibers, which affect dermal collagen remodeling and mechanical properties. Specifically, these crosslinks make individual fibers stiffer in their plastic loading region and lead to increased fragmentation of the collagenous network. To better understand the influence of these changes, we investigated the impact of nonenzymatic crosslink changes on the dermal microstructure using discrete fiber networks representative of the dermal microstructure. Our findings suggest that stiffening the plastic region of collagen's mechanical response has minimal effects on network-level stiffness and failure stresses. Conversely, simulating fragmentation through a loss of connectivity substantially reduces network stiffness and failure stress, while increasing stretch ratios at failure.

Beyond 2D: Novel biomaterial approaches for modeling the placenta

This review considers fully three-dimensional biomaterial environments of varying complexity as these pertain to research on the placenta. The developments in placental cell sources are first considered, along with the corresponding maternal cells with which the trophoblast interact. We consider biomaterial sources, including hybrid and composite biomaterials. Properties and characterization of biomaterials are discussed in the context of material design for specific placental applications. The development of increasingly complicated three-dimensional structures includes examples of advanced fabrication methods such as microfluidic device fabrication and 3D bioprinting, as utilized in a placenta context. The review finishes with a discussion of the potential for in vitro, three-dimensional placenta research to address health disparities and sexual dimorphism, especially in light of the exciting recent changes in the regulatory environment for in vitro devices.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain's white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.

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.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Multiscale simulations suggest a protective role of neo-adventitia in abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) are a dangerous cardiovascular disease, the pathogenesis of which is not yet fully understood. In the present work a recent mechanopathological theory, which correlates AAA progression with microstructural and mechanical alterations in the tissue, is investigated using multiscale models. The goal is to combine these changes, within the framework of mechanobiology, with possible mechanical cues that are sensed by vascular cells along the AAA pathogenesis. Particular attention is paid to the formation of a 'neo-adventitia' on the abluminal side of the aortic wall, which is characterized by a highly random (isotropic) distribution of collagen fibers. Macro- and micro-scale results suggest that the formation of an AAA, as expected, perturbs the micromechanical state of the aortic tissue and triggers a growth and remodeling (G&R) reaction by mechanosensing cells such as fibroblasts. This G&R then leads to the formation of a thick neo-adventitia that appears to bring the micromechanical state of the tissue closer to the original homeostatic level. In this context, this new layer could act like a protective sheath, similar to the tunica adventitia in healthy aortas. This potential 'attempt at healing' by vascular cells would have important implications on the stability of the AAA wall and thus on the risk of rupture. STATEMENT OF SIGNIFICANCE: Current clinical criteria for risk assessment in AAAs are still empirical, as the causes and mechanisms of the disease are not yet fully understood. The strength of the arterial tissue is closely related to its microstructure, which in turn is remodeled by mechanosensing cells in the course of the disease. In this study, multiscale simulations show a possible connection between mechanical cues at the microscopic level and collagen G&R in AAA tissue. It should be emphasized that these micromechanical cues cannot be visualized in vivo. Therefore, the results presented here will help to advance our current understanding of the disease and motivate future experimental studies, with important implications for AAA risk assessment.

Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading

Skin is a complex tissue whose biomechanical properties are generally understood in terms of an incompressible material whose microstructure undergoes affine deformations. A growing number of experiments, however, have demonstrated that skin has a high Poisson's ratio, substantially decreases in volume during uniaxial tensile loading, and demonstrates collagen fiber kinematics that are not affine with local deformation. In order to better understand the mechanical basis for these properties, we constructed multiscale mechanical models (MSM) of mouse skin based on microstructural multiphoton microscopy imaging of the dermal microstructure acquired during mechanical testing. Three models that spanned the cases of highly aligned, moderately aligned, and nearly random fiber networks were examined and compared to the data acquired from uniaxially stretched skin. Our results demonstrate that MSMs consisting of networks of matched fiber organization can predict the biomechanical behavior of mouse skin, including the large decrease in tissue volume and nonaffine fiber kinematics observed under uniaxial tension.

Differential propensity of dissection along the aorta

Aortic dissections progress, in part, by delamination of the wall. Previous experiments on cut-open segments of aorta demonstrated that fluid injected within the wall delaminates the aorta in two distinct modes: stepwise progressive tearing in the abdominal aorta and a more prevalent sudden mode of tearing in the thoracic aorta that can also manifest in other regions. A microstructural understanding that delineates these two modes of tearing has remained wanting. We implemented a phase-field finite-element model of the aortic wall, motivated in part by two-photon imaging, and found correlative relations for the maximum pressure prior to tearing as a function of local geometry and material properties. Specifically, the square of the pressure of tearing relates directly to both tissue stiffness and the critical energy of tearing and inversely to the square root of the torn area; this correlation explains the sudden mode of tearing and, with the microscopy, suggests a mechanism for progressive tearing. Microscopy also confirmed that thick interlamellar radial struts are more abundant in the abdominal region of the aorta, where progressive tearing was observed previously. The computational results suggest that structurally significant radial struts increase tearing pressure by two mechanisms: confining the fluid by acting as barriers to flow and increasing tissue stiffness by holding the adjacent lamellae together. Collectively, these two phase-field models provide new insights into the mechanical factors that can influence intramural delaminations that promote aortic dissection.

Review of Current Advances in the Mechanical Description and Quantification of Aortic Dissection Mechanisms

Aortic dissection is a life-threatening event associated with a very poor outcome. A number of complex phenomena are involved in the initiation and propagation of the disease. Advances in the comprehension of the mechanisms leading to dissection have been made these last decades, thanks to improvements in imaging and experimental techniques. However, the micro-mechanics involved in triggering such rupture events remains poorly described and understood. It constitutes the primary focus of the present review. Towards the goal of detailing the dissection phenomenon, different experimental and modeling methods were used to investigate aortic dissection, and to understand the underlying phenomena involved. In the last ten years, research has tended to focus on the influence of microstructure on initiation and propagation of the dissection, leading to a number of multiscale models being developed. This review brings together all these materials in an attempt to identify main advances and remaining questions.

Bio-chemo-mechanics of the thoracic aorta

The pathophysiology of thoracic aortic aneurysm and dissection is poorly understood, despite high mortality. An evidence review was conducted to examine the biomechanical, chemical and genetic factors involved in thoracic aortic pathology. The composition of connective tissue and smooth muscle cells can mediate important mechanical properties that allow the thoracic aorta to withstand and transmit pressures. Genetic syndromes can affect connective tissue and signalling proteins that interrupt smooth muscle function, leading to tissue failure. There are complex interplaying factors that maintain thoracic aortic function in health and are disrupted in disease, signifying an area for extensive research.

A Novel Anisotropic Failure Criterion With Dispersed Fiber Orientations for Aortic Tissues

Accurate failure criteria play a fundamental role in biomechanical analyses of aortic wall rupture and dissection. Experimental investigations have demonstrated a significant difference of aortic wall strengths in the circumferential and axial directions. Therefore, the isotropic von Mises stress and maximum principal stress, commonly used in computational analysis of the aortic wall, are inadequate for modeling of anisotropic failure properties. In this study, we propose a novel stress-based anisotropic failure criterion with dispersed fiber orientations. In the new failure criterion, the overall failure metric is computed by using angular integration (AI) of failure metrics in all directions. Affine rotations of fiber orientations due to finite deformation are taken into account in an anisotropic hyperelastic constitutive model. To examine fitting capability of the failure criterion, a set of off-axis uniaxial tension tests were performed on aortic tissues of four porcine individuals and 18 human ascending thoracic aortic aneurysm (ATAA) patients. The dispersed fiber failure criterion demonstrates a good fitting capability with the off-axis testing data. Under simulated biaxial stress conditions, the dispersed fiber failure criterion predicts a smaller failure envelope comparing to those predicted by the traditional anisotropic criteria without fiber dispersion, which highlights the potentially important role of fiber dispersion in the failure of the aortic wall. Our results suggest that the deformation-dependent fiber orientations need to be considered when wall strength determined from uniaxial tests are used for in vivo biomechanical analysis. More investigations are needed to determine biaxial failure properties of the aortic wall.

Experimental determination of the suture behavior of aortic tissue in comparison to 3D printed silicone modelling material

The imitation of biological tissue in a synthetic physical model can benefit many medical applications, e.g. pre surgical planning or education. For a quantitative validation of the model's mechanical behavior, standardized testing on both, the biological original and the artificial material, is necessary. In four parts, this study focuses on the biomechanical analysis of the impact of sutures for aortic modelling using 3D printed silicone. Testing methods are developed and executed on biological and synthetic samples. The first part is the determination of the pullout strength of a single stitch. The second part is the investigation of the reduction of the tensile strength and elongation of tensile bars due to stitching. Third, the tensile testing of biological and artificial vessels repaired with an anastomosis gives information about the transferability to real surgical applications. A qualitative feedback study with surgical experts concludes the evaluation. The study reveals that the pullout strength is independent from the fiber or notch direction, but that repaired aortic tensile bars show a dependency on the fiber direction of the tissue. Additionally, the circular seam of the anastomosis provides a more stable connection than multiple single stitches. For the artificial models, the mechanical behavior mainly depends on the mechanical properties of the base silicone, here represented by the Shore A hardness, rather than the manufacturing process. When compared to the biological original the most similar material varies depending on the mechanical property in focus.

Recent Advances in Biomechanical Characterization of Thoracic Aortic Aneurysms

Thoracic aortic aneurysm (TAA) is a focal enlargement of the thoracic aorta, but the etiology of this disease is not fully understood. Previous work suggests that various genetic syndromes, congenital defects such as bicuspid aortic valve, hypertension, and age are associated with TAA formation. Though occurrence of TAAs is rare, they can be life-threatening when dissection or rupture occurs. Prevention of these adverse events often requires surgical intervention through full aortic root replacement or implantation of endovascular stent grafts. Currently, aneurysm diameters and expansion rates are used to determine if intervention is warranted. Unfortunately, this approach oversimplifies the complex aortopathy. Improving treatment of TAAs will likely require an increased understanding of the biological and biomechanical factors contributing to the disease. Past studies have substantially contributed to our knowledge of TAAs using various ex vivo, in vivo, and computational methods to biomechanically characterize the thoracic aorta. However, any singular approach typically focuses on only material properties of the aortic wall, intra-aneurysmal hemodynamics, or in vivo vessel dynamics, neglecting combinatorial factors that influence aneurysm development and progression. In this review, we briefly summarize the current understanding of TAA causes, treatment, and progression, before discussing recent advances in biomechanical studies of TAAs and possible future directions. We identify the need for comprehensive approaches that combine multiple characterization methods to study the mechanisms contributing to focal weakening and rupture. We hope this summary and analysis will inspire future studies leading to improved prediction of thoracic aneurysm progression and rupture, improving patient diagnoses and outcomes.

Avalanches and power law behavior in aortic dissection propagation

Aortic dissection is a devastating cardiovascular disease known for its rapid propagation and high morbidity and mortality. The mechanisms underlying the propagation of aortic dissection are not well understood. Our study reports the discovery of avalanche-like failure of the aorta during dissection propagation that results from the local buildup of strain energy followed by a cascade failure of inhomogeneously distributed interlamellar collagen fibers. An innovative computational model was developed that successfully describes the failure mechanics of dissection propagation. Our study provides the first quantitative agreement between experiment and model prediction of the dissection propagation within the complex extracellular matrix (ECM). Our results may lead to the possibility of predicting such catastrophic events based on microscopic features of the ECM.

A patient-specific numerical modeling of the spontaneous coronary artery dissection in relation to atherosclerosis

The spontaneous coronary artery dissection (SCAD) is a clinical complication of angioplasty leading to an initiation of a tear/crack in the intima layer of the artery. The crack can propagate to the interface of the intima-media layer following by intramural hematoma. The relation between the SCAD and atherosclerosis is a controversial issue, as some studies stated no correlation between them while others showed that a crack can initiate in the intima but cannot propagate into the atrophied media layer. To investigate the relation between the intraluminal crack propagation in the atherosclerotic artery and SCAD, this study numerically investigated the initiation and propagation of a crack in the intraluminal and radial locations of the healthy and atherosclerotic human coronary arterial walls. The energy release rate, namely J-integral, is computed as a numerical derivative of the strain energy with respect to a crack extension using a user-defined virtual crack method (VCE) of extended finite element method (XFEM). Experimental measurements were carried out to calculate the elasto-plastic mechanical properties of the healthy and atherosclerotic human coronary arteries. The experimental data were then assigned to our own established patient-specific FE model of the coronary artery. Cracks were sketched in the intraluminal and radial locations of the arterial wall and allowed to propagate to the virtual interface of the intima-media to form a false lumen. The results revealed a higher stress at the crack tip of the healthy arterial wall compared to the atherosclerotic one. Lower crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were observed in the intraluminal crack of the atherosclerotic artery. J-integral of the atherosclerotic arterial wall was also found to be higher than the healthy one at the intraluminal crack. The results revealed that although a crack can initiate in the intraluminal of an atherosclerotic artery, it cannot propagate into the media layer due to a relatively higher rate of the strain energy release in the atherosclerotic arterial wall compared to the healthy one.

Computational modeling reveals the relationship between intrinsic failure properties and uniaxial biomechanical behavior of arterial tissue

Biomechanical failure of the artery wall can lead to rupture, a catastrophic event with a high rate of mortality. Thus, there is a pressing need to understand failure behavior of the arterial wall. Uniaxial testing remains the most common experimental technique to assess tissue failure properties. However, the relationship between intrinsic failure parameters of the tissue and measured uniaxial failure properties is not fully established. Furthermore, the effect of the experimental variables, such as specimen shape and boundary conditions, on the measured failure properties is not well understood. We developed a finite element model capable of recapitulating pre-failure and post-failure uniaxial biomechanical response of the arterial tissue specimen. Intrinsic stiffness, strength and fracture toughness of the vessel wall tissue were used as the input material parameters to the model. Two uniaxial testing protocols were considered: a conventional setup with a rectangular specimen held at the grips by cardboard inserts, and the other used a dogbone specimen with soft foam inserts at the grips. Our computational study indicated negligible differences in the peak stress and post-peak mechanical behavior between these two testing protocols. It was also found that the tissue experienced only modest localized failure until higher levels of applied stretch beyond the peak stress. A robust cohesive model was capable of modeling the post-peak biomechanical response, which was primarily governed by tissue fracture toughness. Our results suggest that the post-peak region, in conjunction with the peak stress, must be considered to evaluate the complete biomechanical failure behavior of the soft tissue.

Biomechanics of aortic wall failure with a focus on dissection and aneurysm: A review

Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. The maximum diameter criterion, typically used for aneurysm rupture risk estimations, has been challenged by more sophisticated biomechanically motivated models in the past. Although these models are very helpful for the clinicians in decision-making, they do not attempt to capture material failure. Following a short overview of the microstructure of the aorta, we analyze the failure mechanisms involved in the dissection and rupture by considering also traumatic rupture. We continue with a literature review of experimental studies relevant to quantify tissue strength. More specifically, we summarize more extensively uniaxial tensile, bulge inflation and peeling tests, and we also specify trouser, direct tension and in-plane shear tests. Finally we analyze biomechanically motivated models to predict rupture risk. Based on the findings of the reviewed studies and the rather large variations in tissue strength, we propose that an appropriate material failure criterion for aortic tissues should also reflect the microstructure in order to be effective. STATEMENT OF SIGNIFICANCE: Aortic dissections and aortic aneurysms are fatal events characterized by structural changes to the aortic wall. Despite the advances in medical, biomedical and biomechanical research, the mortality rates of aneurysms and dissections remain high. The present review article summarizes experimental studies that quantify the aortic wall strength and it discusses biomechanically motivated models to predict rupture risk. We identified contradictory observations and a large variation within and between data sets, which may be due to biological variations, different sample sizes, differences in experimental protocols, etc. Based on the findings of the reviewed literature and the rather large variations in tissue strength, it is proposed that an appropriate criterion for aortic failure should also reflect the microstructure.

Modeling lamellar disruption within the aortic wall using a particle-based approach

Aortic dissections associate with medial degeneration, thus suggesting a need to understand better the biophysical interactions between the cells and matrix that constitute the middle layer of the aortic wall. Here, we use a recently extended "Smoothed Particle Hydrodynamics" formulation to examine potential mechanisms of aortic delamination arising from smooth muscle cell (SMC) dysfunction or apoptosis, degradation of or damage to elastic fibers, and pooling of glycosaminoglycans (GAGs), with associated losses of medial collagen in the region of the GAGs. First, we develop a baseline multi-layered model for the healthy aorta that delineates medial elastic lamellae and intra-lamellar constituents. Next, we examine stress fields resulting from the disruption of individual elastic lamellae, lost SMC contractility, and GAG production within an intra-lamellar space, focusing on the radial transferal of loading rather than on stresses at the tip of the delaminated tissue. Results suggest that local disruptions of elastic lamellae transfer excessive loads to nearby intra-lamellar constituents, which increases cellular vulnerability to dysfunction or death. Similarly, lost SMC function and accumulations of GAGs increase mechanical stress on nearby elastic lamellae, thereby increasing the chance of disruption. Overall these results suggest a positive feedback loop between lamellar disruption and cellular dropout with GAG production and lost medial collagen that is more pronounced at higher distending pressures. Independent of the initiating event, this feedback loop can catastrophically propagate intramural delamination.

A computational multi-scale approach to investigate mechanically-induced changes in tricuspid valve anterior leaflet microstructure

The tricuspid valve is an atrioventricular valve that prevents blood backflow from the right ventricle into the right atrium during ventricular contractions. It is important to study mechanically induced microstructural alterations in the tricuspid valve leaflets, as this aids both in understanding valvular diseases and in the development of new engineered tissue replacements. The structure and composition of the extracellular matrix (ECM) fiber networks are closely tied to an overall biomechanical function of the tricuspid valve. In this study, we conducted experiments and implemented a multiscale modeling approach to predict ECM microstructural changes to tissue-level mechanical responses in a controlled loading environment. In particular, we characterized a sample of a porcine anterior leaflet at a macroscale using a biaxial mechanical testing method. We then generated a three-dimensional finite element model, to which computational representations of corresponding fiber networks were incorporated based on properties of the microstructural architecture obtained from small angle light scattering. Using five different biaxial boundary conditions, we performed iterative simulations to obtain model parameters with an overall R² value of 0.93. We observed that mechanical loading could markedly alter the underlying ECM architecture. For example, a relatively isotropic fiber network (with an anisotropy index value α of 28%) became noticeably more anisotropic (with an α of 40%) when it underwent mechanical loading. We also observed that the mechanical strain was distributed in a different manner at the ECM/fiber level as compared to the tissue level. The approach presented in this study has the potential to be implemented in pathophysiologically altered biomechanical and structural conditions and to bring insights into the mechanobiology of the tricuspid valve. STATEMENT OF SIGNIFICANCE: Quantifying abnormal cellar/ECM-level deformation of tricuspid valve leaflets subjected to a modified loading environment is of great importance, as it is believed to be linked to valvular remodeling responses. For example, developing surgical procedures or engineered tissue replacements that maintain/mimic ECM-level mechanical homeostasis could lead to more durable outcomes. To quantify leaflet deformation, we built a multiscale framework encompassing the contributions of disorganized ECM components and organized fibers, which can predict the behavior of the tricuspid valve leaflets under physiological loading conditions both at the tissue level and at the ECM level. In addition to future in-depth studies of tricuspid valve pathologies, our model can be used to characterize tissues in other valves of the heart.

Isotropic Failure Criteria Are Not Appropriate for Anisotropic Fibrous Biological Tissues

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

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.

A Uniaxial Testing Approach for Consistent Failure in Vascular Tissues

Although uniaxial tensile testing is commonly used to evaluate failure properties of vascular tissue, there is no established protocol for specimen shape or gripping method. Large percentages of specimens are reported to fail near the clamp and can potentially confound the studies, or, if discarded will result in sample waste. The objective of this study is to identify sample geometry and clamping conditions that can achieve consistent failure in the midregion of small arterial specimens, even for vessels from older individuals. Failure location was assessed in 17 dogbone specimens from human cerebral and sheep carotid arteries using soft inserts. For comparison with commonly used protocols, an additional 22 rectangular samples were tested using either sandpaper or foam tape inserts. Midsample failure was achieved in 94% of the dogbone specimens, while only 14% of the rectangular samples failed in the midregion, the other 86% failing close to the clamps. Additionally, we found midregion failure was more likely to be abrupt, caused by cracking or necking. In contrast, clamp failure was more likely to be gradual and included a delamination mode not seen in midregion failure. Hence, this work provides an approach that can be used to obtain consistent midspecimen failure, avoiding confounding clamp-related artifacts. Furthermore, with consistent midregion failure, studies can be designed to image the failure process in small vascular samples providing valuable quantitative information about changes to collagen and elastin structure during the failure process.

Structural modeling reveals microstructure-strength relationship for human ascending thoracic aorta

High lethality of aortic dissection necessitates accurate predictive metrics for dissection risk assessment. The not infrequent incidence of dissection at aortic diameters <5.5 cm, the current threshold guideline for surgical intervention (Nishimura et al., 2014), indicates an unmet need for improved evidence-based risk stratification metrics. Meeting this need requires a fundamental understanding of the structural mechanisms responsible for dissection evolution within the vessel wall. We present a structural model of the repeating lamellar structure of the aortic media comprised of elastic lamellae and collagen fiber networks, the primary load-bearing components of the vessel wall. This model was used to assess the role of these structural features in determining in-plane tissue strength, which governs dissection initiation from an intimal tear. Ascending aortic tissue specimens from three clinically-relevant patient populations were considered: non-aneurysmal aorta from patients with morphologically normal tricuspid aortic valve (CTRL), aneurysmal aorta from patients with tricuspid aortic valve (TAV), and aneurysmal aorta from patients with bicuspid aortic valve (BAV). Multiphoton imaging derived collagen fiber organization for each patient cohort was explicitly incorporated in our model. Model parameters were calibrated using experimentally-measured uniaxial tensile strength data in the circumferential direction for each cohort, while the model was validated by contrasting simulated tissue strength against experimentally-measured strength in the longitudinal direction. Orientation distribution, controlling the fraction of loaded collagen fibers at a given stretch, was identified as a key feature governing anisotropic tissue strength for all patient cohorts.

Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel-Gasser-Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

Failure of the Porcine Ascending Aorta: Multidirectional Experiments and a Unifying Microstructural Model

The ascending thoracic aorta is poorly understood mechanically, especially its risk of dissection. To make better predictions of dissection risk, more information about the multidimensional failure behavior of the tissue is needed, and this information must be incorporated into an appropriate theoretical/computational model. Toward the creation of such a model, uniaxial, equibiaxial, peel, and shear lap tests were performed on healthy porcine ascending aorta samples. Uniaxial and equibiaxial tests showed anisotropy with greater stiffness and strength in the circumferential direction. Shear lap tests showed catastrophic failure at shear stresses (150-200 kPa) much lower than uniaxial tests (750-2500 kPa), consistent with the low peel tension (∼60 mN/mm). A novel multiscale computational model, including both prefailure and failure mechanics of the aorta, was developed. The microstructural part of the model included contributions from a collagen-reinforced elastin sheet and interlamellar connections representing fibrillin and smooth muscle. Components were represented as nonlinear fibers that failed at a critical stretch. Multiscale simulations of the different experiments were performed, and the model, appropriately specified, agreed well with all experimental data, representing a uniquely complete structure-based description of aorta mechanics. In addition, our experiments and model demonstrate the very low strength of the aorta in radial shear, suggesting an important possible mechanism for aortic dissection.

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.

Crack Propagation and Its Shear Mechanisms in the Bovine Descending Aorta

Aortic dissection and rupture may involve circumferential shear stress in the circumferential-longitudinal plane. Inflation of bovine descending aortic ring specimens provides evidence of such shear from the non-uniform circumferential distortion of radial lines drawn on the circumferential-radial ring face. Delamination without tensile peeling induces cracks that propagate nearly circumferentially in the circumferential-longitudinal plane from the root of a radial cut representing rupture initiation in a ring. Translational shear deformation tests of small rectangular aortic wall blocks in the circumferential and longitudinal direction measure the consequences of such shear on substructures in the aortic wall, in particular the collagen fibers. The two directions of shear deformation produce no statistical difference in the shear stress response of the wall. Possibly, the interfiber connections between collagen fibers are put into tension by either translational shear deformation so that the stress measured reflects the tensile response of these connections. Wall rupture may involve failure of these connections; such failure is supported by the voids parallel to the collagen fibers observed in a histological study after translational shear. Further, interstitial fluid is redistributed by shear as evidenced by the measured weight loss of a set of specimens during the translational shear of blocks. Because the mass changes, mathematical modeling of aortic tissue in vitro as incompressible is an approximation. These observations suggest that no simple modification of classical rupture theories, whether based on energy functions, stress or strain, suffices to predict the rupture of hydrated soft biological tissue that has complex substructures.

Crack Propagation Versus Fiber Alignment in Collagen Gels: Experiments and Multiscale Simulation

It is well known that the organization of the fibers constituting a collagenous tissue can affect its failure behavior. Less clear is how that effect can be described computationally so as to predict the failure of a native or engineered tissue under the complex loading conditions that can occur in vivo. Toward the goal of a general predictive strategy, we applied our multiscale model of collagen gel mechanics to the failure of a double-notched gel under tension, comparing the results for aligned and isotropic samples. In both computational and laboratory experiments, we found that the aligned gels were more likely to fail by connecting the two notches than the isotropic gels. For example, when the initial notches were 30% of the sample width (normalized tip-to-edge distance = 0.7), the normalized tip-to-tip distance at which the transition occurred from between-notch failure to across-sample failure shifted from 0.6 to 1.0. When the model predictions for the type of failure event (between the two notches versus across the sample width) were compared to the experimental results, the two were found to be strongly covariant by Fisher's exact test (p < 0.05) for both the aligned and isotropic gels with no fitting parameters. Although the double-notch system is idealized, and the collagen gel system is simpler than a true tissue, it presents a simple model system for studying failure of anisotropic tissues in a controlled setting. The success of the computational model suggests that the multiscale approach, in which the structural complexity is incorporated via changes in the model networks rather than via changes to a constitutive equation, has the potential to predict tissue failure under a wide range of conditions.

Multimodal optical measurement in vitro of surface deformations and wall thickness of the pressurized aortic arch

Computational modeling of arterial mechanics continues to progress, even to the point of allowing the study of complex regions such as the aortic arch. Nevertheless, most prior studies assign homogeneous and isotropic material properties and constant wall thickness even when implementing patient-specific luminal geometries obtained from medical imaging. These assumptions are not due to computational limitations, but rather to the lack of spatially dense sets of experimental data that describe regional variations in mechanical properties and wall thickness in such complex arterial regions. In this work, we addressed technical challenges associated with in vitro measurement of overall geometry, full-field surface deformations, and regional wall thickness of the porcine aortic arch in its native anatomical configuration. Specifically, we combined two digital image correlation-based approaches, standard and panoramic, to track surface geometry and finite deformations during pressurization, with a 360-deg fringe projection system to contour the outer and inner geometry. The latter provided, for the first time, information on heterogeneous distributions of wall thickness of the arch and associated branches in the unloaded state. Results showed that mechanical responses vary significantly with orientation and location (e.g., less extensible in the circumferential direction and with increasing distance from the heart) and that the arch exhibits a nearly linear increase in pressure-induced strain up to 40%, consistent with other findings on proximal porcine aortas. Thickness measurements revealed strong regional differences, thus emphasizing the need to include nonuniform thicknesses in theoretical and computational studies of complex arterial geometries.

Bio-Chemo-Mechanical Models of Vascular Mechanics

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