Layer-specific damage experiments and modeling of human thoracic and abdominal aortas with non-atherosclerotic intimal thickening

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Growth and remodeling of the dissected membrane in an idealized dissected aorta model

While transitioning from the acute to chronic phase, the wall of a dissected aorta often expands in diameter and adaptations in thickness and microstructure take place in the dissected membrane. Including the mechanisms, leading to these changes, in a computational model is expected to improve the accuracy of predictions of the long-term complications and optimal treatment timing of dissection patients. An idealized dissected wall was modeled to represent the elastin and collagen production and/or degradation imposed by stress- and inflammation-mediated growth and remodeling, using the homogenized constrained mixture theory. As no optimal growth and remodeling parameters have been defined for aortic dissections, a Latin hypercube sampling with 1000 parameter combinations was assessed for four inflammation patterns, with a varying spatial extent (full/local) and temporal evolution (permanent/transient). The dissected membrane thickening and microstructure was considered together with the diameter expansion over a period of 90 days. The highest success rate was found for the transient inflammation patterns, with about 15% of the samples leading to converged solutions after 90 days. Clinically observed thickening rates were found for 2-4% of the transient inflammation samples, which represented median total diameter expansion rates of about 5 mm/year. The dissected membrane microstructure showed an elastin decrease and, in most cases, a collagen increase. In conclusion, the model with the transient inflammation pattern allowed the reproduction of clinically observed dissected membrane thickening rates, diameter expansion rates and adaptations in microstructure, thus providing guidance in reducing the parameter space in growth and remodeling models of aortic dissections.

Nonlocal damage evaluation of a sigmoid-based damage model for fibrous biological soft tissues

The comprehension and modeling of the mechanical behavior of soft biological tissues are essential due to their clinical applications. This knowledge is essential for predicting tissue responses accurately and enhancing our ability to compute the behavior of biological structures and bio-prosthetic devices under specific loading conditions. The current research is centered on modeling the initiation and progression of soft tissues damage, which typically exhibit intricate anisotropic and nonlinear elastic characteristics. For this purpose, the following study presents a comparative analysis of the computational performance of two distinct damage modeling techniques. The first technique employs a well-established damage model, based on a piece-wise exponential damage function as proposed by Calvo et al. (Int J Numer Methods Eng 69:2036-2057, 2007. https://doi.org/10.1002/nme.1825 ). The second approach adopts a sigmoid function, as proposed by López-Campos et al. (Comput Methods Biomech Biomed Eng 23(6):213-223. https://doi.org/10.1080/10255842.2019.1710742 ). The aim of this study is to verify the validity of the López-Campos sigmoid-based damage model to be used in finite element simulation, the implementation of which is unknown. For this proposal, both models were implemented within a commercial Finite Element software package, and their responses to local and non-local damage algorithms were assessed in depth through two standard benchmark tests: a plate with a hole and a ball burst. The results of this study indicate that, for a wide range of cases, such as in-plane stresses, out-plane stresses, stress concentration and contact, all over large displacement conditions, the López-Campos damage model shows a good response to non-local algorithms achieving mesh independence and convergence in all these cases. The results obtained are in line with those obtained for the Calvo's damage model, showing, in addition, larger deformations under in-plane stress and stress concentration conditions and a lower number of iterations under out-plane stress and contact conditions. Consequently, the López-Campos' damage model emerges as a valuable and useful tool in the field of mechanical damage research in biological systems.

Uncertainty quantification of the wall thickness and stiffness in an idealized dissected aorta

Personalized treatment informed by computational models has the potential to markedly improve the outcome for patients with a type B aortic dissection. However, existing computational models of dissected walls significantly simplify the characteristic false lumen, tears and/or material behavior. Moreover, the patient-specific wall thickness and stiffness cannot be accurately captured non-invasively in clinical practice, which inevitably leads to assumptions in these wall models. It is important to evaluate the impact of the corresponding uncertainty on the predicted wall deformations and stress, which are both key outcome indicators for treatment optimization. Therefore, a physiology-inspired finite element framework was proposed to model the wall deformation and stress of a type B aortic dissection at diastolic and systolic pressure. Based on this framework, 300 finite element analyses, sampled with a Latin hypercube, were performed to assess the global uncertainty, introduced by 4 uncertain wall thickness and stiffness input parameters, on 4 displacement and stress output parameters. The specific impact of each input parameter was estimated using Gaussian process regression, as surrogate model of the finite element framework, and a δ moment-independent analysis. The global uncertainty analysis indicated minor differences between the uncertainty at diastolic and systolic pressure. For all output parameters, the 4th quartile contained the major fraction of the uncertainty. The parameter-specific uncertainty analysis elucidated that the material stiffness and relative thickness of the dissected membrane were the respective main determinants of the wall deformation and stress. The uncertainty analysis provides insight into the effect of uncertain wall thickness and stiffness parameters on the predicted deformation and stress. Moreover, it emphasizes the need for probabilistic rather than deterministic predictions for clinical decision making in aortic dissections.

Layer-Specific Properties of the Human Infra-Renal Aorta During Aging Considering Pre/Post-Failure Damage

There is little information on the layer-specific failure properties of the adult human abdominal aorta, and there has been no quantification of postfailure damage. Infra-renal aortas were thus taken from forty-seven autopsy subjects and cut into 870 intact-wall and layer strips that underwent uni-axial-tensile testing. Intact-wall failure stress did not differ significantly (p > 0.05) from the medial value longitudinally, nor from the intimal and medial values circumferentially, which were the lowest recorded values. Intact-wall failure stretch did not differ (p > 0.05) from the medial value in either direction. Intact-wall prefailure stretch (defined as failure stretch-stretch at the initiation of the concave phase of the stress-stretch response) did not differ (p > 0.05) from the intimal and medial values, and intact-wall postfailure stretch (viz., full-rupture stretch-failure stretch) did not differ (p > 0.05) from the adventitial value since the adventitia was the last layer to rupture, being most extensible albeit under residual tension. Intact-wall failure stress and stretch declined from 20 to 60 years, explained by steady declines throughout the lifetime of their medial counterparts, implicating beyond 60 years the less age-varying failure properties of the intima under minimal residual compression. The positive correlation of postfailure stretch with age counteracted the declining failure stretch, serving as a compensatory mechanism against rupture. Hypertension, diabetes, and coronary artery disease adversely affected the intact-wall and layer-specific failure stretches while increasing stiffness.

Sensitivity analysis of the mechanical properties on atherosclerotic arteries rupture risk with an artificial neural network method

Considering the differences between individuals, in this paper, an uncertainty analysis model for predicting rupture risk of atherosclerotic arteries is established based on a back-propagation artificial neural network. The influence of isotropy and anisotropy on the rupture risk of atherosclerotic arteries is analyzed, and the results demonstrate the effectiveness of the artificial neural network in predicting the rupture risk. Moreover, the rupture risk of atherosclerotic arteries at different inflation sizes are simulated. This study contributes to a better understanding of the underlying mechanisms of atherosclerotic arteries rupture and promotes the advancement of artificial neural networks in atherosclerosis research.

Active and passive mechanical characterization of a human descending thoracic aorta with Klippel-Trenaunay syndrome

A human aorta from a female donor affected by Klippel-Trenaunay syndrome was retrieved during a surgery for organ donation for transplant. The aorta was preserved in refrigerated Belzer UW organ preservation solution and tested within a few hours for mechanical characterization with and without vascular smooth muscle activation. KCl and Noradrenaline were used as vasoactive agents in bubbled Krebs-Henseleit buffer solution at 37 °C. A quasi-static and a dynamic mechanical characterization of the full wall and the three individual layers were carried out for strips taken in longitudinal and circumferential directions. The full wall in the descending portion of the aorta underwent mechanical tests with and without smooth muscle activation. Results were compared to data obtained from healthy aortas and show a reduced stiffness of the full wall in circumferential direction. Also, a significant reduction of the response to vasoactive agents in circumferential direction was observed, while the longitudinal response was similar to healthy cases.

Pharmacological modulation of vascular ageing: A review from VascAgeNet

Vascular ageing, characterized by structural and functional changes in blood vessels of which arterial stiffness and endothelial dysfunction are key components, is associated with increased risk of cardiovascular and other age-related diseases. As the global population continues to age, understanding the underlying mechanisms and developing effective therapeutic interventions to mitigate vascular ageing becomes crucial for improving cardiovascular health outcomes. Therefore, this review provides an overview of the current knowledge on pharmacological modulation of vascular ageing, highlighting key strategies and promising therapeutic targets. Several molecular pathways have been identified as central players in vascular ageing, including oxidative stress and inflammation, the renin-angiotensin-aldosterone system, cellular senescence, macroautophagy, extracellular matrix remodelling, calcification, and gasotransmitter-related signalling. Pharmacological and dietary interventions targeting these pathways have shown potential in ameliorating age-related vascular changes. Nevertheless, the development and application of drugs targeting vascular ageing is complicated by various inherent challenges and limitations, such as certain preclinical methodological considerations, interactions with exercise training and sex/gender-related differences, which should be taken into account. Overall, pharmacological modulation of endothelial dysfunction and arterial stiffness as hallmarks of vascular ageing, holds great promise for improving cardiovascular health in the ageing population. Nonetheless, further research is needed to fully elucidate the underlying mechanisms and optimize the efficacy and safety of these interventions for clinical translation.

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.

Layer-Specific Tensile Strength of the Human Aorta: Segmental Variations

Knowledge of the failure properties of the aorta is essential to understand the mechanisms of dissection and rupture. Limited information is, however, available in humans or experimental animals about the layer-specific properties and their segmental variations have not been determined. In this paper, the failure properties of the intima, media, and adventitia were studied in nine consecutive aortic segments and two principal directions. Detailed biomechanical tests were performed with a tensile-testing device on 756 layer strips, harvested from fourteen cadaveric subjects aged 21-82 years. Intimal and medial strength in either direction remained invariant along the aorta, and their extensibility longitudinally decreased, whereas adventitial strength and extensibility longitudinally increased, explaining why the preferential sites for the development of aortic dissection or traumatic rupture are in the proximal aorta. The media was stronger circumferentially than longitudinally in all segments, accounting for the typically transverse tearing in dissection/rupture. The adventitial properties were significantly higher than the intimal and medial in most segments. Still, the intima had similar strength but lower extensibility compared to the media in both directions, and higher maximum stiffness longitudinally in several segments. The rupture surface of all layers was not perpendicular to the loading axis, more so in the circumferential strips compared to longitudinal ones. Aging impaired the extensibility and strength of all layers, particularly the media, but did not affect the maximum stiffness and rupture-surface direction. Females were rarely associated with different failure properties compared to age-matched males.

Strain-induced collagen denaturation is rate dependent in failure of cerebral arteries

While soft tissues are commonly damaged by mechanical loading, the manifestation of this damage at the microstructural level is not fully understood. Specifically, while rate-induced stiffening has been previously observed in cerebral arteries, associated changes in microstructural damage patterns following high-rate loading are largely undefined. In this study, we stretched porcine middle cerebral arteries to failure at 0.01 and >150 s^-1, both axially and circumferentially, followed by probing for denatured tropocollagen using collagen hybridizing peptide (CHP). We found that collagen fibrils aligned with the loading direction experienced less denaturation following failure tests at high than low rates. Others have demonstrated similar rate dependence in tropocollagen denaturation during soft tissue failure, but this is the first study to quantify this behavior using CHP and to report it for cerebral arteries. These findings may have significant implications for traumatic brain injury and intracranial balloon angioplasty. We additionally observed possible tropocollagen denaturation in vessel layers primarily composed of fibrils transversely aligned to the loading axis. To our knowledge, this is the first observation of collagen denaturation due to transverse loading, but further research is needed to confirm this finding. STATEMENT OF SIGNIFICANCE: Previous work shows that collagen hybridizing peptide (CHP) can be used to identify collagen molecule unfolding and denaturation in mechanically overloaded soft tissues, including the cerebral arteries. But experiments have not explored collagen damage at rates relevant to traumatic brain injury. In this work, we quantified collagen damage in cerebral arteries stretched to failure at both high and low rates. We found that the collagen molecule is less damaged at high than at low rates, suggesting that damage mechanisms of either the collagen molecule or other elements of the collagen superstructure are rate dependent. This work implies that arteries failed at high rates, such as in traumatic brain injury, will have different molecular-level damage patterns than arteries failed at low rates. Consequently, improved understanding of damage characteristics may be expanded in the future to better inform clinically relevant cases of collagen damage such as angioplasty and injury healing.

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

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

Effect of aging on the biaxial mechanical behavior of human descending thoracic aorta: Experiments and constitutive modeling considering collagen crosslinking

Collagen crosslinking, an important contributor to the stiffness of soft tissues, was found to increase with aging in the aortic wall. Here we investigated the mechanical properties of human descending thoracic aorta with aging and the role of collagen crosslinking through a combined experimental and modeling approach. A total of 32 samples from 17 donors were collected and divided into three age groups: <40, 40-60 and > 60 years. Planar biaxial tensile tests were performed to characterize the anisotropic mechanical behavior of the aortic samples. A recently developed constitutive model incorporating collagen crosslinking into the two-fiber family model (Holzapfel and Ogden, 2020) was modified to accommodate biaxial deformation of the aorta, in which the extension and rotation kinematics of bonded fibers and crosslinks were decoupled. The mechanical testing results show that the aorta stiffens with aging with a more drastic change in the longitudinal direction, which results in altered aortic anisotropy. Our results demonstrate a good fitting capability of the constitutive model considering crosslinking for the biaxial aortic mechanics of all age groups. Furthermore, constitutive modeling results suggest an increased contribution of crosslinking and strain energy density to the biaxial stress-stretch behaviors with aging and point to excessive crosslinking as a prominent contributor to aortic stiffening.

Tri-layered constitutive modelling unveils functional differences between the pig ascending and lower thoracic aorta

The arterial wall's tri-layered macroscopic and layer-specific microscopic structure determine its mechanical properties, which vary at different arterial locations. Combining layer-specific mechanical data and tri-layered modelling, this study aimed to characterise functional differences between the pig ascending (AA) and lower thoracic aorta (LTA). AA and LTA segments were obtained for n=9 pigs. For each location, circumferentially and axially oriented intact wall and isolated layer strips were tested uniaxially and the layer-specific mechanical response modelled using a hyperelastic strain energy function. Then, layer-specific constitutive relations and intact wall mechanical data were combined to develop a tri-layered model of an AA and LTA cylindrical vessel, accounting for the layer-specific residual stresses. AA and LTA behaviours were then characterised for in vivo pressure ranges while stretched axially to in vivo length. The media dominated the AA response, bearing>2/3 of the circumferential load both at physiological (100 mmHg) and hypertensive pressures (160 mmHg). The LTA media bore most of the circumferential load at physiological pressure only (57±7% at 100 mmHg), while adventitia and media load bearings were comparable at 160 mmHg. Furthermore, increased axial elongation affected the media/adventitia load-bearing only at the LTA. The pig AA and LTA presented strong functional differences, likely reflecting their different roles in the circulation. The media-dominated compliant and anisotropic AA stores large amounts of elastic energy in response to both circumferential and axial deformations, which maximises diastolic recoiling function. This function is reduced at the LTA, where the adventitia shields the artery against supra-physiological circumferential and axial loads.

Location specific multi-scale characterization and constitutive modeling of pig aorta

The mechanical and structural behavior of the aorta depend on physiological functions and vary from proximal to distal. Understanding the relation between regionally varying mechanical and multi-scale structural response of aorta can be helpful to assess the disease outcomes. Therefore, this study investigated the variation in mechanical and multi-scale structural properties among the major segments of aorta such as ascending aorta (AA), descending aorta (DA) and abdominal aorta (ABA), and established a relation between mechanical and multi-structural parameters. The obtained results showed significant increase in anisotropy and nonlinearity from proximal to distal aorta. The change in periphery length and radii between load and stress free configuration was also found increasing far from the heart. Opening angle was significantly large for ABA than AA and DA (AA/DA vs ABA; p = 0.001). Mean circumferential residual stretch (ratio of mean periphery length at load and stress free configurations) was found decreasing between AA and DA, and then increasing between DA to ABA and its value was significantly more for ABA (AA vs DA; p = 0.041, AA vs ABA; p = 0.001, DA vs ABA; p = 0.001). The waviness of collagen fibers, collagen fiber content, collagen fibril diameter and total protein content were found significantly increasing from proximal to distal. Pearson correlation test showed a significant linear correlation between variation in mechanical and multi-scale structural parameters over the aortic length. Residual stretch was found positively correlated with collagen fiber content (r = 0.82) whereas opening angel was found positively correlated with total protein content (TPC) (r = 0.76).

Pulse wave velocity: A clinical measure to aid material parameter estimation in computational arterial biomechanics

Determining proper material parameters from clinical data remains a large, though unavoidable, challenge in patient-specific computational cardiovascular modeling. In an attempt to couple the clinical and modelling practice, this study investigated whether pulse wave velocity (PWV), a clinical arterial stiffness measure, can guide in determining appropriate parameter values for the Gasser-Ogden-Holzapfel (GOH) constitutive model. The reduction and uncertainty analysis was demonstrated on a cylindrical descending thoracic aorta model. Starting from discretized ranges of GOH parameters and using a full factorial design, the parameter sets yielding a physiological PWV (3.5-12.5 m/s) at diastolic pressure (80 mmHg; PWV₈₀) were selected and their PWV at dicrotic notch pressure (110 mmHg; PWV₁₁₀) was determined. These PWV measures were applied to determine the reduction of the 7D GOH parameter space, the 2D subspaces and the remaining uncertainty in case only PWV₈₀ or both measurements are available. The resulting 12,032 parameter sets lead to a 7D parameter space reduction of ≥ 82.5 % using PWV₈₀, which increased to 96.0 % when including PWV₁₁₀, in particular at 3.5-8.5 m/s. A similar trend was observed for the remaining uncertainty and the 2D subspaces comprised of medial collagen fiber parameters, while scarce reductions were found for the adventitial and elastin parameters. In conclusion, PWV₈₀ and PWV₁₁₀ are complementary measures with the potential to reduce the GOH parameter space in arterial models, in particular for media- and collagen-related parameters. Moreover, this approach has the advantage that it allows the estimation of the remaining uncertainty after parameter space reduction.

Effect of balloon pre-dilation on performance of self-expandable nitinol stent in femoropopliteal artery

Balloon pre-dilation is usually performed before implantation of a nitinol stent in a femoropopliteal artery in a case of severe blockage or calcified plaque. However, its effect on performance of the nitinol stent in a diseased femoropopliteal artery has not been studied yet. This study compares the outcomes of stenting with pre-dilation and without it by modelling the entire processes of stent deployment. Fatigue deformation of the implanted stent is also modelled under diastolic-systolic blood pressure, repetitive bending, torsion, axial compression and their combination. Reduced level of stress in the stent occurs after stenting with pre-dilation, but causing the increased damage in the media layer, i.e. the middle layer of the arterial wall. Generally, pre-dilation increases the risk of nitinol stent's fatigue failure. Additionally, the development of in-stent restenosis is predicted based on the stenting-induced tissue damage in the media layer, and no severe mechanical irritation is induced to the media layer by pre-dilation, stent deployment or fatigue loading.

Hyperelastic and damage properties of the hypoxic aorta treated with Cinaciguat

Chronic hypoxia during gestation and postnatal period induces pulmonary hypertension, aorta stiffening and vascular remodeling. In this study, we hypothesized that a postnatal treatment with Cinaciguat, a guanylate cyclase activator, may improve the vascular function by enhancing NO-sGC pathways that induce vasodilation. To assess this, we collected aortas from six lambs gestated, born and raised at 3600 masl. Half of these lambs received a Cinaciguat postnatal treatment, while the other half was used as control (vehicle). Uniaxial tension was applied on samples of each group of aortas (control and Cinaciguat-treated) through cyclic loading. The obtained stress-stretch curves were used to identify constitutive parameters of a hyperelastic damage model. These material constants allowed us to assess the softening/dissipation behavior and to characterize the treatment effects. Results showed that Cinaciguat has an effect on the damage behavior at large strains, altering the damage onset under uniaxial tension. We conclude that Cinaciguat, as a vasodilator, can prevent the very early effects of vascular remodeling caused by perinatal hypoxia, and improve the aortic-tissue damage properties of hypoxic lambs.

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.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed mucosa–submucosa layer under large deformation

Mechanical characterisation of the layer-specific, viscoelastic properties of the human oesophagus is crucial in furthering the development of devices emerging in the field, such as robotic endoscopic biopsy devices, as well as in enhancing the realism, and therefore effectiveness, of surgical simulations. In this study, the viscoelastic and stress-softening behaviour of the passive human oesophagus was investigated through ex vivo cyclic mechanical tests. Due to restrictions placed on the laboratory as a result of COVID-19, only oesophagi from cadavers fixed in formalin were allowed for testing. Three oesophagi in total were separated into their two main layers and the mucosa–submucosa layer was investigated. A series of uniaxial tensile tests were conducted in the form of increasing stretch level cyclic tests at two different strain rates: 1% s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1 and 10% s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document}-1. Rectangular samples in both the longitudinal and circumferential directions were tested to observe any anisotropy. Histological analysis was also performed through a variety of staining methods. Overall, the longitudinal direction was found to be much stiffer than the circumferential direction. Stress-softening was observed in both directions, as well as permanent set and hysteresis. Strain rate-dependent behaviour was also apparent in the two directions, with an increase in strain rate resulting in an increase in stiffness. This strain rate dependency was more pronounced in the longitudinal direction than the circumferential direction. Finally, the results were discussed in regard to the histological content of the layer, and the behaviour was modelled and validated using a visco-hyperelastic matrix-fibre model.

Probing the Mechanical Properties of Large Arteries by Measuring Their Deformation In Vivo with Ultrasound

Aging and cardiovascular diseases (CVDs) may alter the microstructures of arteries and hence their mechanical properties. Therefore, the measurement of intrinsic artery mechanical properties in vivo can provide valuable information in understanding aging and CVDs and is of clinical significance. The accuracy of advanced ultrasound imaging techniques in measuring the deformation of large arteries under blood pressure is good. However, the assessment of arterial stiffness in vivo remains a challenge. An inverse method to infer the constitutive parameters of arteries in vivo from the blood pressure-arterial radius relationship (P-r curve) is proposed here. The stability analysis reveals that a key constitutive parameter, b_θ, which measures the circumferential hardening of an artery, can be reliably identified. An in vivo experiment was performed on the common carotid arteries of 41 healthy volunteers (age: 37 ± 17 y). The value of b_θ varies significantly (from 0.55 ± 0.15 for the young group to 0.93 ± 0.29 for the older group, p < 0.01) and is positively correlated with age (r = 0.673, p < 0.01). Furthermore, our theoretical analysis and experimental study have revealed a strong correlation between the clinic-used stiffness index β and b_θ. This study shows that the arterial material parameter b_θ can be measured in vivo, which makes it promising as a new biomarker in the diagnosis of CVDs.

The Role of Layer-Specific Residual Stresses in Arterial Mechanics: Analysis via a Novel Modelling Framework

The existence of residual stresses in unloaded arteries has long been known. However, their effect is often neglected in experimental studies. Using a recently developed modelling framework, we aimed to investigate the role of residual stresses in the mechanical behaviour of the tri-layered wall of the pig thoracic aorta. The mechanical behaviour of the intact wall and isolated layers of n = 3 pig thoracic aortas was investigated via uniaxial tensile testing. After modelling the layer-specific mechanical data using a hyperelastic strain energy function, the layer-specific deformations in the unloaded vessel were estimated so that the mechanical response of the computationally assembled tri-layered flat wall would match that measured experimentally. Physiological tension–inflation of the cylindrical tri-layered vessel was then simulated, analysing changes in the distribution of stresses in the three layers when neglecting residual stresses. In the tri-layered model with residual stresses, layers exhibited comparable stresses throughout the physiological range of pressure. At 100 mmHg, intimal, medial, and adventitial circumferential load bearings were 16 $$\pm$$ ±  3%, 59 $$\pm$$ ± 4%, and 25 $$\pm$$ ± 2%, respectively. Adventitial stiffening at high pressures produced a shift in load bearing from the media to the adventitia. When neglecting residual stresses, in vivo stresses were highest at the intima and lowest at the adventitia. Consequently, the intimal and adventitial load bearings, 23 $$\pm$$ ± 2% and 18 $$\pm$$ ± 3% at 100 mmHg, were comparable at all pressures. Residual stresses play a crucial role in arterial mechanics guaranteeing a uniform distribution of stresses through the wall thickness. Neglecting these leads to incorrect interpretation of the layers’ role in arterial mechanics.

Viscoelasticity of human descending thoracic aorta in a mock circulatory loop

Healthy human descending thoracic aortas, obtained during organ donation for transplant and research, were tested in a mock circulatory loop to measure the mechanical response to physiological pulsatile pressure and flow. The viscoelastic properties of the aortic segments were investigated at three different pulse rates. The same aortic segments were also subjected to quasi-static pressure tests in order to identify the aortic dynamic stiffness ratio, which is defined as the ratio between the stiffness in case of pulsatile pressure and the stiffness measured for static pressurization, both at the same value of pressure. The loss factor was also identified. The shape of the deformed aorta under static and dynamic pressure was measured by image processing to verify the compatibility of the end supports with the natural deformation of the aorta in the human body. In addition, layer-specific experiments on 10 human descending thoracic aortas allowed to precisely identify the mass density of the aortic tissue, which is an important parameter in cardiovascular dynamic models.

An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load

An insight into changes of soft biological tissue ultrastructures under loading conditions is essential to understand their response to mechanical stimuli. Therefore, this study offers an approach to investigate the arrangement of collagen fibrils and proteoglycans (PGs), which are located within the mechanically loaded aortic wall. The human aortic samples were either fixed directly with glutaraldehyde in the load-free state or subjected to a planar biaxial extension test prior to fixation. The aortic ultrastructure was recorded using electron tomography. Collagen fibrils and PGs were segmented using convolutional neural networks, particularly the ESPNet model. The 3D ultrastructural reconstructions revealed a complex organization of collagen fibrils and PGs. In particular, we observed that not all PGs are attached to the collagen fibrils, but some fill the spaces between the fibrils with a clear distance to the collagen. The complex organization cannot be fully captured or can be severely misinterpreted in 2D. The approach developed opens up practical possibilities, including the quantification of the spatial relationship between collagen fibrils and PGs as a function of the mechanical load. Such quantification can also be used to compare tissues under different conditions, e.g., healthy and diseased, to improve or develop new material models. STATEMENT OF SIGNIFICANCE: The developed approach enables the 3D reconstruction of collagen fibrils and proteoglycans as they are embedded in the loaded human aortic wall. This methodological pipeline comprises the knowledge of arterial mechanics, imaging with transmission electron microscopy and electron tomography, segmentation of 3D image data sets with convolutional neural networks and finally offers a unique insight into the ultrastructural changes in the aortic tissue caused by mechanical stimuli.

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.

Experimental Investigation of the Anisotropic Mechanical Response of the Porcine Thoracic Aorta

Knowledge of the mechanical properties of blood vessels and determining appropriate constitutive relations are essential in developing methodologies for accurate prognosis of vascular diseases. We examine the directional variation of the mechanical properties of the porcine thoracic aorta by performing uniaxial extension tests on dumbbell-shaped specimens cut at five different orientations with respect to the circumferential direction of the aorta. Specimens in all the orientations considered exhibit a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta, and samples oriented at 45[Formula: see text] and 60[Formula: see text] with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response not displayed by axial and circumferential specimens. Failure stress indicates decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction. Furthermore, we determine the material parameters for the four-fiber-family and Gasser-Holzapfel-Ogden models from the mechanical response data of the circumferential and longitudinal specimens. It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.

Role of smooth muscle activation in the static and dynamic mechanical characterization of human aortas

The rupture of aortic aneurysms causes around 10,000 deaths each year in the United States. Prosthetic tubes for aortic repair present a large mismatch of mechanical properties with the natural aorta, which has negative consequences for perfusion. This motivates research into the mechanical characterization of human aortas to develop a new generation of mechanically compatible aortic grafts. Experimental data and a suitable material model for human aortas with vascular smooth muscle (VSM) activation are not available. Hence, the present study provides experimental data that are needed. These data made it possible to develop a precise structure-based model of active aortic tissue. The results show the importance of VSM activation on the static and dynamic mechanical response of human aortas.

Experimental data and a suitable material model for human aortas with smooth muscle activation are not available in the literature despite the need for developing advanced grafts; the present study closes this gap. Mechanical characterization of human descending thoracic aortas was performed with and without vascular smooth muscle (VSM) activation. Specimens were taken from 13 heart-beating donors. The aortic segments were cooled in Belzer UW solution during transport and tested within a few hours after explantation. VSM activation was achieved through the use of potassium depolarization and noradrenaline as vasoactive agents. In addition to isometric activation experiments, the quasistatic passive and active stress–strain curves were obtained for circumferential and longitudinal strips of the aortic material. This characterization made it possible to create an original mechanical model of the active aortic material that accurately fits the experimental data. The dynamic mechanical characterization was executed using cyclic strain at different frequencies of physiological interest. An initial prestretch, which corresponded to the physiological conditions, was applied before cyclic loading. Dynamic tests made it possible to identify the differences in the viscoelastic behavior of the passive and active tissue. This work illustrates the importance of VSM activation for the static and dynamic mechanical response of human aortas. Most importantly, this study provides material data and a material model for the development of a future generation of active aortic grafts that mimic natural behavior and help regulate blood pressure.

Fluid-structure interaction simulation of tissue degradation and its effects on intra-aneurysm hemodynamics

Tissue degradation plays a crucial role in vascular diseases such as atherosclerosis and aneurysms. Computational modeling of vascular hemodynamics incorporating both arterial wall mechanics and tissue degradation has been a challenging task. In this study, we propose a novel finite element method-based approach to model the microscopic degradation of arterial walls and its interaction with blood flow. The model is applied to study the combined effects of pulsatile flow and tissue degradation on the deformation and intra-aneurysm hemodynamics. Our computational analysis reveals that tissue degradation leads to a weakening of the aneurysmal wall, which manifests itself in a larger deformation and a smaller von Mises stress. Moreover, simulation results for different heart rates, blood pressures and aneurysm geometries indicate consistently that, upon tissue degradation, wall shear stress increases near the flow-impingement region and decreases away from it. These findings are discussed in the context of recent reports regarding the role of both high and low wall shear stress for the progression and rupture of aneurysms.

A Review on Damage and Rupture Modelling for Soft Tissues

Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

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

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

Personalised nitinol stent for focal plaques: Design and evaluation

The purpose of this study is to develop personalised nitinol stents for arteries with one and two opposite focal plaques. Novel designs are evaluated through comparison with a commercial stent design, in terms of lumen gain and shape as well as stress levels in the media layer after stenting.

METHODS

Personalised stents are developed for arteries with one and two opposite focal plaques, based on medical imaging of patients and computer simulations. In silico analysis is then carried out for assessment of stent performance in the diseased arteries.

RESULTS

Personalised designs significantly increase the lumen gain, reduce the stresses in the media layer, and improve the lumen shape compared to the commercial nitinol stent.

CONCLUSION

The personalised designs show outstanding performance compared to the commercial stent.

SIGNIFICANCE

This pilot study proves that personalised nitinol stents are able to deliver desirable treatment outcomes.

Pioneering personalised design of femoropopliteal nitinol stents

BACKGROUND/MOTIVATION

Percutaneous femoropopliteal artery intervention moves towards personalised therapy, which requires design of unique lesion-specific stents. However, to date, not much progress has been made in the development of personalised stents.

OBJECTIVE

This paper aims to design personalised nitinol stents for femoropopliteal arteries based on medical imaging of patients and advanced computational mechanics, which is the first attempt to the authors' best knowledge.

METHODS

The design process is based on three objectives: (i) achieving the healthy lumen area; (ii) reducing the stress in the media layer; (iii) improving the lumen shape after stenting. The design parameters include the strut width and thickness, the crown length, the nominal radius and the number of strut units per crown. Using representative unit-cell models, the effects of the five geometric parameters on the stent performance are investigated thoroughly with numerical simulations. Then, design protocols, especially for the circumferentially varying strut size and the oval stent shape, are developed and fully evaluated for an asymmetric stenosis.

RESULTS

Using the design protocols, full personalised stents are designed for arteries with diffuse and focal plaques, based on medical imaging of patients. The personalised stent designs provide a double lumen gain, a reduced stress in the media layer and an improved lumen shape compared to a commercial stent.

CONCLUSIONS

The suggested protocols prove their high effectiveness in design of personalised stents, and the suggested approach can be applied to development of personalised therapies involving the use of stent technology including percutaneous coronary artery intervention, transcatheter aortic valve implantation, endovascular aneurysm repair and ureteric stenting.

Microstructural and mechanical characterization of the layers of human descending thoracic aortas

The mechanical properties of human aortas are linked to the layered tissue and its microstructure at different length scales. Each layer has specific mechanical and structural properties. While the ground substance and the elastin play an important role in tissue stiffness at small strain, collagen fibers carry most of the load at larger strains, which corresponds to the physiological conditions of the aorta at maximum pulsatile blood pressure. In fact, collagen fibers are crimped in the unloaded state. Collagen fibers show different orientation distributions when they are observed in a plane that is tangent to the aortic wall (in-plane section) or along a direction orthogonal to it (out-of-plane section). This was systematically investigated using large images (2500 × 2500 µm) with high resolution obtained by second harmonic generation (SHG) in order to homogenize tissue heterogeneity after a convergence analysis, which is a main goal of the study. In addition, collagen fibers show lateral interactions due to entanglements and the presence of transverse elastin fibers, observed on varying length scales using atomic force microscopy and a three-dimensional rendering obtained by stacking a sequence of SHG and two-photon fluorescence images; this is another important contribution. Human descending thoracic aortas from 13 heartbeat donors aged 28 to 66 years were examined. Uniaxial tensile tests were carried out on the longitudinal and circumferential strips of the aortic wall and the three separated layers (intima, media and adventitia). A structurally-motivated material model with (i) a term to describe the combined response of ground substance and elastin and (ii) terms to consider four families of collagen fibers with different directions was applied. The exclusion of compressed fibers was implemented in the fitting process of the experimental data, which was optimized by a genetic algorithm. The results show that a single fiber family with directional and dispersion parameters measured from SHG images can describe the mechanical response of all 39 layers (3 layers for each of the 13 aortas) with very good accuracy when a second (auxiliary) family of aligned fibers is introduced in the orthogonal direction to account for lateral fiber interaction. Indeed, all observed distributions of collagen directions can be accurately fitted by a single bivariate von Mises distribution. Statistical analysis of in-plane and out-of-plane dispersion of fiber orientations reveals structural differences between the three layers and a change of collagen dispersion parameters with age. STATEMENT OF SIGNIFICANCE: The stiffness of healthy young aortas is adjusted so that a diameter expansion of about 10 % is possible during the heartbeat. This creates the Windkessel effect, which smooths out the pulsating nature of blood flow and benefits organ perfusion. The specific elastic properties of the aorta that are required to achieve this effect are related to the microstructure of the aortic tissue at different length scales. An increase in the aortic stiffness, in addition to reducing cyclic expansion and worsening perfusion, is a risk factor for clinical hypertension. The present study relates the microstructure of healthy human aortas to the mechanical response and examines the changes in microstructural parameters with age, which is a key factor in increasing stiffness.

Angioplasty Induced Changes in Dialysis Vascular Access Compliance

Dialysis vascular access remains vitally important to maintain life and functional capacity with end stage renal disease. Angioplasty is an integral part of maintaining dialysis access function and patency. To understand the effect of angioplasty balloon dilation on vascular wall mechanics, we conducted a clinical study to evaluate the elastic modulus of the anastomosis in five subjects with anastomosis stenoses, before and after six angioplasty procedures, using B-mode ultrasound DICOM data. A novel and open source vascular ultrasound high-resolution speckle tracking software tool was used. The median lumen diameter increased from 3.4 to 5.5 mm after angioplasty. Meanwhile, the median elastic modulus of the 18 measurements at the anastomosis increased by 52.2%, from 2.24 × 10³ to 3.41 × 10³ mmHg. The results support our hypothesis that the structural changes induced in the vessel wall by balloon dilation lead to reduced vascular compliance and a higher elastic modulus of the vessel wall.

Viscoelastic characterization of human descending thoracic aortas under cyclic load

Experiments were carried out on 15 human descending thoracic aortas from heart-beating healthy donors who donated organs for transplant. The aortas were kept refrigerated in organ preservation solution and tested were completed within 48 hours from explant. Donors' age was comprised between 25 and 70 years, with an average of 51.7 ± 12.8 years. Quasi-static and dynamic uniaxial tensile test were carried out in thermally controlled physiological saline solution in order to characterize the viscoelastic behavior. Strips were tested under harmonic deformation of different frequency, between 1 and 11 Hz, at three initial pre-stretches. Cyclic deformations of two different amplitudes were used: a physiological one and a small one, the latter one for comparison purposes to understand the accuracy limits of viscoelastic models. Aortic strips in circumferential and longitudinal directions were cut from each aorta. Some strips were dissected to separate the three layers: intima, media and adventitia. They were tested individually in order to obtain layer-specific data. However, strips of the intact wall were also tested. Therefore, 8 strips per donors were tested. Viscoelastic parameters are accurately evaluated from the hysteresis loops. Results show that small-amplitude cyclic strain over-estimate the storage modulus and under-estimate the loss-factor. Therefore, cyclic deformation of physiological amplitude is necessary to obtain correct viscoelastic data of aortic tissue. The value of the applied pre-stretch is significant on the dynamic stiffness ratio (storage modulus divided by the corresponding quasi-static stiffness), while it is less significant for the loss factor. The median of the dynamic stiffness ratios, in physiological conditions, varies between 1.14 and 1.33 for the different layers and the intact wall; the corresponding median of the loss factors varies between 0.050 and 0.066. The lowest dynamic stiffness ratios and loss factors were obtained from donors of the youngest age group. STATEMENT OF SIGNIFICANCE: There is an increasing interest in replacing traditional Dacron grafts used to repair thoracic aortas after acute dissection and aneurysm, with grafts in innovative biomaterials that mimic the mechanical properties and the dynamic behavior of the aorta. The human aorta is a complex laminated structure with hyperelastic and viscoelastic material properties and residual stresses. This study aims to characterize the nonlinear viscoelastic properties of ex-vivo human descending thoracic aortas by measuring hysteresis loops of physiological amplitude under harmonic strain. Results show the necessity to characterize the viscoelastic material properties of the aorta under physiological conditions, as well as the necessity to introduce improved models that take better into account the influence of the initial pre-stretch and amplitude of the cyclic load.

Failure Properties of Healthy and Diabetic Rabbit Thoracic Aortas and Their Potential Correlation with Mass Fractions of Collagen

PURPOSE

Diabetes Mellitus (DM) plays an important role in aortic remodeling and alters the wall mechanics. The purpose of this study is to investigate and compare multi-directional failure properties of healthy and diabetic thoracic aortas.

METHODS

Thirty adult rabbits (1.6-2.2 kg) were collected and type 1 diabetic rabbit model was induced by injection of alloxan. A total of 10 control and 20 diabetic (with different time exposure to diabetic condition) rabbit descending thoracic aortas were harvested. Uniaxial tensile (UT) and radial tension (RT) tests were performed to determine circumferential, axial and radial failure stresses of the control and diabetic aortas, which were further correlated with mass fractions (MFs) of collagen.

RESULTS

Throughout the UT test, there was a clear indication of anisotropic mechanical responses for some diabetic aorta specimens in the high loading domain. There was a trend towards an increase in the mean circumferential and axial failure stresses for the diabetic aortas when compared to the control aortas. However, differences were not statistically significant. The quantified failure stresses in the circumferential direction were, in general, higher than the stress values in the axial direction for both control and diabetic groups. For the RT test, the radial failure stresses of the diabetic aortas (in 8 weeks) were significantly higher than those of the control aortas (95 ± 17 vs. 63 ± 15 kPa, p = 0.01). Strong correlations were identified between the circumferential failure stresses and the MFs of collagen for both control and diabetic aortas. Nevertheless, this correlation was not present in the axial and radial directions.

CONCLUSION

The results suggest that there is a lower propensity of radial tear occurrence within the diabetic aortic wall. More importantly, time exposure to diabetic condition is not a factor that may change failure properties of the rabbit descending thoracic aortas in the circumferential and axial directions.

From Uniaxial Testing of Isolated Layers to a Tri-Layered Arterial Wall: A Novel Constitutive Modelling Framework

Mechanical testing and constitutive modelling of isolated arterial layers yields insight into the individual layers’ mechanical properties, but per se fails to recapitulate the in vivo loading state, neglecting layer-specific residual stresses. The aim of this study was to develop a testing/modelling framework that integrates layer-specific uniaxial testing data into a three-layered model of the arterial wall, thereby enabling study of layer-specific mechanics under realistic (patho)physiological conditions. Circumferentially and axially oriented strips of pig thoracic aortas (n = 10) were tested uniaxially. Individual arterial layers were then isolated from the wall, tested, and their mechanical behaviour modelled using a hyperelastic strain energy function. Subsequently, the three layers were computationally assembled into a single flat-walled sample, deformed into a cylindrical vessel, and subjected to physiological tension-inflation. At the in vivo axial stretch of 1.10 ± 0.03, average circumferential wall stress was 75 ± 9 kPa at 100 mmHg, which almost doubled to 138 ± 15 kPa at 160 mmHg. A ~ 200% stiffening of the adventitia over the 60 mmHg pressure increase shifted layer-specific load-bearing from the media (65 ± 10% → 61 ± 14%) to the adventitia (28 ± 9% → 32 ± 14%). Our approach provides valuable insight into the (patho)physiological mechanical roles of individual arterial layers at different loading states, and can be implemented conveniently using simple, inexpensive and widely available uniaxial testing equipment.

Computational model of damage-induced growth in soft biological tissues considering the mechanobiology of healing

Healing in soft biological tissues is a chain of events on different time and length scales. This work presents a computational framework to capture and couple important mechanical, chemical and biological aspects of healing. A molecular-level damage in collagen, i.e., the interstrand delamination, is addressed as source of plastic deformation in tissues. This mechanism initiates a biochemical response and starts the chain of healing. In particular, damage is considered to be the stimulus for the production of matrix metalloproteinases and growth factors which in turn, respectively, degrade and produce collagen. Due to collagen turnover, the volume of the tissue changes, which can result either in normal or pathological healing. To capture the mechanisms on continuum scale, the deformation gradient is multiplicatively decomposed in inelastic and elastic deformation gradients. A recently proposed elasto-plastic formulation is, through a biochemical model, coupled with a growth and remodeling description based on homogenized constrained mixtures. After the discussion of the biological species response to the damage stimulus, the framework is implemented in a mixed nonlinear finite element formulation and a biaxial tension and an indentation tests are conducted on a prestretched flat tissue sample. The results illustrate that the model is able to describe the evolutions of growth factors and matrix metalloproteinases following damage and the subsequent growth and remodeling in the respect of equilibrium. The interplay between mechanical and chemo-biological events occurring during healing is captured, proving that the framework is a suitable basis for more detailed simulations of damage-induced tissue response.

Biaxial softening of isolated cerebral arteries following axial overstretch

Arteries play a critical role in carrying essential nutrients and oxygen throughout the brain; however, vessels can become damaged in traumatic brain injury (TBI), putting neural tissue at risk. Even in the absence of hemorrhage, large deformations can disrupt both the physiological and mechanical behavior of the cerebral vessels. Our group recently reported the effect of vessel overstretch on axial mechanics; however, that work did not address possible changes in circumferential mechanics that are critical to the regulation of blood flow. In order to address this in the present work, ovine middle cerebral arteries were isolated and overstretched axially to 10, 20, or 40% beyond the in vivo configuration. Results showed a statistically significant decrease in circumferential stiffness and strain energy, as well as an increase in vessel diameter following 40% overstretch (p < 0.05). These passive changes would lead to a decrease in vascular resistance and likely play a role in previous reports of cellular dysfunction. We anticipate that our findings will both increase understanding of vessel softening phenomena and also promote improved modeling of cerebrovascular mechanics following head trauma.

Sensitivity analysis of non-local damage in soft biological tissues

Computational modeling can provide insight into understanding the damage mechanisms of soft biological tissues. Our gradient-enhanced damage model presented in a previous publication has shown advantages in considering the internal length scales and in satisfying mesh independence for simulating damage, growth and remodeling processes. Performing sensitivity analyses for this model is an essential step towards applications involving uncertain patient-specific data. In this paper, a numerical analysis approach is developed. For that we integrate two existing methods, that is, the gradient-enhanced damage model and the surrogate model-based probability analysis. To increase the computational efficiency of the Monte Carlo method in uncertainty propagation for the nonlinear hyperelastic damage analysis, the surrogate model based on Legendre polynomial series is employed to replace the direct FEM solutions, and the sparse grid collocation method (SGCM) is adopted for setting the collocation points to further reduce the computational cost in training the surrogate model. The effectiveness of the proposed approach is illustrated by two numerical examples, including an application of artery dilatation mimicking to the clinical problem of balloon angioplasty.

The influence of sample geometry and size on porcine aortic material properties from uniaxial tensile tests using custom-designed tissue cutters, clamps and molds

The aim of this study was to identify the influence of specimen geometry and size on the results of aortic uniaxial tensile tests using custom-designed tissue cutters, clamps and molds. Six descending thoracic aortas from pigs were used for rectangular sample tests, in which the circumferential and axial specimens had widths of 6 mm, 8 mm and 10 mm. The other six aortas were used for the dog-bone-shaped sample tests and were punched into circumferential, axial and oblique specimens with widths of 2 mm, 4 mm and 6 mm. We performed uniaxial tensile tests on the specimens and compared the test results. The results showed that mid-sample failure occurred in 85.2% of the dog-bone-shaped specimens and in 11.1% of the rectangular samples, which could be caused by Saint-Venant’s principle. Therefore, rectangular specimens were not suitable for aortic uniaxial tensile testing performed until rupture. The results also showed that the size effect of the aorta conformed to Weibull theory, and dog-bone-shaped specimens with a width of 4 mm were the optimal choice for aortic uniaxial tensile testing performed until rupture.

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.

Review of the Techniques Used for Investigating the Role Elastin and Collagen Play in Arterial Wall Mechanics

The arterial wall is characterised by a complex microstructure that impacts the mechanical properties of the vascular tissue. The main components consist of collagen and elastin fibres, proteoglycans, Vascular Smooth Muscle Cells (VSMCs) and ground matrix. While VSMCs play a key role in the active mechanical response of arteries, collagen and elastin determine the passive mechanics. Several experimental methods have been designed to investigate the role of these structural proteins in determining the passive mechanics of the arterial wall. Microscopy imaging of load-free or fixed samples provides useful information on the structure-function coupling of the vascular tissue, and mechanical testing provides information on the mechanical role of collagen and elastin networks. However, when these techniques are used separately, they fail to provide a full picture of the arterial micromechanics. More recently, advances in imaging techniques have allowed combining both methods, thus dynamically imaging the sample while loaded in a pseudo-physiological way, and overcoming the limitation of using either of the two methods separately. The present review aims at describing the techniques currently available to researchers for the investigation of the arterial wall micromechanics. This review also aims to elucidate the current understanding of arterial mechanics and identify some research gaps.

Influence of Material Model and Aortic Root Motion in Finite Element Analysis of Two Exemplary Cases of Proximal Aortic Dissection

The risk of type-A dissection is increased in subjects with connective tissue disorders and dilatation of the proximal aorta. The location and extents of vessel wall tears in these patients could be potentially missed during prospective imaging studies. The objective of this study is to estimate the distribution of systolic wall stress in two exemplary cases of proximal dissection using finite element analysis (FEA) and evaluate the sensitivity of the distribution to the choice of anisotropic material model and root motion. FEA was performed for predissection aortas, without prior knowledge of the origin and extents of vessel wall tear. The stress distribution was evaluated along the wall tear in the postdissection aortas. The stress distribution was compared for the Fung and Holzapfel models with and without root motion. For the subject with spiral dissection, peak stress coincided with the origin of the tear in the sinotubular junction. For the case with root dissection, maximum stress was obtained at the distal end of the tear. The FEA predicted tear pressure was 20% higher for the subject with root dissection as compared to the case with spiral dissection. The predicted tear pressure was higher (9-11%) for root motions up to 10 mm. The Holzapfel model predicted a tear pressure that was lower (8-15%) than the Fung model. The FEA results showed that both material response and root motion could potentially influence the predicted dissection pressure of the proximal aorta at least for conditions tested in this study.

A generic physics-informed neural network-based constitutive model for soft biological tissues

Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser-Ogden-Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R² value of 0.9632 vs 0.9019, p=0.0053) and testing (R² value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel-Gasser-Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.

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.

On the importance of tunica intima in the aging aorta: a three-layered in silico model for computing wall stresses in abdominal aortic aneurysms

Layer-specific experimental data for human aortic tissue suggest that, in aged arteries and arteries with non-atherosclerotic intimal thickening, the innermost layer of the aorta increases significantly its stiffness and thickness, becoming load-bearing. However, there are very few computational studies of abdominal aortic aneurysms (AAAs) that take into account the mechanical contribution of the three layers that comprise the aneurysmal tissue. In this paper, a three-layered finite element model is proposed from the simplest uniaxial stress state to geometrically parametrized models of AAAs with different asymmetry values. Comparisons are made between a three-layered artery wall and a mono-layered intact artery, which represents the complex behavior of the aggregate adventitia-media-intima in a single layer with averaged mechanical properties. Likewise, the response of our idealized geometries is compared with similar experimental and numerical models. Finally, the mechanical contributions of adventitia, media and intima are analyzed for the three-layered aneurysms through the evaluation of the mean stress absorption percentage. Results show the relevance and necessity of considering the inclusion of tunica intima in multi-layered models of AAAs for getting accurate results in terms of peak wall stresses and displacements.