On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

Significance of Dynamic Axial Stretching on Estimating Biomechanical Behavior and Properties of the Human Ascending Aorta

Contrary to most vessels, the ascending thoracic aorta (ATA) not only distends but also elongates in the axial direction. The purpose of this study is to investigate the biomechanical behavior of the ascending thoracic aorta (ATA) in response to dynamic axial stretching during the cardiac cycle. In addition, the implications of neglecting this dynamic axial stretching when estimating the constitutive model parameters of the ATA are investigated. The investigations were performed through in silico simulations by assuming a Gasser-Ogden-Holzapfel (GOH) constitutive model representative of ATA tissue material. The GOH model parameters were obtained from biaxial tests performed on four human ATA tissues in a previous study. Pressure-diameter curves were simulated as synthetic data to assess the effect of neglecting dynamic axial stretching on estimating constitutive model parameters. Our findings reveal a significant increase in axial stress (~ 16%) and stored strain energy (~ 18%) in the vessel when dynamic axial stretching is considered, as opposed to assuming a fixed axial stretch. All but one artery showed increased volume compliance while considering a dynamic axial stretching condition. Furthermore, we observe a notable difference in the estimated constitutive model parameters when dynamic axial stretching of the ATA is neglected, compared to the ground truth model parameters. These results underscore the critical importance of accounting for axial deformations when conducting in vivo biomechanical characterization of the ascending thoracic aorta.

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

Biaxial stretch can overcome discrepancy between global and local orientations of wavy collagen fibres

Most frequently used structure-based constitutive models of arterial wall apply assumptions on two symmetric helical (and dispersed) fibre families which, however, are not well supported with histological findings where two collagen fibre families are seldom found. Moreover, bimodal distributions of fibre directions may originate also from their waviness combined with ignoring differences between local and global fibre orientations. In contrast, if the model parameters are identified without histological information on collagen fibre directions, the resulting mean angles of both fibre families are close to ±45°, which contradicts nearly all histologic findings. The presented study exploited automated polarized light microscopy for detection of collagen fibre directions in porcine aorta under different biaxial extensions and approximated the resulting histograms with unimodal and bimodal von Mises distributions. Their comparison showed dominantly circumferential orientation of collagen fibres. Their concentration parameter for unimodal distributions increased with circumferential load, no matter if acting uniaxially or equibiaxially. For bimodal distributions, the angle between both dominant fibre directions (chosen as measure of fibre alignment) decreased similarly for both uniaxial and equibiaxial loads. These results indicate the existence of a single family of wavy circumferential collagen fibres in all layers of the aortic wall. Bimodal distributions of fibre directions presented sometimes in literature may come rather from waviness of circumferentially arranged fibres than from two symmetric families of helical fibres. To obtain a final evidence, the fibre orientation should be analysed together with their waviness.

A review on the biomechanical behaviour of the aorta

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo, experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system.

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.

Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Regional variation in biomechanical properties of ascending thoracic aortic aneurysms

OBJECTIVES

This study aims to characterize the material properties of ascending thoracic aortic aneurysmal tissue, using regional biomechanical assessment of both tensile and dissection propagation peel strength.

METHODS

Thirty-four aneurysm specimens (proximal thoracic aorta) were harvested en-bloc from patients undergoing surgery for aneurysm replacement. Specimens were processed into regional samples of similar shapes covering the whole aneurysm isosurface, according to a structured protocol, in both orientations (longitudinal and circumferential). Thickness mapping, uniaxial tensile and peel tests were conducted, enabling calculation of the following parameters: true stress/strain, tangential modulus, tensile strength, peeling force and dissection energy. Two constitutive material models were used (hyperelastic models of Delfino and Ogden) to fit the data. A circumferential strip of tissue was also obtained for computational histology [regional quantification of (i) elastin, (ii) collagen and (iii) smooth muscle cells].

RESULTS

The aortic wall was thinner on the outer curve (2.21, standard deviation (SD) 0.4 mm vs inner curve 2.50, SD 0.12 mm). Advanced patient age and higher pulse wave velocity (externally measured) were predictors of increased aortic wall thickness. Tensile strength was higher in the circumferential versus longitudinal direction when analysed according to anatomical regions. Both peel force (35.5, 22 N/m) and dissection energy (88.5, 69 J/m2) were on average lowest at the outer curve of the aneurysm in the longitudinal orientation. Delfino and Ogden model constants varied throughout anatomical regions, with the outer curve being associated a higher ɑ constant (Delfino) and lower µ1 constant (Ogden) (P < 0.05) indicating increased stiffness. Histologically, collagen abundance was significantly related to circumferential and longitudinal strength (P= 0.010), whilst smooth muscle cell count had no relation with any mechanical property (P > 0.05).

CONCLUSIONS

Our results suggest that the outer aortic curve is more prone to dissection propagation and perhaps less prone to rupture than the inner aortic curve. This strengthens the notion of disease heterogeneity in ascending thoracic aortic aneurysms and has implications for the pathogenesis of aortic dissection.

Mechanical and histological characteristics of aortic dissection tissues

AIMS

This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations.

METHODS

Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C₁, D₁, and D₂) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness.

RESULTS

The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C₁ and D₂, respectively, while the elastin and collagen waviness were negatively correlated with C₁ and D₂, respectively. Elastin dispersion was negatively correlated to D₂. Multivariate analysis showed that D₂ was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip.

CONCLUSION

Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function.

STATEMENT OF SIGNIFICANCE

Aortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.

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.

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.

Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to the development of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model-the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and the polynomial forms (R2=0.92-0.99 versus 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 versus 0.30), indicating a more well-defined search space. Finally, the exponential and the combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential form leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets owing to its superb fitting capabilities and smaller parameter's confidence regions.

Comparative Study of Human and Murine Aortic Biomechanics and Hemodynamics in Vascular Aging

Introduction: Aging has many effects on the cardiovascular system, including changes in structure (aortic composition, and thus stiffening) and function (increased proximal blood pressure, and thus cardiac afterload). Mouse models are often used to gain insight into vascular aging and mechanisms of disease as they allow invasive assessments that are impractical in humans. Translation of results from murine models to humans can be limited, however, due to species-specific anatomical, biomechanical, and hemodynamic differences. In this study, we built fluid-solid-interaction (FSI) models of the aorta, informed by biomechanical and imaging data, to compare wall mechanics and hemodynamics in humans and mice at two equivalent ages: young and older adults. Methods: For the humans, 3-D computational models were created using wall property data from the literature as well as patient-specific magnetic resonance imaging (MRI) and non-invasive hemodynamic data; for the mice, comparable models were created using population-based properties and hemodynamics as well as subject-specific anatomies. Global aortic hemodynamics and wall stiffness were compared between humans and mice across age groups. Results: For young adult subjects, we found differences between species in pulse pressure amplification, compliance and resistance distribution, and aortic stiffness gradient. We also found differences in response to aging between species. Generally, the human spatial gradients of stiffness and pulse pressure across the aorta diminished with age, while they increased for the mice. Conclusion: These results highlight key differences in vascular aging between human and mice, and it is important to acknowledge these when using mouse models for cardiovascular research.

In vivo parameter identification in arteries considering multiple levels of smooth muscle activity

In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.

Intra-Operative Video-Based Measurement of Biaxial Strains of the Ascending Thoracic Aorta

Local biaxial deformation measurements are essential for the in-depth investigation of tissue properties and remodeling of the ascending thoracic aorta, particularly in aneurysm formation. Current clinical imaging modalities pose limitations around the resolution and tracking of anatomical markers. We evaluated a new intra-operative video-based method to assess local biaxial strains of the ascending thoracic aorta. In 30 patients undergoing open-chest surgery, we obtained repeated biaxial strain measurements, at low- and high-pressure conditions. Precision was very acceptable, with coefficients of variation for biaxial strains remaining below 20%. With our four-marker arrangement, we were able to detect significant local differences in the longitudinal strain as well as in circumferential strain. Overall, the magnitude of strains we obtained (range: 0.02–0.05) was in line with previous reports using other modalities. The proposed method enables the assessment of local aortic biaxial strains and may enable new, clinically informed mechanistic studies using biomechanical modeling as well as mechanobiological profiling.

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

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

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

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

Longitudinal histomechanical heterogeneity of the internal thoracic artery

The internal thoracic artery (ITA) is the principal choice for coronary artery bypass grafting (CABG) due to its mechanical compatibility, histological composition, anti-thrombogenic lumen, and single anastomotic junction. Originating at the subclavian artery, traversing the thoracic cavity, and terminating at the superior epigastric and musculophrenic bifurcation, bilateral ITAs follow a protracted circuitous pathway. The physiological hemodynamics, anatomical configuration, and perivascular changes that occur throughout this length influence the tissue's microstructure and gross mechanical properties. Since histomechanics play a major role in premature graft failure we used inflation-extension testing to quantify the regional material and biaxial mechanical properties at four distinct locations along the left (L) and right (R) ITA and fit the results to a structurally-motivated constitutive model. Our comparative analysis of 44 vessel segments revealed a significant increase in the amount of collagen but not smooth muscle and a significant decrease in elastin and elastic lamellae present with distance from the heart. A subsequent decrease in the total deformation energy and isotropic contribution to the strain energy was present in the LITA but not RITA. Circumferential stress and compliance generally decreased along the length of the LITA while axial stress increased in the RITA. When comparing RITAs to LITAs, some morphological and histological differences were found in proximal sections while distal sections revealed differences predominantly in compliance and axial stress. Overall, this information can be used to better guide graft selection, graft preparation, and xenograft-based tissue-engineering strategies for CABG.

Computational Modeling of Mouse Colorectum Capturing Longitudinal and Through-thickness Biomechanical Heterogeneity

Mechanotransduction, the encoding of local mechanical stresses and strains at sensory endings into neural action potentials at the viscera, plays a critical role in evoking visceral pain, e.g., in the distal colon and rectum (colorectum). The wall of the colorectum is structurally heterogeneous, including two major composites: the inner consists of muscular and submucosal layers, and the outer consists of circular muscular, intermuscular, longitudinal muscular, and serosal layers. In fact the colorectum presents biomechanical heterogenity across both the longitudinal and through-thickness directions thus highlighting the differential roles of sensory nerve endings within different regions of the colorectum in visceral mechanotransduction. We determined constitutive models and model parameters for individual layers of the colorectum from three longitudinal locations (colonic, intermediate, and distal) using nonlinear optimization to fit our experimental results from biaxial extension tests on layer-separated colorectal tissues (mouse model, 7×7 mm2, Siri et al., Am. J. Physiol. Gastrointest. Liver Physiol. 316, G473-G481 and 317, G349-G358), and quantified the thicknesses of the layers. In this study we also quantified the residual stretches stemming from separating colorectal specimens into inner and outer composites and we completed new pressure-diameter mechanical testing to provide an additional validation case. We implemented the constitutive equations and created two-layered, 3-D finite element models using FEBio (University of Utah), and incorporated the residual stretches. We validated the modeling framework by comparing FE-predicted results for both biaxial extension testing of bulk specimens of colorectum and pressure-diameter testing of bulk segments against corresponding experimental results independent of those used in our model fitting. We present the first theoretical framework to simulate the biomechanics of distal colorectum, including both longitudinal and through-thickness heterogeneity, based on constitutive modeling of biaxial extension tests of colon tissues from mice. Our constitutive models and modeling framework facilitate analyses of both fundamental questions (e.g., the impact of organ/tissue biomechanics on mechanotransduction of the sensory nerve endings, structure-function relationships, and growth and remodeling in health and disease) and specific applications (e.g., device design, minimally invasive surgery, and biomedical research).

Mechanical, structural, and physiologic differences in human elastic and muscular arteries of different ages: Comparison of the descending thoracic aorta to the superficial femoral artery

Elastic and muscular arteries differ in structure, function, and mechanical properties, and may adapt differently to aging. We compared the descending thoracic aortas (TA) and the superficial femoral arteries (SFA) of 27 tissue donors (average 41±18 years, range 13-73 years) using planar biaxial testing, constitutive modeling, and bidirectional histology. Both TAs and SFAs increased in size with age, with the outer radius increasing more than the inner radius, but the TAs thickened 6-fold and widened 3-fold faster than the SFAs. The circumferential opening angle did not change in the TA, but increased 2.4-fold in the SFA. Young TAs were relatively isotropic, but the anisotropy increased with age due to longitudinal stiffening. SFAs were 51% more compliant longitudinally irrespective of age. Older TAs and SFAs were stiffer, but the SFA stiffened 5.6-fold faster circumferentially than the TA. Physiologic stresses decreased with age in both arteries, with greater changes occurring longitudinally. TAs had larger circumferential, but smaller longitudinal stresses than the SFAs, larger cardiac cycle stretch, 36% lower circumferential stiffness, and 8-fold more elastic energy available for pulsation. TAs contained elastin sheets separated by smooth muscle cells (SMCs), collagen, and glycosaminoglycans, while the SFAs had SMCs, collagen, and longitudinal elastic fibers. With age, densities of elastin and SMCs decreased, collagen remained constant due to medial thickening, and the glycosaminoglycans increased. Elastic and muscular arteries demonstrate different morphological, mechanical, physiologic, and structural characteristics and adapt differently to aging. While the aortas remodel to preserve the Windkessel function, the SFAs maintain higher longitudinal compliance.

The Macro- and Micro-Mechanics of the Colon and Rectum II: Theoretical and Computational Methods

Abnormal colorectal biomechanics and mechanotransduction associate with an array of gastrointestinal diseases, including inflammatory bowel disease, irritable bowel syndrome, diverticula disease, anorectal disorders, ileus, and chronic constipation. Visceral pain, principally evoked from mechanical distension, has a unique biomechanical component that plays a critical role in mechanotransduction, the process of encoding mechanical stimuli to the colorectum by sensory afferents. To fully understand the underlying mechanisms of visceral mechanical neural encoding demands focused attention on the macro- and micro-mechanics of colon tissue. Motivated by biomechanical experiments on the colon and rectum, increasing efforts focus on developing constitutive frameworks to interpret and predict the anisotropic and nonlinear biomechanical behaviors of the multilayered colorectum. We will review the current literature on computational modeling of the colon and rectum as well as the mechanical neural encoding by stretch sensitive afferent endings, and then highlight our recent advances in these areas. Current models provide insight into organ- and tissue-level biomechanics as well as the stretch-sensitive afferent endings of colorectal tissues yet an important challenge in modeling theory remains. The research community has not connected the biomechanical models to those of mechanosensitive nerve endings to create a cohesive multiscale framework for predicting mechanotransduction from organ-level biomechanics.

Role of Fiber Orientations in the Mechanics of Bioinspired Fiber-Reinforced Elastomers

Fiber reinforcement is a crucial attribute of soft-bodied muscular hydrostats that have the ability to undergo large deformations and maintain their posture. Helically wound fibers around the cylindrical worm body help control the tube diameter and length. Geometric considerations show that a fiber winding angle of 54.7°, called the magic angle, results in a maximum enclosed volume. Few studies have combined both experimental and theoretical techniques to explore the effects of fiber winding at varied angles on the large deformation mechanics of fiber-reinforced elastomers (FRE). We fabricated FRE materials in transversely isotropic layouts varying from 0° to 90° using a custom filament winding technique and characterized the nonlinear stress-strain relationships using uniaxial and equibiaxial experiments. We used these data within a continuum mechanical framework to propose a novel constitutive model for incompressible FRE materials with embedded extensible fibers. The model includes individual contributions from the matrix and fibers in addition to coupled terms in strain invariants, I₁ and I₄. The deviatoric stress components show inversion at fiber orientation angles near the magic angle in the FRE composites. These results are useful in soft robotic applications and in the biomechanics of fiber-reinforced tissues such as the myocardium, arteries, and skin.

Characterization of rat tail lymphatic contractility and biomechanics: incorporating nitric oxide-mediated vasoregulation

The lymphatic system transports lymph from the interstitial space back to the great veins via a series of orchestrated contractions of chains of lymphangions. Biomechanical models of lymph transport, validated with ex vivo or in vivo experimental results, have proved useful in revealing novel insight into lymphatic pumping; however, a need remains to characterize the contributions of vasoregulatory compounds in these modelling tools. Nitric oxide (NO) is a key mediator of lymphatic pumping. We quantified the active contractile and passive biaxial biomechanical response of rat tail collecting lymphatics and changes in the contractile response to the exogenous NO administration and integrated these findings into a biomechanical model. The passive mechanical response was characterized with a three-fibre family model. Nonlinear regression and non-parametric bootstrapping were used to identify best-fit material parameters to passive cylindrical biaxial mechanical data, assessing uniqueness and parameter confidence intervals; this model yielded a good fit (R² = 0.90). Exogenous delivery of NO via sodium nitroprusside (SNP) elicited a dose-dependent suppression of contractions; the amplitude of contractions decreased by 30% and the contraction frequency decreased by 70%. Contractile function was characterized with a modified Rachev-Hayashi model, introducing a parameter that is related to SNP concentration; the model provided a good fit (R² = 0.89) to changes in contractile responses to varying concentrations of SNP. These results demonstrated the significant role of NO in lymphatic pumping and provide a predictive biomechanical model to integrate the combined effect of mechanical loading and NO on lymphatic contractility and mechanical response.

Evaluation of the Stress-Growth Hypothesis in Saphenous Vein Perfusion Culture

The great saphenous vein (GSV) has served as a coronary artery bypass graft (CABG) conduit for over 50 years. Despite prevalent use, first-year failure rates remain high compared to arterial autograft options. Amongst other factors, vein graft failure can be attributed to material and mechanical mismatching that lead to apoptosis, inflammation, and intimal-medial hyperplasia. Through the implementation of the continuum mechanical-based theory of "stress-mediated growth and remodeling," we hypothesize that the mechanical properties of porcine GSV grafts can be favorably tuned for CABG applications prior to implantation using a prolonged but gradual transition from venous to arterial loading conditions in an inflammatory and thrombogenic deficient environment. To test this hypothesis, we used a hemodynamic-mimetic perfusion bioreactor to guide remodeling through stepwise incremental changes in pressure and flow over the course of 21-day cultures. Biaxial mechanical testing of vessels pre- and post-remodeling was performed, with results fit to structurally-motivated constitutive models using non-parametric bootstrapping. The theory of "small-on-large" was used to describe appropriate stiffness moduli, while histology and viability assays confirmed microstructural adaptations and vessel viability. Results suggest that stepwise transition from venous-to-arterial conditions results in a partial restoration of circumferential stretch and circumferential, but not axial, stress through vessel dilation and wall thickening in a primarily outward remodeling process. These remodeled tissues also exhibited decreased mechanical isotropy and circumferential, but not axial, stiffening. In contrast, only increases in axial stiffness were observed using culture under venous perfusion conditions and those tissues experienced moderate intimal resorption.

Mechanical and structural changes in human thoracic aortas with age

Aortic mechanical and structural characteristics have profound effects on pathophysiology, but many aspects of physiologic stress-stretch state and intramural changes due to aging remain poorly understood in human tissues. While difficult to assess in vivo due to residual stresses and pre-stretch, physiologic stress-stretch characteristics can be calculated using experimentally-measured mechanical properties and constitutive modeling. Mechanical properties of 76 human descending thoracic aortas (TA) from 13 to 78-year-old donors (mean age 51±18 years) were measured using multi-ratio planar biaxial extension. Constitutive parameters were derived for aortas in 7 age groups, and the physiologic stress-stretch state was calculated. Intramural characteristics were quantified from histological images and related to aortic morphometry and mechanics. TA stiffness increased with age, and aortas became more nonlinear and anisotropic. Systolic and diastolic elastic energy available for pulsation decreased with age from 30 to 8 kPa and from 18 to 5 kPa, respectively. Cardiac cycle circumferential stretch dropped from 1.14 to 1.04, and circumferential and longitudinal physiologic stresses decreased with age from 90 to 72 kPa and from 90 to 17 kPa, respectively. Aortic wall thickness and radii increased with age, while the density of elastin in the tunica media decreased. The number of elastic lamellae and circumferential physiologic stress per lamellae unit remained constant with age at 102±10 and 0.85±0.04 kPa, respectively. Characterization of mechanical, physiological, and structural features in human aortas of different ages can help understand aortic pathology, inform the development of animal models that simulate human aging, and assist with designing devices for open and endovascular aortic repairs. STATEMENT OF SIGNIFICANCE: This manuscript describes mechanical and structural changes occurring in human thoracic aortas with age, and presents material parameters for 4 commonly used constitutive models. Presented data can help better understand aortic pathology, inform the development of animal models that simulate human aging, and assist with designing devices for open and endovascular aortic repairs.

Sensitivity of Arterial Hyperelastic Models to Uncertainties in Stress-Free Measurements

Despite major advances made in modeling vascular tissue biomechanics, the predictive power of constitutive models is still limited by uncertainty of the input data. Specifically, key measurements, like the geometry of the stress-free (SF) state, involve a definite, sometimes non-negligible, degree of uncertainty. Here, we introduce a new approach for sensitivity analysis of vascular hyperelastic constitutive models to uncertainty in SF measurements. We have considered two vascular hyperelastic models: the phenomenological Fung model and the structure-motivated Holzapfel-Gasser-Ogden (HGO) model. Our results indicate up to 160% errors in the identified constitutive parameters for a 5% measurement uncertainty in the SF data. Relative margins of errors of up to 30% in the luminal pressure, 36% in the axial force, and over 200% in the stress predictions were recorded for 10% uncertainties. These findings are relevant to the large body of studies involving experimentally based modeling and analysis of vascular tissues. The impact of uncertainties on calibrated constitutive parameters is significant in context of studies that use constitutive parameters to draw conclusions about the underlying microstructure of vascular tissues, their growth and remodeling processes, and aging and disease states. The propagation of uncertainties into the predictions of biophysical parameters, e.g., force, luminal pressure, and wall stresses, is of practical importance in the design and execution of clinical devices and interventions. Furthermore, insights provided by the present findings may lead to more robust parameters identification techniques, and serve as selection criteria in the trade-off between model complexity and sensitivity.

Computational Modeling Predicts Immuno-Mechanical Mechanisms of Maladaptive Aortic Remodeling in Hypertension

Uncontrolled hypertension is a major risk factor for myriad cardiovascular diseases. Among its many effects, hypertension increases central artery stiffness which in turn is both an initiator and indicator of disease. Despite extensive clinical, animal, and basic science studies, the biochemomechanical mechanisms by which hypertension drives aortic stiffening remain unclear. In this paper, we show that a new computational model of aortic growth and remodeling can capture differential effects of induced hypertension on the thoracic and abdominal aorta in a common mouse model of disease. Because the simulations treat the aortic wall as a constrained mixture of different constituents having different material properties and rates of turnover, one can gain increased insight into underlying constituent-level mechanisms of aortic remodeling. Model results suggest that the aorta can mechano-adapt locally to blood pressure elevation in the absence of marked inflammation, but large increases in inflammation drive a persistent maladaptive phenotype characterized primarily by adventitial fibrosis. Moreover, this fibrosis appears to occur via a marked increase in the rate of deposition of collagen having different material properties in the absence of a compensatory increase in the rate of matrix degradation. Controlling inflammation thus appears to be key to reducing fibrosis, but therapeutic strategies should not compromise the proteolytic activity of the wall that is essential to mechanical homeostasis.

Captopril treatment during development alleviates mechanically induced aortic remodeling in newborn elastin knockout mice

Deposition of elastin and collagen in the aorta correlates with increases in blood pressure and flow during development, suggesting that the aorta adjusts its mechanical properties in response to hemodynamic stresses. Elastin knockout (Eln^-/-) mice have high blood pressure and pathological remodeling of the aorta and die soon after birth. We hypothesized that decreasing blood pressure in Eln^-/- mice during development may reduce hemodynamic stresses and alleviate pathological remodeling of the aorta. We treated Eln^+/+ and Eln^-/- mice with the anti-hypertensive medication captopril throughout embryonic development and then evaluated left ventricular (LV) pressure and aortic remodeling at birth. We found that captopril treatment decreased Eln^-/- LV pressure to values near Eln^+/+ mice and alleviated the wall thickening and changes in mechanical behavior observed in untreated Eln^-/- aorta. The changes in thickness and mechanical behavior in captopril-treated Eln^-/- aorta were not due to alterations in measured elastin or collagen amounts, but may have been caused by alterations in smooth muscle cell (SMC) properties. We used a constitutive model to understand how changes in stress contributions of each wall component could explain the observed changes in composite mechanical behavior. Our modeling results show that alterations in the collagen natural configuration and SMC properties in the absence of elastin may explain untreated Eln^-/- aortic behavior and that partial rescue of the SMC properties may account for captopril-treated Eln^-/- aortic behavior.

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

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

Mechanical damage characterization in human femoropopliteal arteries of different ages

Endovascular treatment of Peripheral Arterial Disease (PAD) is notorious for high failure rates, and interaction between the arterial wall and the repair devices plays a significant role. Computational modeling can help improve clinical outcomes of these interventions, but it requires accurate inputs of elastic and damage characteristics of the femoropopliteal artery (FPA) which are currently not available. Fresh human FPAs from n = 104 tissue donors 14-80 years old were tested using planar biaxial extension to capture elastic and damage characteristics. Damage initiation stretches and stresses were determined for both longitudinal and circumferential directions, and their correlations with age and risk factors were assessed. Two and four-fiber-family invariant-based constitutive models augmented with damage functions were used to describe stress softening with accumulating damage. In FPAs younger than 50 years, damage began accumulating after 1.51 ± 0.13 and 1.49 ± 0.11 stretch, or 196 ± 110 kPa and 239 ± 79 kPa Cauchy stress in the longitudinal and circumferential directions, respectively. In FPAs older than 50 years, damage initiation stretches and stresses decreased to 1.27 ± 0.09 (106 ± 52 kPa) and 1.26 ± 0.09 (104 ± 59 kPa), respectively. Damage manifested primarily as tears at the internal and external elastic laminae and within the tunica media layer. Higher body mass index and presence of diabetes were associated with lower damage initiation stretches and higher stresses. The selected constitutive models were able to accurately portray the FPA behavior in both elastic and inelastic domains, and properties were derived for six age groups. Presented data can help improve fidelity of computational models simulating endovascular PAD repairs that involve arterial damage. STATEMENT OF SIGNIFICANCE: This manuscript describes inelastic, i.e. damage, behavior of human femoropopliteal arteries, and provides values for three constitutive models simulating this behavior computationally. Using a set of 104 human FPAs 14-80 years old, we have investigated stress and stretch levels corresponding to damage initiation, and have studied how these damage characteristics change across different age groups. Presented inelastic arterial characteristics are important for computational simulations modeling balloon angioplasty and stenting of peripheral arterial disease lesions.

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

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

An in vivo parameter identification method for arteries: numerical validation for the human abdominal aorta

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.

Sex-dependent differences in central artery haemodynamics in normal and fibulin-5 deficient mice: implications for ageing

Mouse models provide unique opportunities to study vascular disease, but they demand increased experimental and computational resolution. We describe a workflow for combining in vivo and in vitro biomechanical data to build mouse-specific computational models of the central vasculature including regional variations in biaxial wall stiffness, thickness and perivascular support. These fluid-solid interaction models are informed by micro-computed tomography imaging and in vivo ultrasound and pressure measurements, and include mouse-specific inflow and outflow boundary conditions. Hence, the model can capture three-dimensional unsteady flows and pulse wave characteristics. The utility of this experimental-computational approach is illustrated by comparing central artery biomechanics in adult wild-type and fibulin-5 deficient mice, a model of early vascular ageing. Findings are also examined as a function of sex. Computational results compare well with measurements and data available in the literature and suggest that pulse wave velocity, a spatially integrated measure of arterial stiffness, does not reflect well the presence of regional differences in stiffening, particularly those manifested in male versus female mice. Modelling results are also useful for comparing quantities that are difficult to measure or infer experimentally, including local pulse pressures at the renal arteries and characteristics of the peripheral vascular bed that may differ with disease.

STUDY OF THE TRANSVERSAL DEFORMATION OF CORNEAL STRIP UNDER UNIAXIAL LOADING

Uniaxial test is easy to access and to obtain accuracy data, but it is difficult to acquire two-dimensional deformation information. We investigated the relationship between the two strain components of corneal strip in uniaxial tests, which is the basis for determining of anisotropic strain energy function of cornea via uniaxial tests. Nine rabbits were taken. The left and right corneas were cut along superior-inferior (SI) and nasal-temporal (NT) direction, respectively. For each strip the uniaxial test was carried out, and the tensile displacements, strip images and loads were recorded. Then the stretching strain, the transversal strains and stress were obtained. Optimization based inverse analysis was utilized to find the best among six fitting models that characterizes the relationship between two strain components in uniaxial tests. All models fitted well the experimental data gathered for corneal strips ([Formula: see text]). According to the model selection index, the power model achieved the best performance index: 0.1268 for SI strips and 0.1063 for NT strips versus 0.151 (SI strips) and 0.107 (NT strips) found at most by other models. Thus, it is the most suitable one for describing the relationship between the two strain components of corneal strip during uniaxial stretching.

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.

Loss of anisotropic properties in abdominal aorta aneurysm obtained from the xenograft rat model

BACKGROUND

Cellular treatments using mesenchymal stem cells (MSCs) cultured in 3D conditions constitute a solution to the classical surgery in treating abdominal aortic aneurysm (AAA). The recurrent question is: how this type of biotherapy changes the mechanical behavior of artery?

METHODS

Experiments measurements based on xenograft rat model showed that the proposed cellular treatment leads to a decreasing radius and length of the AAA during its growth. An inverse finite element method was used to investigate the mechanical hyperelastic behavior of the AAA in the untreated case compared to the treated one.

RESULTS

Although AAA leads a loss anisotropy while the cellular treatment does not restore it, it was shown that the stiffness of the arterial wall was improved. The numerical analysis of the stress distributions permitted to localize the stress concentration through the arterial wall and the probable zone of the rupture of the aneurysm developed from the xenograft rat model.

CONCLUSIONS

The treatment of AAA with MSCs cultured in a 3D conditions constitutes a new challenge. Based on xenograft rat model, this study shows the potential of this cellular treatment to reduce the variation of the growth, the stiffness and the stress distributions.

Immuno-driven and Mechano-mediated Neotissue Formation in Tissue Engineered Vascular Grafts

In vivo development of a neovessel from an implanted biodegradable polymeric scaffold depends on a delicate balance between polymer degradation and native matrix deposition. Studies in mice suggest that this balance is dictated by immuno-driven and mechanotransduction-mediated processes, with neotissue increasingly balancing the hemodynamically induced loads as the polymer degrades. Computational models of neovessel development can help delineate relative time-dependent contributions of the immunobiological and mechanobiological processes that determine graft success or failure. In this paper, we compare computational results informed by long-term studies of neovessel development in immuno-compromised and immuno-competent mice. Simulations suggest that an early exuberant inflammatory response can limit subsequent mechano-sensing by synthetic intramural cells and thereby attenuate the desired long-term mechano-mediated production of matrix. Simulations also highlight key inflammatory differences in the two mouse models, which allow grafts in the immuno-compromised mouse to better match the biomechanical properties of the native vessel. Finally, the predicted inflammatory time courses revealed critical periods of graft remodeling. We submit that computational modeling can help uncover mechanisms of observed neovessel development and improve the design of the scaffold or its clinical use.

Compromised mechanical homeostasis in arterial aging and associated cardiovascular consequences

Aging leads to central artery stiffening and associated hemodynamic sequelae. Because healthy arteries exhibit differential geometry, composition, and mechanical behaviors along the central vasculature, we sought to determine whether wall structure and mechanical function differ across five vascular regions-the ascending and descending thoracic aorta, suprarenal and infrarenal abdominal aorta, and common carotid artery-in 20 versus 100-week-old male wild-type mice. Notwithstanding generally consistent changes across these regions, including a marked thickening of the arterial wall, diminished in vivo axial stretch, and loss of elastic energy storage capacity, the degree of changes tended to be slightly greater in abdominal than in thoracic or carotid vessels. Likely due to the long half-life of vascular elastin, most mechanical changes in the arterial wall resulted largely from a distributed increase in collagen, including thicker fibers in the media, and localized increases in glycosaminoglycans. Changes within the central arteries associated with significant increases in central pulse pressure and adverse changes in the left ventricle, including increased cardiac mass and decreased diastolic function. Given the similar half-life of vascular elastin in mice and humans but very different life-spans, there are important differences in the aging of central vessels across these species. Nevertheless, the common finding of aberrant matrix remodeling contributing to a compromised mechanical homeostasis suggests that studies of central artery aging in the mouse can provide insight into mechanisms and treatment strategies for the many adverse effects of vascular aging in humans.

Computational predictions of damage propagation preceding dissection of ascending thoracic aortic aneurysms

Dissections of ascending thoracic aortic aneurysms (ATAAs) cause significant morbidity and mortality worldwide. They occur when a tear in the intima-media of the aorta permits the penetration of the blood and the subsequent delamination and separation of the wall in 2 layers, forming a false channel. To predict computationally the risk of tear formation, stress analyses should be performed layer-specifically and they should consider internal or residual stresses that exist in the tissue. In the present paper, we propose a novel layer-specific damage model based on the constrained mixture theory, which intrinsically takes into account these internal stresses and can predict appropriately the tear formation. The model is implemented in finite-element commercial software Abaqus coupled with user material subroutine. Its capability is tested by applying it to the simulation of different exemplary situations, going from in vitro bulge inflation experiments on aortic samples to in vivo overpressurizing of patient-specific ATAAs. The simulations reveal that damage correctly starts from the intimal layer (luminal side) and propagates across the media as a tear but never hits the adventitia. This scenario is typically the first stage of development of an acute dissection, which is predicted for pressures of about 2.5 times the diastolic pressure by the model after calibrating the parameters against experimental data performed on collected ATAA samples. Further validations on a larger cohort of patients should hopefully confirm the potential of the model in predicting patient-specific damage evolution and possible risk of dissection during aneurysm growth for clinical applications.

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.

Novel Methodology for Characterizing Regional Variations in the Material Properties of Murine Aortas

Many vascular disorders, including aortic aneurysms and dissections, are characterized by localized changes in wall composition and structure. Notwithstanding the importance of histopathologic changes that occur at the microstructural level, macroscopic manifestations ultimately dictate the mechanical functionality and structural integrity of the aortic wall. Understanding structure-function relationships locally is thus critical for gaining increased insight into conditions that render a vessel susceptible to disease or failure. Given the scarcity of human data, mouse models are increasingly useful in this regard. In this paper, we present a novel inverse characterization of regional, nonlinear, anisotropic properties of the murine aorta. Full-field biaxial data are collected using a panoramic-digital image correlation (p-DIC) system. An inverse method, based on the principle of virtual power (PVP), is used to estimate values of material parameters regionally for a microstructurally motivated constitutive relation. We validate our experimental-computational approach by comparing results to those from standard biaxial testing. The results for the nondiseased suprarenal abdominal aorta from apolipoprotein-E null mice reveal material heterogeneities, with significant differences between dorsal and ventral as well as between proximal and distal locations, which may arise in part due to differential perivascular support and localized branches. Overall results were validated for both a membrane and a thick-wall model that delineated medial and adventitial properties. Whereas full-field characterization can be useful in the study of normal arteries, we submit that it will be particularly useful for studying complex lesions such as aneurysms, which can now be pursued with confidence given the present validation.

Limb flexion-induced twist and associated intramural stresses in the human femoropopliteal artery

High failure rates of femoropopliteal artery (FPA) interventions are often attributed to severe mechanical deformations that occur with limb movement. Torsion of the FPA likely plays a significant role, but is poorly characterized and the associated intramural stresses are currently unknown. FPA torsion in the walking, sitting and gardening postures was characterized in n = 28 in situ FPAs using intra-arterial markers. Principal mechanical stresses and strains were quantified in the superficial femoral artery (SFA), adductor hiatus segment (AH) and the popliteal artery (PA) using analytical modelling. The FPA experienced significant torsion during limb flexion that was most severe in the gardening posture. The associated mechanical stresses were non-uniformly distributed along the length of the artery, increasing distally and achieving maximum values in the PA. Maximum twist in the SFA ranged 10-13° cm^-1, at the AH 8-16° cm^-1, and in the PA 14-26° cm^-1 in the walking, sitting and gardening postures. Maximum principal stresses were 30-35 kPa in the SFA, 27-37 kPa at the AH and 39-43 kPa in the PA. Understanding torsional deformations and intramural stresses in the FPA can assist with device selection for peripheral arterial disease interventions and may help guide the development of devices with improved characteristics.