Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

Variability in structure, morphology, and mechanical properties of the descending thoracic and infrarenal aorta around their circumference

Aortic diseases, such as aneurysms, atherosclerosis, and dissections, demonstrate a preferential development and progression around the aortic circumference, resulting in a highly heterogeneous disease state around the circumference. Differences in the aorta's structural composition and mechanical properties may be partly responsible for this phenomenon. Our goal in this study was to analyze the mechanical and structural properties of the human aorta at its lateral, anterior, posterior, and medial quadrants in two regions prone to circumferentially inhomogeneous diseases, descending Thoracic Aorta (TA) and Infrarenal Aorta (IFR). Human aortas were obtained from 10 donors (64 ± 11 years) and dissected from their loose surrounding tissue. Mechanical properties were determined in all four quadrants of TA and IFR using planar biaxial testing and fitted to three common constitutive models. The structure of tissues was assessed using Movat Pentachrome stained histology slides. We observed that the anterior quadrant exhibited the greatest thickness, followed by the lateral region, in both the TA and IFR. In TA, the posterior wall appeared as the stiffest location in most samples, while in IFR, the anterior wall was the stiffest. We observed a higher glycosaminoglycans content in the lateral and posterior regions of the IFR. We found elastin density to be similar in TA lateral, anterior, and posterior quadrants, while in IFR, the anterior region demonstrated the highest elastin density. Despite significant variations between subjects, this study highlights the distinct morphometrical, mechanical, and structural properties between the quadrants of both TA and IFR.

False aneurysms of the thoracic aorta: anastomosis investigation using the inflation-extension test

INTRODUCTION

False aneurysms in the thoracic aorta are dangerous complications that can occur after cardiac surgery. They often result in high mortality rates. These aneurysms are caused by damage to all layers of the aortic wall. This study aimed to pinpoint the area of the experimental specimen (native vessel, anastomosis, or prosthetic graft) with the greatest deformation, to determine whether a false aneurysm is likely to develop in the anastomotic portion.

METHODS

We conducted the inflation-extension test by performing eight cycles ranging from 0 to 20. The pressure sampling frequency was 100 Hz, and each cycle lasted approximately 34 seconds, resulting in a loading frequency of 0.03 Hz. During the experiment, each camera captured 3,000 frames. Based on the data collected, we evaluated and compared the loading stages of cycle 1 and cycle 8.

RESULTS AND DISCUSSION

During loading, the native vessel experienced a dominant deformation of approximately 7% in the circumferential direction. The prosthetic graft, which had a longitudinal construction, deformed by approximately 8% in the axial direction. The prosthetic graft, on the other hand, only experienced a deformation of up to 1.5% in the circumferential direction, which was about 5 times smaller than the deformation of the native vessel. The anastomosis area was very stiff and showed minimal deformation. Additionally, there was little difference in the mechanical response between the first C1 and the eighth C8 cycle.

CONCLUSION

Based on the available evidence, it can be inferred that aortic false aneurysms are more likely to form just behind the suture lines in the native aorta, which is more elastic compared to stiff sections of anastomosis and prosthetic graft. Numerous pulsations of the native vessel will likely cause the impairment of the aorta at the margin of the anastomosis. This will lead to disruption of the aortic wall and false aneurysm formation in the native vessel near the area of anastomosis.

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.

Methodology for estimation of undeformed thickness of arterial tissues

Soft tissue sample thickness measurement is one of the major sources of differences between mechanical responses published by different groups. New method for the estimation of unloaded sample thickness of soft tissues is proposed in this study. Ten 30 × 30 mm and ten 20 × 20 mm samples of porcine anterior thoracic aortas were loaded by gradually increased radial force. Their deformed thickness was then recorded in order to generate a pressure-thickness response. Next, the limit pressure to which the response can be considered linear was estimated. Line was fitted to the linear part of the curve and extrapolated towards zero pressure to estimate unloaded thickness (7 kPa fit). For comparison, data near zero pressure were fitted separately and extrapolated towards zero (Near Zero fit). The limit pressure for the linearity of the response was around 7 kPa. The Unloaded thickness for 30 × 30 mm samples was 2.68 ± 0.31 mm and 2.68 ± 0.3 mm for Near Zero fit and 7 kPa fit, respectively. The Unloaded thickness for 20 × 20 mm samples was 2.60 ± 0.35 mm and 2.59 ± 0.35 mm for Near Zero fit and 7 kPa fit, respectively. The median of thickness difference between smaller and larger samples was not found statistically different. Proposed method can estimate unloaded undeformed sample thickness quickly and reliably.

Measurement of Layer-Specific Mechanical Properties of Intact Blood Vessels Based on Intravascular Optical Coherence Tomography

PURPOSE

The biomechanical analysis of stress and strain state of multilayered blood vessels has shown great importance in vascular pathology and physiology. However, there is a lack of method in measuring the mechanical property of each layer of a vascular sample without splitting up the wall.

METHODS

Here we develop a vascular inflation test method based on intravascular optical coherence tomography (IVOCT) imaging and inverse parametric estimation. We propose a three-step inverse parametric estimation method to solve the six constitutive parameters of the GOH models for the intima-media and adventitia of the coronaries simultaneously. A bilayer silicone vascular phantom inflation test and a virtual deformation test using finite element simulated data are conducted to evaluate the accuracy of the proposed method.

RESULTS

The virtual deformation test demonstrates that the errors of the constitutive constants are less than 2.56% determined by the proposed inverse parametric estimation method. The stress-strain curves of a bilayer silicone vascular phantom obtained based on the parameters determined by the proposed method match well with those obtained by the uniaxial test.

CONCLUSION

The proposed layer-specific vascular mechanical property measurement method provides a new experimental method for mechanical properties characterization of blood vessels. It also has the potential to be used for patient-specific mechanical properties estimation with IVOCT imaging in vivo.

Region-dependent mechanical characterization of porcine thoracic aorta with a one-to-many correspondence method to create virtual datasets using uniaxial tensile tests

The simulation of the cardiovascular system and in silico clinical trials have garnered attention in the biomedical engineering field. Physics-based modeling is essential to associate with physical and clinical features. In physics-based constitutive modeling, the identification of the parameters and estimation of their ranges based on appropriate experiments are required. Uniaxial tests are commonly used in the field of vascular mechanics, but they have limitations in fully characterizing the regional mechanical behavior of the aorta. Therefore, this study is aimed at identifying a method to integrate constitutive models with experimental data to elucidate regional aortic behavior. To create a virtual two-dimensional dataset, a pair of uniaxial experimental datasets in the longitudinal and circumferential directions was combined using a one-to-many correspondence method such as bootstrap aggregation. The proposed approach is subsequently applied to three constitutive models, i.e., the Fung model, Holzapfel model, and constrained mixture model, to estimate the material parameters based on the four test regions of the porcine thoracic aorta. Finally, the regional difference in the mechanical behavior of the aorta, the correlation between the experimental characteristics and model parameters, and the inter-correlation of the material parameters are confirmed. This integrative approach will enhance the prediction capability of the model with respect to the regions of the aorta.

Through the cleared aorta: three-dimensional characterization of mechanical behaviors of rat thoracic aorta under intraluminal pressurization using optical clearing method

The media of aortic wall is characterized by altering layers of elastin and smooth muscle cells (SMCs), along with collagen fibers in both layers, and plays a central role in functional and pathological remodeling such as hypertension and atherosclerosis. Because the arterial function is linked closely to the arterial wall internal structure, it is essential to investigate the alteration of the arterial microstructure during macroscopic deformation to understand cardiovascular pathologies. The present study adopted a tissue clearing method in three-dimensional mechanical characterization of rat thoracic aorta, and successfully observed changes in the structure of each of the three primary components of the aorta under intraluminal pressurization while maintaining tissue mechanical integrity and flexibility. Layers of elastic fibers and SMCs deformed greater on the intimal side than those on the adventitial side. Furthermore, there was a structural agreement in the alignment angle between SMC nuclei and elastic fibers on their intimal side, but not on the adventitial side. This is the first study that changes in the microstructure of three primary components of the aorta were visualized and evaluated through the aorta. The method established here would also be useful to understand tissue mechanics of other load-bearing soft tissues.

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.

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.

Prolonged mechanical ventilation increases diaphragm arteriole circumferential stretch without changes in stress/stretch: Implications for the pathogenesis of ventilator-induced diaphragm dysfunction

INTRODUCTION

Prolonged mechanical ventilation (MV; ≥6 h) results in large, time-dependent reductions in diaphragmatic blood flow and shear stress. We tested the hypothesis that MV would impair the structural and material properties (ie, increased stress/stretch relation and/or circumferential stretch) of first-order arterioles (1A) from the medial costal diaphragm.

METHODS

Shear stress was estimated from isolated arterioles and prior blood flow data from the diaphragm during spontaneous breathing (SB) and prolonged MV (6 h MV). Thereafter, female Sprague-Dawley rats (~5 months) were randomly divided into two groups, SB (n = 6) and 6 h MV (n = 6). Following SB and 6 h MV, 1A medial costal diaphragm arterioles were isolated, cannulated, and subjected to stepwise (0-140 cmH2 O) increases in intraluminal pressure in calcium-free Ringer's solution. Inner diameter and wall thickness were measured at each pressure step and used to calculate wall:lumen ratio, Cauchy-stress, and circumferential stretch.

RESULTS

Compared to SB, there was a ~90% reduction in arteriolar shear stress with prolonged MV (9 ± 2 vs 78 ± 20 dynes/cm2 ; p ≤ .05). In the unloaded condition (0 cmH2 O), the arteriolar intraluminal diameter was reduced (37 ± 8 vs 79 ± 13 μm) and wall:lumen ratio was increased (120 ± 18 vs 46 ± 10%) compared to SB (p ≤ .05). There were no differences in the passive diameter responses or the circumferential stress/stretch relationship between groups (p > .05), but at each pressure step, circumferential stretch was increased with 6 h MV vs SB (p ≤ .05).

CONCLUSION

During prolonged MV, medial costal diaphragm arteriolar shear stress is severely diminished. Despite no change in the material behavior (stress/stretch), prolonged MV resulted in altered structural and mechanical properties (ie, elevated circumferential stretch) of medial costal diaphragm arterioles. This provides important novel mechanistic insights into the impaired diaphragm blood flow capacity and vascular dysfunction following prolonged MV.

Multi-view digital image correlation systems for in vitro testing of arteries from mice to humans

BACKGROUND

Digital image correlation (DIC) methods are increasingly used for non-contact optical assessment of geometry and deformation in soft tissue biomechanics, thus providing the full-field strain estimates needed for robust inverse material characterization. Despite the well-known flexibility and ease of use of DIC, issues related to spatial resolution and depth-of-field remain challenging in studies of quasi-cylindrical biological samples such as arteries.

OBJECTIVE

After demonstrating that standard surrounding multi-view DIC systems are inappropriate for such usage, we submit that both the optical setup and the data analysis need to be specifically designed with respect to the size of the arterial sample of interest. Accordingly, we propose novel and optimized DIC systems for two distinct ranges of arterial diameters: less than 2.5 mm (murine arteries) and greater than 10 mm (human arteries).

METHODS

We designed, set up, and validated a four-camera panoramic-DIC system for testing murine arteries and a multi-biprism DIC system for testing human arteries. Both systems enable dynamic 360-deg measurements with refraction correction over the entire surface of submerged samples in their native geometries.

RESULTS

Illustrative results for 3D shape and full-surface deformation fields were obtained for a mouse infrarenal aorta and a latex cylinder of size similar to the human infrarenal aorta.

CONCLUSION

Results demonstrated the feasibility and accuracy of both proposed methods in providing quantitative information on the regional behavior of arterial samples tested in vitro under physiologically relevant loading.

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.

Potential damage in pulmonary arterial hypertension: An experimental study of pressure-induced damage of pulmonary artery

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. PAH prognosis remains poor with a 15% mortality rate within 1 year, even with modern clinical management. Previous clinical studies proposed wall shear stress (WSS) to be an important hemodynamic factor affecting cell mechanotransduction, growth and remodeling, and disease progress in PAH. However, WSS in vivo is typically at most 2.5 Pa and a doubt has been cast whether WSS alone can drive disease progress. Furthermore, our current understanding of PAH pathology largely comes from small animals' studies in which caliber enlargement, a hallmark of PAH in humans, is rarely reported. Therefore, a large-animal experiment on pulmonary arteries (PAs) is needed to validate whether increased pressure can induce enlargement of PAs caliber. In this study, we use an inflation testing device to characterize the mechanical behavior, both nonlinear elastic behavior and irreversible damage of porcine arteries. The parameters of elastic behavior are estimated from the inflation test at a low-pressure range before and after over-pressurization. Then, histological images are qualitatively examined for medial and adventitial layers. This study sheds light on the relevance of pressure-induced damage mechanism in human PAH.

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

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

Blood Clot Phenotyping by Rheometry: Platelets and Fibrinogen Chemistry Affect Stress-Softening and -Stiffening at Large Oscillation Amplitude

(1) Background: Together with treatment protocols, viscoelastic tests are widely used for patient care. Measuring at broader ranges of deformation than currently done will add information on a clot’s mechanical phenotype because fibrin networks follow different stretching regimes, and blood flow compels clots into a dynamic non-linear response. (2) Methods: To characterize the influence of platelets on the network level, a stress amplitude sweep test (LAOStress) was applied to clots from native plasma with five platelet concentrations. Five species were used to validate the protocol (human, cow, pig, rat, horse). By Lissajous plots the oscillation cycle for each stress level was analyzed. (3) Results: Cyclic stress loading generates a characteristic strain response that scales with the platelet quantity at low stress, and that is independent from the platelet count at high shear stress. This general behavior is valid in the animal models except cow. Here, the specific fibrinogen chemistry induces a stiffer network and a variant high stress response. (4) Conclusions: The protocol provides several thresholds to connect the softening and stiffening behavior of clots with the applied shear stress. This points to the reversible part of deformation, and thus opens a new route to describe a blood clot’s phenotype.

Recent Advances in Biomechanical Characterization of Thoracic Aortic Aneurysms

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

Characterization of chemoelastic effects in arteries using digital volume correlation and optical coherence tomography

Understanding stress-strain relationships in arteries is important for fundamental investigations in mechanobiology. Here we demonstrate the essential role of chemoelasticity in determining the mechanical properties of arterial tissues. Stepwise stress-relaxation uniaxial tensile tests were carried out on samples of porcine thoracic aortas immersed in a hyperosmotic solution. The tissue deformations were tracked using optical coherence tomography (OCT) during the tensile tests and digital volume correlation (DVC) was used to obtain measurements of depth-resolved strains across the whole thickness of the tested aortas. The hyperosmotic solution exacerbated chemoelastic effects, and we were able to measure different manifestations of these chemoelastic effects: swelling of the media inducing a modification of its optical properties, and existence of a transverse tensile strain. For the first time ever to our best knowledge, 3D strains induced by chemoelastic effects in soft tissues were quantified thanks to the OCT-DVC method. Without doubt, chemoelasticity plays an essential role in arterial mechanobiology in vivo and future work should focus on characterizing chemoelastic effects in arterial walls under physiological and disease conditions. STATEMENT OF SIGNIFICANCE: Chemoelasticity, coupling osmotic phenomena and mechanical stresses, is essential in soft tissue mechanobiology. For the first time ever, we measure and analyze 3D strain fields induced by these chemoelastic effects thanks to the unique combination of OCT imaging and digital volume correlation.

Does the Knowledge of the Local Thickness of Human Ascending Thoracic Aneurysm Walls Improve Their Mechanical Analysis?

Ascending thoracic aortic aneurysm (ATAA) ruptures are life threatening phenomena which occur in local weaker regions of the diseased aortic wall. As ATAAs are evolving pathologies, their growth represents a significant local remodeling and degradation of the microstructural architecture and thus their mechanical properties. To address the need for deeper study of ATAAs and their failure, it is required to analyze the mechanical behavior at the sub-millimeter scale by making use of accurate geometrical and kinematical measurements during their deformation. For this purpose, we propose a novel methodology that combined an accurate tool for thickness distribution measurement of the arterial wall, digital image correlation to assess local strain fields and bulge inflation to characterize the physiological and failure response of flat unruptured human ATAA specimens. The analysis of the heterogeneity of the local thickness and local physiological stress and strain was carried out for each investigated subject. At the subject level, our results state the presence of a non-consistent relationship between the local wall thickness and the local physiological strain field and high heterogeneity of the variables. At the inter-subject level, thicknesses were studied in relation to physiological strain and stress and load at rupture. The rupture pressure was correlated with neither the average thickness nor the lowest thickness of the specimens. Our results confirm that intrinsic material strength (hence structure) differs a lot from a subject to another and even within the same subject.

The evaluation of the aortic annulus displacement during cardiac cycle using magnetic resonance imaging

Background

The stress in the ascending aorta results from many biomechanical factors including the geometry of the vessel and its maximum dimensions, arterial blood pressure and longitudinal systolic stretching due to heart motion. The stretching of the ascending aorta resulting from the longitudinal displacement of the aortic annulus during the heart cycle has not been examined in the general population so far. The aim of the study is to evaluate this parameter using cardiovascular magnetic resonance (CMR) imaging in the general population in all age groups.

Methods

The cardiac magnetic resonance images of 73 patients were evaluated. The maximum distance to which the ventriculo-aortic junction was pulled by the contracting heart (LDAA – longitudinal displacement of the aortic annulus) was measured in the cine coronal sequences. Moreover, the maximum dimensions of the aortic root and the ascending aorta were assessed.

Results

The LDAA value was on average 11.6 ± 2.9 mm (range: 3-19 mm; 95% CI: 10.9–12.3 mm) and did not differ between males and females (11.8 ± 2.9 mm vs. 11.2 ± 2.9 mm, p = .408). The diameter of the ascending aorta was 32 ± 6.3 mm (range: 20-57 mm). The maximal dimension of the aortic root was 35 ± 5.1 mm (range: 18-42 mm). There was a statistically significant negative correlation between the LDAA and the age of patients (r = −.38, p = .001). There was no significant correlation between the LDAA and aortic root dimension (r = .1, p = .409) and between the LDAA and diameter of the ascending aorta (r = .16, p = .170).

Conclusions

Human aortic root and ascending aorta are significantly stretched during systole and the distance to which the aorta is stretched decreases with age. The measurement of the longitudinal displacement of the aortic annulus using the CMR is feasible and reproducible.

High Spatial Resolution Multi-Organ Finite Element Modeling of Ventricular-Arterial Coupling

While it has long been recognized that bi-directional interaction between the heart and the vasculature plays a critical role in the proper functioning of the cardiovascular system, a comprehensive study of this interaction has largely been hampered by a lack of modeling framework capable of simultaneously accommodating high-resolution models of the heart and vasculature. Here, we address this issue and present a computational modeling framework that couples finite element (FE) models of the left ventricle (LV) and aorta to elucidate ventricular-arterial coupling in the systemic circulation. We show in a baseline simulation that the framework predictions of (1) LV pressure-volume loop, (2) aorta pressure-diameter relationship, (3) pressure-waveforms of the aorta, LV, and left atrium (LA) over the cardiac cycle are consistent with the physiological measurements found in healthy human. To develop insights of ventricular-arterial interactions, the framework was then used to simulate how alterations in the geometrical or, material parameter(s) of the aorta affect the LV and vice versa. We show that changing the geometry and microstructure of the aorta model in the framework led to changes in the functional behaviors of both LV and aorta that are consistent with experimental observations. On the other hand, changing contractility and passive stiffness of the LV model in the framework also produced changes in both the LV and aorta functional behaviors that are consistent with physiology principles.

Structural and Functional Differences Between Porcine Aorta and Vena Cava

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

Should We Ignore What We Cannot Measure? How Non-Uniform Stretch, Non-Uniform Wall Thickness and Minor Side Branches Affect Computational Aortic Biomechanics in Mice

In order to advance the state-of-the-art in computational aortic biomechanics, we investigated the influence of (i) a non-uniform wall thickness, (ii) minor aortic side branches and (iii) a non-uniform axial stretch distribution on the location of predicted hotspots of principal strain in a mouse model for dissecting aneurysms. After 3 days of angiotensin II infusion, a murine abdominal aorta was scanned in vivo with contrast-enhanced micro-CT. The animal was subsequently sacrificed and its aorta was scanned ex vivo with phase-contrast X-ray tomographic microscopy (PCXTM). An automatic morphing framework was developed to map the non-pressurized, non-stretched PCXTM geometry onto the pressurized, stretched micro-CT geometry. The output of the morphing model was a structural FEM simulation where the output strain distribution represents an estimation of the wall deformation, not only due to the pressurization, but also due to the local axial stretch field. The morphing model also included minor branches and a mouse-specific wall thickness. A sensitivity study was then performed to assess the influence of each of these novel features on the outcome of the simulations. The results were supported by comparing the computed hotspots of principal strain to hotspots of early vascular damage as detected on PCXTM. Non-uniform axial stretch, non-uniform wall thickness and minor subcostal arteries significantly alter the locations of calculated hotspots of maximal principal strain. Even if experimental data on these features are often not available in clinical practice, one should be aware of the important implications that simplifications in the model might have on the final simulated result.

Mechanical behavior of porcine thoracic aorta in physiological and supra-physiological intraluminal pressures

Understanding the mechanical behavior of aorta under supra-physiological loadings is an important aspect of modeling tissue behavior in various applications that involve large deformations. Utilizing inflation–extension experiments, the mechanical behavior of porcine descending thoracic aortic segments under physiological and supra-physiological intraluminal pressures was investigated. The pressure was changed in the range of 0–70 kPa and the deformation of the segment was determined in three dimensions using a custom-made motion capture system. An orthotropic Fung-type constitutive model was characterized by implementing a novel computationally efficient framework that ensured material stability for numerical simulations. The nonlinear rising trend of circumferential stretch ratio [Formula: see text] from outer toward inner wall was significantly increased at higher pressures. The increase in [Formula: see text] from physiological pressure (13 kPa) to 70 kPa was 13% at the outer wall and 22% at the inner wall; in this pressure range, the longitudinal stretch ratio [Formula: see text] increased 20%. A significant nonlinearity in the material behavior was observed as in the same pressure range, and the circumferential and longitudinal Cauchy stresses at the inner wall were increased 16 and 18 times, respectively. The overall constitutive model was verified in several loading paths in the [Formula: see text] space to confirm its applicability in multi-axial loading conditions.

Investigation of inhomogeneous and anisotropic material behavior of porcine thoracic aorta using nano-indentation tests

This study investigates the inhomogeneity and anisotropy of porcine descending thoracic aorta in three dimensions using a custom-made nano-indentation technique and a quasi-linear viscoelastic modeling approach. The indentation tests were conducted in axial, circumferential, and radial orientations with about 100 μm spatial resolution. The ratio of the elastic moduli obtained in different orientations was used to quantify the tissue local anisotropy. The distal sections were generally stiffer than the proximal ones in both axial and circumferential indentations. Four distinct layers were identified across the thickness with significantly different mechanical properties. The stiffness of the medial quadrant was significantly lower than all other quadrants in axial indentation. The anisotropic behavior of the tissue was more pronounced in the lateral quadrant of the distal sections. The results of this study can be used to better understand the mechanisms of aorta deformation and improve the spatial accuracy of computational models of aorta.

Regional distribution of circumferential residual strains in the human aorta according to age and gender

The biomechanical response of the human aorta varies with axial location, but little is known about the respective variation of residual strains. Such data are available for common lab animals, but in the traditional opening angle measurement the aorta is considered as an ideal cylinder and average residual strains are measured, so that the spatial variations of local residual strains are not determined. The present study provides opening angle and residual strain data throughout the course and around the circumference of the aorta harvested during autopsy. Opening angle showed notable topographical variation; the highest value was at the top of aortic arch, declining abruptly toward the ascending aorta and to a near-constant value in the descending aorta, and rising in the abdominal aorta. The variation of curvature and of external but not internal residual stretch resembled that of opening angle. Extensive residual stress and wall thickness differences were evidenced among quadrants, with the more pre-stressed being also the thicker quadrants. Gender had overall minor effects, but aging led to increased parameters, occurring earlier in the distal aorta but at later stages becoming predominant proximally. Differences in caliber were pronounced in older subjects, unlike those in opening angle, residual stretches, and thickness that were striking in middle-aged subjects. By contrast, curvature decreased with aging in relation to the smaller percentwise opening angle differences. Detailed knowledge of the zero-stress/no-load geometry of the human aortic wall is critical for an in-depth understanding of aortic physiology, while providing the basis for comparison with disease.

Biaxial rupture properties of ascending thoracic aortic aneurysms

Although hundreds of samples obtained from ascending thoracic aortic aneurysms (ATAA) of patients undergoing elective surgical repair have already been characterized biomechanically, their rupture properties were always derived from uniaxial tensile tests. Due to their bulge shape, ATAAs are stretched biaxially in vivo. In order to understand the biaxial rupture of ATAAs, our group developed a novel methodology based on bulge inflation and full-field optical measurements. The objective of the current paper is threefold. Firstly, we will review the failure properties (maximum stress, maximum stretch) obtained by bulge inflation testing on a cohort of 31 patients and compare them with failure properties obtained by uniaxial tension in a previously published study. Secondly, we will investigate the relationship between the failure properties and the age of patients, showing that patients below 55years of age display significantly higher strength. Thirdly, we will define a rupture risk based on the extensibility of the tissue and we will show that this rupture risk is strongly correlated with the physiological elastic modulus of the tissue independently of the age, ATAA diameter or the aortic valve phenotype of the patient.

STATEMENT OF SIGNIFICANCE

Despite their medical importance, rupture properties of ascending thoracic aortic aneurysms (ATAA) subjected to biaxial tension were inexistent in the literature. In order to address this lack, our group developed a novel methodology based on bulge inflation and full-field optical measurements. Here we report rupture properties obtained with this methodology on 31 patients. It is shown for the first time that rupture occurs when the stretch applied to ATAAs reaches the maximum extensibility of the tissue and that this maximum extensibility correlates strongly with the elastic properties. The outcome is a better detection of at-risk individuals for elective surgical repair.

Using Digital Image Correlation to Characterize Local Strains on Vascular Tissue Specimens

Characterization of the mechanical behavior of biological and engineered soft tissues is a central component of fundamental biomedical research and product development. Stress-strain relationships are typically obtained from mechanical testing data to enable comparative assessment among samples and in some cases identification of constitutive mechanical properties. However, errors may be introduced through the use of average strain measures, as significant heterogeneity in the strain field may result from geometrical non-uniformity of the sample and stress concentrations induced by mounting/gripping of soft tissues within the test system. When strain field heterogeneity is significant, accurate assessment of the sample mechanical response requires measurement of local strains. This study demonstrates a novel biomechanical testing protocol for calculating local surface strains using a mechanical testing device coupled with a high resolution camera and a digital image correlation technique. A series of sample surface images are acquired and then analyzed to quantify the local surface strain of a vascular tissue specimen subjected to ramped uniaxial loading. This approach can improve accuracy in experimental vascular biomechanics and has potential for broader use among other native soft tissues, engineered soft tissues, and soft hydrogel/polymeric materials. In the video, we demonstrate how to set up the system components and perform a complete experiment on native vascular tissue.

A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis

Biomechanical models have the potential to predict plaque rupture. For reliable models, correct material properties of plaque components are a prerequisite. This study presents a new technique, where high resolution ultrasound displacement imaging and inverse finite element (FE) modeling is combined, to estimate material properties of plaque components. Iliac arteries with plaques were excised from 6 atherosclerotic pigs and subjected to an inflation test with pressures ranging from 10 to 120 mmHg. The arteries were imaged with high frequency 40 MHz ultrasound. Deformation maps of the plaques were reconstructed by cross correlation of the ultrasound radiofrequency data. Subsequently, the arteries were perfusion fixed for histology and structural components were identified. The histological data were registered to the ultrasound data to construct FE model of the plaques. Material properties of the arterial wall and the intima of the atherosclerotic plaques were estimated using a grid search method. The computed displacement fields showed good agreement with the measured displacement fields, implying that the FE models were able to capture local inhomogeneities within the plaque. On average, nonlinear stiffening of both the wall and the intima was observed, and the wall of the atheroslcerotic porcine iliac arteries was markedly stiffer than the intima (877 ± 459 vs. 100 ± 68 kPa at 100 mmHg). The large spread in the data further illustrates the wide variation of the material properties. We demonstrated the feasibility of a mixed experimental–numerical framework to determine the material properties of arterial wall and intima of atherosclerotic plaques from intact arteries, and concluded that, due to the observed variation, plaque specific properties are required for accurate stress simulations.

A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries

The existence of residual stresses in human arteries has long been shown experimentally. Researchers have also demonstrated that residual stresses have a significant effect on the distribution of physiological stresses within arterial tissues, and hence on their development, e.g., stress-modulated remodeling. Through progress in medical imaging, image analysis and finite element (FE) meshing tools it is now possible to construct in vivo patient-specific geometries and thus to study specific, clinically relevant problems in arterial mechanics via FE simulations. Classical continuum mechanics and FE methods assume that constitutive models and the corresponding simulations start from unloaded, stress-free reference configurations while the boundary-value problem of interest represents a loaded geometry and includes residual stresses. We present a pragmatic methodology to simultaneously account for both (i) the three-dimensional (3-D) residual stress distributions in the arterial tissue layers, and (ii) the equilibrium of the in vivo patient-specific geometry with the known boundary conditions. We base our methodology on analytically determined residual stress distributions (Holzapfel and Ogden, 2010, J. R. Soc. Interface 7, 787-799) and calibrate it using data on residual deformations (Holzapfel et al., 2007, Ann. Biomed. Eng. 35, 530-545). We demonstrate our methodology on three patient-specific FE simulations calibrated using experimental data. All data employed here are generated from human tissues - both the aorta and thrombus, and their respective layers - including the geometries determined from magnetic resonance images, and material properties and 3-D residual stretches determined from mechanical experiments. We study the effect of 3-D residual stresses on the distribution of physiological stresses in the aortic layers (intima, media, adventitia) and the layers of the intraluminal thrombus (luminal, medial, abluminal) by comparing three types of FE simulations: (i) conventional calculations; (ii) calculations accounting only for prestresses; (iii) calculations including both 3-D residual stresses and prestresses. Our results show that including residual stresses in patient-specific simulations of arterial tissues significantly impacts both the global (organ-level) deformations and the stress distributions within the arterial tissue (and its layers). Our method produces circumferential Cauchy stress distributions that are more uniform through the tissue thickness (i.e., smaller stress gradients in the local radial directions) compared to both the conventional and prestressing calculations. Such methods, combined with appropriate experimental data, aim at increasing the accuracy of classical FE analyses for patient-specific studies in computational biomechanics and may lead to increased clinical application of simulation tools.

Characterization of regional deformation and material properties of the intact explanted vein by microCT and computational analysis

PURPOSE

Detailed mechanical information of the vein is important to better understand remodeling of the vessel in disease states, but has been difficult to obtain due to its thinness, unique geometry, and limitations of mechanical testing. This study presents a novel method for characterizing deformation of the intact explanted vein under physiological loads and determining its material properties by combining high-resolution imaging and computational analysis.

METHODS

High-resolution CT (microCT) was used to image an iodine-stained, excised porcine internal jugular vein sample under extension to 100% and 120% of in situ length, and inflation and 2, 10, 20 mmHg of pressure, inside a microCT-compatible hydrostatic loading chamber. Regional strains were measured with the finite element (FE) image registration method known as Hyperelastic Warping. Material properties were approximated with inverse FE characterization by optimizing stiffness-related coefficients so to match simulated strains to the experimental measurements.

RESULTS

The observed morphology and regional strain of the vein were found to be relatively heterogeneous. The regional variability in the measured strain was primarily driven by geometry. Although iodine treatment may result in tissue stiffening, which requires additional investigation, it is effective in allowing detailed detection of vein geometry.

CONCLUSIONS

The feasibility and utility of using microCT and computational analysis to characterize mechanical responses and material properties of the vein were demonstrated. The presented method is a promising alternative or addition to mechanical testing for characterizing veins or other similarly delicate vessels in their native anatomical configuration under a wide range of realistic or simulated environmental and loading conditions.

Vascular elastography: a validation study

Vascular elastography techniques are promising tools for mechanical characterization of diseased arteries. These techniques are usually validated with simulations or phantoms or by comparing results with histology or other imaging modalities. In the study described here, vascular elastography was applied to porcine aortas in vitro during inflation testing (n = 10) and results were compared with those of standard bi-axial tensile testing, a technique that directly measures the force applied to the tissue. A neo-Hookean model was fit to the stress-strain data, valid for large deformations. Results indicated good correspondence between the two techniques, with GUS = 110 ± 11 kPa and GTT = 108 ± 10 kPa for ultrasound and tensile testing, respectively. Bland-Altman analysis revealed little bias (GUS-GTT = 2 ± 20 kPa). The next step will be the application of a non-linear material model that is also adaptable for in vivo measurements.

Structural and mechanical characterisation of bridging veins: A review

Bridging veins drain the venous blood from the cerebral cortex into the superior sagittal sinus (SSS) and doing so they bridge the subdural space. Despite their importance in head impact biomechanics, little is known about their properties with respect to histology, morphology and mechanical behaviour. Knowledge of these characteristics is essential for creating a biofidelic finite element model to study the biomechanics of head impact, ultimately leading to the improved design of protective devices by setting up tolerance criteria. This paper presents a comprehensive review of the state-of-the-art knowledge on bridging veins. Tolerance criteria to prevent head injury through impact have been set by a number of research groups, either directly through impact experiments or by means of finite element (FE) simulations. Current state-of-the-art FE head models still lack a biofidelic representation of the bridging veins. To achieve this, a thorough insight into their nature and behaviour is required. Therefore, an overview of the general morphology and histology is provided here, showing the clearly heterogeneous nature of the bridging vein complex, with its three different layers and distinct morphological and histological changes at the region of outflow into the superior sagittal sinus. Apart from a complex morphology, bridging veins also exhibit complex mechanical behaviour, being nonlinear, viscoelastic and prone to damage. Existing material models capable of capturing these properties, as well as methods for experimental characterisation, are discussed. Future work required in bridging vein research is firstly to achieve consensus on aspects regarding morphology and histology, especially in the outflow cuff segment. Secondly, the advised material models need to be populated with realistic parameters through biaxial mechanical experiments adapted to the dimensions of the bridging vein samples. Finally, updating the existing finite element head models with these parameters will render them truly biofidelic, allowing the establishment of accurate tolerance criteria and, ultimately, better head protection devices.

Biomechanical evaluation of ascending aortic aneurysms

The biomechanical properties of ascending aortic aneurysms were investigated only in the last decade in a limited number of studies. Indeed, in recent years, there has been a growing interest in this field in order to identify new predictive parameters of risk of dissection, which may have clinical relevance. The researches performed so far have been conducted according to the methods used in the study of abdominal aortic aneurysms. In most cases, uniaxial or biaxial tensile tests were used, while in a smaller number of studies other methods, such as opening angle, bulge inflation, and inflation-extension tests, were used. However, parameters and protocols of these tests are at present very heterogeneous in the studies reported in the literature, and, therefore, the results are not comparable and are sometimes conflicting. The purpose of this review then thence to provide a comprehensive analysis of the experimental methodology for determination of biomechanical properties in the specific field of aneurysms of the ascending aorta to allow for better comparison and understanding of the results.

The effect of static stretch on elastin degradation in arteries

Previously we have shown that gradual changes in the structure of elastin during an elastase treatment can lead to important transition stages in the mechanical behavior of arteries. However, in vivo arteries are constantly being loaded due to systolic and diastolic pressures and so understanding the effects of loading on the enzymatic degradation of elastin in arteries is important. With biaxial tensile testing, we measured the mechanical behavior of porcine thoracic aortas digested with a mild solution of purified elastase (5 U/mL) in the presence of a static stretch. Arterial mechanical properties and biochemical composition were analyzed to assess the effects of mechanical stretch on elastin degradation. As elastin is being removed, the dimensions of the artery increase by more than 20% in both the longitude and circumference directions. Elastin assays indicate a faster rate of degradation when stretch was present during the digestion. A simple exponential decay fitting confirms the time constant for digestion with stretch (0.11 ± 0.04 h(-1)) is almost twice that of digestion without stretch (0.069 ± 0.028 h(-1)). The transition from J-shaped to S-shaped stress vs. strain behavior in the longitudinal direction generally occurs when elastin content is reduced by about 60%. Multiphoton image analysis confirms the removal/fragmentation of elastin and also shows that the collagen fibers are closely intertwined with the elastin lamellae in the medial layer. After removal of elastin, the collagen fibers are no longer constrained and become disordered. Release of amorphous elastin during the fragmentation of the lamellae layers is observed and provides insights into the process of elastin degradation. Overall this study reveals several interesting microstructural changes in the extracellular matrix that could explain the resulting mechanical behavior of arteries with elastin degradation.

Influence of surrounding tissues on biomechanics of aortic wall

The present study investigates effects of surrounding tissues and non-uniform wall thickness on the biomechanics of the thoracic aorta. We construct two idealised computational models exemplifying the importance of surrounding tissues and non-uniform wall thickness, namely the uniform-thickness model and the histology image-based model. While the former neglects a connective tissue layer surrounding the aorta, the latter takes it into account with non-uniform wall thickness. Using plane strain finite element analysis, stress distributions in the aortic media between the two models are compared. The histology image-based model substantially enhances the uniformity of stress throughout the aortic media. Furthermore, the altered mechanical properties of surrounding tissues change the stress distribution. These results suggest that surrounding tissues and non-uniform wall thickness should be included in biomechanical analysis to better understand regional adaptation of the aortic wall during normal physiological conditions or pathological conditions such as aortic aneurysms and dissections.

Quantification of structural compliance of aged human and porcine aortic root tissues

The structural compliance of the aortic root has a significant implication for valve procedures such as transcatheter aortic valve implantation and valve-sparing aortic root replacement. However, a detailed quantification of human aortic root structural compliance, particularly in different regions, has been incomplete. In this study, the structural properties of human aortic roots (81 ± 8.74 years, n = 10) were characterized and compared with those of porcine ones (6-9 months, n = 10) using a vessel pressure-inflation test. The test involved tracking three-dimensional deformation of the markers affixed on the different surface regions of the aortic roots, including the three sinuses: the noncoronary sinus (NCS), the left-coronary sinus (LCS), and the right-coronary sinus (RCS), and at three regions along the longitudinal direction of each sinus: the upper sinus (US), the middle sinus (MS), and the lower sinus (LS), and the ascending aorta (AA) region above the NCS. We found that tissue stiffness in physiological pressure range was similar among the three human sinuses. A variation in regional structural stiffness of human aorta was observed. In the circumferential direction, the LS regions were the stiffest in the LCS and RCS, whereas NCS had relatively uniform stiffness. In the longitudinal direction, the human AA regions were more compliant than all sinuses. There was a significant difference in tissue stiffness between human and porcine aortic tissues, suggesting that the mechanical properties of porcine tissues may not be analogous to aged human ones.

Fidelity of the estimation of the deformation gradient from data deduced from the motion of markers placed on a body that is subject to an inhomogeneous deformation field

Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error.