Biaxial mechanical properties of intact and layer-dissected human carotid arteries at physiological and supraphysiological loadings

Comparative in vivo analysis of the role of the adventitia and the endothelium on arterial mechanical function: relevance for aortic counterpulsation

PURPOSE

The comparative effect of the intimal and adventitial layers on arterial biomechanics control, in basal and altered conditions, remains to be elucidated. This study aimed (1) to characterize the arterial conduit (CF) and buffering (distensibility) function of the iliac arteries in in vivo animals, in which the intimal and adventitial layers were removed; (2) to determine the effects of intra-aortic ballon pumping (IABP) on simultaneously de-adventitialized (DA) and de-endothelialized (DE) iliac arteries before and after induced heart failure.

METHODS

Pressure and diameter signals were measured in the iliac arteries of sheep (n = 7) in which the adventitial and intima layer were removed. Intra-aortic balloon pump (IABP) assistance was used in a control state and after heart failure induction.

RESULTS

Both DE and DA determined significant changes in arterial diameter, distensibility and CF. Changes were higher after DA than after DE in terms of distensibility and CF (p<0.05). DA followed by DE (DA + DE) showed significant increases in arterial diameter and CF, accompanied by a decrease in distensibility (p<0.05) with respect to intact arteries. Heart failure induction caused significant hemodynamic changes without modifying the already impaired local biomechanical parameters. Nonsignificant improvements in the biomechanical parameters of DA + DE iliac arteries were observed during IABP before and after heart failure induction.

CONCLUSIONS

Biomechanical changes caused by DA of iliac arteries were more important than those observed after DE. The DA + DE arteries showed significant differences with respect to intact arteries and with DA or DE arteries. IABP-related effects on arterial mechanics were absent in DA + DE arteries.

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.

Histology and Biaxial Mechanical Behavior of Abdominal Aortic Aneurysm Tissue Samples

Abdominal aortic aneurysms (AAAs) represent permanent, localized dilations of the abdominal aorta that can be life-threatening if progressing to rupture. Evaluation of risk of rupture depends on understanding the mechanical behavior of patient AAA walls. In this project, a series of patient AAA wall tissue samples have been evaluated through a combined anamnestic, mechanical, and histopathologic approach. Mechanical properties of the samples have been characterized using a novel, strain-controlled, planar biaxial testing protocol emulating the in vivo deformation of the aorta. Histologically, the tissue ultrastructure was highly disrupted. All samples showed pronounced mechanical stiffening with stretch and were notably anisotropic, with greater stiffness in the circumferential than the axial direction. However, there were significant intrapatient variations in wall stiffness and stress. In biaxial tests in which the longitudinal stretch was held constant at 1.1 as the circumferential stretch was extended to 1.1, the maximum average circumferential stress was 330 ± 70 kPa, while the maximum average axial stress was 190 ± 30 kPa. A constitutive model considering the wall as anisotropic with two preferred directions fit the measured data well. No statistically significant differences in tissue mechanical properties were found based on patient gender, age, maximum bulge diameter, height, weight, body mass index, or smoking history. Although a larger patient cohort is merited to confirm these conclusions, the project provides new insight into the relationships between patient natural history, histopathology, and mechanical behavior that may be useful in the development of accurate methods for rupture risk evaluation.

Experimental determination of rupture pressure and stress of adventitia of human middle cerebral arteries

Background Intracranial arterial dissections might be attributed to the particular biomechanical properties of their specific layers. Also, knowledge of adventitia properties would be crucial in the context of intracranial balloon angioplasty. Aims The purpose of this work was to determine the rupture pressure of separated adventitia and compare it to intact cerebral arterial segments. Methods Brain specimens were harvested from 14 autopsy subjects (age range from 23 to 86 years). Pressure-inflation tests were conducted on proximal segments of middle cerebral arteries and separated adventitia layers from contralateral arteries to assess the rupture pressure values. Results The averaged rupture pressure of adventitia layers was 1.41 SD 0.25 atm (1072 SD 190 mmHg), whereas for intact arterial segments it was 2.32 SD 0.70 atm (1763 SD 532 mmHg) and diminished with age according to nonlinear regression trends. The difference beetween the aformentioned rupture pressures was positively correlated with rupture pressure of intact arterial segments ( R²= 0.88; p < 0.001). Conclusions The obtained experimental results indicate a leading role of adventitia in building arterial strength under supraphysiological pressure conditions. The greater the rupture pressure of complete cerebral arteries, the smaller the contribution of adventitia in overall wall resistance.

Mechanical properties and composition of carotid and femoral atherosclerotic plaques: A comparative study

This study compares the mechanical properties of excised carotid and femoral human plaques and also develops a predictor of these properties based on plaque composition. Circumferential planar tension tests were performed on 24 carotid and 16 femoral plaque samples. Composition was characterised using Fourier Transform Infrared spectroscopy. Stretch at failure, strength, and stiffness are significantly higher in the carotid group (P=.012, P<.001 and P=.002, respectively). The ratio of calcified to lipid plaque content demonstrates the strongest correlation with the stretch at failure and strength (R²=.285, P<.001 and R²=.347, P<.001). No composition based parameter correlates significantly with stiffness. The significantly different mechanical properties of the two groups aids in explaining the varying endovascular treatment outcomes clinically observed in these vessels. Furthermore, determining the ratio of calcified to lipid plaque content may be useful in predicting individual plaque mechanical response to endovascular treatment.

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

BACKGROUND

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall's anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example.

METHOD

Porcine common carotid arteries (n=10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF.

RESULTS

Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (κ1,2,3=[13.5,0.0,25.2] and κ1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data.

CONCLUSIONS

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.

STATEMENT OF SIGNIFICANCE

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial and uniaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, an effective orientation density that accounts for cross-links between the main collagen fibers has been porposed. The model provides a good approximation to the experimental data.

Endothelial fluid shear stress sensing in vascular health and disease

Endothelial cells transduce the frictional force from blood flow (fluid shear stress) into biochemical signals that regulate gene expression and cell behavior via specialized mechanisms and pathways. These pathways shape the vascular system during development and during postnatal and adult life to optimize flow to tissues. The same pathways also contribute to atherosclerosis and vascular malformations. This Review covers recent advances in basic mechanisms of flow signaling and the involvement of these mechanisms in vascular physiology, remodeling, and these diseases. We propose that flow sensing pathways that govern normal morphogenesis can contribute to disease under pathological conditions or can be altered to induce disease. Viewing atherosclerosis and vascular malformations as instances of pathological morphogenesis provides a unifying perspective that may aid in developing new therapies.

Quest for the Vulnerable Atheroma: Carotid Stenosis and Diametric Strain--A Feasibility Study

The Bernoulli effect may result in eruption of a vulnerable carotid atheroma, causing a stroke. We measured electrocardiography (ECG)-registered QRS intra-stenotic blood velocity and atheroma strain dynamics in carotid artery walls using ultrasonic tissue Doppler methods, providing displacement and time resolutions of 0.1 μm and 3.7 ms. Of 22 arteries, 1 had a peak systolic velocity (PSV) >280 cm/s, 4 had PSVs between 165 and 280 cm/s and 17 had PSVs <165 cm/s. Eight arteries with PSVs <65 cm/s and 4 of 9 with PSVs between 65 and 165 cm/s had normal systolic diametric expansion (0% and 7%) and corresponding systolic wall thinning. The remaining 10 arteries had abnormal systolic strain dynamics, 2 with diametric reduction (>-0.05 mm), 2 with extreme wall expansion (>0.1 mm), 2 with extreme wall thinning (>-0.1 mm) and 4 with combinations. Decreases in systolic diameter and/or extreme systolic arterial wall thickening may indicate imminent atheroma rupture.

Biomechanical properties and microstructure of human ventricular myocardium

In the multidisciplinary field of heart research it is of utmost importance to identify accurate myocardium material properties for the description of phenomena such as mechano-electric feedback or heart wall thickening. A rationally-based material model is required to understand the highly nonlinear mechanics of complex structures such as the passive myocardium under different loading conditions. Unfortunately, to date there are no experimental data of human heart tissues available to estimate material parameters and to develop adequate material models. This study aimed to determine biaxial extension and triaxial shear properties and the underlying microstructure of the passive human ventricular myocardium. Using new state-of-the-art equipment, planar biaxial extension tests were performed to determine the biaxial extension properties of the passive ventricular human myocardium. Shear properties of the myocardium were examined by triaxial simple shear tests performed on small cubic specimens excised from an adjacent region of the biaxial extension specimens. The three-dimensional microstructure was investigated through second-harmonic generation (SHG) microscopy on optically cleared tissues, which emphasized the 3D orientation and dispersion of the myofibers and adjacent collagen fabrics. The results suggest that the passive human LV myocardium under quasi-static and dynamic multiaxial loadings is a nonlinear, anisotropic (orthotropic), viscoelastic and history-dependent soft biological material undergoing large deformations. Material properties of the tissue components along local microstructural axes drive the nonlinear and orthotropic features of the myocardium. SHG microscopy investigation revealed detailed information about the myocardial microstructure due to its high resolution. It enabled the identification of structural parameters such as the fiber and the sheet orientations and corresponding dispersions. With this complete set of material data, a sophisticated material model and associated material parameters can be defined for a better description of the biomechanical response of the ventricular myocardium in humans. Such a model will lead to more accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases.

STATEMENT OF SIGNIFICANCE

Unfortunately, to date there are no experimental data of human heart tissues available for material parameter estimation and the development of adequate material models. In this manuscript novel biaxial tensile and shear test data at different specimen orientations are presented, which allowed to adequately capture the direction-dependent material response. With these complete sets of mechanical data, combined with their underlying microstructural data (also presented herein), sophisticated material models and associated material parameters can be defined for the description of the mechanical behavior of the ventricular myocardium in humans. Such models will lead to accurate computational simulations to better understand the fundamental underlying ventricular mechanics, a step needed in the improvement of medical treatment of heart diseases.

A New Vascular Coupler Design for End-to-End Anastomosis: Fabrication and Proof-of-Concept Evaluation

Traditional hand-suturing for vascular connection techniques is time consuming, expensive, and requires highly complex instruments and technical expertise. The aim of this study is to develop a new vascular coupler that can be used in end-to-end anastomosis surgery in an easier and more efficient way for both arteries and veins. The vascular coupler has four rotatable wings and one translatable spike in each wing. Prototypes were manufactured using polytetrafluoroethylene (PTFE) and high-density polyethylene (HDPE). A set of installation tools was designed to facilitate the anastomosis process. Proof-of-concept testing with the vascular coupler using plastic tubes and porcine cadaver vessels showed that the coupler should work as designed. A simplified finite element (FE) model assisted in the evaluation of the tearing likelihood of human vessels during installation of the coupler. Results of tests on the coupler showed that the vascular coupler could be efficiently attached to blood vessels, did not leak after the anastomosis was performed, had sufficient joint strength, and had little impact on flow in the vessel. The entire anastomosis process can be completed in 3 min when using the vascular coupler to join porcine cadaver vessels.

Investigation of the optimal collagen fibre orientation in human iliac arteries

The distribution of collagen fibres plays a significant role in the mechanical behaviour of artery walls. Experimental data show that in most artery wall layers there are two (or more) in-plane symmetrically disposed families of fibres. However, a recent investigation revealed that some artery wall layers have only one preferred fibre direction, notably in the medial layer of human common iliac arteries. This paper aims to provide a possible explanation for this intriguing phenomenon. An invariant-based constitutive model is utilized to characterize the mechanical behaviour of tissues. We then use three different hypotheses to determine the 'optimal fibre angle' in an iliac artery model. All three hypotheses lead to the same result that the optimal fibre angle in the medial layer of the iliac artery is close to the circumferential direction. The axial pre-stretch, in particular, is found to play an essential role in determining the optimal fibre angle.

Stretch calculated from grip distance accurately approximates mid-specimen stretch in large elastic arteries in uniaxial tensile tests

The mechanical properties of vascular tissues affect hemodynamics and can alter disease progression. The uniaxial tensile test is a simple and effective method for determining the stress-strain relationship in arterial tissue ex vivo. To enable calculation of strain, stretch can be measured directly with image tracking of markers on the tissue or indirectly from the distance between the grips used to hold the specimen. While the imaging technique is generally considered more accurate, it also requires more analysis, and the grip distance method is more widely used. The purpose of this study is to compare the stretch of the testing specimen calculated from the grip distance method to that obtained from the imaging method for canine descending aortas and large proximal pulmonary arteries. Our results showed a significant difference in stretch between the two methods; however, this difference was consistently less than 2%. Therefore, the grip distance method is an accurate approximation of the stretch in large elastic arteries in the uniaxial tensile test.

Modeling of human artery tissue with probabilistic approach

Accurate modeling of biological soft tissue properties is vital for realistic medical simulation. Mechanical response of biological soft tissue always exhibits a strong variability due to the complex microstructure and different loading conditions. The inhomogeneity in human artery tissue is modeled with a computational probabilistic approach by assuming that the instantaneous stress at a specific strain varies according to normal distribution. Material parameters of the artery tissue which are modeled with a combined logarithmic and polynomial energy equation are represented by a statistical function with normal distribution. Mean and standard deviation of the material parameters are determined using genetic algorithm (GA) and inverse mean-value first-order second-moment (IMVFOSM) method, respectively. This nondeterministic approach was verified using computer simulation based on the Monte-Carlo (MC) method. Cumulative distribution function (CDF) of the MC simulation corresponds well with that of the experimental stress-strain data and the probabilistic approach is further validated using data from other studies. By taking into account the inhomogeneous mechanical properties of human biological tissue, the proposed method is suitable for realistic virtual simulation as well as an accurate computational approach for medical device validation.

Quantification of Shear Deformations and Corresponding Stresses in the Biaxially Tested Human Myocardium

One goal of cardiac research is to perform numerical simulations to describe/reproduce the mechanoelectrical function of the human myocardium in health and disease. Such simulations are based on a complex combination of mathematical models describing the passive mechanical behavior of the myocardium and its electrophysiology, i.e., the activation of cardiac muscle cells. The problem in developing adequate constitutive models is the shortage of experimental data suitable for detailed parameter estimation in specific functional forms. A combination of shear and biaxial extension tests with different loading protocols on different specimen orientations is necessary to capture adequately the direction-dependent (orthotropic) response of the myocardium. In most experimental animal studies, where planar biaxial extension tests on the myocardium have been conducted, the generated shear stresses were neither considered nor discussed. Hence, in this study a method is presented which allows the quantification of shear deformations and related stresses. It demonstrates an approach for experimenters as to how the generation of these shear stresses can be minimized during mechanical testing. Experimental results on 14 passive human myocardial specimens, obtained from nine human hearts, show the efficiency of this newly developed method. Moreover, the influence of the clamping technique of the specimen, i.e., the load transmission between the testing device and the tissue, on the stress response is determined by testing an isotropic material (Latex). We identified that the force transmission between the testing device and the specimen by means of hooks and cords does not influence the performed experiments. We further showed that in-plane shear stresses definitely exist in biaxially tested human ventricular myocardium, but can be reduced to a minimum by preparing the specimens in an appropriate manner. Moreover, we showed whether shear stresses can be neglected when performing planar biaxial extension tests on fiber-reinforced materials. The used method appears to be robust to quantify normal and shear deformations and corresponding stresses in biaxially tested human myocardium. This method can be applied for the mechanical characterization of any fiber-reinforced material using planar biaxial extension tests.

Contribution of collagen fiber undulation to regional biomechanical properties along porcine thoracic aorta

As major extracellular matrix components, elastin, and collagen play crucial roles in regulating the mechanical properties of the aortic wall and, thus, the normal cardiovascular function. The mechanical properties of aorta, known to vary with age and multitude of diseases as well as the proximity to the heart, have been attributed to the variations in the content and architecture of wall constituents. This study is focused on the role of layer-specific collagen undulation in the variation of mechanical properties along the porcine descending thoracic aorta. Planar biaxial tensile tests are performed to characterize the hyperelastic anisotropic mechanical behavior of tissues dissected from four locations along the thoracic aorta. Multiphoton microscopy is used to image the associated regional microstructure. Exponential-based and recruitment-based constitutive models are used to account for the observed mechanical behavior while considering the aortic wall as a composite of two layers with independent properties. An elevated stiffness is observed in distal regions compared to proximal regions of thoracic aorta, consistent with sharper and earlier collagen recruitment estimated for medial and adventitial layers in the models. Multiphoton images further support our prediction that higher stiffness in distal regions is associated with less undulation in collagen fibers. Recruitment-based models further reveal that regardless of the location, collagen in the media is recruited from the onset of stretching, whereas adventitial collagen starts to engage with a delay. A parameter sensitivity analysis is performed to discriminate between the models in terms of the confidence in the estimated model parameters.

Evaluation of Biaxial Mechanical Properties of Aortic Media Based on the Lamellar Microstructure

Evaluation of the mechanical properties of arterial wall components is necessary for establishing a precise mechanical model applicable in various physiological and pathological conditions, such as remodeling. In this contribution, a new approach for the evaluation of the mechanical properties of aortic media accounting for the lamellar structure is proposed. We assumed aortic media to be composed of two sets of concentric layers, namely sheets of elastin (Layer I) and interstitial layers composed of mostly collagen bundles, fine elastic fibers and smooth muscle cells (Layer II). Biaxial mechanical tests were carried out on human thoracic aortic samples, and histological staining was performed to distinguish wall lamellae for determining the dimensions of the layers. A neo-Hookean strain energy function (SEF) for Layer I and a four-parameter exponential SEF for Layer II were allocated. Nonlinear regression was used to find the material parameters of the proposed microstructural model based on experimental data. The non-linear behavior of media layers confirmed the higher contribution of elastic tissue in lower strains and the gradual engagement of collagen fibers. The resulting model determines the nonlinear anisotropic behavior of aortic media through the lamellar microstructure and can be assistive in the study of wall remodeling due to alterations in lamellar structure during pathological conditions and aging.

Feasibility of a Priori Numerical Assessment of Plaque Scaffolding after Carotid Artery Stenting in Clinical Routine: Proof of Concept

Purpose

Carotid artery stenting (CAS) is an alternative procedure for the treatment of severely stenosed carotid artery lesions in high-risk patients. Appropriate patient selection and stent design are paramount to achieve a low stroke and death rate in these complex high-risk procedures. This study introduces and evaluates a novel virtual, patient-specific, pre-operative environment to quantify scaffolding parameters based on routine imaging techniques.

Methods

Two patients who underwent CAS with two different sizes of the Acculink stent (Abbott Vascular, Santa Clara, CA, USA) were studied. Pre-operative data were used to build the numerical models for the virtual procedure. Numerical results were validated with post-operative angiography. Using novel virtual geometrical tools, incomplete stent apposition, free cell area and largest fitting sphere in the stent cell were evaluated in situ as quantitative measures of successful stent placement and to assess potential risk factors for CAS complications.

Results

A quantitative validation of the numerical outcome with post-operative images noted differences in lumen diameter of 5.31 ± 8.05% and 4.12 ± 9.84%, demonstrating the reliability of the proposed methodology. The quantitative measurements of the scaffolding parameters on the virtually deployed stent geometry highlight the variability of the device behavior in relation to the target lesion. The free cell area depends on the target diameter and oversizing, while the largest fitting spheres and apposition values are influenced by the local concavity and convexity of the vessel.

Conclusions

The proposed virtual environment may be an additional tool for endovascular specialists especially in complex anatomical cases where stent design and positioning may have a higher impact on procedural success and outcome.

Determination and modeling of the inelasticity over the length of the porcine carotid artery

The study of the mechanical properties of swine carotids has clinical relevance because it is important for the appropriate design of intravascular devices in the animal trial phases. The inelastic properties of porcine carotid tissue were investigated. Experimental uniaxial cyclic tests were performed along the longitudinal and circumferential directions of vessels. The work focused on the determination, comparison, and constitutive modeling of the softening properties and residual stretch set of the swine carotid artery over long stretches and stress levels in both proximal and distal regions. It was observed that the residual strain depends on the maximum stretch in the previous load cycle. The strain was higher for distal than for proximal samples and for circumferential than for longitudinal samples. In addition, a pseudoelastic model was used to reproduce the residual stretch and softening behavior of the carotid artery. The model presented a good approximation of the experimental data. The results demonstrate that the final results in animal trial studies could be affected by the location studied along the length of the porcine carotid.

Extension of Murray's law including nonlinear mechanics of a composite artery wall

A goal function approach is used to derive an extension of Murray’s law that includes effects of nonlinear mechanics of the artery wall. The artery is modeled as a thin-walled tube composed of different species of nonlinear elastic materials that deform together. These materials grow and remodel in a process that is governed by a target state defined by a homeostatic radius and a homeostatic material composition. Following Murray’s original idea, this target state is defined by a principle of minimum work. We take this work to include that of pumping and maintaining blood, as well as maintaining the materials of the artery wall. The minimization is performed under a constraint imposed by mechanical equilibrium. We derive a condition for the existence of a cost-optimal homeostatic state. We also conduct parametric studies using this novel theoretical frame to investigate how the cost-optimal radius and composition of the artery wall depend on flow rate, blood pressure, and elastin content

A finite viscoelastic-plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress-strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress-strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.

A structural approach including the behavior of collagen cross-links to model patient-specific human carotid arteries

In this work the mechanical response of the carotid arterial wall is studied. Some limitations of previous models of the arterial wall are overcomed and variability of the fitting problem is reduced. We review some experimental data from the literature and provide a constitutive model to characterize such data. A strain energy function is introduced including the behavior of cross-links between the main collagen fibers. With this function we are able to fit experimental data including information about the microstructure that previous models were not able to do. To demonstrate the applicability of the proposed model a patient-specific carotid artery geometry is reconstructed and simulated in a finite element framework, providing a microstructural description of the arterial wall. Our results qualitatively and quantitatively describe the experimental findings given in the literature fitting macroscopic mechanical tests and improving the features of previously developed models.

Differential mechanical response and microstructural organization between non-human primate femoral and carotid arteries

Unique anatomic locations and physiologic functions predispose different arteries to varying mechanical responses and pathologies. However, the underlying causes of these mechanical differences are not well understood. The objective of this study was to first identify structural differences in the arterial matrix that would account for the mechanical differences between healthy femoral and carotid arteries and second to utilize these structural observations to perform a microstructurally motivated constitutive analysis. Femoral and carotid arteries were subjected to cylindrical biaxial loading and their microstructure was quantified using two-photon microscopy. The femoral arteries were found to be less compliant than the carotid arteries at physiologic loads, consistent with previous studies, despite similar extracellular compositions of collagen and elastin ([Formula: see text]). The femoral arteries exhibited significantly less circumferential dispersion of collagen fibers ([Formula: see text]), despite a similar mean fiber alignment direction as the carotid arteries. Elastin transmural distribution, in vivo axial stretch, and opening angles were also found to be distinctly different between the arteries. Lastly, we modeled the arteries' mechanical behaviors using a microstructural-based, distributed collagen fiber constitutive model. With this approach, the material parameters of the model were solved using the experimental microstructural observations. The findings of this study support an important role for microstructural organization in arterial stiffness.

Plaque hemorrhage in carotid artery disease: pathogenesis, clinical and biomechanical considerations

Stroke remains the most prevalent disabling illness today, with internal carotid artery luminal stenosis due to atheroma formation responsible for the majority of ischemic cerebrovascular events. Severity of luminal stenosis continues to dictate both patient risk stratification and the likelihood of surgical intervention. But there is growing evidence to suggest that plaque morphology may help improve pre-existing risk stratification criteria. Plaque components such a fibrous tissue, lipid rich necrotic core and calcium have been well investigated but plaque hemorrhage (PH) has been somewhat overlooked. In this review we discuss the pathogenesis of PH, its role in dictating plaque vulnerability, PH imaging techniques, marterial properties of atherosclerotic tissues, in particular, those obtained based on in vivo measurements and effect of PH in modulating local biomechanics.

Multiaxial mechanical response and constitutive modeling of esophageal tissues: Impact on esophageal tissue engineering

Congenital defects of the esophagus are relatively frequent, with 1 out of 2500 babies suffering from such a defect. A new method of treatment by implanting tissue engineered esophagi into newborns is currently being developed and tested using ovine esophagi. For the reconstruction of the biological function of native tissues with engineered esophagi, their cellular structure as well as their mechanical properties must be considered. Since very limited mechanical and structural data for the esophagus are available, the aim of this study was to investigate the multiaxial mechanical behavior of the ovine esophagus and the underlying microstructure. Therefore, uniaxial tensile, biaxial tensile and extension-inflation tests on esophagi were performed. The underlying microstructure was examined in stained histological sections through standard optical microscopy techniques. Moreover, the uniaxial ultimate tensile strength and residual deformations of the tissue were determined. Both the mucosa-submucosa and the muscle layers showed nonlinear and anisotropic mechanical behavior during uniaxial, biaxial and inflation testing. Cyclical inflation of the intact esophageal tube caused marked softening of the passive esophagi in the circumferential direction. The rupture strength of the mucosa-submucosa layer was much higher than that of the muscle layer. Overall, the ovine esophagus showed a heterogeneous and anisotropic behavior with different mechanical properties for the individual layers. The intact and layer-specific multiaxial properties were characterized using a well-known three-dimensional microstructurally based strain-energy function. This novel and complete set of data serves the basis for a better understanding of tissue remodeling in diseased esophagi and can be used to perform computer simulations of surgical interventions or medical-device applications.

Mechanical, biological and structural characterization of in vitro ruptured human carotid plaque tissue

Recent experimental studies performed on human carotid plaques have focused on mechanical characterization for the purpose of developing material models for finite-element analysis without quantifying the tissue composition or relating mechanical behaviour to preoperative classification. This study characterizes the mechanical and biological properties of 25 human carotid plaques and also investigates the common features that lead to plaque rupture during mechanical testing by performing circumferential uniaxial tests, Fourier transform infrared (FTIR) and scanning electron microscopy (SEM) on each specimen to relate plaque composition to mechanical behaviour. Mechanical results revealed large variations between plaque specimen behaviour with no correlation to preoperative ultrasound prediction. However, FTIR classification demonstrated a statistically significant relationship between stress and stretch values at rupture and the level of calcification (P=0.002 and P=0.009). Energy-dispersive X-ray spectroscopy was carried out to confirm that the calcium levels observed using FTIR analysis were accurate. This work demonstrates the potential of FTIR as an alternative method to ultrasound forpredicting plaque mechanical behaviour. SEM imaging at the rupture sites of each specimen highlighted voids created by the nodes of calcifications in the tissue structure which could lead to increased vulnerability of the plaque.

Non-Euclidean stress-free configuration of arteries accounting for curl of axial strips sectioned from vessels

It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.

Changing views of the biomechanics of vulnerable plaque rupture: a review

This review examines changing perspectives on the biomechanics of vulnerable plaque rupture over the past 25 years from the first finite element analyses (FEA) showing that the presence of a lipid pool significantly increases the local tissue stress in the atheroma cap to the latest imaging and 3D FEA studies revealing numerous microcalcifications in the cap proper and a new paradigm for cap rupture. The first part of the review summarizes studies describing the role of the fibrous cap thickness, tissue properties, and lesion geometry as main determinants of the risk of rupture. Advantages and limitations of current imaging technologies for assessment of vulnerable plaques are also discussed. However, the basic paradoxes as to why ruptures frequently did not coincide with location of PCS and why caps >65 μm thickness could rupture at tissue stresses significantly below the 300 kPa critical threshold still remained unresolved. The second part of the review describes recent studies in the role of microcalcifications, their origin, shape, and clustering in explaining these unresolved issues including the actual mechanism of rupture due to the explosive growth of tiny voids (cavitation) in local regions of high stress concentration between closely spaced microinclusions oriented along their tensile axis.

A mathematical evaluation of hemodynamic parameters after carotid eversion and conventional patch angioplasty

Carotid endarterectomy has a long history in stroke prevention, yet controversy remains concerning optimal techniques. Two methods frequently used are endarterectomy with patch angioplasty (CEAP) and eversion endarterectomy (CEE). The objective of this study was to compare hemodynamics-related stress and strain distributions between arteries repaired using CEAP and CEE. Mathematical models were based on in vivo three-dimensional arterial geometry, pulsatile velocity profiles, and intraluminal pressure inputs obtained from 16 patients with carotid artery disease. These data were combined with experimentally derived nonlinear, anisotropic carotid artery mechanical properties to create fluid-structure interaction models of CEAP and CEE. These models were then used to calculate hemodynamic parameters thought to promote recurrent disease and restenosis. Combining calculations of stress and strain into a composite risk index, called the integral abnormality factor, allowed for an overall comparison between CEAP and CEE. CEE demonstrated lower mechanical stresses in the arterial wall, whereas CEAP straightened the artery and caused high stress and strain concentrations at the suture-artery interface. CEAP produced a larger continuous region of oscillatory, low-shear, vortical flow in the carotid bulb. There was a more than two-fold difference in the integral abnormality factor, favoring CEE. In conclusion, in a realistically simulated carotid artery, fluid-structure interaction modeling demonstrated CEE to produce less mechanical wall stress and improved flow patterns compared with CEAP. Clinical validation with larger numbers of individual patients will ultimately be required to support modeling approaches to help predict arterial disease progression and comparative effectiveness of reconstruction methods and devices.

Patient-specific finite element analysis of carotid artery stenting: a focus on vessel modeling

Finite element analysis is nowadays a well-assessed technique to investigate the impact of stenting on vessel wall and, given the rapid progression of both medical imaging techniques and computational methods, the challenge of using the simulation of carotid artery stenting as procedure planning tool to support the clinical practice can be approached. Within this context, the present study investigates the impact of carotid stent apposition on carotid artery anatomy by means of patient-specific finite element analysis. In particular, we focus on the influence of the vessel constitutive model on the prediction of carotid artery wall tensional state of lumen gain and of vessel straightening. For this purpose, we consider, for a given stent design and CA anatomy, two constitutive models for the CA wall, that is, a hyperelastic isotropic versus a fiber-reinforced hyperelastic anisotropic model. Despite both models producing similar patterns with respect to stress distribution, the anisotropic model predicts a higher vessel straightening and a more evident discontinuity of the lumen area near the stent ends as observed in the clinical practice. Although still affected by several simplifications, the present study can be considered as further step toward a realistic simulation of carotid artery stenting.

Analysis of axial prestretch in the abdominal aorta with reference to post mortem interval and degree of atherosclerosis

It is a well-known fact that the length of an artery in situ and the length of an excised artery differs. Retraction of blood vessels is usually observed. This prestretch plays an important role in arterial physiology. We have recently determined that the decrease of axial prestretch in the human abdominal aorta is so closely correlated with age that it is suitable for forensic applications (estimation of the age at time of death for cadavers of unknown identity). Since post mortem autolysis may affect the reliability of an estimate based on axial prestretch, the present study aims to detail analysis of the effect of post mortem time. The abdominal aorta is a prominent site of atherosclerotic changes (ATH), which may potentially affect longitudinal prestretch. Thus ATH was also involved in the analysis. Axial prestretch in the human abdominal aorta, post mortem interval (PMI), and the degree of ATH were documented in 365 regular autopsies. The data was first age adjusted to remove any supposed correlation with age. After the age adjustment of the sample, the correlation analysis showed no significant PMI effects on the prestretch in non-putrefied bodies. Analysis of the prestretch variance with respect to ATH suggested that ATH is not a suitable factor to explain the prestretch variability remaining after the age adjustment. It was concluded that, although atherosclerotic plaques may certainly change the biomechanics of arteries, they do not significantly affect the longitudinal prestretch in the human abdominal aorta.

Our capricious vessels: The influence of stent design and vessel geometry on the mechanics of intracranial aneurysm stent deployment

There is a growing interest in virtual tools to assist clinicians in evaluating different procedures and devices for endovascular treatment. In the present study we use finite element analysis to investigate the influence of stent design and vessel geometry for stent assisted coiling of intracranial aneurysms. Nine virtual stenting procedures were performed: three nitinol stent designs ((i) an open cell stent resembling the Neuroform, (ii) a generic stiff and (iii) a more flexible closed cell design), were deployed in three patient-specific cerebral aneurysmatic vessels. We investigated the percentage of strut area covering the aneurysm neck, the straightening induced on the cerebrovasculature by the stent placement (quantified by the reduction in tortuosity), and stent apposition to the wall (quantified as the percentage of struts within 0.2mm of the vessel). The results suggest that the open cell design better covers the aneurysm neck (11.0±1.1%) compared to both the stiff (7.8±1.6%) and flexible (8.7±1.6%) closed cell stents, and induces less straightening of the vessel (-5.1±1.6% vs. -42.9±9.8% and -26.9±11.9% ). The open cell design has, however, less struts apposing well to the vessel wall (56.0±6.4%) compared to the flexible (73.4±4.6%) and stiff (70.4±5.1%) closed cell design. With the presented study, we hope to contribute to and improve aneurysm treatment, using a novel patient specific environment as a possible pre-operative tool to evaluate mechanical stent behavior in different vascular geometries.

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

Many treatments for cardiovascular diseases include an endovascular insertion of stents or stent grafts into arteries, a procedure which may cause high tissue stresses and even damage in the arterial wall. In order to study such problems by using finite element methods, both appropriate constitutive models and experimental data on human tissue samples are required. Layer-specific experimental data for human tissue tested up to the supra-physiological loading range are rare in the literature. In this study, intact and layer-separated experimental data from uniaxial extension tests are presented for human thoracic and abdominal aortas with non-atherosclerotic intimal thickening undergoing supra-physiological loading. A novel pseudo-elastic damage model, proposed to describe discontinuous softening in aortic arterial tissues, is fit to the obtained experimental data. Fitting of the model with and without consideration of damage accumulation in the non-collagenous matrix material reveals that tissue damage is primarily related to the collagen fiber fabric. By employing the fit model, the effect of aortic tissue pre-conditioning on the material parameters from the resulting data fits is evaluated. Histological examination of the collagen fibers under different applied stretches is used to gain more insights into the structural changes of the tissue under supra-physiological loading.

Arterial stiffness identification of the human carotid artery using the stress-strain relationship in vivo

Arterial stiffness is well accepted as a reliable indicator of arterial disease. Increase in carotid arterial stiffness has been associated with carotid arterial disease, e.g., atherosclerotic plaque, thrombosis, stenosis, etc. Several methods for carotid arterial stiffness assessment have been proposed. In this study, in vivo noninvasive assessment using applanation tonometry and an ultrasound-based motion estimation technique was applied in seven healthy volunteers (age 28±3.6years old) to determine pressure and wall displacement in the left common carotid artery (CCA), respectively. The carotid pressure was obtained using a calibration method by assuming that the mean and diastolic blood pressures remained constant throughout the arterial tree. The regional carotid arterial wall displacement was estimated using a 1D cross-correlation technique on the ultrasound radio frequency (RF) signals acquired at a frame rate of 505-1010Hz. Young's moduli were estimated under two different assumptions: (i) a linear elastic two-parallel spring model and (ii) a two-dimensional, nonlinear, hyperelastic model. The circumferential stress (σ(θ)) and strain (ɛ(θ)) relationship was then established in humans in vivo. A slope change in the circumferential stress-strain curve was observed and defined as the transition point. The Young's moduli of the elastic lamellae (E(1)), elastin-collagen fibers (E(2)) and collagen fibers (E(3)) and the incremental Young's moduli before ( [Formula: see text] ) and after the transition point ( [Formula: see text] ) were determined from the first and second approach, respectively, to describe the contribution of the complex mechanical interaction of the different arterial wall constituents. The average moduli E(1), E(2) and E(3) from seven healthy volunteers were found to be equal to 0.15±0.04, 0.89±0.27 and 0.75±0.29MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the intact wall (both the tunica adventitia and tunica media layers) were found to be equal to 0.16±0.04MPa and 0.90±0.25MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the tunica adventitia were found to be equal to 0.18±0.05MPa and 0.84±0.22MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the tunica media were found to be equal to 0.19±0.05MPa and 0.90±0.25MPa, respectively. The stiffness of the carotid artery increased with strain during the systolic phase. In conclusion, the feasibility of measuring the regional stress-strain relationship and stiffness of the normal human carotid artery was demonstrated noninvasively in vivo.

Comparative analysis of the biaxial mechanical behavior of carotid wall tissue and biological and synthetic materials used for carotid patch angioplasty

Patch angioplasty is the most common technique used for the performance of carotid endarterectomy. A large number of patching materials are available for use while new materials are being continuously developed. Surprisingly little is known about the mechanical properties of these materials and how these properties compare with those of the carotid artery wall. Mismatch of the mechanical properties can produce mechanical and hemodynamic effects that may compromise the long-term patency of the endarterectomized arterial segment. The aim of this paper was to systematically evaluate and compare the biaxial mechanical behavior of the most commonly used patching materials. We compared PTFE (n  =  1), Dacron (n  =  2), bovine pericardium (n  =  10), autogenous greater saphenous vein (n  =  10), and autogenous external jugular vein (n  =  9) with the wall of the common carotid artery (n  =  18). All patching materials were found to be significantly stiffer than the carotid wall in both the longitudinal and circumferential directions. Synthetic patches demonstrated the most mismatch in stiffness values and vein patches the least mismatch in stiffness values compared to those of the native carotid artery. All biological materials, including the carotid artery, demonstrated substantial nonlinearity, anisotropy, and variability; however, the behavior of biological and biologically-derived patches was both qualitatively and quantitatively different from the behavior of the carotid wall. The majority of carotid arteries tested were stiffer in the circumferential direction, while the opposite anisotropy was observed for all types of vein patches and bovine pericardium. The rates of increase in the nonlinear stiffness over the physiological stress range were also different for the carotid and patching materials. Several carotid wall samples exhibited reverse anisotropy compared to the average behavior of the carotid tissue. A similar characteristic was observed for two of 19 vein patches. The obtained results quantify, for the first time, significant mechanical dissimilarity of the currently available patching materials and the carotid artery. The results can be used as guidance for designing more efficient patches with mechanical properties resembling those of the carotid wall. The presented systematic comparative mechanical analysis of the existing patching materials provides valuable information for patch selection in the daily practice of carotid surgery and can be used in future clinical studies comparing the efficacy of different patches in the performance of carotid endarterectomy.

Nonlinear mechanical behavior of the human common, external, and internal carotid arteries in vivo

BACKGROUND

The mechanical environment and properties of the carotid artery play an important role in the formation and progression of atherosclerosis in the carotid bifurcation. The purpose of this work was to measure and compare the range and variation of circumferential stress and tangent elastic moduli in the human common (CCA), external (ECA), and internal (ICA) carotid arteries over the cardiac cycle in vivo.

METHODS

Measurements were performed in the surgically exposed proximal cervical CCA, distal ECA, and distal ICA of normotensive patients (n = 16) undergoing carotid endarterectomy. All measurements were completed in vivo over the cardiac cycle in the repaired carotid bifurcation after the atherosclerotic plaque was successfully removed. B-mode Duplex ultrasonography was used for measurement of arterial diameter and wall thickness, and an angiocatheter placed in the CCA was used for concurrent measurement of blood pressure. A semiautomatic segmentation algorithm was used to track changes in arterial diameter and wall thickness in response to blood pressure. These measurements were then used to calculate the variation of circumferential (hoop) stresses, tangent elastic moduli (the slope of the stress-strain curve at specified stresses), and strain-induced stiffness of the arterial wall (stiffening in response to the increase of intraluminal blood pressure) for each patient.

RESULTS

The diameter and wall thickness of the segments (CCA, ECA, and ICA) of the carotid bifurcation were found to decrease and strain-induced stiffness to increase from proximal CCA to distal ECA and ICA. The circumferential stress from end-diastole (minimum pressure) to peak-systole (maximum pressure) varied nonlinearly from 25 ± 7 to 63 ± 23 kPa (CCA), from 22 ± 7 to 57 ± 19 kPa (ECA), and from 28 ± 8 to 67 ± 23 kPa (ICA). Tangent elastic moduli also varied nonlinearly from end-diastole to peak-systole as follows: from 0.40 ± 0.25 to 1.50 ± 2.05 MPa (CCA), from 0.49 ± 0.34 to 1.14 ± 0.52 MPa (ECA), and from 0.68 ± 0.31 to 1.51 ± 0.69 MPa (ICA). The strain-induced stiffness of CCA and ECA increased more than 3-fold and the stiffness of ICA increased more than 2.5-fold at peak-systole compared with end-diastole.

CONCLUSIONS

The in vivo mechanical behavior of the three segments of the carotid bifurcation was qualitatively similar, but quantitatively different. All three arteries--CCA, ECA and ICA--exhibited nonlinear variations of circumferential stress and tangent elastic moduli within the normal pressure range. The variability in the properties of the three segments of the carotid bifurcation indicates a need for development of carotid models that match the in vivo properties of the carotid segments. Finally, the observed nonlinear behavior of the artery points to the need for future vascular mechanical studies to evaluate the mechanical factors of the arterial wall over the entire cardiac cycle.

3D constitutive modeling of the biaxial mechanical response of intact and layer-dissected human carotid arteries

Human arteries with non-atherosclerotic intimal thickening consist of three distinct layers: adventitia, media and intima. From a series of axial extension and inflation tests on intact and layer-dissected human carotid arteries (adventitia and media-intima composite), a 3D structurally-based strain-energy function (SEF) is calibrated, and a set of five material parameters is identified which is not yet available in the literature. The zero-stress states of the artery tubes investigated are considered in the calibration process, and the related kinematics for the finite deformation of the individual continuum are described in detail. The SEF employed is capable of describing the different mechanical properties of the intact and layer-dissected tissue tubes (arterial segments) investigated at different pressure domains and axial stretches. The correlation coefficients and error measures determined indicate good correlation between the model and the experimental data for all tested tubes. Mean values of each individual material parameter provide a kind of 'master model' that characterizes the mean response of all mechanical data obtained from the human carotid arteries. The material parameters and the 3D constitutive model serve as a foundation for finite element simulations, and hence the analysis of more complex patient-specific boundary-value problems in the human carotid physiology and pathology.