Characterization of arterial wall mechanical behavior and stresses from human clinical data

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

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

In Vivo Material Properties of Human Common Carotid Arteries: Trends and Sex Differences

INTRODUCTION

In vivo estimation of material properties of arterial tissue can provide essential insights into the development and progression of cardiovascular diseases. Furthermore, these properties can be used as an input to finite element simulations of potential medical treatments.

MATERIALS AND METHODS

This study uses non-invasively measured pressure, diameter and wall thickness of human common carotid arteries (CCAs) acquired in 103 healthy subjects. A non-linear optimization was performed to estimate material parameters of two different constitutive models: a phenomenological, isotropic model and a structural, anisotropic model. The effect of age, sex, body mass index and blood pressure on the parameters was investigated.

RESULTS AND CONCLUSION

Although both material models were able to model in vivo arterial behaviour, the structural model provided more realistic results in the supra-physiological domain. The phenomenological model predicted very high deformations for pressures above the systolic level. However, the phenomenological model has fewer parameters that were shown to be more robust. This is an advantage when only the physiological domain is of interest. The effect of stiffening with age, BMI and blood pressure was present for women, but not always for men. In general, sex had the biggest effect on the mechanical properties of CCAs. Stiffening trends with age, BMI and blood pressure were present but not very strong. The intersubject variability was high. Therefore, it can be concluded that finding a representative set of parameters for a certain age or BMI group would be very challenging. Instead, for purposes of patient-specific modelling of surgical procedures, we currently advise the use of patient-specific parameters.

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

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

Fitting mechanical properties of the aortic wall and individual layers to experimental tensile tests including residual stresses

The authors have observed that a stress-strain curve for uniaxial tension of an aortic intact wall cannot be simply obtained by combining the strain energy functions of the three individual aortic layers - intima, media and adventitia - even taking into account the interaction among the three layers; the strain energy functions of the three layers are obtained fitting tensile tests on strips from the individual layers. Due to the layer separation, the residual stresses are released and thus they do not affect the stress-strain curves of the individual layers. The present study shows that it is instead possible to fit the intact wall experimental curves with the combination of the strain energy functions of the three individual layers if residual strains are added. The residual strains are used as optimization parameters with specific constraints and allowing for the buckling (wrinkling) of the intima under unpressurized condition of the aortic wall, as experimentally observed. By varying these parameters in the experimentally observed range of values, it is possible to find a solution with the combined responses of the individual layers matching the experimental stress-strain curves of the intact wall.

Image-Based Finite Element Modeling Approach for Characterizing In Vivo Mechanical Properties of Human Arteries

Mechanical properties of the arterial walls could provide meaningful information for the diagnosis, management and treatment of cardiovascular diseases. Classically, various experimental approaches were conducted on dissected arterial tissues to obtain their stress-stretch relationship, which has limited value clinically. Therefore, there is a pressing need to obtain biomechanical behaviors of these vascular tissues in vivo for personalized treatment. This paper reviews the methods to quantify arterial mechanical properties in vivo. Among these methods, we emphasize a novel approach using image-based finite element models to iteratively determine the material properties of the arterial tissues. This approach has been successfully applied to arterial walls in various vascular beds. The mechanical properties obtained from the in vivo approach were compared to those from ex vivo experimental studies to investigate whether any discrepancy in material properties exists for both approaches. Arterial tissue stiffness values from in vivo studies generally were in the same magnitude as those from ex vivo studies, but with lower average values. Some methodological issues, including solution uniqueness and robustness; method validation; and model assumptions and limitations were discussed. Clinical applications of this approach were also addressed to highlight their potential in translation from research tools to cardiovascular disease management.

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

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

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

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

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

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

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

Inverse modeling framework for characterizing patient-specific microstructural changes in the pulmonary arteries

Microstructural changes in the pulmonary arteries associated with pulmonary arterial hypertension (PAH) is not well understood and characterized in humans. To address this issue, we developed and applied a patient-specific inverse finite element (FE) modeling framework to characterize mechanical and structural changes of the micro-constituents in the proximal pulmonary arteries using in-vivo pressure measurements and magnetic resonance images. The framework was applied using data acquired from a pediatric PAH patient and a heart transplant patient with normal pulmonary arterial pressure, which serves as control. Parameters of a constrained mixture model that are associated with the structure and mechanical properties of elastin, collagen fibers and smooth muscle cells were optimized to fit the patient-specific pressure-diameter responses of the main pulmonary artery. Based on the optimized parameters, individual stress and linearized stiffness resultants of the three tissue constituents, as well as their aggregated values, were estimated in the pulmonary artery. Aggregated stress resultant and stiffness are, respectively, 4.6 and 3.4 times higher in the PAH patient than the control subject. Stress and stiffness resultants of each tissue constituent are also higher in the PAH patient. Specifically, the mean stress resultant is highest in elastin (PAH: 69.96, control: 14.42 kPa-mm), followed by those in smooth muscle cell (PAH: 13.95, control: 4.016 kPa-mm) and collagen fibers (PAH: 13.19, control: 2.908 kPa-mm) in both the PAH patient and the control subject. This result implies that elastin may be the key load-bearing constituent in the pulmonary arteries of the PAH patient and the control subject.

Analysis of the passive biomechanical behavior of a sheep-specific aortic artery in pulsatile flow conditions

In this work, a novel numerical-experimental procedure is proposed, through the use of the Cardiac Simulation Test (CST), device that allows the exposure of the arterial tissue to in-vitro conditions, mimicking cardiac cycles generated by the heart. The main goal is to describe mechanical response of the arterial wall under physiological conditions, when it is subjected to a variable pressure wave over time, which causes a stress state affecting the biomechanical behavior of the artery wall. In order to get information related to stress and strain states, numerical simulation via finite element method, is performed under a condition of systolic and diastolic pressure. The description of this methodological procedure is performed with a sample corresponding to a sheep aorta without cardiovascular pathologies. There are two major findings: the evaluation of the mechanical properties of the sheep aorta through the above-mentioned tests and, the numerical simulation of the mechanical response under the conditions present in the CST. The results state that differences between numerical and experimental circumferential stretch in diastole and systole to distinct zones studied do not exceed 1%. However, greater discrepancies can be seen in the distensibility and incremental modulus, two main indicators, which are in the order of 30%. In addition, numerical results determine an increase of the principal maximum stress and strain between the case of systolic and diastolic pressure, corresponding to 31.1% and 14.9% for the stress and strain measurement respectively; where maximum values of these variables are located in the zone of the ascending aorta and the aortic arch.

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

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

Identification of in vivo nonlinear anisotropic mechanical properties of ascending thoracic aortic aneurysm from patient-specific CT scans

Accurate identification of in vivo nonlinear, anisotropic mechanical properties of the aortic wall of individual patients remains to be one of the critical challenges in the field of cardiovascular biomechanics. Since only the physiologically loaded states of the aorta are given from in vivo clinical images, inverse approaches, which take into account of the unloaded configuration, are needed for in vivo material parameter identification. Existing inverse methods are computationally expensive, which take days to weeks to complete for a single patient, inhibiting fast feedback for clinicians. Moreover, the current inverse methods have only been evaluated using synthetic data. In this study, we improved our recently developed multi-resolution direct search (MRDS) approach and the computation time cost was reduced to 1~2 hours. Using the improved MRDS approach, we estimated in vivo aortic tissue elastic properties of two ascending thoracic aortic aneurysm (ATAA) patients from pre-operative gated CT scans. For comparison, corresponding surgically-resected aortic wall tissue samples were obtained and subjected to planar biaxial tests. Relatively close matches were achieved for the in vivo-identified and ex vivo-fitted stress-stretch responses. It is hoped that further development of this inverse approach can enable an accurate identification of the in vivo material parameters from in vivo image data.

Iliac Veins Are More Compressible Than Iliac Arteries: A New Method of Testing

Incompressibility implies that a tissue preserves its volume regardless of the loading conditions. Although this assumption is well-established in arterial wall mechanics, it is assumed to apply for the venous wall without validation. The objective of this study is to test whether the incompressibility assumption holds for the venous wall. To investigate the vascular wall volume under different loading conditions, inflation-extension testing protocol was used in conjunction with intravascular ultrasound (IVUS) in both common iliac arteries (n = 6 swine) and common iliac veins (n = 9 dogs). Use of IVUS allows direct visualizations of lumen dimensions simultaneous with direct measurements of outer dimensions during loading. The arterial tissue was confirmed to preserve volume during various load conditions (p = 0.11) consistent with the literature, while the venous tissue was found to lose volume (about 35%) under loaded conditions (p < 0.05). Using a novel methodology, this study shows the incompressibility assumption does not hold for the venous wall especially at higher pressures, which suggests that there may be fluid loss through the vein wall during loading. This has important implications for coupling of fluid transport across the wall and biomechanics of the wall in healthy and diseased conditions.

Validation of the Strain Assessment of a Phantom of Abdominal Aortic Aneurysm: Comparison of Results Obtained From Magnetic Resonance Imaging and Stereovision Measurements

Predicting aortic aneurysm ruptures is a complex problem that has been investigated by many research teams over several decades. Work on this issue is notably complex and involves both the mechanical behavior of the artery and the blood flow. Magnetic resonance imaging (MRI) can provide measurements concerning the shape of an organ and the blood that flows through it. Measuring local distortion of the artery wall is the first essential factor to evaluate in a ruptured artery. This paper aims to demonstrate the feasibility of this measure using MRI on a phantom of an abdominal aortic aneurysm (AAA) with realistic shape. The aortic geometry is obtained from a series of cine-MR images and reconstructed using Mimics software. From 4D flow and MRI measurements, the field of velocity is determined and introduced into a computational fluid dynamic (CFD) model to determine the mechanical boundaries applied on the wall artery (pressure and ultimately wall shear stress (WSS)). These factors are then converted into a solid model that enables wall deformations to be calculated. This approach was applied to a silicone phantom model of an AAA reconstructed from a patient's computed tomography-scan examination. The calculated deformations were then compared to those obtained in identical conditions by stereovision. The results of both methods were found to be close. Deformations of the studied AAA phantom with complex shape were obtained within a gap of 12% by modeling from MR data.

Estimation of in vivo constitutive parameters of the aortic wall using a machine learning approach

The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters are established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training/validation dataset. The accuracy of the ML-model was examined using a testing dataset.

CFD-Based Comparison Study of a New Flow Diverting Stent and Commercially-Available Ones for the Treatment of Cerebral Aneurysms

Flow-diverting stents (FDSs) show considerable promise for the treatment of cerebral aneurysms by diverting blood flow away from the aneurysmal sacs, however, post-treatment complications such as failure of occlusion and subarachnoid haemorrhaging remain and vary with the FDS used. Based on computational fluid dynamics (CFD), this study aimed to investigate the performance of a new biodegradable stent as compared to two metallic commercially available FDSs. CFD models were developed for an idealized cerebral artery with a sidewall aneurysmal sac treated by deploying the aforementioned stents of different porosities (90, 80, and 70 % ) respectively. By using these models, the simulation and analysis were performed, with a focus on comparing the local hemodynamics or the blood flow in the stented arteries as compared to the one without the stent deployment. For the comparison, we computed and compared the flow velocity, wall shear stress (WSS) and pressure distributions, as well as the WSS related indices, all of which are of important parameters for studying the occlusion and potential rupture of the aneurysm. Our results illustrate that the WSS decreases within the aneurysmal sac on the treated arteries, which is more significant for the stents with lower porosity or finer mesh. Our results also show that the maximum WSS near the aneurysmal neck increases regardless of the stents used. In addition, the WSS related indices including the time-average WSS, oscillatory shear index and relative residence time show different distributions, depending on the FDSs. Together, we found that the finer mesh stents provide more flow reduction and smaller region characterized by high oscillatory shear index, while the new stent has a higher relative residence time.

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

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

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

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

Comparative mechanics of diverse mammalian carotid arteries

The prevalence of diverse animal models as surrogates for human vascular pathologies necessitate a comprehensive understanding of the differences that exist between species. Comparative passive mechanics are presented here for the common carotid arteries taken from bovine, porcine, ovine, leporine, murine-rat, and murine-mouse specimens. Data is generated using a scalable biaxial mechanical testing device following consistent circumferential (pressure-diameter) and axial (force-length) testing protocols. The structural mechanical response of carotids under equivalent loading, quantified by the deformed inner radius, deformed wall thickness, lumen area compliance and axial force, varies significantly among species but generally follows allometric scaling. Conversely, descriptors of the local mechanical response within the deformed arterial wall, including mean circumferential stress, mid-wall circumferential stretch, and mean axial stress, are relatively consistent across species. Unlike the larger animals studied, the diameter distensibility curves of murine specimens are non-monotonic and have a significantly higher value at 100 mmHg. Taken together, our results provide baseline structural and mechanical information for carotid arteries across a broad range of common animal models.

A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

Hyperelastic models are of particular interest in modeling biomaterials. In order to implement them, one must derive the stress and elasticity tensors from the given potential energy function explicitly. However, it is often cumbersome to do so because researchers in biomechanics may not be well-exposed to systematic approaches to derive the stress and elasticity tensors as it is vaguely addressed in literature. To resolve this, we present a framework of a general approach to derive the stress and elasticity tensors for hyperelastic models. Throughout the derivation we carefully elaborate the differences between formulas used in the displacement-based formulation and the displacement/pressure mixed formulation. Three hyperelastic models, Mooney-Rivlin, Yeoh and Holzapfel-Gasser-Ogden models that span from first-order to higher order and from isotropic to anisotropic materials, are served as examples. These detailed derivations are validated with numerical experiments that demonstrate excellent agreements with analytical and other computational solutions. Following this framework, one could implement with ease any hyperelastic model as user-defined functions in software packages or develop as an original source code from scratch.

Stiffness Properties of Adventitia, Media, and Full Thickness Human Atherosclerotic Carotid Arteries in the Axial and Circumferential Directions

Arteries can be considered as layered composite material. Experimental data on the stiffness of human atherosclerotic carotid arteries and their media and adventitia layers are very limited. This study used uniaxial tests to determine the stiffness (tangent modulus) of human carotid artery sections containing American Heart Association type II and III lesions. Axial and circumferential oriented adventitia, media, and full thickness specimens were prepared from six human carotid arteries (total tissue strips: 71). Each artery yielded 12 specimens with two specimens in each of the following six categories; axial full thickness, axial adventitia (AA), axial media (AM), circumferential full thickness, circumferential adventitia (CA), and circumferential media (CM). Uniaxial testing was performed using Inspec 2200 controlled by software developed using labview. The mean stiffness of the adventitia was 3570 ± 667 and 2960 ± 331 kPa in the axial and circumferential directions, respectively, while the corresponding values for the media were 1070 ± 186 and 1800 ± 384 kPa. The adventitia was significantly stiffer than the media in both the axial (p = 0.003) and circumferential (p = 0.010) directions. The stiffness of the full thickness specimens was nearly identical in the axial (1540 ± 186) and circumferential (1530 ± 389 kPa) directions. The differences in axial and circumferential stiffness of media and adventitia were not statistically significant.

Comparison of in vivo vs. ex situ obtained material properties of sheep common carotid artery

Patient-specific biomechanical modelling can improve preoperative surgical planning. This requires patient-specific geometry as well as patient-specific material properties as input. The latter are, however, still quite challenging to estimate in vivo. This study focuses on the estimation of the mechanical properties of the arterial wall. Firstly, in vivo pressure, diameter and thickness of the arterial wall were acquired for sheep common carotid arteries. Next, the animals were sacrificed and the tissue was stored for mechanical testing. Planar biaxial tests were performed to obtain experimental stress-stretch curves. Finally, parameters for the hyperelastic Mooney-Rivlin and Gasser-Ogden-Holzapfel (GOH) material model were estimated based on the in vivo obtained pressure-diameter data as well as on the ex situ experimental stress-stretch curves. Both material models were able to capture the in vivo behaviour of the tissue. However, in the ex situ case only the GOH model provided satisfactory results. When comparing different fitting approaches, in vivo vs. ex situ, each of them showed its own advantages and disadvantages. The in vivo approach estimates the properties of the tissue in its physiological state while the ex situ approach allows to apply different loadings to properly capture the anisotropy of the tissue. Both of them could be further enhanced by improving the estimation of the stress-free state, i.e. by adding residual circumferential stresses in vivo and by accounting for the flattening effect of the tested samples ex vivo. • Competing interests: none declared • Word count: 4716.

Population-specific material properties of the implantation site for transcatheter aortic valve replacement finite element simulations

Patient-specific computational models are an established tool to support device development and test under clinically relevant boundary conditions. Potentially, such models could be used to aid the clinical decision-making process for percutaneous valve selection; however, their adoption in clinical practice is still limited to individual cases. To be fully informative, they should include patient-specific data on both anatomy and mechanics of the implantation site. In this work, fourteen patient-specific computational models for transcatheter aortic valve replacement (TAVR) with balloon-expandable Sapien XT devices were retrospectively developed to tune the material parameters of the implantation site mechanical model for the average TAVR population. Pre-procedural computed tomography (CT) images were post-processed to create the 3D patient-specific anatomy of the implantation site. Balloon valvuloplasty and device deployment were simulated with finite element (FE) analysis. Valve leaflets and aortic root were modelled as linear elastic materials, while calcification as elastoplastic. Material properties were initially selected from literature; then, a statistical analysis was designed to investigate the effect of each implantation site material parameter on the implanted stent diameter and thus identify the combination of material parameters for TAVR patients. These numerical models were validated against clinical data. The comparison between stent diameters measured from post-procedural fluoroscopy images and final computational results showed a mean difference of 2.5 ± 3.9%. Moreover, the numerical model detected the presence of paravalvular leakage (PVL) in 79% of cases, as assessed by post-TAVR echocardiographic examination. The final aim was to increase accuracy and reliability of such computational tools for prospective clinical applications.

Estimation of in vivo mechanical properties of the aortic wall: A multi-resolution direct search approach

The patient-specific biomechanical analysis of the aorta requires in vivo mechanical properties of individual patients. Existing approaches for estimating in vivo material properties often demand high computational cost and mesh correspondence of the aortic wall between different cardiac phases. In this paper, we propose a novel multi-resolution direct search (MRDS) approach for estimation of the nonlinear, anisotropic constitutive parameters of the aortic wall. Based on the finite element (FE) updating scheme, the MRDS approach consists of the following three steps: (1) representing constitutive parameters with multiple resolutions using principal component analysis (PCA), (2) building links between the discretized PCA spaces at different resolutions, and (3) searching the PCA spaces in a 'coarse to fine' fashion following the links. The estimation of material parameters is achieved by minimizing a node-to-surface error function, which does not need mesh correspondence. The method was validated through a numerical experiment by using the in vivo data from a patient with ascending thoracic aortic aneurysm (ATAA), the results show that the number of FE iterations was significantly reduced compared to previous methods. The approach was also applied to the in vivo CT data from an aged healthy human patient, and using the estimated material parameters, the FE-computed geometry was well matched with the image-derived geometry. This novel MRDS approach may facilitate the personalized biomechanical analysis of aortic tissues, such as the rupture risk analysis of ATAA, which requires fast feedback to clinicians.

Integrated geometric and mechanical analysis of an image-based lymphatic valve

Lymphatic valves facilitate the lymphatic system's role in maintaining fluid homeostasis. Malformed valves are found in several forms of primary lymphœdema, resulting in incurable swelling of the tissues and immune dysfunction. Their experimental study is complicated by their small size and operation in low pressure and low Reynolds number environments. Mathematical models of these structures can give insight and complement experimentation. In this work, we present the first valve geometry reconstructed from confocal imagery and used in the construction of a subject-specific model in a closing mode. A framework is proposed whereby an image is converted into a valve model. An FEA study was performed to identify the significance of the shear modulus, the consequences of smoothing the leaflet surface and the effect of wall motion on valve behaviour. Smoothing is inherent to any analysis from imagery. The nature of the image, segmentation and meshing all cause attenuation of high-frequency features. Smoothing not only causes loss of surface area but also the loss of high-frequency geometric features which may reduce stiffness. This work aimed to consider these effects and inform studies by taking a manual reconstruction and through manifold harmonic analysis, attenuating higher frequency features to replicate lower resolution images or lower degree-of-freedom reconstructions. In conclusion, two metrics were considered: trans-valvular pressure required to close the valve, ΔP_c, and the retrograde volume displacement after closure. The higher ΔP_c, the greater the volume of lymph that will pass through the valve during closure. Retrograde volume displacement after closure gives a metric of compliance of the valve and for the quality of the valve seal. In the case of the image-specific reconstructed valve, removing features with a wavelength longer than four μm caused changes in ΔP_c. Varying the shear modulus from 10 kPa to 60 kPa caused a 3.85-fold increase in the retrograde volume displaced. The inclusion of a non-rigid wall caused ΔP_c to increase from 1.56 to 2.52 cmH₂O.

A biochemical and mechanical model of injury-induced intimal thickening

In this paper, we investigate an axisymmetric model of intimal thickening using hyperelasticity theory. Our model describes the growth of the arterial intima due to cell proliferation which, in turn, is driven by the release of a cytokine such as platelet-derived growth factor (PDGF). With the growth rate tied to both local stress and the local concentration of PDGF, we derive a quadruple free boundary problem with different regions of the vessel wall characterized by different homeostatic stress. We compare our model predictions to rabbit and rodent models of atherosclerosis and find that in order to achieve the growth rates reported in the experiments, growth must be mainly cytokine induced rather than stress induced. Our model is also able to reproduce Glagov remodelling where, as a vessel becomes more diseased, the lumen expands before rapidly contracting.

Disturbed Cyclical Stretch of Endothelial Cells Promotes Nuclear Expression of the Pro-Atherogenic Transcription Factor NF-κB

Exposure of endothelial cells to low and multidirectional blood flow is known to promote a pro-atherogenic phenotype. The mechanics of the vessel wall is another important mechano-stimulus within the endothelial cell environment, but no study has examined whether changes in the magnitude and direction of cell stretch can be pro-atherogenic. Herein, we developed a custom cell stretching device to replicate the in vivo stretch environment of the endothelial cell and examined whether low and multidirectional stretch promote nuclear translocation of NF-κB. A fluid–structure interaction model of the device demonstrated a nearly uniform strain within the region of cell attachment and a negligible magnitude of shear stress due to cyclical stretching of the cells in media. Compared to normal cyclical stretch, a low magnitude of cyclical stretch or no stretch caused increased expression of nuclear NF-κB (p = 0.09 and p < 0.001, respectively). Multidirectional stretch also promoted significant nuclear NF-κB expression, comparable to the no stretch condition, which was statistically higher than the low (p < 0.001) and normal (p < 0.001) stretch conditions. This is the first study to show that stretch conditions analogous to atherogenic blood flow profiles can similarly promote a pro-atherogenic endothelial cell phenotype, which supports a role for disturbed vessel wall mechanics as a pathological cell stimulus in the development of advanced atherosclerotic plaques.

Behaviour of two typical stents towards a new stent evolution

This study explores the analysis of a new stent geometry from two typical stents used to treat the coronary artery disease. Two different finite element methods are applied with different boundary conditions to investigate the stenosis region. Computational fluid dynamics (CFD) models including fluid-structure interaction are used to assess the haemodynamic impact of two types of coronary stents implantation: (1) type 1-based on a strut-link stent geometry and (2) type 2-a continuous helical stent. Using data from a recent clinical stenosis, flow disturbances and consequent shear stress alterations introduced by the stent treatment are investigated. A relationship between stenosis and the induced flow fields for the two types of stent designs is analysed as well as the correlation between haemodynamics and vessel wall biomechanical factors during the initiation and development of stenosis formation in the coronary artery. Both stents exhibit a good performance in reducing the obstruction artery. However, stent type 1 presents higher radial deformation than the type 2. This deformation can be seen as a limitation with a long-term clinical impact.

FSI Simulations of Pulse Wave Propagation in Human Abdominal Aortic Aneurysm: The Effects of Sac Geometry and Stiffness

This study aims to quantify the effects of geometry and stiffness of aneurysms on the pulse wave velocity (PWV) and propagation in fluid–solid interaction (FSI) simulations of arterial pulsatile flow. Spatiotemporal maps of both the wall displacement and fluid velocity were generated in order to obtain the pulse wave propagation through fluid and solid media, and to examine the interactions between the two waves. The results indicate that the presence of abdominal aortic aneurysm (AAA) sac and variations in the sac modulus affect the propagation of the pulse waves both qualitatively (eg, patterns of change of forward and reflective waves) and quantitatively (eg, decreasing of PWV within the sac and its increase beyond the sac as the sac stiffness increases). The sac region is particularly identified on the spatiotemporal maps with a region of disruption in the wave propagation with multiple short-traveling forward/reflected waves, which is caused by the change in boundary conditions within the saccular region. The change in sac stiffness, however, is more pronounced on the wall displacement spatiotemporal maps compared to those of fluid velocity. We conclude that the existence of the sac can be identified based on the solid and fluid pulse waves, while the sac properties can also be estimated. This study demonstrates the initial findings in numerical simulations of FSI dynamics during arterial pulsations that can be used as reference for experimental and in vivo studies. Future studies are needed to demonstrate the feasibility of the method in identifying very mild sacs, which cannot be detected from medical imaging, where the material property degradation exists under early disease initiation.

Can finite element models of ballooning procedures yield mechanical response of the cardiovascular site to overexpansion?

Patient-specific numerical models could aid the decision-making process for percutaneous valve selection; in order to be fully informative, they should include patient-specific data of both anatomy and mechanics of the implantation site. This information can be derived from routine clinical imaging during the cardiac cycle, but data on the implantation site mechanical response to device expansion are not routinely available.

We aim to derive the implantation site response to overexpansion by monitoring pressure/dimensional changes during balloon sizing procedures and by applying a reverse engineering approach using a validated computational balloon model. This study presents the proof of concept for such computational framework tested in-vitro. A finite element (FE) model of a PTS-X405 sizing balloon (NuMed, Inc., USA) was created and validated against bench tests carried out on an ad hoc experimental apparatus: first on the balloon alone to replicate free expansion; second on the inflation of the balloon in a rapid prototyped cylinder with material deemed suitable for replicating pulmonary arteries in order to validate balloon/implantation site interaction algorithm.

Finally, the balloon was inflated inside a compliant rapid prototyped patient-specific right ventricular outflow tract to test the validity of the approach. The corresponding FE simulation was set up to iteratively infer the mechanical response of the anatomical model. The test in this simplified condition confirmed the feasibility of the proposed approach and the potential for this methodology to provide patient-specific information on mechanical response of the implantation site when overexpanded, ultimately for more realistic computational simulations in patient-specific settings.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the 'computational dissection' of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

MECHANICAL CHARACTERIZATION OF ABDOMINAL AORTIC ANEURYSM WALL IN RAT MODEL TREATED BY MESENCHYMAL STEM CELLS

In this work, we study the mechanical properties of abdominal aortic aneurysms (AAAs) treated by cell therapy. Based on the xenograft model in rats, we analyze the effects of the injection of bone marrow mesenchymal stem cells (MSCs) on the stiffness of the arterial wall. Uniaxial tests performed on control, treated and untreated samples, have led to the identification of a nonlinear behavior law, using a mechanical model based on a stress-stretch exponential relation. The comparison of the mechanical behavior shows the benefits of the proposed cell therapy which improves the mechanical strength of the aneurysmal vessel wall. A histological study has shown the favorable change expression of elastin and collagen which are involved in the mechanical behavior of repaired arterial tissue. Thus, this work is part of MSCs biological understanding and it contributes to evaluate the approaches used in cell therapy and regenerative medicine to treat AAAs.

A novel non-invasive ultrasonic method to assess total axial stress of the common carotid artery wall in healthy and atherosclerotic men

In the present study, developing a new non-invasive method independent from blood flow, we estimated and compared the total axial stress of the common carotid artery wall in healthy and atherosclerotic subjects. Consecutive ultrasonic images of the common carotid artery of 48 male subjects including healthy, with less and more than 50% stenosis in carotid artery were recorded. Longitudinal displacement and acceleration was extracted from ultrasonic image processing using a block matching algorithm. Furthermore, images were examined using a maximum gradient algorithm and time rate changes of the internal diameter and intima-media thickness were extracted. Finally, axial stress was estimated using an appropriate constitutive equation. Statistical analysis results showed that with stenosis initiation and its progression, axial acceleration and stress increase significantly. According to the results of the present study, maximum axial stress of the arterial wall is 1.713±0.546, 1.993±0.731 and 2.610±0.603 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Whereas minimum axial stress is -1.714±0.676, -1.982±0.663 and -2.593±0.661 (kPa) in normal, with less and more than 50% stenosis in carotid artery respectively. Moreover, internal diameter and intima-media thickness of the artery also increase significantly with stenosis initiation and its progression. In this study, the feasibility of axial wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data is concluded. We found a strong and graded association between axial stress and severity of carotid stenosis, which might be used to discriminate healthy from atherosclerotic arteries.

A constitutive modeling interpretation of the relationship among carotid artery stiffness, blood pressure, and age in hypertensive subjects

Aging has a profound influence on arterial wall structure and function. We have previously reported the relationship among pulse wave velocity, age, and blood pressure in hypertensive subjects. In the present study, we aimed for a quantitative interpretation of the observed changes in wall behavior with age using a constitutive modeling approach. We implemented a model of arterial wall biomechanics and fitted this to the group-averaged pressure-area ( P-A) relationship of the “young” subgroup of our study population. Using this model as our take-off point, we assessed which parameters had to be changed to let the model describe the “old” subgroup’s P-A relationship. We allowed elastin stiffness and collagen recruitment parameters to vary and adjusted residual stress parameters according to published age-related changes. We required wall stress to be homogeneously distributed over the arterial wall and assumed wall stress normalization with age by keeping average “old” wall stress at the “young” level. Additionally, we required axial force to remain constant over the cardiac cycle. Our simulations showed an age-related shift in pressure-load bearing from elastin to collagen, caused by a decrease in elastin stiffness and a considerable increase in collagen recruitment. Correspondingly, simulated diameter and wall thickness increased by about 20 and 17%, respectively. The latter compared well with a measured thickness increase of 21%. We conclude that the physiologically realistic changes in constitutive properties we found under physiological constraints with respect to wall stress could well explain the influence of aging in the stiffness-pressure-age pattern observed.

Non-invasive, energy-based assessment of patient-specific material properties of arterial tissue

The mechanical properties of human biological tissue vary greatly. The determination of arterial material properties should be based on experimental data, i.e. diameter, length, intramural pressure, axial force and stress-free geometry. Currently, clinical data provide only non-invasively measured pressure-diameter data for superficial arteries (e.g. common carotid and femoral artery). The lack of information forces us to take into account certain assumptions regarding the in situ configuration to estimate material properties in vivo. This paper proposes a new, non-invasive, energy-based approach for arterial material property estimation. This approach is compared with an approach proposed in the literature. For this purpose, a simplified finite element model of an artery was used as a mock experimental situation. This method enables exact knowledge of the actual material properties, thereby allowing a quantitative evaluation of material property estimation approaches. The results show that imposing conditions on strain energy can provide a good estimation of the material properties from the non-invasively measured pressure and diameter data.

Identification of biomechanical properties in vivo in human uterine cervix

BACKGROUND AND AIMS

The course and outcome of pregnancy is closely correlated to change of biomechanical properties of the uterine cervix. The aim of this study was to build a non-linear, fiber reinforced mechanical model of the cervix for estimation of mechanical characteristics of the cervix in early- and term-pregnant women based on recordings of in vivo pressure and diameter by means of the Functional Luminal Imaging Probe (FLIP) technology.

MATERIALS AND METHODS

Five early- and six term-pregnant women were examined with a FLIP probe. The bag on the probe was inserted into the cervical canal for concomitant measurement of diameters at 16 serial locations along the canal and the bag pressure. The bag was inflated to a maximum volume of 50 ml. A three-fiber-families model including isotropic elastin-dominated matrix and anisotropic collagen was introduced to describe the mechanical behavior of the cervical canal. The unknown geometric and mechanical parameters were calculated on the basis of the mid-cervical diameters and the intraluminal pressures during the inflation.

RESULTS

The wall thickness in the unloaded state (zero pressure applied) and mechanical properties of the matrix material (c) and collagens (c1, c2) were estimated with good fits of the calculated intraluminal pressures to the FLIP recordings during the cervical canal distension. No significant difference in the wall thickness was found between the early- and term-pregnant women (10.3 ± 0.8mm vs. 11.7 ± 2.2mm, p=0.30). The cervical matrix material and the collagen in the early-pregnant women were much stiffer than that in the term-pregnant women (p<0.05).

CONCLUSIONS

The cervical mechanical properties can be obtained from recorded pressure and diameter data in vivo via the established mechanical model. Matrix material and collagens of the cervix wall were remodeled during pregnancy. The mechanical model can be applied to other tubular visceral organs where concomitant measures of pressure and diameter can be obtained for better understanding diseases and their evolution or treatment.

EFFECTS OF OLMESARTAN ON LOCAL AND REGIONAL RIGIDITY OF ARTERIES IN ISCHEMIC HEART DISEASE

Aim. To evaluate 24-week treatment by olmesartan on rigidity of arteries in different vessel areas in patients with coronary heart disease (CHD) with 1–2 grade arterial hypertension (AH).

Material and methods. Into open-label, non-randomized trial 25 patients with CHD and 1–2 grade AH were included. During 24-week treatment period patients received olmesartan medoxomil 20–40 mg daily. Baseline and final parameters of arterial wall stiffness were measured using ultrasound method with echotracking. The thickness of intima-media (TIMC) was defined. To evaluate regional vessel stiffness the volume sphygmography method was used.

Results. Acorrding to the data of volume sphygmography terapy by olmesartan significantly decrease PWVao by 19,4%, R-PWV b L-PWV — by 11,9% and 11,6% (p<0,05). CAVI1 decreased by 9,3%; L–CAVI1 — by 13,7%, CAVI2 — на 14,9% (p<0,05). В-PWV did not change significantly. During 24-week medication treatment the regress of carotid atherosclerosis was marked: decrease of TIMC from 773,6±155,7 μm to 736,3±124,1 μm (p<0,05). The values loc P sys and loc P dia significantly decreased by 13,5% and 11% (p<0,05); rigidity index β by 19,1% (p<0,05). Also we marked the increase of transverse pliability by 3,3% (p<0,05) and decrease of loc PWV by 17% (p<0,05). The coefficient of transverse pliability, locAix and DOCA did not show significant changes.

Conclusion. Addition of olmesartan to the standard treatment of CHD and AH showed significant improvement of local and regional stiffness.

Quantification of regional differences in aortic stiffness in the aging human

There has been a growing awareness over the past decade that stiffening of the aorta, and its attendant effects on hemodynamics, is both an indicator and initiator of diverse cardiovascular, neurovascular, and renovascular diseases. Although different clinical metrics of arterial stiffness have been proposed and found useful in particular situations, there remains a need to understand better the complex interactions between evolving aortic stiffness and the hemodynamics. Computational fluid-solid-interaction (FSI) models are amongst the most promising means to understand such interactions for one can parametrically examine effects of regional variations in material properties and arterial geometry on local and systemic blood pressure and flow. Such models will not only increase our understanding, they will also serve as important steps towards the development of fluid-solid-growth (FSG) models that can further examine interactions between the evolving wall mechanics and hemodynamics that lead to arterial adaptations or disease progression over long periods. In this paper, we present a consistent quantification and comparison of regional nonlinear biaxial mechanical properties of the human aorta based on 19 data sets available in the literature and we calculate associated values of linearized stiffness over the cardiac cycle that are useful for initial large-scale FSI and FSG simulations. It is shown, however, that there is considerable variability amongst the available data and consequently that there is a pressing need for more standardized biaxial testing of the human aorta to collect data as a function of both location and age, particularly for young healthy individuals who serve as essential controls.

Biomechanics of porcine renal arteries and role of axial stretch

It is known that arteries experience significant axial stretches in vivo. Several authors have shown that the axial force needed to maintain an artery at its in vivo axial stretch does not change with transient cyclical pressurization over normal ranges. However, the axial force phenomenon of arteries has never been explained with microstructural considerations. In this paper we propose a simple biomechanical model to relate the specific axial force phenomenon of arteries to the predicted load-dependent average collagen fiber orientation. It is shown that (a) the model correctly predicts the authors' experimentally measured biaxial behavior of pig renal arteries and (b) the model predictions are in agreement with additional experimental results reported in the literature. Finally, we discuss the implications of the model for collagen fiber orientation and deposition in arteries.

Growth and residual stresses of arterial walls

Growth, residual stresses and mechanical responses of arterial walls under the inner pressure are investigated within the framework of a finite deformation hyper-elasticity theory. A biomechanical model for a two-layer thick-walled circular cylindrical tube is proposed to address the mechanical effects of finite volumetric growth and residual stresses of arterial walls. The active stress due to smooth muscle tone in the media and the dispersion of collagen fiber orientations in the adventitia are also considered. The fields of displacements and stress distributions of arterial walls with growth are solved analytically. Analysis of axial, radial and circumferential growth is considered and residual stress distributions of arterial walls in different cases of growth are compared.