A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour

Mechanical characterization and torsional buckling of pediatric cardiovascular materials

In complex cardiovascular surgical reconstructions, conduit materials that avoid possible large-scale structural deformations should be considered. A fundamental mode of mechanical complication is torsional buckling which occurs at the anastomosis site due to the mechanical instability, leading surgical conduit/patch surface deformation. The objective of this study is to investigate the torsional buckling behavior of commonly used materials and to develop a practical method for estimating the critical buckling rotation angle under physiological intramural vessel pressures. For this task, mechanical tests of four clinically approved materials, expanded polytetrafluoroethylene (ePTFE), Dacron, porcine and bovine pericardia, commonly used in pediatric cardiovascular surgeries, are conducted (n = 6). Torsional buckling initiation tests with n = 4 for the baseline case (L = 7.5 cm) and n = 3 for the validation of ePTFE (L = 15 cm) and Dacron (L = 15 cm and L = 25 cm) for each are also conducted at low venous pressures. A practical predictive formulation for the buckling potential is proposed using experimental observations and available theory. The relationship between the critical buckling rotation angle and the lumen pressure is determined by balancing the circumferential component of the compressive principal stress with the shear stress generated by the modified critical buckling torque, where the modified critical buckling torque depends linearly on the lumen pressure. While the proposed technique successfully predicted the critical rotation angle values lying within two standard deviations of the mean in the baseline case for all four materials at all lumen pressures, it could reliably predict the critical buckling rotation angles for ePTFE and Dacron samples of length 15 cm with maximum relative errors of 31% and 38%, respectively, in the validation phase. However, the validation of the performance of the technique demonstrated lower accuracy for Dacron samples of length 25 cm at higher pressure levels of 12 mmHg and 15 mmHg. Applicable to all surgical materials, this formulation enables surgeons to assess the torsional buckling potential of vascular conduits noninvasively. Bovine pericardium has been found to exhibit the highest stability, while Dacron (the lowest) and porcine pericardium have been identified as the least stable with the (unitless) torsional buckling resistance constants, 43,800, 12,300 and 14,000, respectively. There was no significant difference between ePTFE and Dacron, and between porcine and bovine pericardia. However, both porcine and bovine pericardia were found to be statistically different from ePTFE and Dacron individually (p < 0.0001). ePTFE exhibited highly nonlinear behavior across the entire strain range [0, 0.1] (or 10% elongation). The significant differences among the surgical materials reported here require special care in conduit construction and anastomosis design.

Modeling fatigue failure in soft tissue using a visco-hyperelastic model with discontinuous damage

Soft tissue is susceptible to injury from single high-magnitude static loads and from repetitive low-magnitude fatigue loads. While many constitutive formulations have been developed and validated to model static failure in soft tissue, a modeling framework is not well-established for fatigue failure. Here we determined the feasibility of using a visco-hyperelastic damage model with discontinuous damage (strain energy-based damage criterion) to simulate low- and high-cycle fatigue failure in soft fibrous tissue. Cyclic creep data from six uniaxial tensile fatigue experiments of human medial meniscus were used to calibrate the specimen-specific material parameters. The model was able to successfully simulate all three characteristic stages of cyclic creep, and predict the number of cycles until tissue rupture. Mathematically, damage propagated under constant cyclic stress due to time-dependent viscoelastic increases in tensile stretch that in turn increased strain energy. Our results implicate solid viscoelasticity as a fundamental regulator of fatigue failure in soft tissue, where tissue with slow stress relaxation times will be more resistant to fatigue injury. In a validation study, the visco-hyperelastic damage model was able to simulate characteristic stress-strain curves of pull to failure experiments (static failure) when using material parameters curve fit to the fatigue experiments. For the first time, we've shown that a visco-hyperelastic discontinuous damage framework can model cyclic creep and predict material rupture in soft tissue, and may enable the reliable simulation of both fatigue and static failure behavior from a single constitutive formulation.

Hyperelastic and damage properties of the hypoxic aorta treated with Cinaciguat

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

A knowledge map analysis of brain biomechanics: Current evidence and future directions

Although brain, one of the most complex organs in the mammalian body, has been subjected to many studies from physiological and pathological points of view, there remain significant gaps in the available knowledge regarding its biomechanics. This article reviews the research trends in brain biomechanics with a focus on injury. We used published scientific articles indexed by Web of Science database over the past 40 years and tried to address the gaps that still exist in this field. We analyzed the data using VOSviewer, which is a software tool designed for scientometric studies. The results of this study showed that the response of brain tissue to external forces has been one of the significant research topics among biomechanicians. These studies have addressed the effects of mechanical forces on the brain and mechanisms of traumatic brain injury, as well as characterized changes in tissue behavior under trauma and other neurological diseases to provide new diagnostic and monitoring methods. In this study, some challenges in the field of brain injury biomechanics have been identified and new directions toward understanding the gaps in this field are suggested.

In vitro histomechanical effects of enzymatic degradation in carotid arteries during inflation tests with pulsatile loading

In this paper, the objective is to assess the histomechanical effects of collagen proteolysis in arteries under loading conditions reproducing in vivo environment. Thirteen segments of common porcine carotid arteries (8 proximal and 5 distal) were immersed in a bath of bacterial collagenase and tested with a pulsatile tension/inflation machine. Diameter, pressure and axial load were monitored throughout the tests and used to derive the stress-stretch curves and to determine the secant circumferential stiffness. Results were analysed separately for proximal and distal segments, before and after 1, 2 and 3 h of enzymatic degradation. A histological analysis was performed to relate the arterial microstructure to its mechanical behavior under collagen proteolysis. Control (before enzymatic degradation) and treated populations (after 1, 2 or 3 h of enzymatic degradation) were found statistically incomparable, and histology confirmed the alteration of the fibrous structure of collagen bundles induced by the collagenase treatment. A decrease of the secant circumferential stiffness of the arterial wall was noticed mostly at the beginning of the treatment, and was less pronounced after 1 h. These results constitute an important set of enzymatically damaged arteries that can be used to validate biomechanical computational models correlating structure and properties of blood vessels.

Computational Multiscale Solvers for Continuum Approaches

Computational multiscale analyses are currently ubiquitous in science and technology. Different problems of interest-e.g., mechanical, fluid, thermal, or electromagnetic-involving a domain with two or more clearly distinguished spatial or temporal scales, are candidates to be solved by using this technique. Moreover, the predictable capability and potential of multiscale analysis may result in an interesting tool for the development of new concept materials, with desired macroscopic or apparent properties through the design of their microstructure, which is now even more possible with the combination of nanotechnology and additive manufacturing. Indeed, the information in terms of field variables at a finer scale is available by solving its associated localization problem. In this work, a review on the algorithmic treatment of multiscale analyses of several problems with a technological interest is presented. The paper collects both classical and modern techniques of multiscale simulation such as those based on the proper generalized decomposition (PGD) approach. Moreover, an overview of available software for the implementation of such numerical schemes is also carried out. The availability and usefulness of this technique in the design of complex microstructural systems are highlighted along the text. In this review, the fine, and hence the coarse scale, are associated with continuum variables so atomistic approaches and coarse-graining transfer techniques are out of the scope of this paper.

Image-based multi-scale mechanical analysis of strain amplification in neurons embedded in collagen gel

A general multi-scale strategy is presented for modeling the mechanical environment of a group of neurons that were embedded within a collagenous matrix. The results of the multi-scale simulation are used to estimate the local strains that arise in neurons when the extracellular matrix is deformed. The distribution of local strains was found to depend strongly on the configuration of the embedded neurons relative to the loading direction, reflecting the anisotropic mechanical behavior of the neurons. More importantly, the applied strain on the surrounding extracellular matrix is amplified in the neurons for all loading configurations that are considered. In the most severe case, the applied strain is amplified by at least a factor of 2 in 10% of the neurons' volume. The approach presented in this paper provides an extension to the capability of past methods by enabling the realistic representation of complex cell geometry into a multi-scale framework. The simulation results for the embedded neurons provide local strain information that is not accessible by current experimental techniques.

An investigation into the role of different constituents in damage accumulation in arterial tissue and constitutive model development

Carotid atherosclerotic plaque rupture is one of the leading causes of stroke. Treatments for atherosclerosis can induce tissue damage during the deployment of an intravascular device or through external tissue clamping during surgery. In this paper, a constituent specific study was performed to investigate the role of the ground matrix and collagen fibres of arterial tissue in response to supra-physiological loads. Cyclic mechanical tests were conducted on intact and collagenase-digested strips of porcine common carotid arteries. Using these tests, four passive damage-relevant phenomena were studied, namely (i) Mullins effect, (ii) hysteresis, (iii) permanent set and (iv) matrix failure and fibre rupture. A constitutive model was also developed to capture all of these damage-relevant phenomena using a continuum damage mechanics approach. The implemented constitutive model was fit to experimental results for both intact and digested samples. The results of this work demonstrate the important role of the ground matrix in the permanent deformation of the arterial tissue under high loads. Supra-physiological load-induced tissue damage may play a key role in vascular remodelling in arteries with atherosclerosis or following interventional procedures.

Fatigue damage of collagenous tissues: experiment, modeling and simulation studies

Mechanical fatigue damage is a critical issue for soft tissues and tissue-derived materials, particularly for musculoskeletal and cardiovascular applications; yet, our understanding of the fatigue damage process is incomplete. Soft tissue fatigue experiments are often difficult and time-consuming to perform, which has hindered progress in this area. However, the recent development of soft-tissue fatigue-damage constitutive models has enabled simulation-based fatigue analyses of tissues under various conditions. Computational simulations facilitate highly controlled and quantitative analyses to study the distinct effects of various loading conditions and design features on tissue durability; thus, they are advantageous over complex fatigue experiments. Although significant work to calibrate the constitutive models from fatigue experiments and to validate predictability remains, further development in these areas will add to our knowledge of soft-tissue fatigue damage and will facilitate the design of durable treatments and devices. In this review, the experimental, modeling, and simulation efforts to study collagenous tissue fatigue damage are summarized and critically assessed.

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.

Subfailure overstretch induces persistent changes in the passive mechanical response of cerebral arteries

Cerebral blood vessels are critical in maintaining the health of the brain, but their function can be disrupted by traumatic brain injury (TBI). Even in cases without hemorrhage, vessels are deformed with the surrounding brain tissue. This subfailure deformation could result in altered mechanical behavior. This study investigates the effect of overstretch on the passive behavior of isolated middle cerebral arteries (MCAs), with the hypothesis that axial stretch beyond the in vivo length alters this response. Twenty nine MCA sections from 11 ewes were tested. Vessels were subjected to a baseline test consisting of an axial stretch from a buckled state to 1.05* in vivo stretch (λIV) while pressurized at 13.3 kPa. Specimens were then subjected to a target level of axial overstretch between 1.05*λIV (λz = 1.15) and 1.52*λIV (λz = 1.63). Following overstretch, baseline tests were repeated immediately and then every 10 min, for 60 min, to investigate viscoelastic recovery. Injury was defined as an unrecoverable change in the passive mechanical response following overstretch. Finally, pressurized MCAs were pulled axially to failure. Post-overstretch response exhibited softening such that stress values at a given level of stretch were lower after injury. The observed softening also generally resulted in increased non-linearity of the stress-stretch curve, with toe region slope decreasing and large deformation slope increasing. There was no detectable change in reference configuration or failure values. As hypothesized, the magnitude of these alterations increased with overstretch severity, but only once overstretch exceeded 1.2*λIV (p < 0.001). These changes were persistent over 60 min. These changes may have significant implications in repeated TBI events and in increased susceptibility to stroke post-TBI.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

Quantitative diagnostics of soft tissue through viscoelastic characterization using time-based instrumented palpation

Although palpation has been successfully employed for centuries to assess soft tissue quality, it is a subjective test, and is therefore qualitative and depends on the experience of the practitioner. To reproduce what the medical practitioner feels needs more than a simple quasi-static stiffness measurement. This paper assesses the capacity of dynamic mechanical palpation to measure the changes in viscoelastic properties that soft tissue can exhibit under certain pathological conditions. A diagnostic framework is proposed to measure elastic and viscous behaviors simultaneously using a reduced set of viscoelastic parameters, giving a reliable index for quantitative assessment of tissue quality. The approach is illustrated on prostate models reconstructed from prostate MRI scans. The examples show that the change in viscoelastic time constant between healthy and cancerous tissue is a key index for quantitative diagnostics using point probing. The method is not limited to any particular tissue or material and is therefore useful for tissue where defining a unique time constant is not trivial. The proposed framework of quantitative assessment could become a useful tool in clinical diagnostics for soft tissue.

A damage model for the percutaneous triple hemisection technique for tendo-achilles lengthening

A full understanding of the mechanisms of action in the percutaneous triple hemisection technique for tendo-achilles lengthening has yet to be acquired and therefore, an accurate prediction of the amount of lengthening that occurs is difficult to make. The purpose of this research was to develop a phenomenological damage model that utilizes both matrix and fiber damage and replicates the observed behavior of the tendon tissue during the lengthening process. Matrix damage was triggered and evolved relative to shear strain and the fiber damage was triggered and evolved relative to fiber stretch. Three examples are given to show the effectiveness of the model. Implementation of the damage model provides a tool for studying this common procedure, and may allow for numerical investigation of alternative surgical approaches that could reduce the incidence rates of severe over-lengthening.

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.

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.

Finite element analysis of balloon-expandable coronary stent deployment: influence of angioplasty balloon configuration

Today, the majority of coronary stents are balloon-expandable and are deployed using a balloon-tipped catheter. To improve deliverability, the membrane of the angioplasty balloon is typically folded about the catheter in a pleated configuration. As such, the deployment of the angioplasty balloon is governed by the material properties of the balloon membrane, its folded configuration and its attachment to the catheter. Despite this observation, however, an optimum strategy for modelling the configuration of the angioplasty balloon in finite element studies of coronary stent deployment has not been identified, and idealised models of the angioplasty balloon are commonly employed in the literature. These idealised models often neglect complex geometrical features, such as the folded configuration of the balloon membrane and its attachment to the catheter, which may have a significant influence on the deployment of a stent. In this study, three increasingly sophisticated models of a typical semi-compliant angioplasty balloon were employed to determine the influence of angioplasty balloon configuration on the deployment of a stent. The results of this study indicate that angioplasty balloon configuration has a significant influence on both the transient behaviour of the stent and its impact on the mechanical environment of the coronary artery.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

Does microcalcification increase the risk of rupture?

Rupture of atherosclerotic plaque, which is related to maximal stress conditions in the plaque among others, is a major cause of mortality. More careful examination of stress distributions in atherosclerotic plaques reports that it could be due to local stress behaviors at critical sites caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. However, the role of microcalcifications is not yet fully understood, and most finite element models of blood vessels with atheroma plaque ignore the heterogeneity of the plaque constituents at the microscale. The goal of this work is to investigate the effect of microcalcifications on the stress field of an atheroma plaque vessel section. This is achieved by performing a parametric finite element study, assuming a plane strain hypothesis, of a coronary artery section with eccentric atheroma plaque and one microcalcification incorporated. The geometrical parameters used to define and design the idealized coronary plaque anatomy and the microcalcification were the fibrous cap thickness and the microcalcification ratio, angle and eccentricity. We could conclude that microcalcifications should be considered in the modeling of this kind of problems since they cause a significant alteration of the vulnerable risk by increasing the maximum maximal principal stress up to 32%, although this increase of stress is not uniform (12% on average). The obtained results show that the fibrous cap thickness, the microcalcification ratio and the microcalcification eccentricity, in combination with the microcalcification angle, appear to be the key morphological parameters that play a determinant role in the maximal principal stress and accordingly in the rupture risk of the plaque.

Effects of dispersion of fiber orientation on the mechanical property of the arterial wall

Effects of dispersion of the fiber orientation on the mechanical property of the arterial wall in health and disease subjected to the combined internal pressure and axial loading are examined within the framework of the finite deformation hyper-elasticity theory. Taking into account the residual stress, a two layer thick-walled circular cylindrical tube model with the fiber-reinforced incompressible composite hyper-elastic material is employed. Stress-radius curves and stress distributions of the arterial wall are given in health and disease considering dispersion of the fiber orientation. With instability/bifurcation analysis, it is found that not only the uniform inflation of the arterial wall in health, but also the instability or bifurcation problem for the arterial wall in disease may be described by this model.

Identification of heterogeneous elastic properties in stenosed arteries: a numerical plane strain study

Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging. An important issue is to solve the inverse problem that consists in estimating the elastic properties inside the plaque from measured displacements. This study focuses on the identifiability of elastic parameters, e.g. on the compromise between identification time and identification accuracy. An idealised plane strain finite element (FE) model is used. The effects of the FE mesh of the a priori assumptions about the constituents, of the measurement resolution and of the data noise are numerically investigated.

Experimental study and constitutive modelling of the passive mechanical properties of the porcine carotid artery and its relation to histological analysis: Implications in animal cardiovascular device trials

The present study focusses on the determination, comparison and constitutive modelling of the passive mechanical properties of the swine carotid artery over very long stretches in both proximal and distal regions. Special attention is paid to the histological and mechanical variations of these properties depending on the proximity to the heart. The results can have clinical relevance, especially in the research field of intravascular device design. Before the final clinical trials on humans, research in the vascular area is conducted on animal models, swine being the most common due to the similarities between the human and swine cardiovascular systems as well as the fact that the swine size is suitable for testing devices, in this case endovascular carotid systems. The design of devices usually involves numerical techniques, and an important feature is the appropriate modelling of the mechanical properties of the vessel. Fourteen carotid swine arteries were harvested just after sacrifice and cyclic uniaxial tension tests in longitudinal and circumferential directions were performed for distal and proximal samples. The stress-stretch curves obtained were fitted with a hyperelastic anisotropic model. Stress-free configuration states were also analyzed. Finally, human and swine samples were processed in a histological laboratory and images were used to quantify their microconstituents. The statistical analysis revealed significant differences between the mechanical behavior of proximal and distal locations in the circumferential but not in the longitudinal direction. Circumferential direction samples show clear differences both in residual stretches and tensile curves between the two locations, while the features of longitudinal specimens are independent of the axial position. The statistical analysis provides significant evidence of changes depending on the position of the sample, mainly in elastin and SMC quantification.