Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. In this work, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.

The regional-dependent biaxial behavior of young and aged mouse skin: A detailed histomechanical characterization, residual strain analysis, and constitutive model

Skin fulfills several vital functions, many of which are dependent on its mechanical properties. Therefore, as mice have become an invaluable model for skin research, determining murine skin's mechanical properties is important. Specifically, skin's mechanical properties are important for functional tests as well as for prognostic and diagnostic purposes. Additionally, computational simulations of skin behavior are becoming commonplace, rendering accurate models of murine skin's constitutive behavior necessary. To date, our knowledge of mouse skin mechanics shows significant gaps. For example, there are no comprehensive reports correlating skin's mechanical properties with region, age, and direction. Moreover, mouse skin's residual strain behavior has not been reported on. In our current work, we set out to fill these gaps. Based on histology, 2-photon microscopy, and planar biaxial testing, while accurately tracking various reference configurations, we report on differences in gross structure, microstructural organization, and constitutive response of skin, and cast those properties into a versatile Fung-type hyperelastic constitutive law for three reference configurations. Our data is the most comprehensive report contrasting the mechanical properties of young (12 weeks) and aged (52 weeks) mouse skin and will, thus, be valuable to basic science as control data, and provide accurate constitutive laws for mouse skin modeling. STATEMENT OF SIGNIFICANCE: Our findings are significant as they fill several gaps in our understanding of mouse skin mechanics. This is particularly important as mouse skin is becoming a frequent and critical model of human skin for cosmetic and medical science. Specifically, we quantified how mechanical properties of mice skin vary with age, with location, and with direction. Additionally, we cast our findings into constitutive models that can be used by others for predictive computer simulations of skin behavior.

Fabrications of small diameter compliance bypass conduit using electrospinning of clinical grade polyurethane

Objective

Compliance and viscoelastic mismatches of small diameter vascular conduits and host arteries have been the cause of conduit’s failure.

Methods

To reduce these mismatches, the aim of this study was to develop and characterize a polyurethane conduit, which mimics the viscoelastic behaviors of human arteries. Electrospinning technique was used to fabricate tubular polyurethane conduits with similar properties of the human common carotid artery. This was achieved by manipulating the fiber diameter by altering the syringe flow rate of the solution. The mechanical and viscoelastic properties of the fabricated electrospun polyurethane conduits were, then, compared with commercially available vascular conduits, expanded polytetrafluoroethylene, polyethylene terephthalate (Dacron®) and the healthy human common carotid arteries. In addition, a comprehensive constitutive model was proposed to capture the visco-hyperelastic behavior of the synthetic electrospun polyurethanes, commercial conduits and human common carotid arteries.

Results

Results showed that increasing the fiber diameter of electrospun polyurethanes from 114 to 190 nm reduced Young’s modulus from 8 to 2 MPa. Also, thicker fiber diameter yielded in higher conduits’ viscosity. Furthermore, the results revealed that proposed visco-hyperelastic model is strongly able to fit the experimental data with great precision which proofs the reliability of the proposed model to address both nonlinear elasticity and viscoelasticity of the electrospun polyurethanes, commercial conduits and human common carotid arteries.

Conclusions

In conclusion, statistical analysis revealed that the elastic and viscous properties of 190 nm fiber diameter conduit are very similar to that of human common carotid artery in comparison to the commercial expanded polytetrafluoroethylene and Dacron® that are up to nine and seven times stiffer than natural vessels. Therefore, based on our findings, from the mechanical point of view, by considering the amount of Young’s modulus, compliance, distensibility and viscoelastic behavior, the fabricated electrospun polyurethane with fiber diameter of 189.6 ± 52.89 nm is an optimum conduit with promising potential for substituting natural human vessels.

Skin mechanical properties and modeling: A review

The mechanical properties of the skin are important for various applications. Numerous tests have been conducted to characterize the mechanical behavior of this tissue, and this article presents a review on different experimental methods used. A discussion on the general mechanical behavior of the skin, including nonlinearity, viscoelasticity, anisotropy, loading history dependency, failure properties, and aging effects, is presented. Finally, commonly used constitutive models for simulating the mechanical response of skin are discussed in the context of representing the empirically observed behavior.

A combination of experimental and finite element analyses of needle-tissue interaction to compute the stresses and deformations during injection at different angles

One of the main clinical applications of the needles is its practical usage in the femoral vein catheterization. Annually more than two million peoples in the United States are exposed to femoral vein catheterization. How to use the input needles into the femoral vein has a key role in the sense of pain in post-injection and possible injuries, such as tissue damage and bleeding. It has been shown that there might be a correlation between the stresses and deformations due to femoral injection to the tissue and the sense of pain and, consequently, injuries caused by needles. In this study, the stresses and deformations induced by the needle to the femoral tissue were experimentally and numerically investigated in response to an input needle at four different angles, i.e., 30°, 45°, 60°, and 90°, via finite element method. In addition, a set of experimental injections at different angles were carried out to compare the numerical results with that of the experimental ones, namely pain score. The results revealed that by increasing the angle of injection up to 60°, the strain at the interaction site of the needle-tissue is increased accordingly while a significant falling is observed at the angle of 90°. In contrast, the stress due to injection was decreased at the region of needle-tissue interaction with showing the lowest one at the angle of 90°. Experimental results were also well confirmed the numerical observations since the lowest pain score was seen at the angle of 90°. The results suggest that the most effective angle of injection would be 90° due to a lower amount of stresses and deformations compared to the other angles of injection. These findings may have implications not only for understating the stresses and deformations induced during injection around the needle-tissue interaction, but also to give an outlook to the doctors to implement the most suitable angle of injection in order to reduce the pain as well as post injury of the patients.

Numerical investigation of the haemodynamics in the human fetal umbilical vein/ductus venosus based on the experimental data

Abortion of the fetus due to a disease, in an early stage of pregnancy, has been dramatically increased in the last decades. There is a still lack of knowledge on the various types of diseases which lead fetus to a vulnerable circumstance. The transport of oxygenated blood from the placenta to the human fetus has been an important clinical feature in Doppler velocimetry studies, especially the ductus venosus (DV). The DV connects intra-abdominal portion of the umbilical vein and the inferior vena cava (IVC) at the inlet of the right atrium and is, therefore, important when examining the fetus state of health. An abnormal flow in the DV can indicate a fetal disease such as, chromosomal abnormalities, cardiac defect, hypoxaemia and intrauterine growth restriction (IUGR). The blood flow in the fetal circulation has not been investigated much in detail. The blood flow in the fetal circulation provides necessary information for physician to make a suitable decision on abortion or alternative medical practice before or even after birth. The present study performed a comparative study to quantify the blood velocity in DV by a combination approach based on 3D computational simulation and Doppler measurement. The results showed that the velocity value in DV is significant and can be considered as an indicator of any kind of disease in fetal. The nodal displacement of the model was also analysed. It shows that DV tolerates a higher level of displacement compared with the other regions of the model, whereas the nodal pressure shows different results as the lowest values are located in DV.

A combination of experimental and numerical methods to investigate the role of strain rate on the mechanical properties and collagen fiber orientations of the healthy and atherosclerotic human coronary arteries

Atherosclerosis enables to alter not only the microstructural but also the physical properties of the arterial walls by plaque forming. Few studies so far have been conducted to calculate the isotropic or anisotropic mechanical properties of the healthy and atherosclerotic human coronary arteries. To date there is a paucity of knowledge on the mechanical response of the arteries under different strain rates. Therefore, the objective of the concurrent research was to comprehend whether the alteration in the strain rates of the human atherosclerotic arteries in comparison with the healthy ones contribute to the biomechanical behaviors. To do this, healthy and atherosclerotic human coronary arteries were removed from 18 individuals during autopsy. Histological analyses by both an expert histopathologist and an imaged-based recognizer software were performed to figure out the average angle of collagen fibers in the healthy and atherosclerotic arterial walls. Thereafter, the samples were subjected to 3 diverse strain rates, i.e., 5, 20, and 50 mm/min, until the material failure occurs. The stress-strain diagrams of the arterial tissues were calculated in order to capture their linear elastic and nonlinear hyperelastic mechanical properties. In addition, Artificial Neural Networks (ANNs) was employed to predict the alteration of mean angle of collagen fibers during load bearing up to failure. The findings suggest that strain rate has a significant (p < 0.05) role in the linear elastic and nonlinear hyperelastic mechanical properties as well as the mean angle of collagen fibers of the atherosclerotic arteries, whereas no specific impact on the healthy ones. Furthermore, the mean angle of collagen fibers during the load bearing up to the failure at each strain rate was well predicted by the proposed ANNs code.

Dynamic finite element simulation of the gunshot injury to the human forehead protected by polyvinyl alcohol sponge

Although there are some traditional models of the gunshot wounds, there is still a need for more modeling analyses due to the difficulties related to the gunshot wounds to the forehead region of the human skull. In this study, the degree of damage as a consequence of penetrating head injuries due to gunshot wounds was determined using a preliminary finite element (FE) model of the human skull. In addition, the role of polyvinyl alcohol (PVA) sponge, which can be used as an alternative to reinforce the kinetic energy absorption capacity of bulletproof vest and helmet materials, to minimize the amount of skull injury due to penetrating processes was investigated through the FE model. Digital computed tomography along with magnetic resonance imaging data of the human head were employed to launch a three-dimensional (3D) FE model of the skull. Two geometrical shapes of projectiles (steel ball and bullet) were simulated for penetrating with an initial impact velocity of 734 m/s using nonlinear dynamic modeling code, namely LS-DYNA. The role of the damaged/distorted elements were removed during computation when the stress or strain reached their thresholds. The stress distributions in various parts of the forehead and sponge after injury were also computed. The results revealed the same amount of stress for both the steel ball and bullet after hitting the skull. The modeling results also indicated the time that steel ball takes to penetrate into the skull is lower than that of the bullet. In addition, more than 21% of the steel ball's kinetic energy was absorbed by the PVA sponge and, subsequently, injury sternness of the forehead was considerably minimized. The findings advise the application of the PVA sponge as a substitute strengthening material to be able to diminish the energy of impact as well as the load transmitted to the object.

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

The skin tissue has been shown to behave like a nonlinear anisotropic material. This study was aimed to employ a constitutive fiber family equation to characterize the nonlinear anisotropic mechanical behavior of the rat and mice skin tissues in different anatomical locations, including the abdomen and back, using histostructural and uniaxial data. The rat and mice skin tissues were excised from the animals' body and then the histological analyses were performed on each skin type to determine the mean fiber orientation angle. Afterward, the preconditioned skin tissues were subjected to a series of quasi-static axial and circumferential loads until the incidence of failure. The crucial role of fiber orientation was explicitly added into a proposed strain energy density function. The material coefficients were determined using the constrained nonlinear optimization method based on the axial and circumferential extension data of the rat and mice samples at different anatomical locations. The material coefficients of the skins were given with R(2) ≥ 0.998. The results revealed a significant load-bearing capacity and stiffness of the rat abdomen compared to the rat back tissues. In addition, the mice abdomen showed a higher stiffness in the axial direction in comparison with circumferential one, while the mice back displayed its highest stiffness in the circumferential direction. The material coefficients of the rat and mice skin tissues were determined and well compared to the experimental data. The optimized fiber angles were also compared to the experimental histological data, and in all cases less than 11.85% differences were observed in both the skin tissues.

MAGNETIC FLUID HYPERTHERMIA IN A CYLINDRICAL GEL CONTAINS WATER FLOW

In magnetic fluid hyperthermia (MFH), nanoparticles are injected into a diseased tissue and then subjected to an alternating high frequency magnetic field. The produced heat may have a key asset to destroy the cancerous cells. The blood flow in a tissue is considered as the most complicated part of the MFH which should be taken into account in the analysis of the MFH. This study was aimed to perform an experimental study to investigate the heat transfer of agar gel which contains fluid flow. Fe 3 O 4 as a nanoparticle was injected into the center of a cylindrical gel. It was also embedded with other cylindrical gels and subjected to an alternating magnetic field of 7.3 (kA/m) and a frequency of 50 (kHz) for 3600 (s). The temperature of the gel was measured at three points. The temperature distribution was measured via the experimental data. Moreover, specific absorption rate (SAR) was quantified with time differential temperature function at t = 0 by means of experimental data. Finite element method (FEM) was employed to establish a model to validate the SAR function. Results revealed the effects of fluid flow and accuracy of the SAR function for heat production in gel. The proposed function have implications in hyperthermia studies as a heat generation source. Finally, the condition of experimental setup was simulated to find the blood perfusion.

Resolving the viscoelasticity and anisotropy dependence of the mechanical properties of skin from a porcine model

The mechanical response of skin to external loads is influenced by anisotropy and viscoelasticity of the tissue, but the underlying mechanisms remain unclear. Here, we report a study of the main effects of tissue orientation (TO, which is linked to anisotropy) and strain rate (SR, a measure of viscoelasticity), as well as the interaction effects between the two factors, on the tensile properties of skin from a porcine model. Tensile testing to rupture of porcine skin tissue was conducted to evaluate the sensitivity of the tissue modulus of elasticity (E) and fracture-related properties, namely maximum stress (σU) and strain (εU) at σU, to varying SR and TO. Specimens were excised from the abdominal skin in two orientations, namely parallel (P) and right angle (R) to the torso midline. Each TO was investigated at three SR levels, namely 0.007-0.015 s(-1) (low), 0.040 s(-1) (mid) and 0.065 s(-1) (high). Two-factor analysis of variance revealed that the respective parameters responded differently to varying SR and TO. Significant changes in the σU were observed with different TOs but not with SR. The εU decreased significantly with increasing SR, but no significant variation was observed for different TOs. Significant changes in E were observed with different TOs; E increased significantly with increasing SR. More importantly, the respective mechanical parameters were not significantly influenced by interactions between SR and TO. These findings suggest that the trends associated with the changes in the skin mechanical properties may be attributed partly to differences in the anisotropy and viscoelasticity but not through any interaction between viscoelasticity and anisotropy.

A computational fluid–structure interaction model of the blood flow in the healthy and varicose saphenous vein

Objective

Varicose vein has become enlarged and twisted and, consequently, has lost its mechanical strength. As a result of the varicose saphenous vein (SV) mechanical alterations, the hemodynamic parameters of the blood flow, such as blood velocity as well as vein wall stress and strain, would change accordingly. However, little is known about stress and strain and there consequences under experimental conditions on blood flow and velocity within normal and varicose veins. In this study, a three-dimensional (3D) computational fluid–structure interaction (FSI) model of a human healthy and varicose SVs was established to determine the hemodynamic characterization of the blood flow as a function of vein wall mechanical properties, i.e. elastic and hyperelastic.

Methods

The mechanical properties of the human healthy and varicose SVs were experimentally measured and implemented into the computational model. The fully coupled fluid and structure models were solved using the explicit dynamics finite element code LS-DYNA.

Results

The results revealed that, regardless of healthy and varicose, the elastic walls reach to the ultimate strength of the vein wall, whereas the hyperelastic wall can tolerate more stress. The highest von Mises stress compared to the healthy ones was seen in the elastic and hyperelastic varicose SVs with 1.412 and 1.535 MPa, respectively. In addition, analysis of the resultant displacement in the vein wall indicated that the varicose SVs experienced a higher displacement compared to the healthy ones irrespective of elastic and hyperelastic material models. The highest blood velocity was also observed for the healthy hyperelastic SV wall.

Conclusion

The findings of this study may have implications not only for determining the role of the vein wall mechanical properties in the hemodynamic alterations of the blood, but also for employing as a null information in balloon-angioplasty and bypass surgeries.

An experimental-nonlinear finite element study of a balloon expandable stent inside a realistic stenotic human coronary artery to investigate plaque and arterial wall injury

The stresses induced within plaque tissues and arterial layers during stent expansion inside an atherosclerotic artery can be exceeded from the yield stresses of those tissues and, consequently, lead to plaque or arterial wall rupture. The distribution and magnitude of the stresses in the plaque-artery-stent structure might be distinctly different for different plaque types. In this study, the mechanical properties of six healthy and atherosclerotic human coronary arteries were determined for application in plaque and arterial vulnerability assessment. A nonlinear finite element simulation based on an Ogden material model was established to investigate the effect of plaque types on the stresses induced in the arterial wall during implantation of a balloon expandable coronary stent. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results indicated a significant influence of plaque types on the maximum stresses induced within the plaque wall and arterial wall during stenting but not when computing maximum stress on the stent. The stress on the stiffest calcified plaque wall was 3.161 MPa, whereas cellular and hypocellular plaques showed relatively less stress on their wall. The highest von Mises stresses within the arterial wall were observed on the hypocellular plaque, whereas the lowest stresses were seen to be located in the calcified and cellular plaques. Although the computed stresses on the arterial wall for the calcified and cellular plaques were not high enough to invoke a rupture, the stress on the hypocellular plaque was relatively higher than that of the strength of the arterial wall. These findings may have implications not only for understanding the stresses induced in plaque and the arterial wall, but also for developing surgeries such as balloon-angioplasty and stenting.

Measurement of the axial and circumferential mechanical properties of rat skin tissue at different anatomical locations

Skin tissue is not only responsible for thermoregulation but also for protecting the human body from mechanical, bacterial, and viral insults. The mechanical properties of skin tissue may vary according to the anatomical locations in the body. However, the linear elastic and nonlinear hyperelastic mechanical properties of the skin in different anatomical regions and at different loading directions (axial and circumferential) so far have not been determined. In this study, the mechanical properties during tension of the rat abdomen and back were calculated at different loading directions using linear elastic and nonlinear hyperelastic material models. The skin samples were subjected to a series of tensile tests. The elastic modulus and maximum stress of the skin tissues were measured before the incidence of failure. The nonlinear mechanical behavior of the skin tissues was also computationally investigated through a constitutive equation. Hyperelastic strain energy density function was calibrated using the experimental data. The results revealed the anisotropic mechanical behavior of the abdomen and the isotropic mechanical response of the back skin. The highest elastic modulus was observed in the abdomen skin under the axial direction (10 MPa), while the lowest one was seen in the back skin under axial loading (5 MPa). The Mooney-Rivlin material model closely addressed the nonlinear mechanical behavior of the skin at different loading directions, which can be implemented in the future biomechanical models of skin tissue. The results might have implications not only for understanding of the isotropic and anisotropic mechanical behavior of skin tissue at different anatomical locations but also for providing more information for a diversity of disciplines, including dermatology, cosmetics industry, clinical decision making, and clinical intervention.

A comparative study on the uniaxial mechanical properties of the umbilical vein and umbilical artery using different stress-strain definitions

The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress-strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney-Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress-strain diagram, the maximum strain of UV was 92 % higher, while the elastic modulus and maximum stress were 162 and 42 % lower than that of UA. The Mooney-Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.

A nonlinear finite element simulation of balloon expandable stent for assessment of plaque vulnerability inside a stenotic artery

The stresses induced on plaque wall during stent implantation inside a stenotic artery are associated with plaque rupture. The stresses in the plaque-artery-stent structure appear to be distinctly different for different plaque types in terms of both distribution and magnitude. In this study, a nonlinear finite element simulation was executed to analyze the influence of plaque composition (calcified, cellular, and hypocellular) on plaque, artery layers (intima, media, and adventitia), and stent stresses during implantation of a balloon expandable coronary stent into a stenosed artery. The atherosclerotic artery was assumed to consist of a plaque and normal arterial tissues on its outer side. The results revealed a significant influence of plaque types on the maximum stresses induced within plaque wall and artery layers during stenting, but not when calculating maximum stress on stent. The stress on stiffer calcified plaque wall was in the fracture level (2.21 MPa), whereas cellular and hypocellular plaques play a protective role by displaying less stress on their wall. The highest von Mises stresses were observed on less stiff media layer. The findings of this study suggest a lower risk of arterial vascular injury for calcified plaque, while higher risk of plaque ruptures for cellular and hypocellular plaques.

Finite element simulation of an artificial intervertebral disk using fiber reinforced laminated composite model

Degeneration of intervertebral disk (IVD) has been increased in recent years. The lumbar herniation can be cured using conservative and surgical procedures. Surgery is considered after failure of conservative treatment. Partial discectomy, fusion, and total disk replacement (TDR) are also common surgical treatments for degenerative disk disease. However, due to limitations and disadvantages of the current treatments, many studies have been carried out to approach the best design of mimicking natural disk. Recently, a new method of TDRs has been introduced using nature deformation of IVD by reinforced fibers of annulus fibrosis. Nonetheless, owing to limitations of experimental works on the human body, numerical studies of IVD may help to understand load transfer and biomechanical properties within the disks with reinforced fibers. In this study, a three-dimensional (3D) finite element model of the L2-L3 disk vertebrae unit with 12 vertical fibers embedded into annulus fibrosis was constructed. The IVD was subjected to compressive force, bending moment, and axial torsion. The most important parameters of disk failures were compared to that of experimental data. The results showed that the addition of reinforced fibers into the disk invokes a significant decrease of stress in the nucleus and annulus. The findings of this study may have implications not only for developing IVDs with reinforced fibers but also for the application of fiber reinforced IVD in orthopedics surgeries as a suitable implant.