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

Energetically stable curve fitting to hyperelastic models based on uniaxial and biaxial tensile tests

Hyperelastic constitutive laws in biomechanics are used to model soft tissues, and material model parameters are often determined by performing curve fitting on data from uniaxial or biaxial tensile tests. The strain energy function of the applied constitutive law must to be energetically stable; however, this condition is not inherently provided by most currently available models. This study provides a procedure to determine stable strain energy functions in a biaxial strain space based on either uniaxial or biaxial tensile tests. Instead of conservative, strain-independent conditions, a stability region is defined in the strain space based on the sample's tensile tests, thus allowing optimisation within a wider parameter space, resulting in better approximations. An extension of the Levenberg-Marquardt algorithm incorporating user-defined stability constraints is proposed, and the constrained optimisation algorithm is applied to isotropic and anisotropic models. The uniqueness of solutions of the Fung model is also discussed. The material model parameters of stable solutions for soft tissue measurements from various literature sources are determined to demonstrate the proposed procedure. Applying appropriate constraints in the optimisation algorithm resulted in stable and physically permissible constrained solutions for the strain energy function, in contrast to the results of most unconstrained optimisation cases.

Dynamic traction force in trabecular meshwork cells: A 2D culture model for normal and glaucomatous states

Glaucoma, which is associated with intraocular pressure (IOP) elevation, results in trabecular meshwork (TM) cellular dysfunction, leading to increased rigidity of the extracellular matrix (ECM), larger adhesion forces between the TM cells and ECM, and higher resistance to aqueous humor drainage. TM cells sense the mechanical forces due to IOP dynamic and apply multidimensional forces on the ECM. Recognizing the importance of cellular forces in modulating various cellular activities and development, this study is aimed to develop a 2D in vitro cell culture model to calculate the 3D, depth-dependent, dynamic traction forces, tensile/compressive/shear strain of the normal and glaucomatous human TM cells within a deformable polyacrylamide (PAM) gel substrate. Normal and glaucomatous human TM cells were isolated, cultured, and seeded on top of the PAM gel substrate with embedded FluoSpheres, spanning elastic moduli of 1.5 to 80 kPa. Sixteen-hour post-seeding live confocal microscopy in an incubator was conducted to Z-stack image the 3D displacement map of the FluoSpheres within the PAM gels. Combined with the known PAM gel stiffness, we ascertained the 3D traction forces in the gel. Our results revealed meaningfully larger traction forces in the glaucomatous TM cells compared to the normal TM cells, reaching depths greater than 10-µm in the PAM gel substrate. Stress fibers in TM cells increased with gel rigidity, but diminished when stiffness rose from 20 to 80 kPa. The developed 2D cell culture model aids in understanding how altered mechanical properties in glaucoma impact TM cell behavior and aqueous humor outflow resistance. STATEMENT OF SIGNIFICANCE: Glaucoma, a leading cause of irreversible blindness, is intricately linked to elevated intraocular pressures and their subsequent cellular effects. The trabecular meshwork plays a pivotal role in this mechanism, particularly its interaction with the extracellular matrix. This research unveils an advanced 2D in vitro cell culture model that intricately maps the complex 3D forces exerted by trabecular meshwork cells on the extracellular matrix, offering unparalleled insights into the cellular biomechanics at play in both healthy and glaucomatous eyes. By discerning the changes in these forces across varying substrate stiffness levels, we bridge the gap in understanding between cellular mechanobiology and the onset of glaucoma. The findings stand as a beacon for potential therapeutic avenues, emphasizing the gravity of cellular/extracellular matrix interactions in glaucoma's pathogenesis and setting the stage for targeted interventions in its early stages.

Segmental biomechanics of the normal and glaucomatous human aqueous outflow pathway

The conventional aqueous outflow pathway, encompassing the trabecular meshwork (TM), juxtacanalicular connective tissue (JCT), and inner wall endothelium of Schlemm's canal (SC), governs intraocular pressure (IOP) regulation. This study targets the biomechanics of low-flow (LF) and high-flow (HF) regions within the aqueous humor outflow pathway in normal and glaucomatous human donor eyes, using a combined experimental and computational approach. LF and HF TM/JCT/SC complex tissues from normal and glaucomatous eyes underwent uniaxial tensile testing. Dynamic motion of the TM/JCT/SC complex was recorded using customized green-light optical coherence tomography during SC pressurization in cannulated anterior segment wedges. A hyperviscoelastic model quantified TM/JCT/SC complex properties. A fluid-structure interaction model simulated tissue-aqueous humor interaction. FluoSpheres were introduced into the pathway via negative pressure in the SC, with their motion tracked using two-photon excitation microscopy. Tensile test results revealed that the elastic moduli of the LF and HF regions in glaucomatous eyes are 3.5- and 1.5-fold stiffer than the normal eyes, respectively. The FE results also showed significantly larger shear moduli in the TM, JCT, and SC of the glaucomatous eyes compared to the normal subjects. The LF regions in normal eyes demonstrated larger elastic moduli compared to the HF regions in glaucomatous eyes. The resultant strain in the outflow tissues and velocity of the aqueous humor in the FSI models were in good agreement with the digital volume correlation and 3D particle image velocimetry data, respectively. This study uncovers stiffer biomechanical responses in glaucomatous eyes, with LF regions stiffer than HF regions in both normal and glaucomatous eyes. STATEMENT OF SIGNIFICANCE: This study delves into the biomechanics of the conventional aqueous outflow pathway, a crucial regulator of intraocular pressure and ocular health. By analyzing mechanical differences in low-flow and high-flow regions of normal and glaucomatous eyes, this research unveils the stiffer response in glaucomatous eyes. The distinction between regions' properties offers insights into aqueous humor outflow regulation, while the integration of experimental and computational methods enhances credibility. These findings have potential implications for disease management and present a vital step toward innovative ophthalmic interventions. This study advances our understanding of glaucoma's biomechanical basis and its broader impact on ocular health.

Effect of Extra-abdominal Vein Varix on the Stress Distribution in Umbilical Cord: A Simulation Study

The umbilical cord is a critical structure linking the fetus to the placenta and is surrounded by the amniotic fluid. It is composed of a vein, two arteries coiled around the vein, and Wharton's jelly surrounding the blood vessels. In this study, the stress distribution of the arteries, vein, and Wharton's jelly of an umbilical cord with extra-abdominal umbilical vein varix is analyzed for varying amniotic pressure using finite element analysis. Four diameters are considered for the umbilical vein, 6.5 mm, 11 mm, 15.5 mm, and 20 mm, with 6.5 mm corresponding to the normal vein diameter. The amniotic pressure is varied from 15-105 mmHg in steps of 15 mmHg, to simulate contractions during labour. Stress distribution is obtained and the peak stresses are analyzed. According to the results, the peak stress in the Wharton's jelly and the umbilical vein increases nonlinearly with increasing amniotic pressure. The peak stress in umbilical arteries initially decreases till the amniotic pressure reaches 45 mmHg and thereafter increases. This might be due to asymmetric deformation of the Wharton's jelly at the pressure range below arterial pressure.Clinical Relevance- This study could be useful in understanding the fundamental mechanics of extra-abdominal umbilical vein varix and help in development of better treatment protocols.

Interaction of the Blood Components with Ascending Thoracic Aortic Aneurysm Wall: Biomechanical and Fluid Analyses

Background: Ascending thoracic aortic aneurysm (ATAA) is an asymptomatic localized dilation of the aorta that is prone to rupture with a high rate of mortality. While diameter is the main risk factor for rupture assessment, it has been shown that the peak wall stress from finite element (FE) simulations may contribute to refinement of clinical decisions. In FE simulations, the intraluminal boundary condition is a single-phase blood flow that interacts with the thoracic aorta (TA). However, the blood is consisted of red blood cells (RBCs), white blood cells (WBCs), and plasma that interacts with the TA wall, so it may affect the resultant stresses and strains in the TA, as well as hemodynamics of the blood. Methods: In this study, discrete elements were distributed in the TA lumen to represent the blood components and mechanically coupled using fluid–structure interaction (FSI). Healthy and aneurysmal human TA tissues were subjected to axial and circumferential tensile loadings, and the hyperelastic mechanical properties were assigned to the TA and ATAA FE models. Results: The ATAA showed larger tensile and shear stresses but smaller fluid velocity compared to the ATA. The blood components experienced smaller shear stress in interaction with the ATAA wall compared to TA. The computational fluid dynamics showed smaller blood velocity and wall shear stress compared to the FSI. Conclusions: This study is a first proof of concept, and future investigations will aim at validating the novel methodology to derive a more reliable ATAA rupture risk assessment considering the interaction of the blood components with the TA wall.

Biomechanical tensile behavior of human Wharton's jelly

Wharton's jelly (WJ) is a mucous connective tissue of the umbilical cord. It shows high healing capabilities, mainly attributed to the chemical composition and to the presence of stem cells, growth factors and peptides. Although WJ biological properties are well documented in vitro and in vivo, there is still a lack of mechanical data on this tissue, which is paramount for its use as a biomaterial for medical applications. In this study, mechanical responses of ten WJ samples within close physiological conditions were registered undergoing quasi static cyclic tensile tests followed by a load up to failure. This protocol aimed on one hand to provide biomechanical data to feed predictive numerical models and on the other hand increase WJ knowledge in view of its potential use in biomedical field. In spite of the WJ harvest, the resulting viscous nonlinear elastic response obtained is fully in tune with the literature confirming the database quality. A side of the knowledge improvement on WJ mechanical response, this paper provides accurate data that will enhance predictive simulation work such as finite element analysis. The mechanical step-through brought by the analytical nonlinear characterization over cyclic and ultimate loads is to predict WJ behavior. Actually, principal component analysis highlighted its quality while pointing out indicators, such as failure or hydration criteria, as well as models' limitations.

A computational fluid dynamics modelling of maternal-fetal heat exchange and blood flow in the umbilical cord

Human fetal thermoregulation, maternal-fetal heat exchange, and the role of the umbilical cord in these processes are not well understood. Ethical and technical limitations have restricted current knowledge to animal studies, that do not reflect human morphology. Here, we present the first 3-dimensional computational model of the human umbilical cord with finite element analysis, aiming to compute the maternal-fetal heat exchange. By modelling both the umbilical vein and the two umbilical arteries, we found that the coiled geometry of the umbilical artery, in comparison with the primarily straight umbilical vein, affects blood flow parameters such as velocity, pressure, temperature, shear strain rate and static entropy. Specifically, by enhancing the heat transfer coefficient, we have shown that the helical structure of the umbilical arteries plays a vital role in the temperature drop of the blood, along the arterial length from the fetal end to the placental end. This suggests the importance of the umbilical cord structure in maternal-fetal heat exchange and fetal heat loss, opening the way for future research with modified models and scenarios, as the basis for early detection of potential heat-transfer related complications, and/or assurance of fetal wellbeing.

A patient-specific numerical modeling of the spontaneous coronary artery dissection in relation to atherosclerosis

The spontaneous coronary artery dissection (SCAD) is a clinical complication of angioplasty leading to an initiation of a tear/crack in the intima layer of the artery. The crack can propagate to the interface of the intima-media layer following by intramural hematoma. The relation between the SCAD and atherosclerosis is a controversial issue, as some studies stated no correlation between them while others showed that a crack can initiate in the intima but cannot propagate into the atrophied media layer. To investigate the relation between the intraluminal crack propagation in the atherosclerotic artery and SCAD, this study numerically investigated the initiation and propagation of a crack in the intraluminal and radial locations of the healthy and atherosclerotic human coronary arterial walls. The energy release rate, namely J-integral, is computed as a numerical derivative of the strain energy with respect to a crack extension using a user-defined virtual crack method (VCE) of extended finite element method (XFEM). Experimental measurements were carried out to calculate the elasto-plastic mechanical properties of the healthy and atherosclerotic human coronary arteries. The experimental data were then assigned to our own established patient-specific FE model of the coronary artery. Cracks were sketched in the intraluminal and radial locations of the arterial wall and allowed to propagate to the virtual interface of the intima-media to form a false lumen. The results revealed a higher stress at the crack tip of the healthy arterial wall compared to the atherosclerotic one. Lower crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were observed in the intraluminal crack of the atherosclerotic artery. J-integral of the atherosclerotic arterial wall was also found to be higher than the healthy one at the intraluminal crack. The results revealed that although a crack can initiate in the intraluminal of an atherosclerotic artery, it cannot propagate into the media layer due to a relatively higher rate of the strain energy release in the atherosclerotic arterial wall compared to the healthy one.

The biomechanics of the umbilical cord Wharton Jelly: Roles in hemodynamic proficiency and resistance to compression

The umbilical cord is a complex structure containing three vessels, one straight vein and two coiled arteries, encased by the Wharton Jelly (WJ) a spongy structure made of collagen and hydrated macromolecules. Fetal blood reaches the placenta through the arteries and flows back to the fetus through the vein. The role of the WJ in maintaining cord circulation proficiency and the ultimate reason for arterial coiling still lack of reasonable mechanistic interpretations. We performed biaxial tension tests and evidenced significant differences in the mechanical properties of the core and peripheral WJ. The core region, located between the arteries and the vein, resulted rather stiffer close to the fetus. Finite element modelling and optimization based inverse method were used to create 2D and 3D models of the cord and to simulate stress distribution in different hemodynamic conditions, compressive loads and arterial coiling. We recorded a facilitated stress transmission from the arteries to the vein through the soft core of periplacental WJ. This condition generates a pressure gradient that boosts the venous backflow circulation towards the fetus. Peripheral WJ allows arteries to act as pressure buffering chambers during the cardiac diastole and helps to dissipate compressive forces away from vessels. Altered WJ biomechanics may represent the structural basis of cord vulnerability in many high-risk clinical conditions.

A numerical study on the application of the functionally graded materials in the stent design

Undesirable deformation of the stent can induce a significant amount of injure not only to the blood vessel but also to the plaque. The objective of this study was to reduce/minimize these undesirable deformations by the application of Functionally Graded Materials (FGM). To do this, Finite Element (FE) method was employed to simulate the expansion of a stent and the corresponding displacement of the stenosis plaque. Three hyperelastic plaque types as well as five elastoplastic stents were simulated. Dogboning, foreshortening, maximum stress in the plaque, and the pressure which is needed to fully expand the stent for different stent materials, were acquired. While all FGMs had lower dogboning in comparison to the stents made of the uniform materials, the stent with the lowest heterogeneous index displayed the lowest amount of dogboning. Steel stent showed the lowest foreshortening and fully expansion pressure but the difference was much lower than that the one for dogboning. Therefore, the FGM with the heterogeneous index of 0.5 is expected to exhibit the most suitable results. In addition, the results revealed that the material parameters has crucial effects on the deformation of the stent and, as a result, as a design point of view the FGM parameters can be tailored to achieve the goal of the biomechanical optimization.

A Combination of Constitutive Damage Model and Artificial Neural Networks to Characterize the Mechanical Properties of the Healthy and Atherosclerotic Human Coronary Arteries

It has been indicated that the content and structure of the elastin and collagen of the arterial wall can subject to a significant alteration due to the atherosclerosis. Consequently, a high tissue stiffness, stress, and even damage/rupture are triggered in the arterial wall. Although many studies so far have been conducted to quantify the mechanical properties of the coronary arteries, none of them consider the role of collagen damage of the healthy and atherosclerotic human coronary arterial walls. Recently, a fiber family-based constitutive equation was proposed to capture the anisotropic mechanical response of the healthy and atherosclerotic human coronary arteries via both the histostructural and uniaxial data. In this study, experimental mechanical measurements along with histological data of the healthy and atherosclerotic arterial walls were employed to determine the constitutive damage parameters and remodeling of the collagen fibers. To do this, the preconditioned arterial tissues were excised from human cadavers within 5-h postmortem, and the mean angle of their collagen fibers was precisely determined. Thereafter, a group of quasistatic axial and circumferential loadings were applied to the arterial walls, and the constrained nonlinear minimization method was employed to identify the arterial parameters according to the axial and circumferential extension data. The remodeling of the collagen fibers during the tensile test was also predicted via Artificial Neural Networks algorithm. Regardless of loading direction, the results presented a noteworthy load-bearing capability and stiffness of the atherosclerotic arteries compared to the healthy ones (P < 0.005). Theoretical fiber angles were found to be consistent with the experimental histological data with less than 2 and 5° difference for the healthy and atherosclerotic arterial walls, respectively. The pseudoelastic damage model data were also compared with that of the experimental data, and interestingly, the arterial mechanical behavior for both the primary loading (up to the elastic region) and the discontinuous softening (up to the ultimate stress) was well addressed. The proposed model predicted well the mechanical response of the arterial tissue considering the damage of collagen fibers for both the healthy and atherosclerotic arterial walls.

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.

Fabrication of a Functionalized Magnetic Bacterial Nanocellulose with Iron Oxide Nanoparticles

In this study, bacterial nanocellulose (BNC) produced by the bacteria Gluconacetobacter xylinus is synthesized and impregnated in situ with iron oxide nanoparticles (IONP) (Fe3O4) to yield a magnetic bacterial nanocellulose (MBNC). The synthesis of MBNC is a precise and specifically designed multi-step process. Briefly, bacterial nanocellulose (BNC) pellicles are formed from preserved G. xylinus strain according to our experimental requirements of size and morphology. A solution of iron(III) chloride hexahydrate (FeCl3·6H2O) and iron(II) chloride tetrahydrate (FeCl2·4H2O) with a 2:1 molar ratio is prepared and diluted in deoxygenated high purity water. A BNC pellicle is then introduced in the vessel with the reactants. This mixture is stirred and heated at 80 °C in a silicon oil bath and ammonium hydroxide (14%) is then added by dropping to precipitate the ferrous ions into the BNC mesh. This last step allows forming in situ magnetite nanoparticles (Fe3O4) inside the bacterial nanocellulose mesh to confer magnetic properties to BNC pellicle. A toxicological assay was used to evaluate the biocompatibility of the BNC-IONP pellicle. Polyethylene glycol (PEG) was used to cover the IONPs in order to improve their biocompatibility. Scanning electron microscopy (SEM) images showed that the IONP were located preferentially in the fibril interlacing spaces of the BNC matrix, but some of them were also found along the BNC ribbons. Magnetic force microscope measurements performed on the MBNC detected the presence magnetic domains with high and weak intensity magnetic field, confirming the magnetic nature of the MBNC pellicle. Young's modulus values obtained in this work are also in a reasonable agreement with those reported for several blood vessels in previous studies.

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.

A comparative study on the mechanical properties of the healthy and varicose human saphenous vein under uniaxial loading

Saphenous Vein (SV) due to fatness, age, inactiveness, etc. can be afflicted with varicose. The main reason of the varicose vein is believed to be related to the leg muscle pump which is unable to return the blood to the heart in contradiction of the effect of gravity. As a result of the varicose vein, both the structure and mechanical properties of the vein wall would alter. However, so far there is a lack of knowledge on the mechanical properties of the varicose vein. In this study, a comparative study was carried out to measure the elastic and hyperelastic mechanical properties of the healthy and varicose SVs. Healthy and varicose SVs were removed at autopsy and surgery from seven individuals and then axial tensile load was applied to them up to the failure point. In order to investigate the mechanical behaviour of the vein, this study was benefitted from three different stress definitions, such as 2nd Piola-Kichhoff, engineering and true stresses and four different strain definitions, i.e. Almansi-Hamel, Green-St. Venant, engineering and true strains, to determine the linear mechanical properties of the SVs. A Digital Image Correlation (DIC) technique was used to measure the true strain of the vein walls during load bearing. The non-linear mechanical behaviour of the SVs was also computationally evaluated via the Mooney-Rivlin material model. The true/Cauchy stress-strain diagram exhibited the elastic modulus of the varicose SVs as 45.11% lower than that of the healthy ones. Furthermore, by variation of the stress a significant alteration on the maximum stress of the healthy SVs was observed, but then not for the varicose veins. Additionally, the highest stresses of 4.99 and 0.65 MPa were observed for the healthy and varicose SVs, respectively. These results indicate a weakness in the mechanical strength of the SV when it becomes varicose, owing to the degradation of the elastin and collagen content of the SV. The Mooney-Rivlin hyperelastic and the Finite Element (FE) data were finally well compared to the experimental data.

A combination of histological analyses and uniaxial tensile tests to determine the material coefficients of the healthy and atherosclerotic human coronary arteries

Atherosclerosis is considered as the most severe form of cardiovascular diseases as it alters the structure of the elastin and collagen and, consequently, the mechanical properties of the artery wall. The role of collagen fibers orientations in the mechanical properties of the healthy and atherosclerotic human coronary arteries so far has not been well determined. In this study, a fiber family based constitutive equation was employed to address the mechanical behavior of healthy and atherosclerotic human coronary arteries using the combination of histostructural and uniaxial data. A group of six healthy and atherosclerotic human coronary arteries was excised at autopsy and histological analyses were performed on each artery to determine the mean angle of collagen fibers. The preconditioned arterial tissues were then subjected to a series of quasi-static axial and circumferential loadings. The key role of fiber orientation was explicitly added into a proposed strain energy density function. The constrained nonlinear optimization method was used to determine the material coefficients based on the axial and circumferential extension data of the arteries. The material coefficients of coronary arteries were given with R(2)≥0.991. The results regardless of loading direction revealed a significant load-bearing capacity and stiffness of atherosclerotic arteries compared to the healthy ones (p<0.005). The optimized fiber angles were in good agreement with the experimental histological data as only 2.52% and 10.10% differences were observed for the healthy and atherosclerotic arteries, respectively. The stored energy function of the healthy arteries was found to be higher than that of atherosclerotic ones. These findings help us to understand the directional mechanical properties of coronary arteries which may have implications for different types of interventions and surgeries, including bypass, stenting, and balloon-angioplasty.