The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.

Pulmonary arterial hypertension (PAH) commonly leads to right ventricular (RV) hypertrophy and fibrosis that affect the mechanical properties of the RV myocardium (MYO). To investigate the effects of PAH on the mechanics of the RV MYO and extracellular matrix (ECM), we compared RV wall samples, isolated from rats in which PAH was induced using the SuHx protocol, with samples from control animals before and after the tissues were decellularized. Planar biaxial mechanical testing, a technique first adapted to living soft biological tissues by Fung, was performed on intact and decellularized samples. Fung's anisotropic exponential strain energy function fitted the full range of biaxial test results with high fidelity in control and PAH samples both before and after they were decellularized. Mean RV myocardial apex-to-outflow tract and circumferential stresses during equibiaxial strain were significantly greater in PAH than control samples. Mean RV ECM circumferential but not apex-to-outflow tract stresses during equibiaxial strain were significantly greater in the PAH than control group. The ratio of ECM to myocardial stresses at matched strains did not change significantly between groups. Circumferential stresses were significantly higher than apex-to-outflow tract stresses for all groups. These findings confirm the predictions of a mathematical model based on changes in RV hemodynamics and morphology in rat PAH, and may provide a foundation for a new constitutive analysis of the contributions of ECM remodeling to changes in RV filling properties during PAH.

The cervix is essential to a healthy pregnancy as it must bear the increasing load caused by the growing fetus. Preterm birth is suspected to be caused by the premature softening and mechanical failure of the cervix. The objective of this paper is to measure the anisotropic mechanical properties of human cervical tissue using indentation and video extensometry. The human cervix is a layered structure, where its thick stromal core contains preferentially aligned collagen fibers embedded in a soft ground substance. The fiber composite nature of the tissue provides resistance to the complex three-dimensional loading environment of pregnancy. In this work, we detail an indentation mechanical test to obtain the force and deformation response during loading which closely matches in vivo conditions. We postulate a constitutive material model to describe the equilibrium material behavior to ramp-hold indentation, and we use an inverse finite element method based on genetic algorithm (GA) optimization to determine best-fit material parameters. We report the material properties of human cervical slices taken at different anatomical locations from women of different obstetric backgrounds. In this cohort of patients, the anterior internal os (the area where the cervix meets the uterus) of the cervix is stiffer than the anterior external os (the area closest to the vagina). The anatomic anterior and posterior quadrants of cervical tissue are more anisotropic than the left and right quadrants. There is no significant difference in material properties between samples of different parities (number of pregnancies reaching viable gestation age).

This paper describes the propagation of shear waves in a Holzapfel-Gasser-Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (pre-deformation) can influence plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after an imposed pre-deformation in simple shear. These analytical expressions show that shear wave speeds are affected by the parameters (µ_0,k_1,k_2,?) of the HGO model and the direction and amplitude of the pre-deformation shear, ?. Simulations of corresponding finite element models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, closed-form expressions for the wave speed in terms of the parameters of the HGO model will allow efficient estimation of material parameters from experimental data.

This paper presents in vivo mechanical characterization of the muscularis, submucosa, and mucosa of the porcine stomach wall under large deformation loading. This is particularly important for the development of gastrointestinal pathology-specific surgical intervention techniques. The study is based on testing the cardiac and fundic glandular stomach regions using a custom-developed compression ultrasound elastography system. Particular attention has been paid to elucidate the heterogeneity and anisotropy of tissue response. A Fung hyperelastic material model has been used to model the mechanical response of each tissue layer. A univariate analysis comparing the initial shear moduli of the three layers indicates that the muscularis (5.69 ± 4.06 kPa) is the stiffest followed by the submucosa (3.04 ± 3.32 kPa) and the mucosa (0.56 ± 0.28 kPa). The muscularis is found to be strongly distinguishable from the mucosa tissue in the cardiac and fundic regions based on a multivariate discriminant analysis. The cardiac muscularis is observed to be stiffer than the fundic muscularis tissue (shear moduli of 7.96 ± 3.82 kPa versus 3.42 ± 2.96 kPa), more anisotropic (anisotropic parameter of 2.21 ± 0.77 versus 1.41 ± 0.38), and strongly distinguishable from its fundic counterpart. The results are consistent with the tissue morphology and are in accordance with our previous ex vivo tissue study. Finally, a univariate comparison of the in vivo and ex vivo initial shear moduli for each layer shows that the muscularis and submucosa tissues are softer while in vivo, but the mucosa tissue is stiffer while in vivo. The results concerning the mechanical properties highlight the inhomogeneity and anisotropy of multilayer stomach tissue.

The fracture properties of cortical bone are directly coupled to its complex hierarchical structure. The limited availability of bone material from many anatomic locations creates challenges for assessing the effect of bone heterogeneity and anisotropy on fracture properties. The small punch technique (SPT) was employed to examine the fracture behavior of cortical bone in terms of area under the curve values obtained from load-load point displacement behavior. Fracture toughness of cortical bone was also determined in terms of J-toughness values obtained using a compact tension (CT) test. Area under the curve values obtained from the small punch test were correlated with the J-toughness values of cortical bone. The effects of bone density and compositional parameters on area under the curve and J-toughness values were also analyzed using linear and multiple regression analysis. Area under the curve and J-toughness values are strongly and positively correlated. Bone density and %mineral content are positively correlated with both area under the curve and J-toughness values. The multiple regression analysis outcomes support these results. Overall, the findings support the hypothesis that area under the curve values obtained from small punch tests can be used to assess the fracture behavior of cortical bone.

Predicting the mechanical behavior of the intervertebral disk (IVD) in health and in disease requires accurate spatial mapping of its compressive mechanical properties. Previous studies confirmed that residual strains in the annulus fibrosus (AF) of the IVD, which result from nonuniform extracellular matrix deposition in response to in vivo loads, vary by anatomical regions (anterior, posterior, and lateral) and zones (inner, middle, and outer). We hypothesized that as the AF is composed of a nonlinear, anisotropic, viscoelastic material, the state of residual strain in the transverse plane would influence the apparent values of axial compressive properties. To test this hypothesis, axial creep indentation tests were performed, using a 1.6 mm spherical probe, at nine different anatomical locations on bovine caudal AFs in both the intact (residual strain present) and strain relieved states. The results showed a shift toward increased spatial homogeneity in all measured parameters, particularly instantaneous strain. This shift was not observed in control AFs, which were tested twice in the intact state. Our results confirm that time-dependent axial compressive properties of the AF are sensitive to the state of residual strain in the transverse plane, to a degree that is likely to affect whole disk behavior.

While the anisotropic behavior of the complex composite myocardial tissue has been well characterized in recent years, the compressibility of the tissue has not been rigorously investigated to date. In the first part of this study, we present experimental evidence that passive-excised porcine myocardium exhibits volume change. Under tensile loading of a cylindrical specimen, a volume change of 4.1 ± 1.95 % is observed at a peak stretch of 1.3. Confined compression experiments also demonstrate significant volume change in the tissue (loading applied up to a volumetric strain of 10%). In order to simulate the multiaxial passive behavior of the myocardium, a nonlinear volumetric hyperelastic component is combined with the well-established Holzapfel–Ogden anisotropic hyperelastic component for myocardium fibers. This framework is shown to describe the experimentally observed behavior of porcine and human tissues under shear and biaxial loading conditions. In the second part of the study, a representative volumetric element (RVE) of myocardium tissue is constructed to parse the contribution of the tissue vasculature to observed volume change under confined compression loading. Simulations of the myocardium microstructure suggest that the vasculature cannot fully account for the experimentally measured volume change. Additionally, the RVE is subjected to six modes of shear loading to investigate the influence of microscale fiber alignment and dispersion on tissue-scale mechanical behavior.

The tricuspid valve is a one-way valve on the pulmonary side of the heart, which prevents backflow of blood during ventricular contractions. Development of computational models of the tricuspid valve is important both in understanding the normal valvular function and in the development/improvement of surgical procedures and medical devices. A key step in the development of such models is quantification of the mechanical properties of the tricuspid valve leaflets. In this study, after examining previously measured five-loading-protocol biaxial stress–strain response of porcine tricuspid valves, a phenomenological constitutive framework was chosen to represent this response. The material constants were quantified for all three leaflets, which were shown to be highly anisotropic with average anisotropy indices of less than 0.5 (an anisotropy index value of 1 indicates a perfectly isotropic response, whereas a smaller value of the anisotropy index indicates an anisotropic response). To obtain mean values of material constants, stress–strain responses of the leaflet samples were averaged and then fitted to the constitutive model (average R 2 over 0.9 ). Since the sample thicknesses were not hugely different, averaging the data using the same tension levels and stress levels produced similar average material constants for each leaflet.

There is lack of investigation capturing the complex mechanical interaction of tissue-engineered intervertebral disk (IVD) constructs in physiologically relevant environmental conditions. In this study, mechanical characterization of anisotropic electrospinning (ES) substrates made of polycaprolactone (PCL) was carried out in wet and dry conditions and viability of human bone marrow derived mesenchymal stem cells (hMSCs) seeded within double layers of ES PCL were also studied. Cyclic compression of IVD-like constructs composed of an agarose core confined by ES PCL double layers was implemented using a bioreactor and the cellular response to the mechanical stimulation was evaluated. Tensile tests showed decrease of elastic modulus of ES PCL as the angle of stretching increased, and at 60 deg stretching angle in wet, the maximum ultimate tensile strength (UTS) was observed. Based on the configuration of IVD-like constructs, the calculated circumferential stress experienced by the ES PCL double layers was 40 times of the vertical compressive stress. Confined compression of IVD-like constructs at 5% and 10% displacement dramatically reduced cell viability, particularly at 10%, although cell presence in small and isolated area can still be observed after mechanical conditioning. Hence, material mechanical properties of tissue-engineered scaffolds, composed of fibril structure of polymer with low melting point, are affected by the testing condition. Circumferential stress induced by axial compressive stimulation, conveyed to the ES PCL double layer wrapped around an agarose core, can affect the viability of cells seeded at the interface, depending on the mechanical configuration and magnitude of the load.

Progress toward understanding the underlying mechanisms of pelvic organ prolapse (POP) is limited, in part, due to a lack of information on the biomechanical properties and microstructural composition of the vaginal wall. Compromised vaginal wall integrity is thought to contribute to pelvic floor disorders; however, normal structure–function relationships within the vaginal wall are not fully understood. In addition to the information produced from uniaxial testing, biaxial extension–inflation tests performed over a range of physiological values could provide additional insights into vaginal wall mechanical behavior (i.e., axial coupling and anisotropy), while preserving in vivo tissue geometry. Thus, we present experimental methods of assessing murine vaginal wall biaxial mechanical properties using extension–inflation protocols. Geometrically intact vaginal samples taken from 16 female C57BL/6 mice underwent pressure–diameter and force–length preconditioning and testing within a pressure-myograph device. A bilinear curve fit was applied to the local stress–stretch data to quantify the transition stress and stretch as well as the toe- and linear-region moduli. The murine vaginal wall demonstrated a nonlinear response resembling that of other soft tissues, and evaluation of bilinear curve fits suggests that the vagina exhibits pseudoelasticity, axial coupling, and anisotropy. The protocols developed herein permit quantification of biaxial tissue properties. These methods can be utilized in future studies in order to assess evolving structure–function relationships with respect to aging, the onset of prolapse, and response to potential clinical interventions.

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.

Homografts and synthetic grafts are used in surgery for congenital heart disease (CHD). Determining these materials' mechanical properties will aid in understanding tissue behavior when subjected to abnormal CHD hemodynamics. Homograft tissue samples from anterior/posterior aspects, of ascending/descending aorta (AA, DA), innominate artery (IA), left subclavian artery (LScA), left common carotid artery (LCCA), main/left/right pulmonary artery (MPA, LPA, RPA), and synthetic vascular grafts, were obtained in three orientations: circumferential, diagonal (45 deg relative to circumferential direction), and longitudinal. Samples were subjected to uniaxial tensile testing (UTT). True strain-Cauchy stress curves were individually fitted for each orientation to calibrate Fung model. Then, they were used to calibrate anisotropic Holzapfel–Gasser model (R 2 > 0.95). Most samples demonstrated a nonlinear hyperelastic strain–stress response to UTT. Stiffness (measured by tangent modulus at different strains) in all orientations were compared and shown as contour plots. For each vessel segment at all strain levels, stiffness was not significantly different among aspects and orientations. For synthetic grafts, stiffness was significantly different among orientations (p < 0.042). Aorta is significantly stiffer than pulmonary artery at 10% strain, comparing all orientations, aspects, and regions (p = 0.0001). Synthetic grafts are significantly stiffer than aortic and pulmonary homografts at all strain levels (p < 0.046). Aortic, pulmonary artery, and synthetic grafts exhibit hyperelastic biomechanical behavior with anisotropic effect. Differences in mechanical properties among vascular grafts may affect native tissue behavior and ventricular/arterial mechanical coupling, and increase the risk of deformation due to abnormal CHD hemodynamics.

Elastin and collagen fibers are the major load-bearing extracellular matrix (ECM) constituents of the vascular wall. Arteries function differently than veins in the circulatory system; however as a result from several treatment options, veins are subjected to sudden elevated arterial pressure. It is thus important to recognize the fundamental structure and function differences between a vein and an artery. Our research compared the relationship between biaxial mechanical function and ECM structure of porcine thoracic aorta and inferior vena cava. Our study suggests that aorta contains slightly more elastin than collagen due to the cyclical extensibility, but vena cava contains almost four times more collagen than elastin to maintain integrity. Furthermore, multiphoton imaging of vena cava showed longitudinally oriented elastin and circumferentially oriented collagen that is recruited at supraphysiologic stress, but low levels of strain. However in aorta, elastin is distributed uniformly, and the primarily circumferentially oriented collagen is recruited at higher levels of strain than vena cava. These structural observations support the functional finding that vena cava is highly anisotropic with the longitude being more compliant and the circumference stiffening substantially at low levels of strain. Overall, our research demonstrates that fiber distributions and recruitment should be considered in addition to relative collagen and elastin contents. Also, the importance of accounting for the structural and functional differences between arteries and veins should be taken into account when considering disease treatment options.

The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R 2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.

The stress in a cell due to extracellular mechanical stimulus is determined by its mechanical properties, and the structural organization of many adherent cells suggests that their properties are anisotropic. This anisotropy may significantly influence the cells' mechanotransductive response to complex loads, and has important implications for development of accurate models of tissue biomechanics. Standard methods for measuring cellular mechanics report linear moduli that cannot capture large-deformation anisotropic properties, which in a continuum mechanics framework are best described by a strain energy density function (SED). In tissues, the SED is most robustly measured using biaxial testing. Here, we describe a cellular microbiaxial stretching (CμBS) method that modifies this tissue-scale approach to measure the anisotropic elastic behavior of individual vascular smooth muscle cells (VSMCs) with nativelike cytoarchitecture. Using CμBS, we reveal that VSMCs are highly anisotropic under large deformations. We then characterize a Holzapfel–Gasser–Ogden type SED for individual VSMCs and find that architecture-dependent properties of the cells can be robustly described using a formulation solely based on the organization of their actin cytoskeleton. These results suggest that cellular anisotropy should be considered when developing biomechanical models, and could play an important role in cellular mechano-adaptation.

Indentation experiments offer a robust, fast, and repeatable testing method for evaluating the mechanical properties of the solid-state materials in a wide stiffness range. With the advantage of requiring a minimal sample preparation and multiple tests on a small piece of specimen, this method has recently become a popular technique for measuring the elastic properties of the biological materials, especially the brain tissue whose ultrasoft nature makes its mechanical characterization very challenging. Nevertheless, some limitations are associated with the indentation of the brain tissue, such as improper surface detection, negative initial contact force due to tip-tissue moisture interaction, and partial contact between the tip and the sample. In this study, an indirect indentation scheme is proposed to overcome the aforementioned difficulties. In this way, the indentation force is transferred from a sharp tip to the surface of the tissue slices via a rigid coverslip. To demonstrate the accuracy of this method, the linear viscoelastic properties of the white and gray matters of the bovine brain samples are measured by imposing small cyclic loads at different frequencies. The rate, regional, directional, and postmortem time dependence of the viscoelastic moduli are investigated and compared with the previous results from cyclic shear and monotonic experiments on the brain tissue. While findings of this research present a comprehensive set of information for the viscoelastic properties of the brain at a wide frequency range, the central goal of this paper is to introduce a novel experimentation technique with noticeable advantages for biomechanical characterization of the soft tissue.

Located on the right side of the heart, the tricuspid valve (TV) prevents blood backflow from the right ventricle to the right atrium. Similar to other cardiac valves, quantification of TV biaxial mechanical properties is essential in developing accurate computational models. In the current study, for the first time, the biaxial stress–strain behavior of porcine TV was measured ex vivo under different loading protocols using biaxial tensile testing equipment. The results showed a highly nonlinear response including a compliant region followed by a rapid transition to a stiff region for all of the TV leaflets both in the circumferential and in the radial directions. Based on the data analysis, all three leaflets were found to be anisotropic, and they were stiffer in the circumferential direction in comparison to the radial direction. It was also concluded that the posterior leaflet was the most anisotropic leaflet.

The rostral-caudally aligned fiber-reinforced structure of spinal cord white matter (WM) gives rise to transverse isotropy in the material. Stress and strain patterns generated in the spinal cord parenchyma following spinal cord injury (SCI) are multidirectional and dependent on the mechanism of the injury. Our objective was to develop a WM constitutive model that captures the material transverse isotropy under dynamic loading. The WM mechanical behavior was extracted from the published tensile and compressive experiments. Combinations of isotropic and fiber-reinforcing models were examined in a conditional quasi-linear viscoelastic (QLV) formulation to capture the WM mechanical behavior. The effect of WM transverse isotropy on SCI model outcomes was evaluated by simulating a nonhuman primate (NHP) contusion injury experiment. A second-order reduced polynomial hyperelastic energy potential conditionally combined with a quadratic reinforcing function in a four-term Prony series QLV model best captured the WM mechanical behavior (0.89 < R 2 < 0.99). WM isotropic and transversely isotropic material models combined with discrete modeling of the pia mater resulted in peak impact forces that matched the experimental outcomes. The transversely isotropic WM with discrete pia mater resulted in maximum principal strain (MPS) distributions which effectively captured the combination of ipsilateral peripheral WM sparing, ipsilateral injury and contralateral sparing, and the rostral/caudal spread of damage observed in in vivo injuries. The results suggest that the WM transverse isotropy could have an important role in correlating tissue damage with mechanical measures and explaining the directional sensitivity of the spinal cord to injury.

Styrene-based block copolymers are promising materials for the development of a polymeric heart valve prosthesis (PHV), and the mechanical properties of these polymers can be tuned via the manufacturing process, orienting the cylindrical domains to achieve material anisotropy. The aim of this work is the development of a computational tool for the optimization of the material microstructure in a new PHV intended for aortic valve replacement to enhance the mechanical performance of the device. An iterative procedure was implemented to orient the cylinders along the maximum principal stress direction of the leaflet. A numerical model of the leaflet was developed, and the polymer mechanical behavior was described by a hyperelastic anisotropic constitutive law. A custom routine was implemented to align the cylinders with the maximum principal stress direction in the leaflet for each iteration. The study was focused on valve closure, since during this phase the fibrous structure of the leaflets must bear the greatest load. The optimal microstructure obtained by our procedure is characterized by mainly circumferential orientation of the cylinders within the valve leaflet. An increase in the radial strain and a decrease in the circumferential strain due to the microstructure optimization were observed. Also, a decrease in the maximum value of the strain energy density was found in the case of optimized orientation; since the strain energy density is a widely used criterion to predict elastomer's lifetime, this result suggests a possible increase of the device durability if the polymer microstructure is optimized. The present method represents a valuable tool for the design of a new anisotropic PHV, allowing the investigation of different designs, materials, and loading conditions.