Mechanical characterization of anisotropic planar biological soft tissues using finite indentation: experimental feasibility

Heart valve tissue engineering offers a promising alternative for current treatment and replacement strategies, e.g., synthetic or bioprosthetic heart valves. In vitro mechanical conditioning is an important tool for engineering strong, implantable heart valves. Detailed knowledge of the mechanical properties of the native tissue as well as the developing tissue construct is vital for a better understanding and control of the remodeling processes induced by mechanical conditioning. The nonlinear, anisotropic and inhomogeneous mechanical behavior of heart valve tissue necessitates a mechanical characterization method that is capable of dealing with these complexities. In a recent computational study we showed that one single indentation test, combining force and deformation gradient data, provides sufficient information for local characterization of nonlinear soft anisotropic tissue properties. In the current study this approach is validated in two steps. First, indentation tests with varying indenter sizes are performed on linear elastic PDMS rubbers and compared to tensile tests on the same specimen. For the second step, tissue constructs are engineered using uniaxial or equibiaxial static constrained culture conditions. Digital image correlation (DIC) is used to quantify the anisotropy in the tissue constructs. For both validation steps, material parameters are estimated by inverse fitting of a computational model to the experimental results.     

Functional analysis of bioprosthetic heart valves

Glutaraldehyde-treated bovine pericardium is used successfully as bioprosthetic material in the manufacturing of heart valves leaflets. The mechanical properties of bovine pericardial aortic valve leaflets seem to influence its mechanical behaviour and the failure mechanisms. In this study the effect of orthotropy on tricuspid bioprosthetic aortic valve was analysed, using a three-dimensional finite element model, during the entire cardiac cycle. Multiaxial tensile tests were also performed to determine the anisotropy of pericardium. Seven different models of the same valve were analysed using different values of mechanical characteristics from one leaflet to another, considering pericardium as an orthotropic material. The results showed that even a small difference between values along the two axes of orthotropy can negatively influence leaflets performance as regard both displacement and stress distribution. Leaflets of bovine pericardium bioprostheses could be manufactured to be similar to natural human heart valves reproducing their well-known anisotropy. In this way it could be possible to improve the manufacturing process, durability and function of pericardial bioprosthetic valves.     

On the biaxial mechanical properties of the layers of the aortic valve leaflet

All existing constitutive models for heart valve leaflet tissues either assume a uniform transmural stress distribution or utilize a membrane tension formulation. Both approaches ignore layer specific mechanical contributions and the implicit nonuniformity of the transmural stress distribution. To begin to address these limitations, we conducted novel studies to quantify the biaxial mechanical behavior of the two structurally distinct, load bearing aortic valve (AV) leaflet layers: the fibrosa and ventricularis. Strip biaxial tests, with extremely sensitive force sensing capabilities, were further utilized to determine the mechanical behavior of the separated ventricularis layer at very low stress levels. Results indicated that both layers exhibited very different nonlinear, highly anisotropic mechanical behaviors. While the leaflet tissue mechanical response was dominated by the fibrosa layer, the ventricularis contributed double the amount of the fibrosa to the total radial tension and experienced four times the stress level. The strip biaxial test results further indicated that the ventricularis exhibited substantial anisotropic mechanical properties at very low stress levels. This result suggested that for all strain levels, the ventricularis layer is dominated by circumferentially oriented collagen fibers, and the initial loading phase of this layer cannot be modeled as an isotropic material. Histological-based thickness measurements indicated that the fibrosa and ventricularis constitute 41% and 29% of the total layer thickness, respectively. Moreover, the extensive network of interlayer connections and identical strains under biaxial loading in the intact state suggests that these layers are tightly bonded. In addition to advancing our knowledge of the subtle but important mechanical properties of the AV leaflet, this study provided a comprehensive database required for the development of a true 3D stress constitutive model for the native AV leaflet.     

Bioprosthetic heart valve leaflet motion monitored by dual camera stereo photogrammetry

Dual camera stereo photogrammetry (DCSP) was applied to investigate the leaflet motion of bioprosthetic heart valves (BHVs) in a physiologic pulse flow loop (PFL). A 25-mm bovine pericardial valve was installed in the aortic valve position of the PFL, which was operated at a pulse rate of 70 beats/min and a cardiac output of 5 l/min. The systolic/diastolic aortic pressure was maintained at 120/80 mmHg to mimic the physiologic load experienced by the aortic valve. The leaflet of the test valve was marked with 80 India ink dots to form a fan-shaped matrix. From the acquired image sequences, 3-D coordinates of the marker matrix were derived and hence the surface contour, local mean and Gaussian curvatures at each opening and closing phase during one cardiac cycle were reconstructed. It is generally believed that the long-term failure rate of BHV is related to the uneven distribution of mechanical stresses occurring in the leaflet material during opening and closing. Unfortunately, a quantitative analysis of the leaflet motion under physiological conditions has not been reported. The newly developed technique permits frame-by-frame mapping of the leaflet surface, which is essential for dynamic analysis of stress-strain behavior in BHV.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Improved prediction of the collagen fiber architecture in the aortic heart valve

Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively with the predicted fiber directions. The results of the present model might be used to gain further insight into the response of tissue engineered constructs during mechanical conditioning.     

A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics

This paper presents a finite element formulation suitable for large-strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue. First, an experimentally derived strain energy function is obtained from literature. This function is implemented in finite elements using the mixed pressure-displacement formulation. A modification is made to aid in maintaining positive definiteness of the stiffness matrix at low strains. The numerical implementation is shown to be accurate in representing the analytical model of material behavior. The mixed formulation is useful for modeling of soft biological tissues in general, and the model presented here is applicable to finite element simulation of mitral valve mechanics.     

Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test

Predicting the injury risk in automotive collisions requires accurate knowledge of human tissues, more particularly their mechanical properties under dynamic loadings. The present methodology aims to determine the failure characteristics of planar soft tissues such as skin, hollow organs and large vessel walls. This consists of a dynamic tensile test, which implies high-testing velocities close to those in automotive collisions. To proceed, I-shaped tissue samples are subjected to dynamic tensile tests using a customized tensile device based on the drop test principle. Data acquisition has especially been adapted to heterogeneous and soft biological tissues given that standard measurement systems (considered to be global) have been completed with a non-contact and full-field strain measurement (considered to be local). This local measurement technique, called the Image Correlation Method (ICM) provides an accurate strain analysis by revealing strain concentrations and avoids damaging the tissue. The methodology has first been applied to human forehead skin and can be further expanded to other planar soft tissues. The failure characteristics for the skin in terms of ultimate stress are 3 MPa +/- 1.5 MPa. The ultimate global longitudinal strains are equal to 9.5%+/-1.9% (Green-Lagrange strain), which contrasts with the ultimate local longitudinal strain values of 24.0%+/-5.3% (Green-Lagrange strain). This difference is a consequence of the tissue heterogeneity, clearly illustrated by the heterogeneous distribution of the local strain field. All data will assist in developing the tissue constitutive law that will be implemented in finite element models.     

Biaxial mechanical properties of bovine jugular venous valve leaflet tissues

Venous valve incompetence has been implicated in diseases ranging from chronic venous insufficiency (CVI) to intracranial venous hypertension. However, while the mechanical properties of venous valve leaflet tissues are central to CVI biomechanics and mechanobiology, neither stress–strain curves nor tangent moduli have been reported. Here, equibiaxial tensile mechanical tests were conducted to assess the tangent modulus, strength and anisotropy of venous valve leaflet tissues from bovine jugular veins. Valvular tissues were stretched to 60% strain in both the circumferential and radial directions, and leaflet tissue stress–strain curves were generated for proximal and distal valves (i.e., valves closest and furthest from the right heart, respectively). Toward linking mechanical properties to leaflet microstructure and composition, Masson’s trichrome and Verhoeff–Van Gieson staining and collagen assays were conducted. Results showed: (1) Proximal bovine jugular vein venous valves tended to be bicuspid (i.e., have two leaflets), while distal valves tended to be tricuspid; (2) leaflet tissues from proximal valves exhibited approximately threefold higher peak tangent moduli in the circumferential direction than in the orthogonal radial direction (i.e., proximal valve leaflet tissues were anisotropic; \(p<0.01\)); (3) individual leaflets excised from the same valve apparatus appeared to exhibit different mechanical properties (i.e., intra-valve variability); and (4) leaflets from distal valves exhibited a trend of higher soluble collagen concentrations than proximal ones (i.e., inter-valve variability). To the best of the authors’ knowledge, this is the first study reporting biaxial mechanical properties of venous valve leaflet tissues. These results provide a baseline for studying venous valve incompetence at the tissue level and a quantitative basis for prosthetic venous valve design.     

Anomalous rate dependence of the preconditioned response of soft tissue during load controlled deformation

It has been observed in load controlled laboratory tests of myocardium and skin that the tissues can exhibit a decrease in nonlinear stiffness with an increase in loading rate: the faster a test is performed, the more compliant is the preconditioned material behavior. This response seems to conflict with what is generally expected of soft tissues based on stretch or strain controlled tests, in which an increased rate of deformation results in a stiffer material response. It is hypothesized that this anomalous behavior has not been observed previously due to the small number of cyclic load controlled mechanical characterization tests that are geared specifically towards viscoelastic tissue response. The goal of this paper is to examine the preconditioned response of soft tissue to load controlled deformation using nonlinear viscoelastic material models including quasi-linear viscoelasticity, and to determine under what conditions this anomalous behavior becomes apparent. Results from this study suggest that this behavior is a true phenomenon unique to load controlled deformations that results from the interplay of nonlinear effects and creep behavior. These results call for increased attention to experimental parameters when testing and modeling nonlinear viscoelastic material behavior.     

Modelling and simulation of porcine liver tissue indentation using finite element method and uniaxial stress–strain data

We hypothesize that both compression and elongation stress–strain data should be considered for modeling and simulation of soft tissue indentation. Uniaxial stress–strain data were obtained from in vitro loading experiments of porcine liver tissue. An axisymmetric finite element model was used to simulate liver tissue indentation with tissue material represented by hyperelastic models. The material parameters were derived from uniaxial stress–strain data of compressions, elongations, and combined compression and elongation of porcine liver samples. in vitro indentation tests were used to validate the finite element simulation. Stress–strain data from the simulation with material parameters derived from the combined compression and elongation data match the experimental data best. This is due to its better ability in modeling 3D deformation since the behavior of biological soft tissue under indentation is affected by both its compressive and tensile characteristics. The combined logarithmic and polynomial model is somewhat better than the 5-constant Mooney–Rivlin model as the constitutive model for this indentation simulation.     

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.     

Mapping the spatial variation of mitral valve elastic properties using air-pulse optical coherence elastography

The mitral valve is a highly heterogeneous tissue composed of two leaflets, anterior and posterior, whose unique composition and regional differences in material properties are essential to overall valve function. While mitral valve mechanics have been studied for many decades, traditional testing methods limit the spatial resolution of measurements and can be destructive. Optical coherence elastography (OCE) is an emerging method for measuring viscoelastic properties of tissues in a noninvasive, nondestructive manner. In this study, we employed air-pulse OCE to measure the spatial variation in mitral valve elastic properties with micro-scale resolution at 1 mm increments along the radial length of the leaflets. We analyzed differences between the leaflets, as well as between regions of the valve. We found that the anterior leaflet has a higher elastic wave velocity, which is reported as a surrogate for stiffness, than the posterior leaflet, most notably at the annular edge of the sample. In addition, we found a spatial elastic gradient in the anterior leaflet, where the annular edge was found to have a greater elastic wave velocity than the free edge. This gradient was less pronounced in the posterior leaflet. These patterns were confirmed using established uniaxial tensile testing methods. Overall, the anterior leaflet was stiffer and had greater heterogeneity in its mechanical properties than the posterior leaflet. This study measures differences between the two mitral leaflets with greater resolution than previously feasible and demonstrates a method that may be suitable for assessing valve mechanics following repair or during the engineering of synthetic valve replacements.     

Time-dependent biaxial mechanical behavior of the aortic heart valve leaflet

Despite continued progress in the treatment of aortic valve (AV) disease, current treatments continue to be challenged to consistently restore AV function for extended durations. Improved approaches for AV repair and replacement rests upon our ability to more fully comprehend and simulate AV function. While the elastic behavior the AV leaflet (AVL) has been previously investigated, time-dependent behaviors under physiological biaxial loading states have yet to be quantified. In the current study, we performed strain rate, creep, and stress-relaxation experiments using porcine AVL under planar biaxial stretch and loaded to physiological levels (60 N/m equi-biaxial tension), with strain rates ranging from quasi-static to physiologic. The resulting stress-strain responses were found to be independent of strain rate, as was the observed low level of hysteresis ( approximately 17%). Stress relaxation and creep results indicated that while the AVL exhibited significant stress relaxation, it exhibited negligible creep over the 3h test duration. These results are all in accordance with our previous findings for the mitral valve anterior leaflet (MVAL) [Grashow, J.S., Sacks, M.S., Liao, J., Yoganathan, A.P., 2006a. Planar biaxial creep and stress relaxatin of the mitral valve anterior leaflet. Annals of Biomedical Engineering 34 (10), 1509-1518; Grashow, J.S., Yoganathan, A.P., Sacks, M.S., 2006b. Biaxial stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Annals of Biomedical Engineering 34 (2), 315-325], and support our observations that valvular tissues are functionally anisotropic, quasi-elastic biological materials. These results appear to be unique to valvular tissues, and indicate an ability to withstand loading without time-dependent effects under physiologic loading conditions. Based on a recent study that suggested valvular collagen fibrils are not intrinsically viscoelastic [Liao, J., Yang, L., Grashow, J., Sacks, M.S., 2007. The relation between collagen fibril kinematics and mechanical properties in the mitral valve anterior leaflet. Journal of Biomechanical Engineering 129 (1), 78-87], we speculate that the mechanisms underlying this quasi-elastic behavior may be attributed to inter-fibrillar structures unique to valvular tissues. These mechanisms are an important functional aspect of native valvular tissues, and are likely critical to improve our understanding of valvular disease and help guide the development of valvular tissue engineering and surgical repair.     

An inverse modeling approach for semilunar heart valve leaflet mechanics: exploitation of tissue structure

Determining the biomechanical behavior of heart valve leaflet tissues in a noninvasive manner remains an important clinical goal. While advances in 3D imaging modalities have made in vivo valve geometric data available, optimal methods to exploit such information in order to obtain functional information remain to be established. Herein we present and evaluate a novel leaflet shape-based framework to estimate the biomechanical behavior of heart valves from surface deformations by exploiting tissue structure. We determined accuracy levels using an “ideal” in vitro dataset, in which the leaflet geometry, strains, mechanical behavior, and fibrous structure were known to a high level of precision. By utilizing a simplified structural model for the leaflet mechanical behavior, we were able to limit the number of parameters to be determined per leaflet to only two. This approach allowed us to dramatically reduce the computational time and easily visualize the cost function to guide the minimization process. We determined that the image resolution and the number of available imaging frames were important components in the accuracy of our framework. Furthermore, our results suggest that it is possible to detect differences in fiber structure using our framework, thus allowing an opportunity to diagnose asymptomatic valve diseases and begin treatment at their early stages. Lastly, we observed good agreement of the final resulting stress–strain response when an averaged fiber architecture was used. This suggests that population-averaged fiber structural data may be sufficient for the application of the present framework to in vivo studies, although clearly much work remains to extend the present approach to in vivo problems.     

Elastic characterization of transversely isotropic soft materials by dynamic shear and asymmetric indentation

The mechanical characterization of soft anisotropic materials is a fundamental challenge because of difficulties in applying mechanical loads to soft matter and the need to combine information from multiple tests. A method to characterize the linear elastic properties of transversely isotropic soft materials is proposed, based on the combination of dynamic shear testing (DST) and asymmetric indentation. The procedure was demonstrated by characterizing a nearly incompressible transversely isotropic soft material. A soft gel with controlled anisotropy was obtained by polymerizing a mixture of fibrinogen and thrombin solutions in a high field magnet (B?=?11.7 T); fibrils in the resulting gel were predominantly aligned parallel to the magnetic field. Aligned fibrin gels were subject to dynamic (20-40 Hz) shear deformation in two orthogonal directions. The shear storage modulus was 1.08?±?0. 42 kPa (mean?±?std. dev.) for shear in a plane parallel to the dominant fiber direction, and 0.58?±?0.21 kPa for shear in the plane of isotropy. Gels were indented by a rectangular tip of a large aspect ratio, aligned either parallel or perpendicular to the normal to the plane of transverse isotropy. Aligned fibrin gels appeared stiffer when indented with the long axis of a rectangular tip perpendicular to the dominant fiber direction. Three-dimensional numerical simulations of asymmetric indentation were used to determine the relationship between direction-dependent differences in indentation stiffness and material parameters. This approach enables the estimation of a complete set of parameters for an incompressible, transversely isotropic, linear elastic material.     

Stresses in the closed mitral valve: a model study

In the present model study on the closed mitral valve, tensile force in the chordae tendineae is related to transvalvular pressure using a mathematical model of mechanics of the closed mitral valve. Circumferential stress as well as bending stress in the valve leaflets were neglected. Without precisely knowing the mechanical properties of the leaflet material, geometry of the leaflets was estimated by applying Laplace's law, which relates leaflet stress to leaflet curvature. Independent of shape of the mitral valve orifice, under all circumstances tensile force in the chordae tendineae was calculated to be equal or greater than half the force exerted on the mitral valve orifice by the transvalvular pressure.     

A nonlinear anisotropic model for porcine aortic heart valves

The anisotropic property of porcine aortic valve leaflet has potentially significant effects on its mechanical behaviour and the failure mechanisms. However, due to its complex nature, testing and modelling the anisotropic porcine aortic valves remains a continuing challenge to date. This study has developed a nonlinear anisotropic finite element model for porcine heart valves. The model is based on the uniaxial experimental data of porcine aortic heart valve leaflet and the properties of nonlinear composite material. A finite element code is developed to solve this problem using the 8-node super-parameter nonlinear shells and the update Lagrangian method. The stress distribution and deformation of the porcine aortic valves with either uniform and non-uniform thicknesses in closed phase and loaded condition are calculated. The results showed significant changes in the stress distributions due to the anisotropic property of the leaflets. Compared with the isotropic valve at the same loading condition, it is found that the site of the peak stress of the anisotropic leaflet is different; the maximum longitudinal normal stress is increased, but the maximum transversal normal stress and in-plane shear stress are reduced. We conclude that it is very important to consider the anisotropic property of the porcine heart valves in order to understand the failure mechanism of such valves in vivo.     

A Computational Model of Aging and Calcification in the Aortic Heart Valve

The aortic heart valve undergoes geometric and mechanical changes over time. The cusps of a normal, healthy valve thicken and become less extensible over time. In the disease calcific aortic stenosis (CAS), calcified nodules progressively stiffen the cusps. The local mechanical changes in the cusps, due to either normal aging or pathological processes, affect overall function of the valve. In this paper, we propose a computational model for the aging aortic valve that connects local changes to overall valve function. We extend a previous model for the healthy valve to describe aging. To model normal/uncomplicated aging, leaflet thickness and extensibility are varied versus age according to experimental data. To model calcification, initial sites are defined and a simple growth law is assumed. The nodules then grow over time, so that the area of calcification increases from one model to the next model representing greater age. Overall valve function is recorded for each individual model to yield a single simulation of valve function over time. This simulation is the first theoretical tool to describe the temporal behavior of aortic valve calcification. The ability to better understand and predict disease progression will aid in design and timing of patient treatments for CAS.