Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear

Utilization of novel biologically-derived biomaterials in bioprosthetic heart valves (BHV) requires robust constitutive models to predict the mechanical behavior under generalized loading states. Thus, it is necessary to perform rigorous experimentation involving all functional deformations to obtain both the form and material constants of a strain-energy density function. In this study, we generated a comprehensive experimental biaxial mechanical dataset that included high in-plane shear stresses using glutaraldehyde treated bovine pericardium (GLBP) as the representative BHV biomaterial. Compared to our previous study (Sacks, JBME, v.121, pp. 551-555, 1999), GLBP demonstrated a substantially different response under high shear strains. This finding was underscored by the inability of the standard Fung model, applied successfully in our previous GLBP study, to fit the high-shear data. To develop an appropriate constitutive model, we utilized an interpolation technique for the pseudo-elastic response to guide modification of the final model form. An eight parameter modified Fung model utilizing additional quartic terms was developed, which fitted the complete dataset well. Model parameters were also constrained to satisfy physical plausibility of the strain energy function. The results of this study underscore the limited predictive ability of current soft tissue models, and the need to collect experimental data for soft tissue simulations over the complete functional range.     

A homogenization model of the annulus fibrosus

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli (E theta and E z) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus (G thetaz) was two orders of magnitude larger than directly measured values. The values of E theta and E z were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure-function relationships in disc degeneration and for functional tissue engineering.     

Eicosapentaenoic acid prevents atrial fibrillation associated with heart failure in a rabbit model

Atrial fibrillation (AF) is associated with morbidity and mortality of heart failure. Eicosapentaenoic acid (EPA), which is contained in fish oil, was shown to reduce the risk of cardiovascular diseases. We investigated the effects of EPA on AF associated with heart failure in a rabbit model. Rabbits were subjected to ventricular tachypacing (VTP) for 4 wk with or without EPA treatment. Continuous VTP induced heart failure status in these rabbits. The duration of AF (DAF) induced by burst pacing was analyzed by electrophysiological studies. VTP resulted in increased DAF following burst pacing. EPA treatment attenuated increased DAF. Atrial fibrosis increased in response to VTP, accompanied by extracellular signal-regulated kinase (ERK) phosphorylation and transforming growth factor-β1 (TGF-β1) expression in the atrium. Treatment with EPA attenuated atrial fibrosis, ERK phosphorylation, and TGF-β1 expression in response to VTP. EPA treatment increased adiponectin as an anti-inflammatory adipokine and decreased tumor necrosis factor-α as a proinflammatory adipokine in the atrium and epicardial adipose tissues. EPA attenuated VTP-induced AF promotion and atrial remodeling, which was accompanied by modulating the profiles of adipokine production from epicardial adipose tissue. EPA may be useful for prevention and treatment of AF associated with heart failure.     

Material characterization of human medial collateral ligament.

The objectives of this study were to determine the longitudinal and transverse material properties of the human medial collateral ligament (MCL) and to evaluate the ability of three existing constitutive models to describe the material behavior of MCL. Uniaxial test specimens were punched from ten human cadaveric MCLs and tensile tested along and transverse to the collagen fiber direction. Using load and optical strain analysis information, the tangent modulus, tensile strength and ultimate strain were determined. The material coefficients for each constitutive model were determined using nonlinear regression. All specimens failed within the substance of the tissue. Specimens tested along the collagen fiber direction exhibited the typical nonlinear behavior reported for ligaments. This behavior was absent from the stress-strain curves of the transverse specimens. The average tensile strength, ultimate strain, and tangent modulus for the longitudinal specimens was 38.6 +/- 4.8 MPa, 17.1 +/- 1.5 percent, and 332.2 +/- 58.3 MPa, respectively. The average tensile strength, ultimate strain, and tangent modulus for the transverse specimens was 1.7 +/- 0.5 MPa, 11.7 +/- 0.9 percent, and 11.0 +/- 3.6 MPa, respectively. All three constitutive models described the longitudinal behavior of the ligament equally well. However, the ability of the models to describe the transverse behavior of the ligament varied.     

A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: Potential application to hypercompliant soft tissues

A dual-indentation creep and stress relaxation methodology was developed and validated for the material characterization of very soft biological tissue within the framework of the biphasic poroviscoelastic (BPVE) constitutive model. Agarose hydrogel, a generic porous medium with mobile fluid, served as a mechanical tissue analogue for validation of the experimental procedure. Indentation creep and stress relaxation tests with a solid plane-ended cylindrical indenter were performed at identical sites on a gel sample with dimensions large enough with respect to indenter size in order to satisfy an infinite layer assumption. A finite element (FE) formulation coupled to a global optimization algorithm was utilized to simultaneously curve-fit the creep and stress relaxation data and extract the BPVE model parameters for the agarose gel. A numerical analysis with artificial data was conducted to validate the uniqueness of the computational procedure. The BPVE model was able to successfully cross-predict both creep and stress relaxation behavior for each pair of experiments with a single unique set of material parameters. Optimized elastic moduli were consistent with those reported in the literature for agarose gel. With the incorporation of appropriately-sized indenters to satisfy more stringent geometric constraints, this simple yet powerful indentation methodology can provide a straightforward means by which to obtain the BPVE model parameters of biological soft tissues that are difficult to manipulate (such as brain and adipose) while maintaining a realistic in situ loading environment.     

The effects of aneurysm on the biaxial mechanical behavior of human abdominal aorta

The biomechanical response of normal and pathologic human abdominal aortic tissue to uniaxial loading conditions is insufficient for the characterization of its three-dimensional (3D) mechanical behavior. Planar biaxial mechanical evaluation allows for 3D constitutive modeling of nearly incompressible tissues, as well as the investigation of the nature of mechanical anisotropy. In the current study, 26 abdominal aortic aneurysm (AAA) tissue samples and 8 age-matched (> 60 years of age) nonaneurysmal abdominal aortic (AA) tissue samples were obtained and tested using a tension-controlled biaxial testing protocol. Graphical response functions (Sun et al., 2003. J. Biomech. Eng. 125, 372-380) were used as a guide to describe the pseudo-elastic response of AA and AAA. Based on the observed pseudo-elastic response, a four-parameter exponential strain energy function developed by Vito (1990. J. Biomech. Eng. 112, 153-159) was used from which both an individual specimen and group material parameter sets were determined for both AA and AAA. Peak Green strain values in the circumferential (Ethetatheta,max) and longitudinal (ELL,max) directions under an equibiaxial tension of 120 N/m were also compared. The strain energy function fit all of the individual specimens well with an average R2 of 0.95 +/- 0.02 and 0.90 +/- 0.02 (mean +/- SEM) for the AA and AAA groups, respectively. The average Ethetatheta,max at 200 N/m equibiaxial tension was found to be significantly smaller for AAAs as compared to AAs (0.07 +/- 0.01 versus 0.13 +/- 0.03, respectively; p < 0.01). There was also a pronounced increase in the circumferential stiffness for AAA tissue as compared to AA tissue, indicating a larger degree of anisotropy for this tissue as compared to age-matched AA tissue. We also observed that the four-parameter Fung-elastic model was not able to fit the AAA tissue mechanical response using physically realistic material parameter values. It was concluded that aneurysmal degeneration of the abdominal aorta is associated with an increase in mechanical anisotropy, with preferential stiffening in the circumferential direction.     

Specimen-specific predictions of contact stress under physiological loading in the human hip: validation and sensitivity studies

Hip osteoarthritis may be initiated and advanced by abnormal cartilage contact mechanics, and finite element (FE) modeling provides an approach with the potential to allow the study of this process. Previous FE models of the human hip have been limited by single specimen validation and the use of quasi-linear or linear elastic constitutive models of articular cartilage. The effects of the latter assumptions on model predictions are unknown, partially because data for the instantaneous behavior of healthy human hip cartilage are unavailable. The aims of this study were to develop and validate a series of specimen-specific FE models, to characterize the regional instantaneous response of healthy human hip cartilage in compression, and to assess the effects of material nonlinearity, inhomogeneity and specimen-specific material coefficients on FE predictions of cartilage contact stress and contact area. Five cadaveric specimens underwent experimental loading, cartilage material characterization and specimen-specific FE modeling. Cartilage in the FE models was represented by average neo-Hookean, average Veronda Westmann and specimen- and region-specific Veronda Westmann hyperelastic constitutive models. Experimental measurements and FE predictions compared well for all three cartilage representations, which was reflected in average RMS errors in contact stress of less than 25 %. The instantaneous material behavior of healthy human hip cartilage varied spatially, with stiffer acetabular cartilage than femoral cartilage and stiffer cartilage in lateral regions than in medial regions. The Veronda Westmann constitutive model with average material coefficients accurately predicted peak contact stress, average contact stress, contact area and contact patterns. The use of subject- and region-specific material coefficients did not increase the accuracy of FE model predictions. The neo-Hookean constitutive model underpredicted peak contact stress in areas of high stress. The results of this study support the use of average cartilage material coefficients in predictions of cartilage contact stress and contact area in the normal hip. The regional characterization of cartilage material behavior provides the necessary inputs for future computational studies, to investigate other mechanical parameters that may be correlated with OA and cartilage damage in the human hip. In the future, the results of this study can be applied to subject-specific models to better understand how abnormal hip contact stress and contact area contribute to OA.     

Modeling electrical power absorption and thermally-induced biological tissue damage

This work develops a model for thermally induced damage from high current flow through biological tissue. Using the first law of thermodynamics, the balance of energy produced by the current and the energy absorbed by the tissue are investigated. The tissue damage is correlated with an evolution law that is activated upon exceeding a temperature threshold. As an example, the Fung material model is used. For certain parameter choices, the Fung material law has the ability to absorb relatively significant amounts of energy, due to its inherent exponential response character, thus, to some extent, mitigating possible tissue damage. Numerical examples are provided to illustrate the model’s behavior.     

A description of arterial wall mechanics using limiting chain extensibility constitutive models

Certain aspects of the mechanical response of arterial walls can be described using nonlinear elasticity theory. Uniaxial tests on vascular walls reveal nonlinear stress-strain behavior, with higher extensibility in the low stretch range and progressively lower extensibility with increasing stretch. This phenomenon is well known in the framework of rubber-like materials where it is called a strain-hardening or strain-stiffening effect. Constitutive models of incompressible hyperelasticity that take this into account include power-law models and limiting chain extensibility models. Our purpose in this paper is to bring to the attention of the biomechanics community some essential features of one such model of the latter type due to Gent. This model is compared with isotropic versions of biomechanical constitutive models by Takamizawa-Hayashi and Fung; the latter is a limiting version of a power-law material. Two particular problems are considered for which experimental data on arterial wall deformations are available. The first concerns small oscillations superposed on a large static stretch of a vertical string of arterial tissue. It is shown that the exponential model of Fung and the Gent model match well with the experimental data. The second problem is the extension of an internally pressurized circular cylindrical tube. It is shown that an inversion phenomenon observed experimentally for the human iliac artery can be described within a membrane theory by the Gent model whereas this cannot be described using the exponential model. The foregoing considerations are carried out for isotropic elastic materials in the absence of residual stress. Extensions to include anisotropy are also indicated.     

Two-dimensional stress-strain relationship for canine pericardium

Two-dimensional pseudoelastic mechanical properties of the canine pericardium were investigated in vitro. The pericardium was assumed to be orthotropic. The material symmetry axis was determined a priori and aligned with the stretching axis. Various biaxial stretching tests were then performed and a set of data covering a wide range of strains was constructed. This complete data set was fitted to a new exponential type constitutive model, and a set of true material constants was determined for each specimen. Using the constitutive model and the true material constants, the results from constant lateral force tests and constant lateral displacement tests were predicted and compared with experiment.     

Confocal arthroscopy-based patient-specific constitutive models of cartilaginous tissues - II: prediction of reaction force history of meniscal cartilage specimens

The theoretical framework developed in a companion paper (Part I) is used to derive estimates of mechanical response of two meniscal cartilage specimens. The previously developed framework consisted of a constitutive model capable of incorporating confocal image-derived tissue microstructural data. In the present paper (Part II) fibre and matrix constitutive parameters are first estimated from mechanical testing of a batch of specimens similar to, but independent from those under consideration. Image analysis techniques which allow estimation of tissue microstructural parameters form confocal images are presented. The constitutive model and image-derived structural parameters are then used to predict the reaction force history of the two meniscal specimens subjected to partially confined compression. The predictions are made on the basis of the specimens' individual structural condition as assessed by confocal microscopy and involve no tuning of material parameters. Although the model does not reproduce all features of the experimental curves, as an unfitted estimate of mechanical response the prediction is quite accurate. In light of the obtained results it is judged that more general non-invasive estimation of tissue mechanical properties is possible using the developed framework.     

Confocal arthroscopy-based patient-specific constitutive models of cartilaginous tissues—II: prediction of reaction force history of meniscal cartilage specimens

The theoretical framework developed in a companion paper (Part I) is used to derive estimates of mechanical response of two meniscal cartilage specimens. The previously developed framework consisted of a constitutive model capable of incorporating confocal image-derived tissue microstructural data. In the present paper (Part II) fibre and matrix constitutive parameters are first estimated from mechanical testing of a batch of specimens similar to, but independent from those under consideration. Image analysis techniques which allow estimation of tissue microstructural parameters form confocal images are presented. The constitutive model and image-derived structural parameters are then used to predict the reaction force history of the two meniscal specimens subjected to partially confined compression. The predictions are made on the basis of the specimens' individual structural condition as assessed by confocal microscopy and involve no tuning of material parameters. Although the model does not reproduce all features of the experimental curves, as an unfitted estimate of mechanical response the prediction is quite accurate. In light of the obtained results it is judged that more general non-invasive estimation of tissue mechanical properties is possible using the developed framework.     

Region-specific constitutive modeling of the plantar soft tissue

Recent research has shown that hyperelastic properties of the plantar soft tissue consisting of adipose tissue and fibrous septa change from region to region. However, relatively little research has been conducted to develop analytical or computational models to describe the region-specific behavior of the plantar soft tissue. The objective of the research is to develop a region-specific constitutive model of the plantar soft tissue. Plantar soft tissue specimens were dissected from six regions [subcalcaneal (CA), sublateral (LA), subnavicular (Nav), 1st, 3rd, and 5th submetatarsal (M1, M3, M5)] from cadaveric foot samples, and a picrosirius red staining technique was used to visualize the collagen fibers in fibrous septa. The volume fractions of adipose tissue and fibrous septa and the volume fractions of the principal orientations of the fibrous septa were calculated with the intensity gradient method. Region-specific constitutive models were then developed in finite element analysis considering the microstructure of the plantar soft tissue. The hyperelastic region specific material properties of the plantar soft tissue were validated with experimental unconfined compression tests and indentation tests from the literature. The results show that the models give reasonable predictions of the stiffness of the soft tissue within a standard deviation of the tests. The region-specific constitutive models help to explain how changes in the constituents are related to mechanical behavior of the soft tissue on a region specific basis.     

Simulation of soft tissue failure using the material point method

Understanding the factors that control the extent of tissue damage as a result of material failure in soft tissues may provide means to improve diagnosis and treatment of soft tissue injuries. The objective of this research was to develop and test a computational framework for the study of the failure of anisotropic soft tissues subjected to finite deformation. An anisotropic constitutive model incorporating strain-based failure criteria was implemented in an existing computational solid mechanics software based on the material point method (MPM), a quasi-meshless particle method for simulations in computational mechanics. The constitutive model and the strain-based failure formulations were tested using simulations of simple shear and tensile mechanical tests. The model was then applied to investigate a scenario of a penetrating injury: a low-speed projectile was released through a myocardial material slab. Sensitivity studies were performed to establish the necessary grid resolution and time-step size. Results of the simple shear and tensile test simulations demonstrated the correct implementation of the constitutive model and the influence of both fiber family and matrix failure on predictions of overall tissue failure. The slab penetration simulations produced physically realistic wound tracts, exhibiting diameter increase from entrance to exit. Simulations examining the effect of bullet initial velocity showed that the anisotropy influenced the shape and size of the exit wound more at lower velocities. Furthermore, the size and taper of the wound cavity was smaller for the higher bullet velocity. It was concluded that these effects were due to the amount of momentum transfer. The results demonstrate the feasibility of using MPM and the associated failure model for large-scale numerical simulations of soft tissue failure.     

Changes to the mechanical properties of the glenohumeral capsule during anterior dislocation

The glenohumeral joint is the most frequently dislocated major joint in the body, and instability due to permanent deformation of the glenohumeral capsule is a common pathology. The corresponding change in mechanical properties may have implications for the ideal location and extent of plication, which is a common clinical procedure used to repair the capsule. Therefore, the objective of this study was to quantify the mechanical properties of four regions of the glenohumeral capsule after anterior dislocation and compare the properties to the normal glenohumeral capsule. Six fresh-frozen cadaveric shoulders were dislocated in the anterior direction with the joint in the apprehension position using a robotic testing system. After dislocation, mechanical testing was performed on the injured glenohumeral capsule by loading the tissue samples in tension and shear. An inverse finite element optimization routine was used to simulate the experiments and obtain material coefficients for each tissue sample. Cauchy stress–stretch curves were then generated to represent the mechanical response of each tissue sample to theoretical loading conditions. Based on several comparisons (average of the material coefficients, average stress–stretch curve for each region, and coefficients representing the average curves) between the normal and injured tissue samples, the mechanical properties of the injured tissue samples from multiple regions were found to be lower than those of the normal tissue in tension but not in shear. This finding indicates that anterior dislocation primarily affects the tensile behavior of the glenohumeral capsule rather than the shear behavior, and this phenomenon could be caused by plastic deformation of the matrix, permanent collagen fiber rotation, and/or collagen fiber failure. These results suggest that plication and suturing may not be sufficient to return stability to the shoulder after dislocation in all individuals. Thus, surgeons may need to perform a procedure that reinforces or stiffens the tissue itself, such as reconstruction or augmentation, to improve repair procedures.     

Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation

High-resolution architecture-based finite element models are commonly used for characterizing the mechanical behavior of cancellous bone. The vast majority of studies use homogeneous material properties to model trabecular tissue. The objectives of this study were to demonstrate that inhomogeneous finite element models that account for microcomputed tomography-measured tissue modulus variability more accurately predict the apparent stiffness of cancellous bone than homogeneous models, and to examine the sensitivity of an inhomogeneous model to the degree of tissue property variability. We tested five different material cases in finite element models of ten cancellous cubes in simulated uniaxial compression. Three of these cases were inhomogeneous and two were homogeneous. Four of these cases were unique to each specimen, and the remaining case had the same tissue modulus for all specimens. Results from all simulations were compared with measured elastic moduli from previous experiments. Tissue modulus variability for the most accurate of the three inhomogeneous models was then artificially increased to simulate the effects of non-linear CT-attenuation-modulus relationships. Uniqueness of individual models was more critical for model accuracy than level of inhomogeneity. Both homogeneous and inhomogeneous models that were unique to each specimen had at least 8% greater explanatory power for apparent modulus than models that applied the same material properties to all specimens. The explanatory power for apparent modulus of models with a tissue modulus coefficient of variation (COV) range of 21-31% was 13% greater than homogeneous models (COV=0). The results of this study indicate that inhomogenous finite element models that have tissue moduli unique to each specimen more accurately predict the elastic behavior of cancellous cubic specimens than models that have common tissue moduli between all specimens.     

A frame-invariant formulation of Fung elasticity

Fung elasticity refers to the hyperelasticity constitutive relation proposed by Fung and co-workers for describing the pseudo-elastic behavior of biological soft tissues undergoing finite deformation. A frame-invariant formulation of Fung elasticity is provided for material symmetries ranging from orthotropy to isotropy, which uses Lamé-like material constants. In the orthotropic case, three orthonormal vectors are used to define mutually orthogonal planes of symmetry and associated texture tensors. The strain energy density is then formulated as an isotropic function of the Lagrangian strain and texture tensors. The cases of isotropy and transverse isotropy are derived from the orthotropic case. Formulations are provided for both material and spatial frames. These formulations are suitable for implementation into finite element codes. It is also shown that the strain energy function can be naturally uncoupled into a dilatational and a distortional part, to facilitate the computational implementation of incompressibility.