Influence of stent height upon stresses on the cusps of closed bioprosthetic valves

A finite element model of a bioprosthetic heart valve was developed to determine the influence of the stent height on leaflet stresses under various pressure loading conditions after valve closure. A nonlinear solution was used to obtain the stresses in the leaflets for stent heights of 14.6 mm, 19.0 mm and 22.0 mm respectively. The basic assumptions included an elliptic-paraboloid for a relaxed leaflet shape, a rigid stent, isotropic leaflet material property with a Poisson's ratio of 0.45, a uniform leaflet thickness and a stress dependent Young's modulus. The model predicted an increase of stresses on the closed leaflets as the stent height was reduced. This observation appears to mitigate, to some extent, the hemodynamic benefits thought to accompany the reduction of stent height of bioprosthetic valves.     

Simulation of long-term fatigue damage in bioprosthetic heart valves: effects of leaflet and stent elastic properties

One of the major failure modes of bioprosthetic heart valves (BHVs) is noncalcific structural deterioration due to fatigue of the tissue leaflets; yet, the mechanisms of fatigue are not well understood. BHV durability is primarily assessed based on visual inspection of the leaflets following accelerated wear testing. In this study, we developed a computational framework to simulate BHV leaflet fatigue, which is both efficient and quantitative, making it an attractive alternative to traditional accelerated wear testing. We utilize a phenomenological soft tissue fatigue damage model developed previously to describe the stress softening and permanent set of the glutaraldehyde-treated bovine pericardium leaflets in BHVs subjected to cyclic loading. A parametric study was conducted to determine the effects of altered leaflet and stent elastic properties on the fatigue of the leaflets. The simulation results show that heterogeneity of the leaflet elastic properties, poor leaflet coaptation, and little stent-tip deflection may accelerate leaflet fatigue, which agrees with clinical findings. Therefore, the developed framework may be an invaluable tool for evaluating leaflet durability in new tissue valve designs, including traditional BHVs as well as new transcatheter valves.     

Stress distribution on the cusps of a polyurethane trileaflet heart valve prosthesis in the closed position.

In this paper, a finite element analysis of the stress distribution on the cusps of a polyurethane trileaflet heart valve prosthesis in the closed position is presented. The geometry of the valve was modified from a relationship proposed by Ghista and Reul (J. Biomechanics 10, 313-324, 1977). The effects of variations in stent height, leaflet thickness and coaptation area on the stress distribution were also analyzed. Analyses were performed with both rigid and flexible stents for the trileaflet valve in order to delineate the effect of stent flexibility on the leaflet stress distribution. The results showed that regions of stress concentration were present near the commissural attachment similar to those predicted with the bioprostheses. The stresses on the leaflets were reduced by increasing the stent height with both rigid and flexible stents. Selectively increasing the leaflet thickness near the commissures and also increasing the coaptation area did not prove to reduce the leaflet stresses when the stent flexibility was taken into account. The possible effect of high stresses on the structural integrity of polyurethane leaflets and its relationship with calcification is yet to be investigated.     

Aortic valve leaflet mechanical properties facilitate diastolic valve function

This work was concerned with the numerical simulation of the behaviour of aortic valves whose material can be modelled as non-linear elastic anisotropic. Linear elastic models for the valve leaflets with parameters used in previous studies were compared with hyperelastic models, incorporating leaflet anisotropy with pronounced stiffness in the circumferential direction through a transverse isotropic model. The parameters for the hyperelastic models were obtained from fits to results of orthogonal uniaxial tensile tests on porcine aortic valve leaflets. The computational results indicated the significant impact of transverse isotropy and hyperelastic effects on leaflet mechanics; in particular, increased coaptation with peak values of stress and strain in the elastic limit. The alignment of maximum principal stresses in all models follows approximately the coarse collagen fibre distribution found in aortic valve leaflets. The non-linear elastic leaflets also demonstrated more evenly distributed stress and strain which appears relevant to long-term scaffold stability and mechanotransduction.     

Dynamic simulation pericardial bioprosthetic heart valve function

While providing nearly trouble-free function for 10-12 years, current bioprosthetic heart valves (BHV) continue to suffer from limited long-term durability. This is usually a result of leaflet calcification and/or structural degeneration, which may be related to regions of stress concentration associated with complex leaflet deformations. In the current work, a dynamic three-dimensional finite element analysis of a pericardial BHV was performed with a recently developed FE implementation of the generalized nonlinear anisotropic Fung-type elastic constitutive model for pericardial BHV tissues (W. Sun and M.S. Sacks, 2005, [Biomech. Model. Mechanobiol., 4(2-3), pp. 190-199]). The pericardial BHV was subjected to time-varying physiological pressure loading to compute the deformation and stress distribution during the opening phase of the valve function. A dynamic sequence of the displacements revealed that the free edge of the leaflet reached the fully open position earlier and the belly region followed. Asymmetry was observed in the resulting displacement and stress distribution due to the fiber direction and the anisotropic characteristics of the Fung-type elastic constitutive material model. The computed stress distribution indicated relatively high magnitudes near the free edge of the leaflet with local bending deformation and subsequently at the leaflet attachment boundary. The maximum computed von Mises stress during the opening phase was 33.8 kPa. The dynamic analysis indicated that the free edge regions of the leaflets were subjected to significant flexural deformation that may potentially lead to structural degeneration after millions of cycles of valve function. The regions subjected to time varying flexural deformation and high stresses of the present study also correspond to regions of tissue valve calcification and structural failure reported from explanted valves. In addition, the present simulation also demonstrated the importance of including the bending component together with the in-plane material behavior of the leaflets towards physiologically realistic deformation of the leaflets. Dynamic simulations with experimentally determined leaflet material specification can be potentially used to modify the valve towards an optimal design to minimize regions of stress concentration and structural failure.     

Computational model of aortic valve surgical repair using grafted pericardium

Aortic valve reconstruction using leaflet grafts made from autologous pericardium is an effective surgical treatment for some forms of aortic regurgitation. Despite favorable outcomes in the hands of skilled surgeons, the procedure is underutilized because of the difficulty of sizing grafts to effectively seal with the native leaflets. Difficulty is largely due to the complex geometry and function of the valve and the lower distensibility of the graft material relative to native leaflet tissue. We used a structural finite element model to explore how a pericardial leaflet graft of various sizes interacts with two native leaflets when the valve is closed and loaded. Native leaflets and pericardium are described by anisotropic, hyperelastic constitutive laws, and we model all three leaflets explicitly and resolve leaflet contact in order to simulate repair strategies that are asymmetrical with respect to valve geometry and leaflet properties. We ran simulations with pericardial leaflet grafts of various widths (increase of 0%, 7%, 14%, 21% and 27%) and heights (increase of 0%, 13%, 27% and 40%) relative to the native leaflets. Effectiveness of valve closure was quantified based on the overlap between coapting leaflets. Results showed that graft width and height must both be increased to achieve proper valve closure, and that a graft 21% wider and 27% higher than the native leaflet creates a seal similar to a valve with three normal leaflets. Experimental validation in excised porcine aortas (n=9) corroborates the results of simulations.     

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.     

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.     

Finite element analysis of the mitral apparatus: annulus shape effect and chordal force distribution

This study presents a three-dimensional finite element model of the mitral apparatus using a hyperelastic transversely isotropic material model for the leaflets. The objectives of this study are to illustrate the effects of the annulus shape on the chordal force distribution and on the mitral valve response during systole, to investigate the role of the anterior secondary (strut) chordae and to study the influence of thickness of the leaflets on the leaflets stresses. Hence, analyses are conducted with a moving and fixed saddle shaped annulus and with and without anterior secondary chordae. We found that the tension in the secondary chordae represents 31% of the load carried by the papillary muscles. When removing the anterior secondary chordae, the tension in the primary anterior chordae is almost doubled, the displacement of the anterior leaflet toward the left atrium is also increased. The moving annulus configuration with an increasing annulus saddle height does not give significant changes in the chordal force distribution and in the leaflet stress compared to the fixed annulus. The results also show that the maximum principle stresses in the anterior leaflet are carried by the collagen fibers. The stresses calculated in the leaflets are very sensitive to the thickness employed.     

A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis

Failure of bioprosthetic and synthetic three-leaflet valves has been shown to occur as a consequence of high tensile and bending stresses, acting on the leaflets during opening and closing. Moreover, in the stented prostheses, whether synthetic or biological, the absence of contraction of the aortic base, due to the rigid stent, causes the leaflets to be subjected to an unphysiological degree of flexure, which is related to calcification. It is shown that the absence of the stent, which gives a flexible aortic base and leaflet attachment, and leaflet fibre-reinforcement result in reduced stresses in the weaker parts of the leaflets in their closed configuration. It is postulated that this leads to a decrease of tears and perforations, which may result in a improved long-term behaviour. The effect of a flexible leaflet attachment and aortic base of a synthetic valve is investigated with a finite element model. Different fibre-reinforced structures are analysed with respect to the stresses that are likely to contribute to the failure of fibre-reinforced prostheses and compared with the results obtained for a stented prosthesis. Results show that for the stentless models a reduction of stresses up to 75% is obtained with respect to stented models with the same type of reinforcement.     

Modeling of long-term fatigue damage of soft tissue with stress softening and permanent set effects

One of the major failure modes of bioprosthetic heart valves is non-calcific structural deterioration due to fatigue of the tissue leaflets. Experimental methods to characterize tissue fatigue properties are complex and time-consuming. A constitutive fatigue model that could be calibrated by isolated material tests would be ideal for investigating the effects of more complex loading conditions. However, there is a lack of tissue fatigue damage models in the literature. To address these limitations, in this study, a phenomenological constitutive model was developed to describe the stress softening and permanent set effects of tissue subjected to long-term cyclic loading. The model was used to capture characteristic uniaxial fatigue data for glutaraldehyde-treated bovine pericardium and was then implemented into finite element software. The simulated fatigue response agreed well with the experimental data and thus demonstrates feasibility of this approach.     

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.     

Analysis of the bending behaviour of porcine xenograft leaflets and of neutral aortic valve material: bending stiffness, neutral axis and shear measurements

Flexibility of the materials used in the construction of bioprosthetic heart valves is essential for proper valve operation. We therefore examined the bending behaviour of glutaraldehyde treated porcine aortic valve cusps in comparison with fresh aortic valve tissue. We repeatedly bent a total of 35 strips of fresh and treated tissue to curvatures ranging from 0.2 to 2.2 mm-1. We compared the stiffness of the two materials between circumferential and radial bending, natural and reverse curvatures and constant or variable tensile stress (0.8-40 kPa). Our results showed a weak positive relationship between bending stiffness and applied tensile stress and a strong positive dependance of stiffness on tissue thickness (t). For the fresh tissue, the bending stiffness increased in proportion to t1.14 while for the glutaraldehyde treated tissue it increased with t2.18. Fourteen strips of fresh and treated tissue were also histologically processed, sectioned and examined with polarized light microscopy. Collagen fiber wavelengths and shear deformations were measured utilizing the tissue banding patterns produced by polarized light microscopy. The neutral axis of bending was found to lie very close to the outer surface of the tissue, suggesting that aortic leaflets have a very low compressive elastic modulus. The shear strains measured in fresh tissue were 10 +/- 2.7% vs 3 +/- 4.4% for the treated, indicating a stiffening of the tissue following glutaraldehyde fixation. We conclude that both natural and bioprosthetic valve cusps have a complex flexural behaviour that cannot be modeled using simple bending principles, although the bioprosthetic material more closely approximates the simple beam than does the fresh. The non-linear elastic modulus, high compressibility and shearing between fiber layers are likely responsible for the observed behaviour of the fresh tissue, while the cross-linking and dehydrating effects of glutaraldehyde are believed to be responsible for the alteration in bending properties observed in the treated tissue. Our study suggests that bioprosthetic valve material does not adequately mimic the mechanics of the natural valve tissue, and that the current glutaraldehyde fixation process eliminates many of the beneficial, stress-reducing properties of the aortic leaflet.     

Stress related collagen ultrastructure in human aortic valves--implications for tissue engineering

Understanding the response of tissue structures to mechanical stress is crucial for optimization of mechanical conditioning protocols in the field of heart valve tissue engineering. In heart valve tissue, it is unclear to what extent mechanical loading affects the collagen fibril morphology. To determine if local stress affects the collagen fibril morphology, in terms of fibril diameter, its distribution, and the fibril density, this was investigated in adult native human aortic valve leaflets. Transmission electron microscopy images of collagen fibrils were analyzed at three locations: the commissures, the belly, and the fixed edge of the leaflets. Subsequently, the mechanical behavior of human aortic valves was used in a computational model to predict the stress distribution in the valve leaflet during the diastolic phase of the cardiac cycle. The local stresses at the three locations were related to the collagen fibril morphology. The fibril diameter and density varied significantly between the measured locations, and appeared inversely related. The average fibril diameter increased from the fixed edge, to the belly, and to the commissures of the leaflets, while fibril density decreased. Interestingly, these differences corresponded well with the level of stress at the locations. The presented data showed that large tissue stress is associated with greater average fibril diameter, lower fibril density, and wider fibril size distribution compared with low stress locations in the leaflets. The findings here provide insight in the effect of mechanical loading on the collagen ultrastructure, and are valuable to improve conditioning protocols for tissue engineering.     

Computational assessment of bicuspid aortic valve wall-shear stress: implications for calcific aortic valve disease

The bicuspid aortic valve (BAV) is associated with a high prevalence of calcific aortic valve disease (CAVD). Although abnormal hemodynamics has been proposed as a potential pathogenic contributor, the native BAV hemodynamic stresses remain largely unknown. Fluid-structure interaction models were designed to quantify the regional BAV leaflet wall-shear stress over the course of CAVD. Systolic flow and leaflet dynamics were computed in two-dimensional tricuspid aortic valve (TAV) and type-1 BAV geometries with different degree of asymmetry (10 and 16% eccentricity) using an arbitrary Lagrangian–Eulerian approach. Valvular performance and regional leaflet wallshear stress were quantified in terms of valve effective orifice area (EOA), oscillatory shear index (OSI) and temporal shear magnitude (TSM). The dependence of those characteristics on the degree of leaflet calcification was also investigated. The models predicted an average reduction of 49% in BAV peak-systolic EOA relative to the TAV. Regardless of the anatomy, the leaflet wall-shear stress was side-specific and characterized by high magnitude and pulsatility on the ventricularis and low magnitude and oscillations on the fibrosa. While the TAV and non-coronary BAV leaflets shared similar shear stress characteristics, the base of the fused BAV leaflet fibrosa exhibited strong abnormalities, which were modulated by the degree of calcification (6-fold, 10-fold and 16-fold TSM increase in the normal, mildly and severely calcified BAV, respectively, relative to the normal TAV). This study reveals the existence of major differences in wall-shear stress pulsatility and magnitude on TAV and BAV leaflets. Given the ability of abnormal fluid shear stress to trigger valvular inflammation, the results support the existence of a mechano-etiology of CAVD in the BAV.     

Prediction of matrix-to-cell stress transfer in heart valve tissues

Non-linear and anisotropic heart valve leaflet tissue mechanics manifest principally from the stratification, orientation, and inhomogeneity of their collagenous microstructures. Disturbance of the native collagen fiber network has clear consequences for valve and leaflet tissue mechanics and presumably, by virtue of their intimate embedment, on the valvular interstitial cell stress–strain state and concomitant phenotype. In the current study, a set of virtual biaxial stretch experiments were conducted on porcine pulmonary valve leaflet tissue photomicrographs via an image-based finite element approach. Stress distribution evolution during diastolic valve closure was predicted at both the tissue and cellular levels. Orthotropic material properties consistent with distinct stages of diastolic loading were applied. Virtual experiments predicted tissue- and cellular-level stress fields, providing insight into how matrix-to-cell stress transfer may be influenced by the inhomogeneous collagen fiber architecture, tissue anisotropic material properties, and the cellular distribution within the leaflet tissue. To the best of the authors’ knowledge, this is the first study reporting on the evolution of stress fields at both the tissue and cellular levels in valvular tissue and thus contributes toward refining our collective understanding of valvular tissue micromechanics while providing a computational tool enabling the further study of valvular cell–matrix interactions.     

A functionally graded material model for the transmural stress distribution of the aortic valve leaflet

Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.     

A two-dimensional finite element analysis of a bioprosthetic heart valve

A finite element scheme has been developed using total Lagrangian techniques for the two-dimensional analysis of bioprosthetic heart valve leaflets undergoing large deformation. Two models of a leaflet, namely a radial and a circumferential slice, have been analysed. The attachment of the slice to the stent was simulated by progressive contact on a circular former and the coaptation of the leaflets in the centre of a heart valve by a straight line of contact. For the circumferential model, different initial configurations have been considered. The prolapse pressure under which the heart valve closes has been shown to be small in comparison with the normal pressure a heart valve sustains. The regions of the valve that are most heavily stressed are subjected to a strong component of bending. The amount is sensitive to the details of the boundary conditions and to the initial configuration of the valve. These observations are likely to be significant in the use of this kind of stress analysis to improve the design of this type of valve.     

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.     

Reduced Leaflet Stress in the Stentless Quadrileaflet Mitral Valve: A Finite Element Model

Background

Failure of bioprosthetics is usually caused by calcification of the leaflets as a consequence of high tensile stresses. The stentless valve resembles native mitral valve anatomy, has a flexible leaflet attachment and a suspension at the papillary muscles, and preserves annuloventricular continuity. In this study, the effects of the stentless valve design on leaflet stress were investigated with a finite element model.

Methods

Finite element models of the stentless quadrileaflet mitral valve were created in the close and open configurations. The geometry of the stented trileaflet mitral valve was also analyzed for comparative purposes. Under the designated pressures, the regional stresses were evaluated, and the distributions of stresses were assessed.

Results

Regardless of whether the valve is in the open or close configuration, the maximum first principal stress was significantly lower in the stentless valve than in the stented valve. For the stentless valves, limited stress concentration was discretely distributed in the papillary flaps under both close and open conditions. In contrast, in the stented valve, increased stress concentration was evident at the central belly under the open condition and at the commissural attachment under close condition. In either configuration, the maximum second principal stress was markedly lower in the stentless valve than in the stented valve.

Conclusions

The stentless valve was associated with a significant reduction in leaflet stress and a more homogeneous stress distribution compared to the stented valve. These findings are consistent with recent reports of the clinical effectiveness of the stentless quadrileaflet mitral valve.