Numerical simulation of leaflet flexure in bioprosthetic valves mounted on rigid and expansile stents

Effect of bioprosthetic leaflet anisotropy on stent dynamics of Transcatheter Aortic Valve Replacement devices

The assessment of stent fatigue in Transcatheter Aortic Valve Replacement (TAVR) systems is critical for the design of next-generation devices, both in vitro and in vivo. The mechanical properties of the bioprosthetic heart valves (BHVs) have a significant impact on the fatigue life of the metallic stent and thus must be taken into consideration when evaluating new TAVR device designs. This study aims to investigate the relationship between BHV anisotropic behaviour and the asymmetric deflections of the stent frame observed during in vitro testing. An explicit dynamics finite element model of the nitinol stent with attached bioprosthetic valve leaflets was developed to evaluate the deflections of the TAVR device under haemodynamic loading. Our results demonstrate that pericardium behaviour plays a dominant role in determining stent frame deflection. The anisotropic behaviour of the leaflets, resulting from collagen fibre orientation, affects the extent of deflection encountered by each commissure of the frame. This leads to asymmetric variation in frame deflection that can influence the overall fatigue life of the nitinol stent. This study highlights the importance of considering both the flexible nature of the metallic stent as well as the leaflet anisotropic behaviour in the design and fatigue assessment of TAVR systems.

Proposed percutaneous aortic valve prosthesis made of cryogel

Transcatheter heart valves are promising for high-risk patients. Generally, their leaflets are made of pericardium stented in a Nitinol basket. Despite their relative success, they are associated with significant complications such as valve migration, implantation risks, stroke, coronary obstruction, myocardial infraction, acute kidney injury (which all are due to the release of detached solid calcific pieces in to the blood stream) and expected issues existing with tissue valves such as leaflet calcification. This study is an attempt to fabricate the first ever polymeric percutaneous valves made of cryogel following the geometry and mechanical properties of porcine aortic valve to address some of the above-mentioned shortcomings. A novel, one-piece, tricuspid percutaneous valve, consisting of leaflets made entirely from the hydrogel, polyvinyl alcohol cryogel reinforced by bacterial cellulose natural nanocomposite, attached to a Nitinol basket was developed and demonstrated. Following the natural geometry of the valve, a novel approach was applied based on the revolution about an axis of a hyperboloid shape. The geometry was modified based on avoiding sharp warpage of leaflets and removal of the central opening orifice area of the valve when valve is fully closed using the finite element analysis. The modified geometry was replaced by a cloud of (control) points and was essentially converted to Bezier surfaces for further adjustment. A cavity mold was then designed and fabricated to form the valve. The fabricated valve was sewn into the Nitinol basket which is covered by Dacron cloth. The models presented in this study merit further development and revisions for both aortic and mitral positions.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Computational methods for the aortic heart valve and its replacements

INTRODUCTION

Replacement with a prosthetic device remains a major treatment option for the patients suffering from heart valve disease, with prevalence growing resulting from an ageing population. While the most popular replacement heart valve continues to be the bioprosthetic heart valve (BHV), its durability remains limited. There is thus a continued need to develop a general understanding of the underlying mechanisms limiting BHV durability to facilitate development of a more durable prosthesis. In this regard, computational models can play a pivotal role as they can evaluate our understanding of the underlying mechanisms and be used to optimize designs that may not always be intuitive. Areas covered: This review covers recent progress in computational models for the simulation of BHV, with a focus on aortic valve (AV) replacement. Recent contributions in valve geometry, leaflet material models, novel methods for numerical simulation, and applications to BHV optimization are discussed. This information should serve not only to infer reliable and dependable BHV function, but also to establish guidelines and insight for the design of future prosthetic valves by analyzing the influence of design, hemodynamics and tissue mechanics. Expert commentary: The paradigm of predictive modeling of heart valve prosthesis are becoming a reality which can simultaneously improve clinical outcomes and reduce costs. It can also lead to patient-specific valve design.

Characterization of mechanical properties of pericardium tissue using planar biaxial tension and flexural deformation

Flexure is an important mode of deformation for native and bioprosthetic heart valves. However, mechanical characterization of bioprosthetic leaflet materials has been done primarily through planar tensile testing. In this study, an integrated experimental and computational cantilever beam bending test was performed to characterize the flexural properties of glutaraldehyde-treated bovine and porcine pericardium of different thicknesses. A strain-invariant based structural constitutive model was used to model the pericardial mechanical behavior quantified through the bending tests of this study and the planar biaxial tests previously performed. The model parameters were optimized through an inverse finite element (FE) procedure in order to describe both sets of experimental data. The optimized material properties were implemented in FE simulations of transcatheter aortic valve (TAV) deformation. It was observed that porcine pericardium TAV leaflets experienced significantly more flexure than bovine when subjected to opening pressurization, and that the flexure may be overestimated using a constitutive model derived from purely planar tensile experimental data. Thus, modeling of a combination of flexural and biaxial tensile testing data may be necessary to more accurately describe the mechanical properties of pericardium, and to computationally investigate bioprosthetic leaflet function and design.

Effects of Leaflet Design on Transvalvular Gradients of Bioprosthetic Heart Valves

Bioprosthetic aortic valves (BAVs) are becoming the prostheses of choice in heart valve replacement. The objective of this paper is to assess the effects of leaflet geometry on the mechanics and hemodynamics of BAVs in a fluid structure interaction model. The curvature and angle of leaflets were varied in 10 case studies whereby the following design parameters were altered: a circular arch, a line, and a parabola for the radial curvature, and a circular arch, a spline, and a parabola for the circumferential curvature. Six different leaflet angles (representative of the inclination of the leaflets toward the surrounding aortic wall) were analyzed. The 3-dimensional geometry of the models were created using SolidWorks, Pointwise was used for meshing, and Comsol Multiphysics was used for implicit finite element calculations. Realistic loading was enforced by considering the time-dependent strongly-coupled interaction between blood flow and leaflets. Higher mean pressure gradients as well as von Mises stresses were obtained with a parabolic or circular curvature for radial curvature or a parabolic or spline curvature for the circumferential curvature. A smaller leaflet angle was associated with a lower pressure gradient, and, a lower von Mises stress. The leaflet curvature and angle noticeably affected the speed of valve opening, and closing. When a parabola was used for circumferential or radial curvature, leaflets displacements were asymmetric, and they opened and closed more slowly. A circular circumferential leaflet curvature, a linear leaflet radial curvature, and leaflet inclination toward the surrounding aortic wall were associated with superior BAVs mechanics.

Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance

The use of replacement heart valves continues to grow due to the increased prevalence of valvular heart disease resulting from an ageing population. Since bioprosthetic heart valves (BHVs) continue to be the preferred replacement valve, there continues to be a strong need to develop better and more reliable BHVs through and improved the general understanding of BHV failure mechanisms. The major technological hurdle for the lifespan of the BHV implant continues to be the durability of the constituent leaflet biomaterials, which if improved can lead to substantial clinical impact. In order to develop improved solutions for BHV biomaterials, it is critical to have a better understanding of the inherent biomechanical behaviors of the leaflet biomaterials, including chemical treatment technologies, the impact of repetitive mechanical loading, and the inherent failure modes. This review seeks to provide a comprehensive overview of these issues, with a focus on developing insight on the mechanisms of BHV function and failure. Additionally, this review provides a detailed summary of the computational biomechanical simulations that have been used to inform and develop a higher level of understanding of BHV tissues and their failure modes. Collectively, this information should serve as a tool not only to infer reliable and dependable prosthesis function, but also to instigate and facilitate the design of future bioprosthetic valves and clinically impact cardiology.

Coupled Simulation of Heart Valves: Applications to Clinical Practice

The last few decades have seen great advances in the understanding of heart valves, and consequently, in the development of novel treatment modalities and surgical procedures for valves afflicted by disease. This is due in part to the profound advancements in computing technology and noninvasive medical imaging techniques that have made it possible to numerically model the complex heart valve systems characterized by distinct features at different length scales and various interacting processes. In this article, we highlight the importance of explicitly coupling these multiple scales and diverse processes to accurately simulate the true behavior of the heart valves, in health and disease. We examine some of the computational modeling studies that have a direct consequence on clinical practice.

Structural analysis of a stented pericardial heart valve with leaflets mounted externally

Our aim was to understand the structural and functional behaviour of a pericardial heart valve with biological leaflets attached externally to a stent. To our knowledge, there is little if any literature concerning these kinds of bioprosthetic heart valves, while there is more concerning bioprosthetic heart valves with leaflets mounted internally. We studied the problem using a finite element approach considering leaflets and stent interaction, the influence of leaflet anisotropy and stent stiffness, by comparing quasi-static and dynamic loadings. Although we considered the problem to be symmetric and fluid-structure interaction was not implemented, we believe that our results could be a solid basis for valve optimization. We found regions of high stress concentration at the commissure near the stent tip and at the base of the leaflet cusp. The structural behaviour in the first region was complex, while the stress in the second region acted radially because of high bending. Although leaflet tissue anisotropy and stent stiffness exerted a significant influence on the structural and functional behaviours, they had a contrasting effect on leaflet stress state, coaptation and valve opening. Therefore, a good optimization should take into account both structural and functional requirements when tuning tissue properties and stent stiffness.

Computational modeling of cardiac valve function and intervention

In the past two decades, major advances have been made in the clinical evaluation and treatment of valvular heart disease owing to the advent of noninvasive cardiac imaging modalities. In clinical practice, valvular disease evaluation is typically performed on two-dimensional (2D) images, even though most imaging modalities offer three-dimensional (3D) volumetric, time-resolved data. Such 3D data offer researchers the possibility to reconstruct the 3D geometry of heart valves at a patient-specific level. When these data are integrated with computational models, native heart valve biomechanical function can be investigated, and preoperative planning tools can be developed. In this review, we outline the advances in valve geometry reconstruction, tissue property modeling, and loading and boundary definitions for the purpose of realistic computational structural analysis of cardiac valve function and intervention.

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.

Effects of Leaflet Stiffness on In Vitro Dynamic Bioprosthetic Heart Valve Leaflet Shape

Advances in the development of replacement heart valves require a deeper understanding of the valve dynamics. In the present study, dynamic aortic valve (AV) leaflet geometries were quantified in vitro using a structured laser-light imaging system (Iyengar et al., ABME 29(11):963-973, 2001). Native AV leaflets were first imaged under simulated physiological flow conditions within a rigid glass conduit with simulated anatomic sinuses. Next, the valve/glass conduit combination was removed from the loop and immersed in a 0.625% aqueous glutaraldehyde solution at room temperature for 24 h to produce a bioprosthetic heart valve (BHV). The BHV leaflets were then re-imaged under identical flow conditions while kept in the same position in the glass conduit to minimize artifacts associated with removal/reinsertion of the valve. We observed that: (1) the native leaflet exhibited small, high frequency shifts in shape; (2) the BHV leaflet demonstrated a more stabile shape, as well as focal regions of prolonged, high curvature; (3) the BHV leaflet opened and closed faster by ~10 ms compared to native leaflet; (4) in both the BHV and native states, the AV opened from basal region leading to free edge (5) when closing, both the native and BHV close with both free edge and circumferential together. The high bending observed in the BHV leaflet correlated with known locations of tissue deterioration previously reported in our laboratory. Thus, in order to minimize leaflet tissue damage, methods of chemical modification utilized in BHVs that maintain leaflet flexibility are necessary to minimize the onset and progression of tissue damage. We conclude that leaflet stiffness can have a considerable effect on dynamic valve motion, and can induce deleterious bending behaviors that may be associated with tissue breakdown and valve failure. Moreover, these unique data can provide much needed quantitative information for computational simulation of heart valve leaflet stiffness on heart valve function.

Prosthetic aortic heart valves: modeling and design

Although heart valve replacement is among the most common cardiovascular surgical procedures, their outcome is often difficult to predict. One of the reasons is the design and choice of the materials used for the fabrication of the prostheses. This review paper describes the use of modeling techniques in prosthetic heart valve (HV) design and aims at the justification and development of a polymer based trileaflet mechanical heart valve (MHV). The closing/opening phase behavior of the bileaflet MHV was investigated. The potential problem of valve failure due to crack propagation in the brittle pyrolytic carbon leaflet was also discussed. These studies suggest that although bileaflet MHV performs satisfactorily, there are justifications for improvement. Since the native aortic HV is trileaflet and made of anisotropic and hyperelastic tissue, one possible approach to a better MHV design is based on our ability to closely mimic the natural geometry and biomaterial properties.

Design of a novel polymeric heart valve

Polymeric heart valves could offer an optimum alternative to current prostheses, by joining the advantages of mechanical and bioprosthetic valves. Though a number of materials suitable for this application have recently become available, significant improvements in the valve design are still needed. In this paper, a novel polymeric heart valve design is proposed and its optimization procedure, based on the use of finite elements, is described. The design strategy was aimed at reducing the energy absorbed during the operating cycle, resulting in high hydrodynamic performances and reduced stress levels. The efficacy of the design strategy was assessed by comparing the valve dynamics and stress levels predicted numerically during the cycle with those of an existing and well qualified polymeric valve design. The improved hydrodynamic performance of the proposed design was confirmed experimentally, by in vitro testing in a pulse duplicator.

On the opening mechanism of the aortic valve: some observations from simulations

Viewed from the standpoint of mechanical engineering design, the aortic valve is impressive. However, our understanding of its mechanics is limited by our inability to study its in vivo function closely and in detail. Computer simulation methods offer an alternative approach and a first step towards the construction of a more complete cardiac model is described. The model includes the aortic valve, its leaflets and their supporting root, and the sinuses modelled as nonlinear materials. An explicit finite element code has been used to examine the time-varying displacements of the structure that was subject to pressure distributions, which included left ventricular, aortic and thoracic pressures. It was shown that the leaflets of the valve open by a combination of root expansion in a radial direction and leaflet movement in the direction of blood flow. This was compared to a model in which the aortic root was stiffened significantly, and it was found that this modified valve opened by leaflet folding to give a much smaller orifice. These findings, concerning the importance of root expansion, are in agreement with earlier experimental observations.

Design and simulation of a poly(vinyl alcohol)—bacterial cellulose nanocomposite mechanical aortic heart valve prosthesis

In this study, a polymeric aortic heart valve made of poly(vinyl alcohol) (PVA)—bacterial cellulose (BC) nanocomposite is simulated and designed using a hyperelastic non-linear anisotropic material model. A novel nanocomposite biomaterial combination of 15 wt % PVA and 0.5 wt % BC is developed in this study. The mechanical properties of the synthesized PVA—BC are similar to those of the porcine heart valve in both the principal directions. To design the geometry of the leaflets an advance surfacing technique is employed. A Galerkin-based non-linear finite element method is applied to analyse the mechanical behaviour of the leaflet in the closing and opening phases under physiological conditions. The model used in this study can be implemented in mechanical models for any soft tissues such as articular cartilage, tendon, and ligament.

In vivo dynamic deformation of the mitral valve annulus

Though mitral valve (MV) repair surgical procedures have increased in the United States [Gammie, J. S., et al. Ann. Thorac. Surg. 87(5):1431-1437, 2009; Nowicki, E. R., et al. Am. Heart J. 145(6):1058-1062, 2003], studies suggest that altering MV stress states may have an effect on tissue homeostasis, which could impact the long-term outcome [Accola, K. D., et al. Ann. Thorac. Surg. 79(4):1276-1283, 2005; Fasol, R., et al. Ann. Thorac. Surg. 77(6):1985-1988, 2004; Flameng, W., P. Herijgers, and K. Bogaerts. Circulation 107(12):1609-1613, 2003; Gillinov, A. M., et al. Ann. Thorac. Surg. 69(3):717-721, 2000]. Improved computational modeling that incorporates structural and geometrical data as well as cellular components has the potential to predict such changes; however, the absence of important boundary condition information limits current efforts. In this study, novel high definition in vivo annular kinematic data collected from surgically implanted sonocrystals in sheep was fit to a contiguous 3D spline based on quintic-order hermite shape functions with C(2) continuity. From the interpolated displacements, the annular axial strain and strain rate, bending, and twist along the entire annulus were calculated over the cardiac cycle. Axial strain was shown to be regionally and temporally variant with minimum and maximum values of -10 and 4%, respectively, observed. Similarly, regionally and temporally variant strain rate values, up to 100%/s contraction and 120%/s elongation, were observed. Both annular bend and twist data showed little deviation from unity with limited regional variations, indicating that most of the energy for deformation was associated with annular axial strain. The regionally and temporally variant strain/strain rate behavior of the annulus are related to the varied fibrous-muscle structure and contractile behavior of the annulus and surrounding ventricular structures, although specific details are still unavailable. With the high resolution shape and displacement information described in this work, high fidelity boundary conditions can be prescribed in future MV finite element models, leading to new insights into MV function and strategies for repair.

Bioprosthetic heart valve heterograft biomaterials: structure, mechanical behavior and computational simulation

The present review surveys significant developments in the biomechanical characterization and computational simulation of biologically derived chemically cross-linked soft tissues, or 'heterograft' biomaterials, used in replacement bioprosthetic heart valve (BHV). A survey of mechanical characterization techniques, relevant mechanical properties and computational simulation approaches is presented for both the source tissues and cross-linked biomaterials. Since durability remains the critical problem with current bioprostheses, changes with the mechanical behavior with fatigue are also presented. Moreover, given the complex nature of the mechanical properties of heterograft biomaterials it is not surprising that most constitutive (stress-strain) models, historically used to characterize their behavior, were oversimplified. Simulations of BHV function utilizing these models have inevitably been inaccurate. Thus, more recent finite element simulations utilizing nonlinear constitutive models, which achieve greater model fidelity, are reviewed. An important conclusion of this review is the need for accurate constitutive models, rigorously validated with appropriate experimental data, in order that the design benefits of computational models can be realized. Finally, for at least the coming 20 years, BHVs fabricated from heterograft biomaterials will continue to be extensively used, and will probably remain as the dominant valve design. We should thus recognize that rational, scientifically based approaches to BHV biomaterial development and design can lead to significantly improved BHV, over the coming decades, which can potentially impact millions of patients worldwide with heart valve disease.

Effects of collagen fiber orientation on the response of biologically derived soft tissue biomaterials to cyclic loading

In the present study, the effects of initial collagen fiber orientation on the medium-term (up to 50 x 10(6) cycles) fatigue response of heart valve soft tissue biomaterials was investigated. Glutaraldehyde treated bovine pericardium (GLBP), preselected for uniform structure and collagen fiber orientation, was used as the representative heart valve biomaterial. Using specialized instrumentation, GLBP specimens were subjected to cyclic tensile loading to maximum stress levels of 500 +/- 50 kPa at a frequency of 22 Hz. Two sample groups were examined, one with the preferred collagen fiber direction parallel (PD) and perpendicular (XD) to the direction of applied strain. The primary findings indicated that GLBP fatigue response was highly sensitive to the direction of loading with respect to fiber orientation. Specifically, when loading perpendicular to the preferred collagen fiber orientation, fiber reorientation is the dominant mechanism. In contrast, when loaded parallel to the preferred fiber direction a reduction in both collagen fiber crimp and fiber reorientation occurred. Moreover, alterations in the degree and direction of mechanical anisotropy can be inducted by cyclic loading when specimens are loaded perpendicular to the preferred fiber direction. Fourier Transform Infrared Spectroscopy (FT-IR) results indicate that molecular-level damage to collagen occurs in both groups after only 20 x 10(6) cycles. Taken as a whole, the results of this study suggest that initial collagen orientation plays a critical role in bioprosthetic heart valve biomaterial fatigue response.

Effect of fiber orientation on the stress distribution within a leaflet of a polymer composite heart valve in the closed position

Polymer trileaflet valves offer natural hemodynamics with the potential for better durability than commercially available tissue valves. Strength and durability of polymer-based valves may be increased through fiber reinforcement. A finite element analysis of the mechanics of a statically loaded polymer trileaflet aortic heart valve has been conducted. A parametric analysis was performed to determine the effects of fiber orientation and volume density in a single and double ply model. A maximum stress value of 1.02MPa was obtained in the non-reinforced model for a transvalvular load (downstream-upstream) of 120mmHg. The maximum stress on the downstream side of the leaflet was approximately twice the maximum stress on the upstream side, and always occurred on the interface with the valve stent. The single ply model reduced the stress on the polymer matrix, with the maximum reduction of at least 64% occurring when the fiber orientation was such that the fibers ran perpendicular to the stent edge. The double ply model further reduced the stress on the polymer matrix, with the maximum reduction of greater than 86% now occurring when the fibers are oriented most perpendicular to one another.

The flexural rigidity of the aortic valve leaflet in the commissural region

Flexure is a major deformation mode of the aortic valve (AV) leaflet, particularly in the commissural region where the upper portion of the leaflet joins the aortic root. However, there are no existing data known on the mechanical properties of leaflet in the commissural region. To address this issue, we quantified the effective stiffness of the commissural region using a cantilever beam method. Ten specimens were prepared, with each specimen flexed in the direction of natural leaflet motion (forward) and against the natural motion (reverse). At a flexure angle (phi) of 30 degrees , the effective forward direction modulus E was 42.63+/-4.44 kPa and the reverse direction E was 75.01+/-14.53 kPa (p=0.049). Further, E-phi response was linear (r(2) approximately 0.9) in both flexural directions. Values for dE/dphi were -2.24+/-0.6 kPa/ degrees and -1.90+/-0.3 kPa/ degrees in the forward and reverse directions, respectively (not statistically different, p=0.424), indicating a consistent decrease in stiffness with increased flexure. In comparison, we have reported that the effective tissue stiffness of AV leaflet belly region was 150-200 kPa [Merryman, W.D., Huang, H.Y.S., Schoen, F.J., Sacks, M.S. (2006). The effects of cellular contraction on AV leaflet flexural stiffness. Journal of Biomechanics 39 (1), 88-96], which was also independent of direction and amount of flexure. Histological studies of the commissure region indicated that tissue buckling was a probable mechanism for decrease in E with increasing flexure. The observed change in E with flexural angle in the commissural region is a subtle aspect of valve function. From a valve design perspective, these findings can be used as design criteria in fabricating prosthetic devices AV resulting in better functional performance.

Simulated Bioprosthetic Heart Valve Deformation under Quasi-Static Loading

For more than 40years, the replacement of diseased natural heart valves with prosthetic devices has dramatically extended the quality and length of the lives of millions of patients worldwide. However, bioprosthetic heart valves (BHV) continue to fail due to structural failure resulting from poor tissue durability and faulty design. Clearly, an in-depth understanding of the biomechanical behavior of BHV at both the tissue and functional prosthesis levels is essential to improving BHV design and to reduce rates of failure. In this study, we simulated quasi-static BHV leaflet deformation under 40, 80, and 120mmHg quasi-static transvalvular pressures. A Fung-elastic material model was used that incorporated material parameters and axes derived from actual leaflet biaxial tests and measured leaflet collagen fiber structure. Rigorous experimental validation of predicted leaflet strain field was used to validate the model results. An overall maximum discrepancy of 2.36% strain between the finite element (FE) results and experiment measurements was obtained, indicating good agreement between computed and measured major principal strains. Parametric studies utilizing the material parameter set from one leaflet for all three leaflets resulted in substantial variations in leaflet stress and strain distributions. This result suggests that utilization of actual leaflet material properties is essential for accurate BHV FE simulations. The present study also underscores the need for rigorous experimentation and accurate constitutive models in simulating BHV function and design.

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 modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

An approach to the simulation of fluid-structure interaction in the aortic valve

A pair of finite element models has been employed to study the interaction of blood flow with the operation of the aortic valve. A three-dimensional model of the left ventricle with applied wall displacements has been used to generate data for the spatially and time-varying blood velocity profile across the aortic aperture. These data have been used as the inlet loading conditions in a three-dimensional model of the aortic valve and its surrounding structures. Both models involve fluid-structure interaction and simulate the cardiac cycle as a dynamic event. Confidence in the models was obtained by comparison with data obtained in a pulse duplicator. The results show a circulatory flow being generated in the ventricle which produces a substantially axial flow through the aortic aperture. The aortic valve behaves in an essentially symmetric way under the action of this flow, so that the pressure difference across the leaflets is approximately uniform. This work supports the use of spatially uniform but temporally variable pressure distributions across the leaflets in dry or structural models of aortic valves. The study is a major advance through its use of truly three-dimensional geometry, spatially non-uniform loading conditions for the valve leaflets and the successful modelling of progressive contact of the leaflets in a fluid environment.

Design and manufacture of a polyvinyl alcohol (PVA) cryogel tri-leaflet heart valve prosthesis

Although current artificial heart valves are life sustaining medical devices, improvements are still necessary to address deficiencies. Bioprosthetic valves have a compromised fatigue life, while mechanical valves have better durability but are prone to thromboembolic complications. A novel, one-piece, tricuspid valve, consisting of leaflets, stent and sewing ring, made entirely from the hydrogel, polyvinyl alcohol cryogel (PVA-C), has been developed and demonstrated. This valve has three thin leaflets attached to a cylindrical stent. In order to approximate the complex shape of the surface of the natural heart valve leaflets, two different geometries have been proposed: revolution about an axis of a hyperboloid shape and revolution about an axis of an arc subtending (joining) two straight lines. The parameters of both geometries were examined based on a compromise between avoiding sharp curvature of leaflets and minimization of the central opening of the valve when closed. The revolution of an arc subtending two straight lines was selected as the preferred geometry since it has the benefit of a smaller central opening when the value of the maximum curvature for the leaflets is the same for each valve geometry. A cavity mold has been designed and constructed to form the PVA-C heart valve. The three leaflets were formed and integrated into the stent and sewing ring in a single process. Prototype heart valves were manufactured in the mold from a solution of PVA and water, by controlled freezing and thawing cycles.

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.

Multiaxial mechanical behavior of biological materials

For native and engineered biological tissues, there exist many physiological, surgical, and medical device applications where multiaxial material characterization and modeling is required. Because biological tissues and many biocompatible elastomers are incompressible, planar biaxial testing allows for a two-dimensional (2-D) stress-state that can be used to fully characterize their three-dimensional (3-D) mechanical properties. Biological tissues exhibit complex mechanical behaviors not easily accounted for in classic elastomeric constitutive models. Accounting for these behaviors by careful experimental evaluation and formulation of constitutive models continues to be a challenging area in biomechanical modeling and simulation. The focus of this review is to describe the application of multiaxial testing techniques to soft tissues and their relation to modern biomechanical constitutive theories.

Response of heterograft heart valve biomaterials to moderate cyclic loading

We have recently demonstrated that noncalcific tissue damage can lead to significant collagen degradation in clinically explanted bioprosthetic heart valves (BHVs). In the present study we quantified the early response of glutaraldehyde treated bovine pericardium (GLBP) to cyclic tensile loading to begin to elucidate the mechanisms of noncalcific tissue degeneration in BHV biomaterials. GLBP specimens were cycled at 30 Hz to a maximum uniaxial strain of 16% (corresponding to approximately 1-MPa peak stress), with the loading direction parallel to the preferred collagen fiber (PD) direction. After 30 x 10(6) cycles, specimens were subjected to biaxial mechanical testing, then cycled until 65 x 10(6) cycles. The results indicated a permanent change in the unloaded tissue dimensions of +7.1% strain in the PD direction and -7.7% strain in the cross fiber direction (XD) after 65 x 10(6) cycles and an increase of the collagen crimp period from 40.6 to 45.2 microm by 65 x 10(6) cycles (p = 0.05). Fourier transform IR spectroscopy analysis indicated that cyclic fatigue of GLBP leads to both collagen conformational changes and early denaturation. Furthermore, no significant changes in areal strain were found under 1-MPa equibiaxial stress, indicating that cyclic loading changed the collagen fiber orientation but not the overall tissue compliance. These observations suggest that while deterioration of collagen begins immediately, fiber straightening and reorientation dominates the changes in the mechanical behavior up to 65 x 10(6) cycles. The present study underscores the complexity of the response of biologically derived biomaterials to cyclic mechanical loading. Improved understanding of these phenomena can potentially guide the development of novel chemical treatment methods that seek to improve BHV durability by minimizing these degenerative processes.

Geometrical Stress-Reducing Factors in the Anisotropic Porcine Heart Valves

This study carries out a detailed parameter study based on a nonlinear anisotropic finite-element model published previously. The aim of this study is to identify the stress-reducing influences from geometrical parameters such as stent height, valve diameter, and the nonuniform thickness of porcine aortic valves under static loading condition. The anisotropy of the valve is considered to be transversely isotropic with fibers oriented along the circumferential directions, which enables us to use a simple anisotropic constitutive model using uniaxial experimental data. The results showed that in general, higher stent height and smaller diameter combined with nonuniform thickness give rise to a much more reduced overall stress level. Although the absolute values of the peak stresses may be influenced by the detailed orientations of fibers, the trends of the stress variation with the geometrical factors seem to be qualitatively consistent within the parameter ranges considered.

The evolution of bioprosthetic heart valve design and its impact on durability

Bioprosthetic heart valves have evolved over the years into remarkably useful and predictable devices. During this process, a number of specific designs have come and gone, and a few have remained. Many design changes were successful, and many were not. This article will describe the successes and failures of the various bioprosthetic valve designs and will detail the specific reasons why a particular design change succeeded or failed to improve bioprosthetic valve performance.

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 three-dimensional computational analysis of fluid-structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valve's behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.

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.

Finite-element analysis of aortic valve-sparing: influence of graft shape and stiffness

Aortic valve incompetence due to aortic root dilation may be surgically corrected by resuspension of the native valve within a vascular graft. This study was designed to examine the effect of graft shape and material properties on aortic valve function, using a three-dimensional finite-element model of the human aortic valve and root. First, the normal root elements in the model were replaced with graft elements, in either a cylindrical or a "pseudosinus" shape. Next, the elements were assigned the material properties of either polyethylene terephthalate, expanded polytetrafluoroethylene, or polyurethane. Diastolic pressures were applied, and stresses, strains, and coaptation were recorded for the valve, root, and graft. Regarding shape, the cylindrical graft models increased the valve stresses by up to 173%, whereas the root-shaped graft model increased valve stresses by up to 40% as compared to normal. Regarding material properties, the polyurethane models demonstrated valve stress, strain, and coaptation values closest to normal, for either root shape. Graft shape had a greater effect on the simulated valve function than did the material property of the graft. Optimizing the shape and material design of the graft may result in improved longevity of the spared valve if a normal environment is restored.

Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II--A structural constitutive model

We have formulated the first constitutive model to describe the complete measured planar biaxial stress-strain relationship of the native and glutaraldehyde-treated aortic valve cusp using a structurally guided approach. When applied to native, zero-pressure fixed, and low-pressure fixed cusps, only three parameters were needed to simulate fully the highly anisotropic, and nonlinear in-plane biaxial mechanical behavior. Differences in the behavior of the native and zero- and low-pressure fixed cusps were found to be primarily due to changes in the effective fiber stress-strain behavior. Further, the model was able to account for the effects of small (< 10 deg) misalignments in the cuspal specimens with respect to the biaxial test axes that increased the accuracy of the model material parameters. Although based upon a simplified cuspal structure, the model underscored the role of the angular orientation of the fibers that completely accounted for extreme mechanical anisotropy and pronounced axial coupling. Knowledge of the mechanics of the aortic cusp derived from this model may aid in the understanding of fatigue damage in bioprosthetic heart valves and, potentially, lay the groundwork for the design of tissue-engineered scaffolds for replacement heart valves.

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.

Simulation of damage in a porcine prosthetic heart valve

A model of a bioprosthetic porcine valve has been produced which simulates the non-linear elastic behaviour of the fixed tissue and the re-inforcement of the leaflets by collagen fibre bundles. The loading on the model is a spatially uniform but temporally varying distribution of pressure. Bending is allowed in the tissue of the leaflets and is shown to be significant in determining the behaviour and failure modes of the leaflets. The simulation of the undamaged valve is validated against in vitro pulse duplicator studies and a simple fluid--solid interaction simulation. Progressive damage is introduced into three models of the valve at a location where tears have been commonly found in vivo. It was found that during the opening and closing of the valve the tip of the tears were subject to mode III or tearing displacements, but that in the fully closed or diastolic state the tear tip was subject to mode I or opening displacements such that it would be expected to propagate parallel to the line of attachment to the stent. The tear tip stresses increased with the length of the tear so that the rate of tearing would be expected to increase with length.

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

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. It is postulated that leaflet fibre-reinforcement leads to a decrease of tears and perforations as a result of reduced stresses in the weaker parts of the leaflets. A three-dimensional finite element model of a reinforced three-leaflet valve prosthesis was developed to analyse the stress reduction. Different fibre reinforcements were investigated and the model responses were analysed for stresses that are expected to contribute to failure of fibre-reinforced valve prostheses. Results of these simulations show that, in peak stress areas of reinforced models, up to 60% of the maximum principal stresses is taken over by fibres and that, in some cases of reinforcement, a more homogeneous stress distribution is obtained.

Optimisation of a Stentless Valve Prosthesis Based on an Analytic Parametric Model of the Aortic Valve

An analytical mathematical model of a stentless aortic valve has been implemented. The valve is characterised by a trileaflet geometry, cilindrical leaflets; the aortic root is schematised by a conical surface which includes the leaflet attachments.

The model Is defined through six geometric parameters: the base radius, the valve height, the commissure radius, the leaflet radial, circumferential and attachment line lengths. Five performance indexes have been used to optimise the valve geometry, namely: the systolic area, the leaflet circumferential stress in diastole, the leaflet bending strain in systole and two bending angles related to the rotation of the leaflets from the diastolic to the systolic configuration.

The sensitivity analysis is carried out which can identify the influence of each geometric parameter on the performance indexes adopted for the optimum valve design.

The analysis of the results provides the geometric configuration which optimises the overall function of the valve throughout the cardiac cycle.

Three-dimensional stress analysis of polypropylene leaflets for prosthetic heart valves

The effect of changing the modulus and thickness of the material in the leaflets of an artificial heart valve has been investigated. This has been achieved with a finite element model of the valve having approximately 2300 thin shell elements. The valve motion and the resulting stresses are modelled dynamically during closure, and subsequent pressurisation. The stresses decrease as the leaflets are made thicker and the modulus is increased. Local and global thickening has been investigated. The highest stresses appear at the tops of the stent posts in the regions of the commissures. When the modulus is too low, or the leaflets are too thin, the valve prolapsed.

Laser Profiling of Bovine Pericardial Heart Valves

Laser profiling techniques have been used to examine the 2-dimensional and 3-dimensional patterns of leaflet motion in functioning bovine pericardial heart valves (1 normal valve and 1 fatigued/calcified). In the normal valve the general patterns of opening and closing were similar for all leaflets; however, localised variations such as areas of high curvature, retarded motion and high speed motion were identified. In the fatigued/calcified valve significant differences from the normal leaflet motion were observed e.g. increased crimping, gross leaflet lag and irregular deformation. The laser profiling technique was able to reveal changes in the functional dynamics of pericardial valve leaflets not otherwise detectable by conventional hydrodynamic measurements of valve performance.

A comparative study of linear and nonlinear simulations of the leaflets in a bioprosthetic heart valve during the cardiac cycle

Two geometrically identical models of the leaflets of a bicuspid bioprosthetic heart valve have been constructed using finite elements. The boundary conditions applied to the models were also identical but a linear material model has been used in one and a nonlinear elastic model in the other. The models were fullscale and contained 2600 Belytschko-Lin-Tsai shell elements which allowed the variation of stress through the thickness of the leaflet to be modelled. A time-varying, spatially-uniform pressure differential was applied across the leaflets to model their behaviour during a complete cardiac cycle. The simulation was performed using a dynamic, explicit, time-stepping, finite element code. A comparison of the two models showed that the nonlinear model was more responsive to the time-varying pressure wave, and deformed into more complex shapes during the opening and closing phases which induced lower compressive but higher tensile stresses in the leaflets.

In vitro determination of the curvatures and bending strains acting on the leaflets of polyurethane trileaflet heart valves during leaflet motion

Leaflet tears originating from the free leaflet edge and calcification around the commissural region are common modes of failure exhibited by explanted bioprosthetic trileaflet heart valves. These may be a result of the cyclic bending and high levels of curvature that affect the leaflets within these areas during normal valve operation. These high levels of curvature occur in a short time period (approximately 20 ms) during rapid leaflet opening and to a lesser degree during leaflet closure. The curvatures that occur at the free leaflet edge of two designs of polyurethane trileaflet heart valve were determined in vitro at various stages during a cardiac cycle using a high-speed video camera (1000 frames/s). Significant deformations at the free leaflet edge were observed and bending radii as low as 0.55 +/- 0.125 mm (mean +/- standard deviation) were present during leaflet opening, 0.76 +/- 0.24 mm during leaflet closure and 1.01 +/- 0.27 mm while the valve was fully open during peak systole. The values of curvature were used to determine the values of bending strain and bending stress acting at the free leaflet edge using thin shell bending theory. The calculated values of bending strain were a maximum during the leaflet flexure associated with valve opening. These high levels of bending strain, which occur for short periods of time, are likely to be an important determinant of the valve's durability. It has been shown that the method of manufacture significantly influenced the level of bending strain in the valve leaflets. Valves manufactured using a dip-casting technique resulted in open leaflet bending strains up to 31 per cent lower than valves manufactured from solvent-cast sheets of polyurethane.