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

Isogeometric finite element-based simulation of the aortic heart valve: Integration of neural network structural material model and structural tensor fiber architecture representations

The functional complexity of native and replacement aortic heart valves (AVs) is well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis framework. A high-order structural tensor (HOST)-based method was developed for efficient storage and mapping the two-dimensional fiber structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed meso-structural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population-based bicuspid AV fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves.

A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis

Numerous studies have suggested that medical image derived computational mechanics models could be developed to reduce mortality and morbidity due to cardiovascular diseases by allowing for patient-specific surgical planning and customized medical device design. In this work, we present a novel framework for designing prosthetic heart valves using a parametric design platform and immersogeometric fluid-structure interaction (FSI) analysis. We parameterize the leaflet geometry using several key design parameters. This allows for generating various perturbations of the leaflet design for the patient-specific aortic root reconstructed from the medical image data. Each design is analyzed using our hybrid arbitrary Lagrangian-Eulerian/immersogeometric FSI methodology, which allows us to efficiently simulate the coupling of the deforming aortic root, the parametrically designed prosthetic valves, and the surrounding blood flow under physiological conditions. A parametric study is performed to investigate the influence of the geometry on heart valve performance, indicated by the effective orifice area and the coaptation area. Finally, the FSI simulation result of a design that balances effective orifice area and coaptation area reasonably well is compared with patient-specific phase contrast magnetic resonance imaging data to demonstrate the qualitative similarity of the flow patterns in the ascending aorta.

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.

Imaging analysis of collagen fiber networks in cusps of porcine aortic valves: effect of their local distribution and alignment on valve functionality

The cusps of native aortic valve (AV) are composed of collagen bundles embedded in soft tissue, creating a heterogenic tissue with asymmetric alignment in each cusp. This study compares native collagen fiber networks (CFNs) with a goal to better understand their influence on stress distribution and valve kinematics. Images of CFNs from five porcine tricuspid AVs are analyzed and fluid-structure interaction models are generated based on them. Although the valves had similar overall kinematics, the CFNs had distinctive influence on local mechanics. The regions with dilute CFN are more prone to damage since they are subjected to higher stress magnitudes.

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.

Application of finite element analysis to the design of tissue leaflets for a percutaneous aortic valve

Percutaneous Aortic Valve (PAV) replacement is an attractive alternative to open heart surgery, especially for patients considered to be poor surgical candidates. Despite this, PAV replacement still has its limitations and associated risks. Bioprosthetic heart valves still have poor long-term durability due to calcification and mechanical failure. In addition, the implantation procedure often presents novel challenges, including damage to the expandable stents and bioprosthetic leaflets. In this study, a simplified version of Fung's elastic constitutive model for skin, developed by Sun and Sacks, was implemented using finite element analysis (FEA) and applied to the modelling of bovine and kangaroo pericardium. The FEA implementation was validated by simulating biaxial tests and by comparing the results with experimental data. Concepts for different PAV geometries were developed by incorporating valve design and performance parameters, along with stent constraints. The influence of effects such as different leaflet material, material orientation and abnormal valve dilation on the valve function was investigated. The stress distribution across the valve leaflet was also examined to determine the appropriate fibre direction for the leaflet. The simulated attachment forces were compared with suture tearing tests performed on the pericardium to evaluate suture density. It is concluded that kangaroo pericardium is suitable for PAV applications, and superior to bovine pericardium, due to its lower thickness and greater extensibility.

Role of Computational Simulations in Heart Valve Dynamics and Design of Valvular Prostheses

Computational simulations are playing an increasingly important role in enhancing our understanding of the normal human physiological function, etiology of diseased states, surgical and interventional planning, and in the design and evaluation of artificial implants. Researchers are taking advantage of computational simulations to speed up the initial design of implantable devices before a prototype is developed and hence able to reduce animal experimentation for the functional evaluation of the devices under development. A review of the reported studies to date relevant to the simulation of the native and prosthetic heart valve dynamics is the subject of the present paper. Potential future directions toward multi-scale simulation studies for our further understanding of the physiology and pathophysiology of heart valve dynamics and valvular implants are also discussed.

Advanced modeling strategy for the analysis of heart valve leaflet tissue mechanics using high-order finite element method

Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation.

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.

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.

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.

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.

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 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.

New polyurethane heart valve prosthesis: design, manufacture and evaluation

In light of the thrombogenicity of mechanical valves and the limited durability of bioprosthetic valves, alternative designs and materials are being considered for prosthetic heart valves. A new tri-leaflet valve, made entirely from polyurethane, has been developed. The valve comprises three thin polyurethane leaflets (approximately 100 microns thick) suspended from the inside of a flexible polyurethane frame. The closed leaflet geometry is elliptical in the radial direction and hyperbolic in the circumferential direction. Valve leaflets are formed and integrated with their support frame in a single dip coating operation. The dipping process consistently gives rise to tolerably uniform leaflet thickness distributions. In hydrodynamic tests, the polyurethane valve exhibits pressure gradients similar to those for a bioprosthetic valve (St Jude Bioimplant), and levels of regurgitation and leakage are considerably less than those for either a bi-leaflet mechanical valve (St Jude Medical) or the bioprosthetic valve. Six out of six consecutively manufactured polyurethane valves have exceeded the equivalent of 10 years function without failure in accelerated fatigue tests. The only failure to date occurred after the equivalent of approximately 12 years cycling, and three valves have reached 527 million cycles (approximately 13 years equivalent). The simplicity of valve manufacture, combined with promising results from in vitro testing, indicate that further evaluation is warranted.

In vitro function and durability assessment of a novel polyurethane heart valve prosthesis

While flexible-leaflet, central-flow prosthetic heart valves promise relief from anticoagulation therapy, they continue to be restricted by inadequate durability. In consequence, a novel trileaflet valve, made entirely from polyurethane, has been developed. A batch of 6 consecutively manufactured polyurethane valves was subjected to hydrodynamic function and accelerated fatigue testing. Computerized data acquisition and control systems have been introduced to improve valve testing methodologies. In terms of hydrodynamic function, the polyurethane valve demonstrates transvalvular pressure gradients similar to those for a bioprosthetic valve (Carpentier-Edwards) and levels of retrograde flow significantly less than those for either the bioprosthetic valve or a bileaflet mechanical valve (St Jude Medical). The equivalent of 10 years of cycling without failure has been exceeded by all 6 polyurethane valves in accelerated fatigue tests with 2 valves remaining intact after 674 million cycles (equivalent to approximately 17 years) in continuing tests. Highspeed photography revealed considerable differences in leaflet motion between valves cycled at accelerated and physiological rates.

Finite element stress analysis of a new design of synthetic leaflet heart valve

This paper presents a parametric finite element analysis of the stresses in the leaflets of a new design of polyurethane heart valve in the closed position. The alpharabola geometry of the valve has previously been reported by Leat and Fisher (1) and has been shown to demonstrate good opening characteristics. The effects of variations in leaflet offset parameter, g, length, h, and local thickening have been determined for a valve where the frame is assumed rigid. A spherical leaflet geometry has also been analysed for comparative purposes. Results have shown that the alpharabola leaflet geometry can reduce the maximum principal tensile stress to 60 per cent of that for a spherical valve of the same mesh density.

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.

Determination of the curvatures and bending strains in open trileaflet heart valves

The leaflets of trileaflet artificial heart valves manufactured from polyurethane, gluteraldehyde-treated porcine aortic valves and pericardial tissue are subject to cyclic stresses and strains which can reduce the lifetime of the implanted valves through leaflet calcification and fatigue failure. A detailed knowledge of the stress state within a valve leaflet throughout a cardiac cycle is desirable in order to improve the geometry of the valve leaflets and ultimately improve the valve performance. An experimental method to evaluate the radius of curvature at the free edge of the open valve leaflet is presented. The technique has been applied to polyurethane trileaflet heart valves manufactured within the authors' laboratory and to commercially available bioprosthetic valves in the fully open position under steady and pulsatile flow conditions. Simple bending theory has been applied to the polyurethane valves to calculate bending stresses and strains at the free leaflet edge based on the measured curvature. The results showed that in the fully open position the highest curvatures occurred at the commissural regions for all the valves analysed. Additional areas of high curvature were present along the free leaflet edge. Average curvatures as high as 0.85 mm-1 were observed at the leaflet commissures for the polyurethane valves with a resultant bending stress of 0.72 MPa. The porcine bioprosthetic valves showed average curvatures as high as 2.5 mm-1 which also occurred at the leaflet commissures. The results of the study have been compared to values of stress obtained from numerical analysis of closed polyurethane valve leaflets reported in the literature.(ABSTRACT TRUNCATED AT 250 WORDS)

Calcification and fatigue failure in a polyurethane heart value

The prosthetic heart valves were fabricated from a polyurethane containing a 4,4'-diphenylmethane diisocyanate hard segment, chain-extended with butanediol and with a polyether soft segment. The rate of calcification of these polyurethane heart valves was much slower in a dynamic in vitro test system than similar bioprosthetic heart valves. The calcified deposits were located exclusively at regions of material failure. Fourier transform infrared (FTIR) spectroscopy indicated the involvement of the polyether soft segments of the polymer directly in the calcification process. Calcification of polymer fractions also suggested that small molecular weight extractable components are accelerating factors in the calcification process.