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

Mechanical Behaviour of Silicone Membranes Saturated with Short Strand, Loose Polyester Fibres for Prosthetic and Rehabilitative Surrogate Skin Applications

Silicone-based elastomers saturated with embedded, short-strand fibres are used for their ability to mimic the aesthetic qualities of skin in clinical and theatrical maxillofacial appliance design. Well-known to prostheses fabricators and technicians, the mechanical impact of fibre addition on elastomeric behaviour endures as tacit, embodied knowledge of the craft, almost unknown in the literature. To examine mechanical changes caused by fibre addition, 100 modified polydimethylsiloxane (PDMS) elastomeric compounds containing incremental amounts of loose polyester fibres were prepared and examined in a variety of mechanical tests. It was found that elasticity and strain percentage at breaking point was reduced by increasing fibre content, but Young’s modulus and ultimate tensile strength (UTS) increased. As fibre content was increased, strain hardening was seen at low strain rates, but exaggerated plastic deformation at high strain rates. PDMS hardness increased by 5 degrees of hardness (Shore-00 scale) for every additional percentage of fibres added and a strong positive linear coefficient (0.993 and 0.995) was identified to reach the hardness values given in the literature for living human skin. The apparent reorienting of loose fibres in the PDMS interrupts and absorbs stress during the loading process similar to the organic response to soft tissue loading, except in extension.

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.

Simplified Multistage Computational Approach to Assess the Fatigue Behavior of a Niti Transcatheter Aortic Valve During In Vitro Tests: A Proof-of-Concept Study

Nowadays, transcatheter aortic valve (TAV) replacement is an alternative to surgical therapy in selected high risk patients for the treatment of aortic stenosis. However, left ventricular contraction determines a severe cyclic loading for the implanted stent-frame, undermining its long-term durability. Technical standards indicate in vitro tests as a suitable approach for the assessment of TAV fatigue behavior: generally, they do not specify test methods but require to test TAV in the worst loading conditions. The most critical conditions could be different according to the specific valve design, hence the compartment where deploying the valve has to be properly identified. A fast and reliable computational methodology could significantly help to face this issue. In this paper, a numerical approach to analyze Nickel-Titanium TAV stent-frame behavior during in vitro durability tests is proposed. A simplified multistage strategy was adopted where, in each stage, only two of the three involved components are considered. As a proof-of-concept, the method was applied to a TAV prototype. Despite its simplifications, the developed computational framework gave useful insights into the stent-frame failures behavior during a fatigue test. Numerical results agree with experimental findings. In particular, the most dangerous condition was identified among a number of experimental tests, where different compartments and pressure gradients were investigated. The specific failure location was also correctly recognized. In conclusion, the presented methodology provides a tool to support the choice of proper testing conditions for the in vitro assessment of TAV fatigue behavior.

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.

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.

A bio-inspired microstructure induced by slow injection moulding of cylindrical block copolymers

It is well known that block copolymers with cylindrical morphology show alignment with shear, resulting in anisotropic mechanical properties. Here we show that well-ordered bi-directional orientation can be achieved in such materials by slow injection moulding. This results in a microstructure, and anisotropic mechanical properties, similar to many natural tissues, making this method attractive for engineering prosthetic fibrous tissues. An application of particular interest to us is prosthetic polymeric heart valve leaflets, mimicking the shape, microstructure and hence performance of the native valve. Anisotropic layers have been observed for cylinder-forming block copolymers centrally injected into thin circular discs. The skin layers exhibit orientation parallel to the flow direction, whilst the core layer shows perpendicularly oriented domains; the balance of skin to core layers can be controlled by processing parameters such as temperature and injection rate. Heart valve leaflets with a similar layered structure have been prepared by injection moulding. Numerical modelling demonstrates that such complex orientation can be explained and predicted by the balance of shear and extensional flow.

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.

Straightening of curved pattern of collagen fibers under load controls aortic valve shape

The network of collagen fibers in the aortic valve leaflet is believed to play an important role in the strength and durability of the valve. However, in addition to its stress-bearing role, such a fiber network has the potential to produce functionally important shape changes in the closed valve under pressure load. We measured the average pattern of the collagen network in porcine aortic valve leaflets after staining for collagen. We then used finite element simulation to explore how this collagen pattern influences the shape of the closed valve. We observed a curved or bent pattern, with collagen fibers angled downward from the commissures toward the center of the leaflet to form a pattern that is concave toward the leaflet free edge. Simulations showed that these curved fiber trajectories straighten under pressure load, leading to functionally important changes in closed valve shape. Relative to a pattern of straight collagen fibers running parallel to the leaflet free edge, the concave pattern of curved fibers produces a closed valve with a 40% increase in central leaflet coaptation height and with decreased leaflet billow, resulting in a more physiological closed valve shape. Furthermore, simulations show that these changes in loaded leaflet shape reflect changes in leaflet curvature due to modulation of in-plane membrane stress resulting from straightening of the curved fibers. This effect appears to play an important role in normal valve function and may have important implications for the design of prosthetic and tissue engineered replacement valves.

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.

Electrospinning versus knitting: two scaffolds for tissue engineering of the aortic valve

Two types of scaffolds were developed for tissue engineering of the aortic valve; an electrospun valvular scaffold and a knitted valvular scaffold. These scaffolds were compared in a physiologic flow system and in a tissue-engineering process. In fibrin gel enclosed human myofibroblasts were seeded onto both types of scaffolds and cultured for 23 days under continuous medium perfusion. Tissue formation was evaluated by confocal laser scanning microscopy, histology and DNA quantification. Collagen formation was quantified by a hydroxyproline assay. When subjected to physiologic flow, the spun scaffold tore within 6 h, whereas the knitted scaffold remained intact. Cells proliferated well on both types of scaffolds, although the cellular penetration into the spun scaffold was poor. Collagen production, normalized to DNA content, was not significantly different for the two types of scaffolds, but seeding efficiency was higher for the spun scaffold, because it acted as a cell impermeable filter. The knitted tissue constructs showed complete cellular in-growth into the pores. An optimal scaffold seems to be a combination of the strength of the knitted structure and the cell-filtering ability of the spun structure.

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.

Design and validation of a novel bioreactor to subject aortic valve leaflets to side-specific shear stress

Hemodynamic stresses are presumed to play an important role in the development of calcific aortic valve disease (CAVD). The elucidation of the shear stress mechanisms involved in the pathogenesis of CAVD has been hampered by the complexity of the native unsteady and side-specific valvular flow environment. To address this gap, this article describes the design and validation of a novel device to expose leaflet samples to time-dependent side-specific shear stress. The device built on a double cone-and-plate geometry was dimensioned based on our previous single-sided shear stress device that minimizes secondary flow effects inherent to this geometry. A fluid-structure interaction (FSI) model was designed to predict the actual shear stress produced on a tissue sample mounted in the new device. Staining was performed on porcine leaflets conditioned in the new bioreactor to assess endothelial integrity and cellular apoptosis. The FSI results demonstrated good agreement between the target (native) and the actual side-specific shear stress produced on a tissue sample. No significant difference in endothelial integrity and cellular apoptosis was detected between samples conditioned for 96 h and fresh controls. This new device will enable the investigation of valvular response to normal and pathologic hemodynamics and the potential mechano-etiology of CAVD.

Patient-specific modeling and quantification of the aortic and mitral valves from 4-D cardiac CT and TEE

As decisions in cardiology increasingly rely on noninvasive methods, fast and precise image processing tools have become a crucial component of the analysis workflow. To the best of our knowledge, we propose the first automatic system for patient-specific modeling and quantification of the left heart valves, which operates on cardiac computed tomography (CT) and transesophageal echocardiogram (TEE) data. Robust algorithms, based on recent advances in discriminative learning, are used to estimate patient-specific parameters from sequences of volumes covering an entire cardiac cycle. A novel physiological model of the aortic and mitral valves is introduced, which captures complex morphologic, dynamic, and pathologic variations. This holistic representation is hierarchically defined on three abstraction levels: global location and rigid motion model, nonrigid landmark motion model, and comprehensive aortic-mitral model. First we compute the rough location and cardiac motion applying marginal space learning. The rapid and complex motion of the valves, represented by anatomical landmarks, is estimated using a novel trajectory spectrum learning algorithm. The obtained landmark model guides the fitting of the full physiological valve model, which is locally refined through learned boundary detectors. Measurements efficiently computed from the aortic-mitral representation support an effective morphological and functional clinical evaluation. Extensive experiments on a heterogeneous data set, cumulated to 1516 TEE volumes from 65 4-D TEE sequences and 690 cardiac CT volumes from 69 4-D CT sequences, demonstrated a speed of 4.8 seconds per volume and average accuracy of 1.45 mm with respect to expert defined ground-truth. Additional clinical validations prove the quantification precision to be in the range of inter-user variability. To the best of our knowledge this is the first time a patient-specific model of the aortic and mitral valves is automatically estimated from volumetric sequences.

Structural analysis of the natural aortic valve in dynamics: from unpressurized to physiologically loaded

A novel finite element model of the natural aortic valve was developed implementing anisotropic hyperelastic material properties for the leaflets and aortic tissues, and starting from the unpressurized geometry. Static pressurization of the aortic root, silicone rubber moulds and published data helped to establish the model parameters, while high-speed video recording of the leaflet motion in a left-heart simulator allowed for comparisons with simulations. The model was discretized with brick elements and loaded with time-varying pressure using an explicit commercial solver. The aortic valve model produced a competent valve whose dynamic behavior (geometric orifice area vs. time) closely matched that observed in the experiment. In both cases, the aortic valve took approximately 30 ms to open to an 800 mm(2) orifice and remained completely or more than half open for almost 200 ms, after which it closed within 30-50 ms. The highest values of stress were along the leaflet attachment line and near the commissure during diastole. Von Mises stress in the leaflet belly reached 600-750 kPa from early to mid-diastole. While the model using the unpressurized geometry as initial configuration was specially designed to satisfy the requirements of continuum mechanics for large deformations of hyperelastic materials, it also clearly demonstrated that dry models can be adequate to analyze valve dynamics. Although improvements are still needed, the advanced modeling and validation techniques used herein contribute toward improved and quantified accuracy over earlier simplified models.

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.

Structural simulations of prosthetic tri-leaflet aortic heart valves

This study presents a combined computational and experimental approach for the nonlinear structural simulations of polymeric tri-leaflet aortic valves (PAVs). Nonlinear shell-based and quasi-static finite-element (FE) structural models are generated for a prosthetic valve geometry that includes the leaflets, stents and root materials, such as the bottom base and outside walls. The PAV structural model is subject to an ensemble averaged transvalvular pressure waveform measured from repeated in vitro tests conducted with a left heart simulator. High-resolution optical measurements are used to measure the in vitro kinematics of the leaflets and the stents. Qualitative and quantitative deformation measures are defined in order to compare the predicted kinematics from the PAV models with the in vitro measurements. Six new quantitative deformation metrics are introduced. They include three distances measuring the current PAV geometric center to the leaflet edges while additional three distances define the stent post-to-stent post (SPTSP) distances. The structural model is able to predict the kinematic deformation metrics with maximum errors around 10% especially in systole where the displacements are larger in magnitude. The combined structural modeling with experimental simulations along with the new proposed deformation metrics provide an effective way to study the PAV structural behavior and a path for improving the structural design of prosthetic valves.

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.

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.

A Knitted, Fibrin-Covered Polycaprolactone Scaffold for Tissue Engineering of the Aortic Valve

State-of-the-art tissue engineered heart valves are not strong enough to withstand aortic blood pressure levels. When a strong and slowly degrading scaffold is used, the starting position of valvular tissue engineering is a stronger valve and seeded cells are allowed more time to create a strong extracellular matrix. A polycaprolactone knitted patch with leaflets was developed as a valvular scaffold. It was sutured into a tube and covered with fibrin gel. The opening and closing behavior and leakage of knitted scaffolds without cells were studied and compared to those of stentless porcine valves. An MTT test was performed on polycaprolactone and fibrin. A loading device was developed to study the durability of the knitted scaffold. The scaffold showed proper opening and it showed coaptation upon closing, but a 39 +/- 3% (n = 3) leakage, compared to a 8 +/- 1% (n = 3) leakage of tested porcine valves. MTT tests showed that polycaprolactone and fibrin are biocompatible materials. Durability testing of the knitted scaffold (n = 1) did not show rupture after ten million loading cycles. A tissue engineering process that includes cell culture will have to show whether this scaffold, besides mechanically reliable and biocompatible, is suitable to lead to a functional, nonregurgitant, durable aortic valve.

Effects of atrial contraction, atrioventricular interaction and heart valve dynamics on human cardiovascular system response

Various simulation models of different complexity have been proposed to model the dynamic response of the human cardiovascular system. In a related paper we proposed an improved numerical model to study the dynamic response of the cardiovascular system, and the pressures, volumes and flow-rates in the four chambers of the heart, which included the effects of atrial contraction, atrioventricular interaction, and heart valve dynamics. This paper investigates the effects of each one of these aspects of the model on the overall dynamic system response. The dynamic response is studied under different situations, with and without including the effect of various features of the model, and these situations are studied and compared among themselves and to detailed aspects of expected healthy-system response. As an important contribution with potential clinical applications, this paper examines the corresponding effects of atrioventricular interaction, and heart valve opening and closing dynamics to the general system dynamic response. This isolation of physical cause-effect relationships is difficult to study with purely experimental methods. The simulation results agree well with results in the open literature. Comparison shows that introduction of these new features greatly improves the simulation accuracy of the effects of a, v and c waves, and in predicting regurgitant valve flow, the dichrotic notch, and E/A velocity ratio.

A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction

Numerical modeling of the human cardiovascular system has always been an active research direction since the 19th century. In the past, various simulation models of different complexities were proposed for different research purposes. In this paper, an improved numerical model to study the dynamic function of the human circulation system is proposed. In the development of the mathematical model, the heart chambers are described with a variable elastance model. The systemic and pulmonary loops are described based on the resistance-compliance-inertia concept by considering local effects of flow friction, elasticity of blood vessels and inertia of blood in different segments of the blood vessels. As an advancement from previous models, heart valve dynamics and atrioventricular interaction, including atrial contraction and motion of the annulus fibrosus, are specifically modeled. With these improvements the developed model can predict several important features that were missing in previous numerical models, including regurgitant flow on heart valve closure, the value of E/A velocity ratio in mitral flow, the motion of the annulus fibrosus (called the KG diaphragm pumping action), etc. These features have important clinical meaning and their changes are often related to cardiovascular diseases. Successful simulation of these features enhances the accuracy of simulations of cardiovascular dynamics, and helps in clinical studies of cardiac function.

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.

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.

Dynamic analysis of the aortic valve using a finite element model

BACKGROUND

The major aim of this study was to examine the leaflet/aortic root interaction during the cardiac cycle, including the stresses developed during the interaction.

METHODS

Dynamic finite element analysis was used along with a geometrically accurate model of the aortic valve and the sinuses. Shell elements along with proper contact conditions were also used in the model. Pressure patterns during the cardiac cycle were given as an input, and a linear elastic model was assumed for the material.

RESULTS

We found that aortic root dilation starts before the opening of the leaflet and is substantial by the time leaflet opens. Dilation of the root alone helps in opening the leaflet to about 20%. The equivalent stress pattern shows an instantaneous increase in stress at the coaptation surface during closure. Stresses increase as the point of attachment is approached from the free surface.

CONCLUSIONS

The complex interplay of the geometry of the valve system can be effectively analyzed using a sophisticated dynamic finite element model. Results not previously brought out by the earlier static analysis shed new light on the root/valve interaction.

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.

A synthetic fiber-reinforced stentless heart valve

There is strong evidence that failure of bioprosthetic and synthetic valves occurs as a consequence of high tensile and bending stresses, acting on the leaflets during opening and closing. In stented prostheses, whether synthetic or biological, the absence of contraction of the aortic base causes the leaflets to be subjected to an unphysiological degree of flexure, which is also related to calcification. However, a stentless synthetic valve, which has a flexible aorta base, can be a good alternative for stented synthetic valves. Moreover, fiber-reinforcement is assumed to lead to a decrease of tears and perforation as a result of reduced stresses in the weaker parts of the leaflets in their closed configuration. The manufacturing method for a stentless, fiber-reinforced, synthetic valve is presented. Prototypes are tested in a pulse duplicator system. The results show that the mean systolic pressure difference is very low, while the high regurgitation (up to 26%) is probably caused by a too small coaptation area of the leaflets.