Electromechanical models of the ventricles

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.     

A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis

Patients with bicuspid aortic valve (BAV) are more likely to develop a calcific aortic stenosis (CAS), as well as a number of other ailments, as compared to their cohorts with normal tricuspid aortic valves (TAV). It is currently unknown whether the increase in risk of CAS is caused by the geometric differences between the tricuspid and bicuspid valves or whether the increase in risk is caused by the same underlying factors that produce the geometric difference. CAS progression is understood to be a multiscale process, mediated at the cell level. In this study, we employ multiscale finite-element simulations of the valves. We isolate the effect of one geometric factor, the number of cusps, in order to explore its effect on multiscale valve mechanics, particularly in relation to CAS. The BAV and TAV are modeled by a set of simulations describing the cell, tissue, and organ length scales. These simulations are linked across the length scales to create a coherent multiscale model. At each scale, the models are three-dimensional, dynamic, and incorporate accurate nonlinear constitutive models of the valve leaflet tissue. We compare results between the TAV and BAV at each length scale. At the cell-scale, our region of interest is the location where calcification develops, near the aortic-facing surface of the leaflet. Our simulations show the observed differences between the tricuspid and bicuspid valves at the organ scale: the bicuspid valve shows greater flexure in the solid phase and stronger jet formation in the fluid phase relative to the tricuspid. At the cell-scale, however, we show that the region of interest is shielded against strain by the wrinkling of the fibrosa. Thus, the cellular deformations are not significantly different between the TAV and BAV in the calcification-prone region. This result supports the assertion that the difference in calcification observed in the BAV versus TAV may be due primarily to factors other than the simple geometric difference between the two valves.     

Heart valve macro- and microstructure

Each heart valve is composed of different structures of which each one has its own histological profile. Although the aortic and the pulmonary valves as well as the mitral and the tricuspid valves show similarities in their architecture, they are individually designed to ensure optimal function with regard to their role in the cardiac cycle.In this article, we systematically describe the structural elements of the four heart valves by different anatomical, light- and electron-microscopic techniques that have been presented. Without the demand of completeness, we describe main structural features that are in our opinion of importance in understanding heart valve performance. These features will also have important implications in the treatment of heart valve disease. They will increase the knowledge in the design of valve substitutes or partial substitutes and may participate to improve reconstructive techniques. In addition, understanding heart valve macro- and microstructure may also be of benefit in heart valve engineering techniques.     

Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in fluent

Simulations of coupled problems such as fluid-structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

A calcified polymeric valve for valve-in-valve applications

The prevalence of aortic valve stenosis (AS) is increasing in the aging society. More recently, novel treatments and devices for AS, especially transcatheter aortic valve replacement (TAVR) have significantly changed the therapeutic approach to this disease. Research and development related to TAVR require testing these devices in the calcified heart valves that closely mimic a native calcific valve. However, no animal model of AS has yet been available. Alternatively, animals with normal aortic valve that are currently used for TAVR experiments do not closely replicate the aortic valve pathology required for proper testing of these devices. To solve this limitation, for the first time, we developed a novel polymeric valve whose leaflets possess calcium hydroxyapatite inclusions immersed in them. This study reports the characteristics and feasibility of these valves. Two types of the polymeric valve, i.e., moderate and severe calcified AS models were developed and tested by deploying a transcatheter valve in those and measuring the related hemodynamics. The valves were tested in a heart flow simulator, and were studied using echocardiography. Our results showed high echogenicity of the polymeric valve, that was correlated to the severity of the calcification. Aortic valve area of the polymeric valves was measured, and the severity of stenosis was defined according to the clinical guidelines. Accordingly, we showed that these novel polymeric valves closely mimic AS, and can be a desired cost-saving solution for testing the performance of the transcatheter aortic valve systems in vitro.     

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r² = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.     

Age-Dependent Changes in Geometry,Tissue Composition and Mechanical Properties of Fetal to Adult Cryopreserved Human Heart Valves

There is limited information about age-specific structural and functional properties of human heart valves, while this information is key to the development and evaluation of living valve replacements for pediatric and adolescent patients. Here, we present an extended data set of structure-function properties of cryopreserved human pulmonary and aortic heart valves, providing age-specific information for living valve replacements. Tissue composition, morphology, mechanical properties, and maturation of leaflets from 16 pairs of structurally unaffected aortic and pulmonary valves of human donors (fetal-53 years) were analyzed. Interestingly, no major differences were observed between the aortic and pulmonary valves. Valve annulus and leaflet dimensions increase throughout life. The typical three-layered leaflet structure is present before birth, but becomes more distinct with age. After birth, cell numbers decrease rapidly, while remaining cells obtain a quiescent phenotype and reside in the ventricularis and spongiosa. With age and maturation–but more pronounced in aortic valves–the matrix shows an increasing amount of collagen and collagen cross-links and a reduction in glycosaminoglycans. These matrix changes correlate with increasing leaflet stiffness with age. Our data provide a new and comprehensive overview of the changes of structure-function properties of fetal to adult human semilunar heart valves that can be used to evaluate and optimize future therapies, such as tissue engineering of heart valves. Changing hemodynamic conditions with age can explain initial changes in matrix composition and consequent mechanical properties, but cannot explain the ongoing changes in valve dimensions and matrix composition at older age.     

Validation of a Fluid–Structure Interaction Model of a Heart Valve using the Dynamic Mesh Method in Fluent

Simulations of coupled problems such as fluid–structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

Multi-Scale Biomechanical Remodeling in Aging and Genetic Mutant Murine Mitral Valve Leaflets: Insights into Marfan Syndrome

Mitral valve degeneration is a key component of the pathophysiology of Marfan syndrome. The biomechanical consequences of aging and genetic mutation in mitral valves are poorly understood because of limited tools to study this in mouse models. Our aim was to determine the global biomechanical and local cell-matrix deformation relationships in the aging and Marfan related Fbn1 mutated murine mitral valve. To conduct this investigation, a novel stretching apparatus and gripping method was implemented to directly quantify both global tissue biomechanics and local cellular deformation and matrix fiber realignment in murine mitral valves. Excised mitral valve leaflets from wild-type and Fbn1 mutant mice from 2 weeks to 10 months in age were tested in circumferential orientation under continuous laser optical imaging. Mouse mitral valves stiffen with age, correlating with increases in collagen fraction and matrix fiber alignment. Fbn1 mutation resulted in significantly more compliant valves (modulus 1.34±0.12 vs. 2.51±0.31 MPa, respectively, P<.01) at 4 months, corresponding with an increase in proportion of GAGs and decrease in elastin fraction. Local cellular deformation and fiber alignment change linearly with global tissue stretch, and these slopes become more extreme with aging. In comparison, Fbn1 mutated valves have decoupled cellular deformation and fiber alignment with tissue stretch. Taken together, quantitative understanding of multi-scale murine planar tissue biomechanics is essential for establishing consequences of aging and genetic mutations. Decoupling of local cell-matrix deformation kinematics with global tissue stretch may be an important mechanism of normal and pathological biomechanical remodeling in valves.     

A detailed fluid mechanics study of tilting disk mechanical heart valve closure and the implications to blood damage

Hemolysis and thrombosis are among the most detrimental effects associated with mechanical heart valves. The strength and structure of the flows generated by the closure of mechanical heart valves can be correlated with the extent of blood damage. In this in vitro study, a tilting disk mechanical heart valve has been modified to measure the flow created within the valve housing during the closing phase. This is the first study to focus on the region just upstream of the mitral valve occluder during this part of the cardiac cycle, where cavitation is known to occur and blood damage is most severe. Closure of the tilting disk valve was studied in a "single shot" chamber driven by a pneumatic pump. Laser Doppler velocimetry was used to measure all three velocity components over a 30 ms period encompassing the initial valve impact and rebound. An acrylic window placed in the housing enabled us to make flow measurements as close as 200 microm away from the closed occluder. Velocity profiles reveal the development of an atrial vortex on the major orifice side of the valve shed off the tip of the leaflet. The vortex strength makes this region susceptible to cavitation. Mean and maximum axial velocities as high as 7 ms and 20 ms were recorded, respectively. At closure, peak wall shear rates of 80,000 s(-1) were calculated close to the valve tip. The region of the flow examined here has been identified as a likely location of hemolysis and thrombosis in tilting disk valves. The results of this first comprehensive study measuring the flow within the housing of a tilting disk valve may be helpful in minimizing the extent of blood damage through the combined efforts of experimental and computational fluid dynamics to improve mechanical heart valve designs.     

Velocity and turbulence measurements past mitral valve prostheses in a model left ventricle

Thrombogenesis and hemolysis have both been linked to the flow dynamics past heart valve prostheses. To learn more about the particular flow dynamics past mitral valve prostheses in the left ventricle under controlled experimental conditions, an in vitro study was performed. The experimental methods included velocity and turbulent shear stress measurements past caged-ball, tilting disc, bileaflet, and polyurethane trileaflet mitral valves in an acrylic rigid model of the left ventricle using laser Doppler anemometry. The results indicate that all four prosthetic heart valves studied create at least mildly disturbed flow fields. The effect of the left ventricular geometry on the flow development is to produce a stabilizing vortex which engulfs the entire left ventricular cavity, depending on the orientation of the valve. The measured turbulent shear stress magnitudes for all four valves did not exceed the reported value for hemolytic damage. However, the measured turbulent shear stresses were near or exceeded the critical shear stress reported in the literature for platelet lysis, a known precursor to thrombus formation.     

Numerical simulation of steady turbulent flow through trileaflet aortic heart valves—II. Results on five models

Turbulent flow simulations are run for five aortic trileaflet valve geometries, ranging from a valve leaflet orifice area of 1.1 cm² (Model A1—very stenotic) to 5.0 cm² (Model A5—natural valve). The simulated data compares well with experimental measurements made downstream of various aortic trileaflet valves by Woo (PhD Thesis, 1984). The location and approximate width and length of recirculation regions are correctly predicted. The less stenotic valve models reattach at the end of the aortic sinus region, 1.1 diameters downstream of the valve. The central jet exiting the less stenotic valve models is not significantly different from fully developed flow, and therefore recovers very quickly downstream of the reattachment point. The more stenotic valves disturb the flow to a greater degree, generating recirculation regions large enough to escape the sinuses and reattach further downstream. Peak turbulent shear stress values downstream of the aortic valve models which approximated prosthetic valves are 125 and 300 N m⁻², very near experimental observations of 150 to 350 N m⁻². The predicted Reynolds stress profiles also present the correct shape, a double peak profile, with the location of the peak occuring at the location of maximum velocity gradient, which occurs near the recirculation region. The pressure drop across model A2 (leaflet orifice area 1.6 cm²) is 20 mmHg at 1.6 diameters downstream. This compares well with values ranging from 19.5 to 26.2 mmHg for valves of similar orifice areas. The pressure drop decreases with decreasing valve stenosis, to a negligible value across the least stenotic valve model. Based on the good agreement between experimental measurements of velocity, shear stress and pressure drop, compared to the simulated data, the model has the potential to be a valuable tool in the analysis of heart valve designs.     

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.     

Geometric modeling of functional trileaflet aortic valves: development and clinical applications

The dimensions of the aortic valve components condition its ability to prevent blood from flowing back into the heart. While the theoretical parameters for best trileaflet valve performance have already been established, an effective approach to describe other less optimal, but functional models has been lacking. Our goal was to establish a method to determine by how much the dimensions of the aortic valve components can vary while still maintaining proper function. Measurements were made on silicone rubber casts of human aortic valves to document the range of dimensional variability encountered in normal adult valves. Analytical equations were written to describe a fully three-dimensional geometric model of a trileaflet valve in both the open and closed positions. A complete set of analytical, numerical and graphical tools was developed to explore a range of component dimensions within functional aortic valves. A list of geometric guidelines was established to ensure safe operation of the valve during the cardiac cycle, with practical safety margins. The geometry-based model presented here allows determining quickly if a certain set of valve component dimensions results in a functional valve. This is of great interest to designers of new prosthetic heart valve models, as well as to surgeons involved in valve-sparing surgery.     

Biomechanical properties of native and tissue engineered heart valve constructs

Due to the increasing number of heart valve diseases, there is an urgent clinical need for off-the-shelf tissue engineered heart valves. While significant progress has been made toward improving the design and performance of both mechanical and tissue engineered heart valves (TEHVs), a human implantable, functional, and viable TEHV has remained elusive. In animal studies so far, the implanted TEHVs have failed to survive more than a few months after transplantation due to insufficient mechanical properties. Therefore, the success of future heart valve tissue engineering approaches depends on the ability of the TEHV to mimic and maintain the functional and mechanical properties of the native heart valves. However, aside from some tensile quasistatic data and flexural or bending properties, detailed mechanical properties such as dynamic fatigue, creep behavior, and viscoelastic properties of heart valves are still poorly understood. The need for better understanding and more detailed characterization of mechanical properties of tissue engineered, as well as native heart valve constructs is thus evident. In the current review we aim to present an overview of the current understanding of the mechanical properties of human and common animal model heart valves. The relevant data on both native and tissue engineered heart valve constructs have been compiled and analyzed to help in defining the target ranges for mechanical properties of TEHV constructs, particularly for the aortic and the pulmonary valves. We conclude with a summary of perspectives on the future work on better understanding of the mechanical properties of TEHV constructs.     

Structural bioinformatics of the human spliceosomal proteome

In this work, we describe the results of a comprehensive structural bioinformatics analysis of the spliceosomal proteome. We used fold recognition analysis to complement prior data on the ordered domains of 252 human splicing proteins. Examples of newly identified domains include a PWI domain in the U5 snRNP protein 200K (hBrr2, residues 258-338), while examples of previously known domains with a newly determined fold include the DUF1115 domain of the U4/U6 di-snRNP protein 90K (hPrp3, residues 540-683). We also established a non-redundant set of experimental models of spliceosomal proteins, as well as constructed in silico models for regions without an experimental structure. The combined set of structural models is available for download. Altogether, over 90% of the ordered regions of the spliceosomal proteome can be represented structurally with a high degree of confidence. We analyzed the reduced spliceosomal proteome of the intron-poor organism Giardia lamblia, and as a result, we proposed a candidate set of ordered structural regions necessary for a functional spliceosome. The results of this work will aid experimental and structural analyses of the spliceosomal proteins and complexes, and can serve as a starting point for multiscale modeling of the structure of the entire spliceosome.