Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.     

Vortex shedding as a mechanism for free emboli formation in mechanical heart valves

The high incidence of thromboembolic complications of mechanical heart valves (MHV) limits their success as permanent implants. The thrombogenicity of all MHV is primarily due to platelet activation by contact with foreign surfaces and by nonphysiological flow patterns. The latter include elevated flow stresses and regions of recirculation of blood that are induced by valve design characteristics. A numerical simulation of unsteady turbulent flow through a bileaflet MHV was conducted, using the Wilcox k-omega turbulence model for internal low-Reynolds-number flows, and compared to quantitative flow visualization performed in a pulse duplicator system using Digital Particle Image Velocimetry (DPIV). The wake of the valve leaflet during the deceleration phase revealed an intricate pattern of interacting shed vortices. Particle paths showed that platelets that were exposed to the highest flow stresses around the leaflets were entrapped within the shed vortices. Potentially activated, such platelets may tend to aggregate and form free emboli. Once formed, such free emboli would be convected downstream by the shed vortices, increasing the risk of systemic emboli.     

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.     

The congenital bicuspid aortic valve can experience high-frequency unsteady shear stresses on its leaflet surface

The bicuspid aortic valve (BAV) is a common congenital malformation of the aortic valve (AV) affecting 1% to 2% of the population. The BAV is predisposed to early degenerative calcification of valve leaflets, and BAV patients constitute 50% of AV stenosis patients. Although evidence shows that genetic defects can play a role in calcification of the BAV leaflets, we hypothesize that drastic changes in the mechanical environment of the BAV elicit pathological responses from the valve and might be concurrently responsible for early calcification. An in vitro model of the BAV was constructed by surgically manipulating a native trileaflet porcine AV. The BAV valve model and a trileaflet AV (TAV) model were tested in an in vitro pulsatile flow loop mimicking physiological hemodynamics. Laser Doppler velocimetry was used to make measurements of fluid shear stresses on the leaflet of the valve models using previously established methodologies. Furthermore, particle image velocimetry was used to visualize the flow fields downstream of the valves and in the sinuses. In the BAV model, flow near the leaflets and fluid shear stresses on the leaflets were much more unsteady than for the TAV model, most likely due to the moderate stenosis in the BAV and the skewed forward flow jet that collided with the aorta wall. This additional unsteadiness occurred during mid- to late-systole and was composed of cycle-to-cycle magnitude variability as well as high-frequency fluctuations about the mean shear stress. It has been demonstrated that the BAV geometry can lead to unsteady shear stresses under physiological flow and pressure conditions. Such altered shear stresses could play a role in accelerated calcification in BAVs.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part II - Valve Studies

Abstract

Using a coupled Lagrangian dynamic leaflet model and an unsteady potential flow solver the motion of a polyurethane type heart valve is simulated in the aortic position. The simulations incorporate two flow domains; the first comprises only the leaflets which are embedded within an unsteady flow of infinite expanse, and the second incorporates the influence of the aortic geometry via a conformal mapping. Simulations are performed for a cardiac output of 51itres/min and a beat period of 72 b.p.m. corresponding to a typical aortic pulse. Resulting valve motions are computed for various leaflet bending stiffnesses in both flow domains. In addition both the bending stress and strain and their time rate of change are evaluated. Valve motion displays the characteristic rapid opening, stable opening and slow closing phases as detailed in the literature. The computed stress values along the leaflet surface are of the order of those found experimentally.     

Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. Although exact causes and mechanisms of AV calcification are unclear, previous studies suggest that mechanical forces play a role. Since calcium deposits occur almost exclusively on the aortic surfaces of AV leaflets, it has been hypothesized that adverse patterns of fluid shear stress on the aortic surface of AV leaflets promote calcification. The current study characterizes AV leaflet aortic surface fluid shear stresses using Laser Doppler velocimetry and an in vitro pulsatile flow loop. The valve model used was a native porcine valve mounted on a suturing ring and preserved using 0.15% glutaraldehyde solution. This valve model was inserted in a mounting chamber with sinus geometries, which is made of clear acrylic to provide optical access for measurements. To understand the effects of hemodynamics on fluid shear stress, shear stress was measured across a range of conditions: varying stroke volumes at the same heart rate and varying heart rates at the same stroke volume. Systolic shear stress magnitude was found to be much higher than diastolic shear stress magnitude due to the stronger flow in the sinuses during systole, reaching up to 20 dyn/cm² at mid-systole. Upon increasing stroke volume, fluid shear stresses increased due to stronger sinus fluid motion. Upon increasing heart rate, fluid shear stresses decreased due to reduced systolic duration that restricted the formation of strong sinus flow. Significant changes in the shear stress waveform were observed at 90 beats/min, most likely due to altered leaflet dynamics at this higher heart rate. Overall, this study represents the most well-resolved shear stress measurements to date across a range of conditions on the aortic side of the AV. The data presented can be used for further investigation to understand AV biological response to shear stresses.     

Fluid-structure interaction of deformable aortic prostheses with a bileaflet mechanical valve

Two different aortic prostheses can be used for performing the Bentall procedure: a standard straight graft and the Valsalva graft that better reproduces the aortic root anatomy. The aim of the present work is to study the effect of the graft geometry on the blood flow when a bileaflet mechanical heart valve is used, as well as to evaluate the stress concentration near the suture line where the coronary arteries are connected to graft. An accurate three-dimensional numerical method is proposed, based on the immersed boundary technique. The method accounts for the interactions between the flow and the motion of the rigid leaflets and of the deformable aortic root, under physiological pulsatile conditions. The results show that the graft geometry only slightly influences the leaflets dynamics, while using the Valsalva graft the stress level near the coronary-root anastomoses is about half that obtained using the standard straight graft.     

Passive flow control of bileaflet mechanical heart valve leakage flow

Blood damage and platelet activation are inherent problems with present day mechanical heart valve designs. We investigate the approach of passive flow control applied to bileaflet mechanical heart valve (BMHV) flows as a means of optimizing leakage flow hemodynamics at length scales relevant to blood damage and platelet activation. Rectangular and hemispherical vortex generator (VG) arrays were mounted on the downstream surfaces of a 25 mm St. Jude Medical valve adjacent to the b-datum leaflet edge (central line where the two leaflets touch in closed position). The effect of VGs on the flow structure emanating from the b-datum line under both pulsatile and steady flow conditions was measured using high resolution particle image velocimetry technique. The VGs were seen to spatially disperse and dissipate the coherent leakage jet structure emanating from the b-datum line. This resulted in a significant diminution of turbulence stresses, particularly with the rectangular VG configuration. This study shows that passive flow control techniques deployed on BHMVs is potentially beneficial as significant control of flow at small length scales may be achieved without altering large scale designs of the valve.     

Dynamics of flow in a mechanical heart valve: the role of leaflet inertia and leaflet compliance

In this work, we examine the dynamics of fluid flow in a mechanical heart valve when the solid inertia and leaflet compliance are important. The fluid is incompressible and Newtonian, and the leaflet is an incompressible neo-Hookean material. In the case of an inertialess leaflet, we find that the maximum valve opening angle and the time that the valve remains closed increase as the shear modulus of the leaflet decreases. More importantly, the regurgitant volume decreases with decreasing shear modulus. When we examined the forces exerted on the leaflet, we found that the downward motion of the leaflet is initiated by a vertical force exerted on its right side and, later on, by a vertical force exerted on the top side of the leaflet. In the case of solid inertia, we find that the maximum valve opening angle and the regurgitant volume are larger than in the case of an inertialess leaflet. These results highlight the importance of solid compliance in the dynamics of blood flow in a mechanical heart valve. More importantly, they indicate that mechanical heart valves with compliant leaflets may have smaller regurgitant volumes and smaller shear stresses than the ones with rigid leaflets.     

Flow in a mechanical bileaflet heart valve at laminar and near-peak systole flow rates: CFD simulations and experiments

Time-accurate, fully 3D numerical simulations and particle image velocity laboratory experiments are carried out for flow through a fully open bileaflet mechanical heart valve under steady (nonpulsatile) inflow conditions. Flows at two different Reynolds numbers, one in the laminar regime and the other turbulent (near-peak systole flow rate), are investigated. A direct numerical simulation is carried out for the laminar flow case while the turbulent flow is investigated with two different unsteady statistical turbulence modeling approaches, unsteady Reynolds-averaged Navier-Stokes (URANS) and detached-eddy simulation (DES) approach. For both the laminar and turbulent cases the computed mean velocity profiles are in good overall agreement with the measurements. For the turbulent simulations, however, the comparisons with the measurements demonstrate clearly the superiority of the DES approach and underscore its potential as a powerful modeling tool of cardiovascular flows at physiological conditions. The study reveals numerous previously unknown features of the flow.     

Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method

Current artificial heart valves either have limited lifespan or require the recipient to be on permanent anticoagulation therapy. In this paper, effort is made to assess a newly developed bileaflet valve prosthesis made of synthetic flexible leaflet materials, whose geometry and material properties are based on those of the native mitral valve, with a view to providing superior options for mitral valve replacement. Computational analysis is employed to evaluate the geometric and material design of the valve, by investigation of its mechanical behaviour and unsteady flow characteristics. The immersed boundary (IB) method is used for the dynamic modelling of the large deformation of the valve leaflets and the fluid-structure interactions. The IB simulation is first validated for the aortic prosthesis subjected to a hydrostatic loading. The predicted displacement fields by IB are compared with those obtained using ANSYS, as well as with experimental measurements. Good quantitative agreement is obtained. Moreover, known failure regions of aortic prostheses are identified. The dynamic behaviour of the valve designs is then simulated under four physiological pulsatile flows. Experimental pressure gradients for opening and closure of the valves are in good agreement with IB predictions for all flow rates for both aortic and mitral designs. Importantly, the simulations predicted improved physiological haemodynamics for the novel mitral design. Limitation of the current IB model is also discussed. We conclude that the IB model can be developed to be an extremely effective dynamic simulation tool to aid prosthesis design.     

The influence of the leaflets' curvature on the flow field in two bileaflet prosthetic heart valves

A successful mechanical prosthetic heart valve design is the bileaflet valve, which has been implanted for the first time more than 20 years ago. A key feature of bileaflet valves is the geometry of the two leaflets, which can be very important in determining the flow field. Laser Doppler anemometry (LDA) was used to perform an accurate study of the velocity and turbulence shear stress peak values (TSS(max)) fields at four distances from the valve plane. TSS(max) is a relevant parameter to assess the risk of hemolysis and platelet activation associated to the implantation of a prosthetic device, continuously interacting with blood. Two bileaflet valves were tested: the St. Jude HP and the Sorin Bicarbon, of the same nominal size (19mm). The former has flat leaflets, whereas the latter's leaflets have a cylindrical surface. A high regime (CO: 6l/min) was imposed, in order to test the two valves at maximum Reynolds number and consequent turbulence generation. The flat-leaflet design of the St. Jude generates a TSS field constant with distance; on the contrary, the Bicarbon's shear stress field undergoes an evident development, with an unexpected central peak at a distance comparable to the valve's dimensions (21mm). The two bileaflet valves tested, although very similar in design, behave very differently as for their turbulence properties. In particular, the concept of curved wake leads to conclude that the curvature of the leaflets' surface must be identified as an important parameter, which deserves careful attention in PHV design and development.     

Near valve flows and potential blood damage during closure of a bileaflet mechanical heart valve

Blood damage and thrombosis are major complications that are commonly seen in patients with implanted mechanical heart valves. For this in vitro study, we isolated the closing phase of a bileaflet mechanical heart valve to study near valve fluid velocities and stresses. By manipulating the valve housing, we gained optical access to a previously inaccessible region of the flow. Laser Doppler velocimetry and particle image velocimetry were used to characterize the flow regime and help to identify the key design characteristics responsible for high shear and rotational flow. Impact of the closing mechanical leaflet with its rigid housing produced the highest fluid stresses observed during the cardiac cycle. Mean velocities as high as 2.4 m/s were observed at the initial valve impact. The velocities measured at the leaflet tip resulted in sustained shear rates in the range of 1500-3500 s(-1), with peak values on the order of 11,000-23,000 s(-1). Using velocity maps, we identified regurgitation zones near the valve tip and through the central orifice of the valve. Entrained flow from the transvalvular jets and flow shed off the leaflet tip during closure combined to generate a dominant vortex posterior to both leaflets after each valve closing cycle. The strength of the peripheral vortex peaked within 2 ms of the initial impact of the leaflet with the housing and rapidly dissipated thereafter, whereas the vortex near the central orifice continued to grow during the rebound phase of the valve. Rebound of the leaflets played a secondary role in sustaining closure-induced vortices.     

Numerical simulation of steady flow in a two-dimensional total artificial heart model.

In this paper, a numerical simulation of steady laminar and turbulent flow in a two-dimensional model for the total artificial heart is presented. A trileaflet polyurethane valve was simulated at the outflow orifice while the inflow orifice had a trileaflet or a flap valve. The finite analytic numerical method was employed to obtain solutions to the governing equations in the Cartesian coordinates. The closure for turbulence model was achieved by employing the k-epsilon-E model. The SIMPLER algorithm was used to solve the problem in primitive variables. The numerical solutions of the simulated model show that regions of relative stasis and trapped vortices were smaller within the ventricular chamber with the flap valve at the inflow orifice than that with the trileaflet valve. The predicted Reynolds stresses distal to the inflow valve within the ventricular chamber were also found to be smaller with the flap valve than with the trileaflet valve. These results also suggest a correlation between high turbulent stresses and the presence of thrombus in the vicinity of the valves in the total artificial hearts. The computed velocity vectors and turbulent stresses were comparable with previously reported in vitro measurements in artificial heart chambers. Analysis of the numerical solutions suggests that geometries similar to the flap valve (or a tilting disk valve) results in a better flow dynamics within the total artificial heart chamber compared to a trileaflet valve.     

Estimation of turbulent shear stresses in pulsatile flow immediately downstream of two artificial aortic valves in vitro

Measuring turbulent shear stresses is of major importance in artificial heart valve evaluation. Bi- and unidirectional fluid velocity measurements enable calculation of Reynolds shear stress ( ) and Reynolds normal stress ( ). τ is important due to the relation to hemolysis and thrombus formation, but σ is the only obtainable parameter in vivo. Therefore, determination of a correlation factor between τ and σ is pertinent.

In a pulsatile flow model, laser Doppler (LDA) and hot-film (HFA) anemometry were used for simultaneous bi- and unidirectional fluid velocity measurements downstream of a Hall Kaster and a Hancock Porcine aortic valve. Velocities were registered in two flow field locations and at four cardiac outputs. The velocity signals were subjected to analog signal processing prior to digital turbulence analysis, as a basis for calculation of τ and σ.

A correlation factor of 0.5 with a correlation coefficient of 0.97 was found between the maximum Reynolds shear stress and Reynolds normal stress, implying . In vitro estimation of turbulent shear stresses downstream of artificial aortic valves, based on the axial velocity component alone, seems possible.     

Mechano-potential etiologies of aortic valve disease

Aortic valve leaflets experience varying applied loads during the cardiac cycle. These varying loads act on both cell types of the leaflets, endothelial and interstitial cells, and cause molecular signaling events that are required for repairing the leaflet tissue, which is continually damaged from the applied loads. However, with increasing age, this reparative mechanism appears to go awry as valve interstitial cells continue to remain in their ‘remodeling’ phenotype and subsequently cause the tissue to become stiff, which results in heart valve disease. The etiology of this disease remains elusive; however, multiple clues are beginning to coalesce and mechanical cues are turning out to be large predicators of cellular function in the aortic valve leaflets, when compared to the cells from the pulmonary valve leaflets, which are under a significantly less demanding mechanical loading regime. Finally, this paper discusses the mechanical environment of the constitutive cell populations, mechanobiological processes that are currently unclear, and a mechano-potential etiology of aortic disease will be presented.     

High resolution three-dimensional strain mapping of bioprosthetic heart valves using digital image correlation

Transcatheter aortic valve replacement (TAVR) is a safe and effective treatment option for patients deemed at high and intermediate risk for surgical aortic valve replacement. Similar to surgical aortic valves (SAVs), transcatheter aortic valves (TAVs) undergo calcification and mechanical wear over time. However, to date, there have been limited publications on the long-term durability of TAV devices. To assess longevity and mechanical strength of TAVs in comparison to surgical bioprosthetic valves, three-dimensional deformation analysis and strain measurement of the leaflets become an inevitable part of the evaluation. The goal of this study was to measure and compare leaflet displacement and strain of two commonly used TAVs in a side-by-side comparison with a commonly used SAV using a high-resolution digital image correlation (DIC) system. 26-mm Edwards SAPIEN 3, 26-mm Medtronic CoreValve, and 25-mm Carpentier-Edwards PERIMOUNT Magna surgical bioprosthesis were examined in a custom-made valve testing apparatus. A time-varying, spatially uniform pressure was applied to the leaflets at different loading rates. GOM ARAMIS® software was used to map leaflet displacement and strain fields during loading and unloading. High displacement regions were found to be at the leaflet belly region of the three bioprosthetic valves. In addition, the frame of the surgical bioprosthesis was found to be remarkably flexible, in contrary to CoreValve and SAPIEN 3 in which the stent was nearly rigid under a similar loading condition. The experimental DIC measurements can be used to characterize the anisotropic materiel behavior of the bioprosthetic heart valve leaflets and validate heart valve computational simulations.