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.     

An in vitro comparative study of St. Jude Medical and Edwards-Duromedics bileaflet valves using laser anemometry

An in vitro comparative study of St. Jude (SJ) and Edwards-Duromedics (DM) Bileaflet valves was performed under steady and physiological pulsatile flow conditions in an axisymmetric chamber using Laser Doppler Anemometry (LDA). LDA measurements were conducted in two different orientations; in the first orientation, the LDA traverse was perpendicular and, in the second orientation, parallel to the tilt axis of the leaflets. The axial velocities were measured in both orientations at two different locations distal to the valves. The velocity profiles at peak systole show the presence of stronger vortex in the sinus region for flow past SJ valve in the first orientation compared to the DM valve. Velocity profile distal to the SJ valve in second orientation was relatively flat where as for the DM valve, a jet-like flow was present. The differences found in the velocity profiles between the two valves can be attributed to the differences in geometry with thicker leaflets, smaller angle of leaflets opening and the presence of the leaflet curvature for the DM valve. The results obtained in this study do not show any fluid dynamic advantages due to the curved leaflet geometry of the DM 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.     

A note on the blood analog for in-vitro testing of heart valve bioprostheses

Glycerol solution with the viscosity coefficient similar to that of blood is used in evaluating the performance characteristics of prosthetic heart valves in the laboratory. However, physiological saline solution is used as a test fluid in testing tissue heart valves even though the viscosity coefficient does not match that of human blood. It is commonly believed that glycerol is absorbed by the tissue valves and hence the leaflets become stiff, making the test results invalid. However, in our laboratory a comparison of tissue valves exposed to glycerine solution at various times does not indicate any difference in the leaflet opening characteristics. Hence, it is suggested that glycerine solution be used as a test fluid for the evaluation of tissue valves also.     

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.     

Simulation of long-term fatigue damage in bioprosthetic heart valves: effects of leaflet and stent elastic properties

One of the major failure modes of bioprosthetic heart valves (BHVs) is noncalcific structural deterioration due to fatigue of the tissue leaflets; yet, the mechanisms of fatigue are not well understood. BHV durability is primarily assessed based on visual inspection of the leaflets following accelerated wear testing. In this study, we developed a computational framework to simulate BHV leaflet fatigue, which is both efficient and quantitative, making it an attractive alternative to traditional accelerated wear testing. We utilize a phenomenological soft tissue fatigue damage model developed previously to describe the stress softening and permanent set of the glutaraldehyde-treated bovine pericardium leaflets in BHVs subjected to cyclic loading. A parametric study was conducted to determine the effects of altered leaflet and stent elastic properties on the fatigue of the leaflets. The simulation results show that heterogeneity of the leaflet elastic properties, poor leaflet coaptation, and little stent-tip deflection may accelerate leaflet fatigue, which agrees with clinical findings. Therefore, the developed framework may be an invaluable tool for evaluating leaflet durability in new tissue valve designs, including traditional BHVs as well as new transcatheter valves.     

In vitro assessment of a combined radiofrequency ablation and cryo-anchoring catheter for treatment of mitral valve prolapse

Percutaneous approaches to mitral valve repair are an attractive alternative to surgical repair or replacement. Radiofrequency ablation has the potential to approximate surgical leaflet resection by using resistive heating to reduce leaflet size, and cryogenic temperatures on a percutaneous catheter can potentially be used to reversibly adhere to moving mitral valve leaflets for reliable application of radiofrequency energy. We tested a combined cryo-anchoring and radiofrequency ablation catheter using excised porcine mitral valves placed in a left heart flow loop capable of reproducing physiologic pressure and flow waveforms. Transmitral flow and pressure were monitored during the cryo-anchoring procedure and compared to baseline flow conditions, and the extent of radiofrequency energy delivery to the mitral valve was assessed post-treatment. Long term durability of radiofrequency ablation treatment was assessed using statically treated leaflets placed in a stretch bioreactor for four weeks. Transmitral flow and pressure waveforms were largely unaltered during cryo-anchoring. Parameter fitting to mechanical data from leaflets treated with radiofrequency ablation and cryo-anchoring revealed significant mechanical differences from untreated leaflets, demonstrating successful ablation of mitral valves in a hemodynamic environment. Picrosirius red staining showed clear differences in morphology and collagen birefringence between treated and untreated leaflets. The durability study indicated that statically treated leaflets did not significantly change size or mechanics over four weeks. A cryo-anchoring and radiofrequency ablation catheter can adhere to and ablate mitral valve leaflets in a physiologic hemodynamic environment, providing a possible percutaneous alternative to surgical leaflet resection of mitral valve tissue.     

A nonlinear anisotropic model for porcine aortic heart valves

The anisotropic property of porcine aortic valve leaflet has potentially significant effects on its mechanical behaviour and the failure mechanisms. However, due to its complex nature, testing and modelling the anisotropic porcine aortic valves remains a continuing challenge to date. This study has developed a nonlinear anisotropic finite element model for porcine heart valves. The model is based on the uniaxial experimental data of porcine aortic heart valve leaflet and the properties of nonlinear composite material. A finite element code is developed to solve this problem using the 8-node super-parameter nonlinear shells and the update Lagrangian method. The stress distribution and deformation of the porcine aortic valves with either uniform and non-uniform thicknesses in closed phase and loaded condition are calculated. The results showed significant changes in the stress distributions due to the anisotropic property of the leaflets. Compared with the isotropic valve at the same loading condition, it is found that the site of the peak stress of the anisotropic leaflet is different; the maximum longitudinal normal stress is increased, but the maximum transversal normal stress and in-plane shear stress are reduced. We conclude that it is very important to consider the anisotropic property of the porcine heart valves in order to understand the failure mechanism of such valves in vivo.     

Modeling leaflet correction techniques in aortic valve repair: A finite element study

In aortic valve sparing surgery, cusp prolapse is a common cause of residual aortic insufficiency. To correct cusp pathology, native leaflets of the valve frequently require adjustment which can be performed using a variety of described correction techniques, such as central or commissural plication, or resuspension of the leaflet free margin. The practical question then arises of determining which surgical technique provides the best valve performance with the most physiologic coaptation. To answer this question, we created a new finite element model with the ability to simulate physiologic function in normal valves, and aortic insufficiency due to leaflet prolapse in asymmetric, diseased or sub-optimally repaired valves. The existing leaflet correction techniques were simulated in a controlled situation, and the performance of the repaired valve was quantified in terms of maximum leaflets stress, valve orifice area, valve opening and closing characteristics as well as total coaptation area in diastole. On the one hand, the existing leaflet correction techniques were shown not to adversely affect the dynamic properties of the repaired valves. On the other hand, leaflet resuspension appeared as the best technique compared to central or commissural leaflet plication. It was the only method able to achieve symmetric competence and fix an individual leaflet prolapse while simultaneously restoring normal values for mechanical stress, valve orifice area and coaptation area.     

FSI simulation of asymmetric mitral valve dynamics during diastolic filling

In this article, we present a fluid-structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.     

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.     

Functional analysis of bioprosthetic heart valves

Glutaraldehyde-treated bovine pericardium is used successfully as bioprosthetic material in the manufacturing of heart valves leaflets. The mechanical properties of bovine pericardial aortic valve leaflets seem to influence its mechanical behaviour and the failure mechanisms. In this study the effect of orthotropy on tricuspid bioprosthetic aortic valve was analysed, using a three-dimensional finite element model, during the entire cardiac cycle. Multiaxial tensile tests were also performed to determine the anisotropy of pericardium. Seven different models of the same valve were analysed using different values of mechanical characteristics from one leaflet to another, considering pericardium as an orthotropic material. The results showed that even a small difference between values along the two axes of orthotropy can negatively influence leaflets performance as regard both displacement and stress distribution. Leaflets of bovine pericardium bioprostheses could be manufactured to be similar to natural human heart valves reproducing their well-known anisotropy. In this way it could be possible to improve the manufacturing process, durability and function of pericardial bioprosthetic valves.     

Biaxial mechanical properties of bovine jugular venous valve leaflet tissues

Venous valve incompetence has been implicated in diseases ranging from chronic venous insufficiency (CVI) to intracranial venous hypertension. However, while the mechanical properties of venous valve leaflet tissues are central to CVI biomechanics and mechanobiology, neither stress–strain curves nor tangent moduli have been reported. Here, equibiaxial tensile mechanical tests were conducted to assess the tangent modulus, strength and anisotropy of venous valve leaflet tissues from bovine jugular veins. Valvular tissues were stretched to 60% strain in both the circumferential and radial directions, and leaflet tissue stress–strain curves were generated for proximal and distal valves (i.e., valves closest and furthest from the right heart, respectively). Toward linking mechanical properties to leaflet microstructure and composition, Masson’s trichrome and Verhoeff–Van Gieson staining and collagen assays were conducted. Results showed: (1) Proximal bovine jugular vein venous valves tended to be bicuspid (i.e., have two leaflets), while distal valves tended to be tricuspid; (2) leaflet tissues from proximal valves exhibited approximately threefold higher peak tangent moduli in the circumferential direction than in the orthogonal radial direction (i.e., proximal valve leaflet tissues were anisotropic; \(p<0.01\)); (3) individual leaflets excised from the same valve apparatus appeared to exhibit different mechanical properties (i.e., intra-valve variability); and (4) leaflets from distal valves exhibited a trend of higher soluble collagen concentrations than proximal ones (i.e., inter-valve variability). To the best of the authors’ knowledge, this is the first study reporting biaxial mechanical properties of venous valve leaflet tissues. These results provide a baseline for studying venous valve incompetence at the tissue level and a quantitative basis for prosthetic venous valve design.     

Cell-mediated retraction versus hemodynamic loading – A delicate balance in tissue-engineered heart valves

Preclinical studies of tissue-engineered heart valves (TEHVs) showed retraction of the heart valve leaflets as major failure of function mechanism. This retraction is caused by both passive and active cell stress and passive matrix stress. Cell-mediated retraction induces leaflet shortening that may be counteracted by the hemodynamic loading of the leaflets during diastole. To get insight into this stress balance, the amount and duration of stress generation in engineered heart valve tissue and the stress imposed by physiological hemodynamic loading are quantified via an experimental and a computational approach, respectively.     

Influence of stent height upon stresses on the cusps of closed bioprosthetic valves

A finite element model of a bioprosthetic heart valve was developed to determine the influence of the stent height on leaflet stresses under various pressure loading conditions after valve closure. A nonlinear solution was used to obtain the stresses in the leaflets for stent heights of 14.6 mm, 19.0 mm and 22.0 mm respectively. The basic assumptions included an elliptic-paraboloid for a relaxed leaflet shape, a rigid stent, isotropic leaflet material property with a Poisson's ratio of 0.45, a uniform leaflet thickness and a stress dependent Young's modulus. The model predicted an increase of stresses on the closed leaflets as the stent height was reduced. This observation appears to mitigate, to some extent, the hemodynamic benefits thought to accompany the reduction of stent height of bioprosthetic valves.     

Personalized Computational Modeling of Mitral Valve Prolapse: Virtual Leaflet Resection

Posterior leaflet prolapse following chordal elongation or rupture is one of the primary valvular diseases in patients with degenerative mitral valves (MVs). Quadrangular resection followed by ring annuloplasty is a reliable and reproducible surgical repair technique for treatment of posterior leaflet prolapse. Virtual MV repair simulation of leaflet resection in association with patient-specific 3D echocardiographic data can provide quantitative biomechanical and physiologic characteristics of pre- and post-resection MV function. We have developed a solid personalized computational simulation protocol to perform virtual MV repair using standard clinical guidelines of posterior leaflet resection with annuloplasty ring implantation. A virtual MV model was created using 3D echocardiographic data of a patient with posterior chordal rupture and severe mitral regurgitation. A quadrangle-shaped leaflet portion in the prolapsed posterior leaflet was removed, and virtual plication and suturing were performed. An annuloplasty ring of proper size was reconstructed and virtual ring annuloplasty was performed by superimposing the ring and the mitral annulus. Following the quadrangular resection and ring annuloplasty simulations, patient-specific annular motion and physiologic transvalvular pressure gradient were implemented and dynamic finite element simulation of MV function was performed. The pre-resection MV demonstrated a substantial lack of leaflet coaptation which directly correlated with the severe mitral regurgitation. Excessive stress concentration was found along the free marginal edge of the posterior leaflet involving the chordal rupture. Following the virtual resection and ring annuloplasty, the severity of the posterior leaflet prolapse markedly decreased. Excessive stress concentration disappeared over both anterior and posterior leaflets, and complete leaflet coaptation was effectively restored. This novel personalized virtual MV repair strategy has great potential to help with preoperative selection of the patient-specific optimal MV repair techniques, allow innovative surgical planning to expect improved efficacy of MV repair with more predictable outcomes, and ultimately provide more effective medical care for the patient.     

A fast strong coupling algorithm for the partitioned fluid–structure interaction simulation of BMHVs

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluid–structure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time.     

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.     

Particle Image Velocimetry Study of Pulsatile Flow in Bi-leaflet Mechanical Heart Valves with Image Compensation Method

Particle Image Velocimetry (PIV) is an important technique in studying blood flow in heart valves. Previous PIV studies of flow around prosthetic heart valves had different research concentrations, and thus never provided the physical flow field pictures in a complete heart cycle, which compromised their pertinence for a better understanding of the valvular mechanism. In this study, a digital PIV (DPIV) investigation was carried out with improved accuracy, to analyse the pulsatile flow field around the bi-leaflet mechanical heart valve (MHV) in a complete heart cycle. For this purpose a pulsatile flow test rig was constructed to provide the necessary in vitro test environment, and the flow field around a St. Jude size 29 bi-leaflet MHV and a similar MHV model were studied under a simulated physiological pressure waveform with flow rate of 5.2 l/min and pulse rate at 72 beats/min. A phase-locking method was applied to gate the dynamic process of valve leaflet motions. A special image-processing program was applied to eliminate optical distortion caused by the difference in refractive indexes between the blood analogue fluid and the test section. Results clearly showed that, due to the presence of the two leaflets, the valvular flow conduit was partitioned into three flow channels. In the opening process, flow in the two side channels was first to develop under the presence of the forward pressure gradient. The flow in the central channel was developed much later at about the mid-stage of the opening process. Forward flows in all three channels were observed at the late stage of the opening process. At the early closing process, a backward flow developed first in the central channel. Under the influence of the reverse pressure gradient, the flow in the central channel first appeared to be disturbed, which was then transformed into backward flow. The backward flow in the central channel was found to be the main driving factor for the leaflet rotation in the valve closing process. After the valve was fully closed, local flow activities in the proximity of the valve region persisted for a certain time before slowly dying out. In both the valve opening and closing processes, maximum velocity always appeared near the leaflet trailing edges. The flow field features revealed in the present paper improved our understanding of valve motion mechanism under physiological conditions, and this knowledge is very helpful in designing the new generation of MHVs.     

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.