Background
Since the first successful implantation of a prosthetic heart valve four decades ago, over 50 different designs have been developed including both mechanical and bioprosthetic valves. Today, with over 200,000 implants worldwide each year, the most widely implanted design is the mechanical bileaflet prosthesis. Several other mechanical valves are currently available and many of them have good bulk forward flow hemodynamics. However, mechanical valve implants suffer from complications resulting from thrombus deposition and patients implanted with these valves need to be under long-term anti-coagulant therapy. In general blood thinners are not needed with bioprosthetic implants, but tissue valves suffer from structural failure with an average life-time of 10-12 years before replacement is needed.
Flow-induced stresses on the formed elements in blood have been implicated in thrombus initiation within the mechanical valve prostheses. Regions of stress concentration on the leaflets during the complex motion of the leaflets have been implicated with structural failure of the leaflets with bioprosthetic valves. In vivo and in vitro experimental studies have yielded valuable information on the relationship between hemodynamic stresses and the problems associated with the implants. More recently, Computational Fluid Dynamics (CFD) has emerged as a promising tool, which, alongside experimentation, can yield insights of unprecedented detail into the hemodynamics of prosthetic heart valves. For CFD to realize its full potential, however, it must rely on numerical techniques that can handle the enormous geometrical complexities of prosthetic devices with spatial and temporal resolution sufficiently high to accurately capture all hemodynamically relevant scales of motion. Such algorithms do not exist today and their development is at the forefront of ongoing research. For CFD to further gain the confidence of valve designers and medical practitioners it must also undergo comprehensive validation with experimental data. Such validation requires the use of high-resolution flow measuring tools and techniques and the integration of experimental studies with CFD modeling.
The link between hemodynamics and clinical complications
Platelets can become hyper-activated due to shear forces and they present a risk for the development of a thrombotic event. As early as 1970, Harker and Slichter13 showed that patients with first-generation mechanical valves such as the ball-and-cage and tilting-disc had a shortened platelet half-life due to increased incidence of platelet destruction and activation.
Direct mechanical trauma by impact with the valve supra-structure and shearing forces induced by turbulent flow are two possible mechanisms accounting for this destruction. Also, continuous sub lethal hemolysis can lead to alterations in red cell membrane morphology and reduced membrane flexibility.18,23 Such alterations can upset the balance of hemostasis as the endothelial lining appears to be very vulnerable to even low wall shear stresses generated in the forward flow fields of bileaflet valves in the aortic position.9,27 These findings have particular importance for prosthetic mitral valve recipients who may be in atrial fibrillation.20,25 In such patients, elevated plasma fibrinogen levels have been detected, indicating a heightened thrombotic tendency compared to population controls in normal sinus rhythm.20
The realization that blood flow induced stresses can trigger bio-chemical responses at the cellular level and cause clinical complications led to the need for a systematic characterization and quantification of the hemodynamical properties of prosthetic heart valves. Such undertaking, however, is far from trivial. Prosthetic valves are geometrically very complex and the shape and motion of their leaflets evolve dynamically in response to the instantaneous flow conditions. The pulsatile nature of blood flow and the ensuing fluid/structure interaction give rise to very complex and highly unsteady, borderline turbulent flow, characterized by regions of flow reversal, three-dimensional separation and vortex formation and shedding. Furthermore, non-Newtonian effects can also become very important and need to be accounted for especially when analyzing the flow within valve components whose scale is comparable to that of formed blood elements, such as the hinge region of mechanical valves. Given these enormous complexities, sophisticated fluid dynamics testing of prosthetic heart valve flows requires a close synergy between advanced experimental and computational fluid dynamics techniques.
Experimental work
Yoganathan et al.27 employed 2D LDV to conduct the first detailed investigations of the pulsatile forward flow fields of the SJM bileaflet valve in the aortic position and the Medtronic-Hall and Bjork-Shiley tilting disc valves.They reported maximum turbulent shear stresses downstream of the leaflets ranging from 1,200 dynes/cm2 for the SJM valve to 2,000 dynes/cm2 for the Medtronic-Hall valve.
Using 1D LDV, Chandran et al2 investigated the flow past different caged ball and tilting disc aortic valve prostheses. Chandran et al3 also investigated the flow downstream of the Bjork-Shirley tilting disc valves in a human aorta model illustrating the influence of valve orientation on the downstream velocity profile in the mid-arch and brachio-cephalic arterial branch of the aorta.Walker and Yoganathan26 looked at the Omni-Carbon tilting disc valve and the Duromedics bileaflet valve. The Omni-Carbon valve design produced turbulent shear stresses up to 2,000 dynes/cm2.The velocity profile taken across the central orifice of the Duromedics bileaflet valve showed a large region of flow separation around its pivots. Turbulent shear stresses as high as 1,700 dynes/cm2 were found adjacent to these separated zones. Fontaine et al.10 were the first to study the Bjork-Shiley and SJM aortic valve flow fields with a 3D LDV. They reported relatively small differences between Reynolds stresses calculated by three-component vs. two-component LDV-within 10 to 20 percent.
The design of mechanical heart valves deliberately includes some degree of leakage, or retrograde, flow upon valve closure. This reverse flow is intended to scour critical areas of the valve, such as the hinges and the areas between the leaflet edges and the housing. Yoganathan et al.27 found that under aortic pulsatile flow conditions the peak reverse velocity through the Medtronic-Hall tilting disc was 0.28 m/s, with a peak turbulent shear stress of 680 dynes/cm2. They also found a peak reverse velocity of 0.22 m/s through the Bjork-Shiley tilting disc with a peak turbulent shear stress of 430 dynes/cm2.These values were measured 10 mm upstream of the valves.They also reported leakage flow 10 mm upstream of the SJM valve and noted a maximum reverse velocity of 0.16 m/s and turbulent shear stresses as high as 325 dynes/cm2. Baldwin et al.1 conducted two-component LDV measurements at 100 near-wall positions upstream of the minor orifices of the mitral and aortic Bjork-Shiley Delrin tilting disc prosthetic valves in the Penn State Electric Left Ventricular Assist Device (PSLVAD). The highest turbulent shear stress near the aortic valve was found to be 9,900 dynes/cm2 and the corresponding peak velocity in the leakage jet was 2.8 m/s. Near the mitral valve, the highest turbulent shear stress was 9,000 dynes/cm2 with a peak leakage velocity of 4.4 m/s. These peak turbulent shear stresses and velocities were detected 1 mm upstream of the valves and approximately 0.6 mm from the adjacent wall of the PSLVAD.Meyer et al22 acquired 3D LDV measurements in the regurgitant flow region proximal of a Bjork-Shiley mono-strut valve in the mitral position.
The study recorded a maximum velocity of 3.7 m/s and peak turbulent shear stresses of 10,000 dyne/cm2. Subsequent experiments4-8,19 with CarboMedics (CM), Medtronic Hall, and SJM bi-leaflet valves found maximum regurgitant flow velocities ranging from 0.7 to 2.6 m/s, with corresponding maximum Reynolds shear stress of between 450 and 3,600 dyne/cm2.These studies demonstrate that turbulent jets in leakage flow can generate elevated levels of turbulent shear stress, even in bileaflet valves. Recent studies4-6,19 have shown that the hinge mechanism is a critical part of the bileaflet MHV. The hinge not only directly influences valve durability and functionality, but the high levels of turbulent shear stress in the hinge region may also lead to thrombus formation.
The basic geometry of the hinge regions in the SJM and CM are characterized by projections on the leaflets which mate to a similarly shaped recess in the valve housing. Both the SJM and CM valves have similar semicircular projections on the leaflet, except that in the former the hinge is streamlined and has a curved profile while in the latter the hinge geometry has sharper corners and is less streamlined edges. LDV studies by Ellis4 found peak leakage velocities and turbulent shear stresses in a 25 mm SJM standard valve of 3.5 m/s and 7,200 dynes/cm2, respectively. An improved equivalent valve model SJM 23mm Regent achieved lower maximum leakage velocity and turbulent shear stress levels of 1.5 m/s and 2,600 dynes/cm2, respectively.7 The highest peak leakage velocity and turbulent shear stress observed in the hinge during the leakage phase in the CM valve were 3.17 m/s and 5510 dynes/cm2, respectively.19
Computational work
The first application of CFD to study flow through MPHVs began in the early 1970s, approximately one decade after the first successfully implanted aortic valve. Early studies employed over-simplified, axisymmetric and/or two-dimensional numerical models to simulate flows in natural and prosthetic heart valves at Reynolds numbers much lower than the physiological range. Full, three-dimensional simulations started appearing only in the late 1980s and early 1990s with the advent of powerful desktop workstations. Such studies included both steady24 and unsteady15-17,24 simulations of the bulk flow through various valve designs as well as simulations aimed at elucidating local phenomena within small scale geometrical features, such as the valve housing and hinges.12
These studies provided the first glimpse into the complex, and highly three-dimensional structure of the flow in heart valves and yielded insights, which further strengthened the presumed link between complex hemodynamics and clinical complications. These studies also underscored the need for substantial computational research and development if CFD is to realize its full potential in the analysis and design of heart valves. Most of these studies, for instance, assumed the flow to be symmetric with respect to one or more geometric axes of symmetry of the valve, focused on Reynolds numbers much lower than the physiological range, and/or employed computational meshes far too coarse to resolve most hemodynamically relevant scales of motion. All these assumptions were dictated almost entirely by the need for computational expedience and the lack of numerical algorithms that are powerful enough to resolve all aspects of heart valve flows under physiological flow conditions.
The first numerical algorithm capable of highly resolved simulations of mechanical heart valves was developed recently by Ge et al.11 They carried out the first direct numerical simulations for typical bileaflet heart valve geometry with the leaflets fixed in the fully open position without adopting any simplifying symmetry assumptions on grids that were one to two orders of magnitude finer (1.5 million grid nodes) than those used in previously reported studies in the literature. Even though these first simulations focused on relatively low Reynolds numbers (300Figure 1. Figure 1a shows an instantaneous snapshot of particle paths in the vicinity of the leaflets. The orderly approach flow encounters the leaflets and the rapid geometrical changes of the model aortic root and is rapidly disorganized developing complex swirling flow patterns, regions of flow reversal, and strong vortical motions. As seen in Figure 1b, multiple pairs of streamwise vortices develop, which (as video animations show) appear and disappear randomly in time and engage in complex interactions with the surrounding walls. Such complex flow patterns could have important biological implications as the pockets of high turbulent stresses they induce can promote platelet activation. Furthermore, damaged blood elements could be captured into regions of recirculating flow and begin to aggregate.
For medical practitioners to be convinced that they can rely on CFD modeling tools to make decisions that could ultimately affect the span and quality of the life of the patient, experimental validation is necessary to ensure that the virtual blood flow environment shown in Figure 1. In-vitro laboratory experiments are currently under way at the Georgia Tech Cardiovascular Fluid Mechanics Laboratory to validate the numerical model. Preliminary comparisons showed very good agreement between data and simulations. A comprehensive validation study is in preparation and will be reported in future publications.
In spite of the progress we have made so far, much remains to be done before CFD can realize its full potential in heart valve design. Namely, the predictive capabilities of the CFD tools need to be demonstrated for the full, coupled fluid/structure interaction problem, where the leaflets are free to move in an anatomically realistic aorta under the action of flow induced forces, at physiological, pulsatile flow conditions. Work to accomplish this objective, which integrates both experiments and CFD modeling, is currently under way with funding from the National Institutes of Health.
Future outlook
With the advent of high performance computers and advances in computational flow dynamics algorithms, more detailed three-dimensional unsteady laminar and disturbed flow simulations are becoming a reality today. Development of high-resolution fluid-structure interaction algorithms, inclusion of detailed structural analysis of biological leaflet valves during the valve function, and particle dynamics analysis with the fluid dynamic analysis to simulate the platelet and red blood cell motion in the crevices with mechanical valve function are crucial for our further understanding of the valve function mechanics. However, complementary experimental studies to validate the simulations are also essential to gain confidence in the results of the complicated numerical simulations. The results from such simulations will provide valuable information towards design improvements to minimize the problems associated with implanted valve prostheses towards the goal of developing an ideal valve replacement. These studies will also provide valuable information towards the development of tissue engineered valve replacements.
Acknowledgements
This research is currently supported by a grant from the National Heart, Lung, and Blood Institute # R01-HL-07262.