Bioprosthetic Heart Valve Leaflet Deformation Monitored by Double-Pulse Stereo Photogrammetry

A double-pulse stereo photogrammetry technique has been developed for the dynamic assessment of the leaflet deformation of bioprosthetic heart valves under simulated physiological conditions. By using a specially designed triggering technique, which takes the advantage of the field transfer mechanisms of the charge coupled device camera, two consecutive images separated by a time interval as short as 5 ms were captured. This made it possible to investigate the realistic leaflet deformation during the valve opening and closing processes which typically last 25–45 ms. This technique was applied to assess a newly developed pericardial valve leaflet in a physiological pulse flow loop. Quantitative leaflet deformations of the valve opening and closing were generated from sequences of digital images. The results can later be applied to finite element analysis of bioprosthetic heart valve leaflet stress and strain during a complete cardiac cycle. © 2002 Biomedical Engineering Society. PAC02: 8719Hh, 8768+z, 8719Rr, 8719Uv     

Surface Geometric Analysis of Anatomic Structures Using Biquintic Finite Element Interpolation

The surface geometry of anatomic structures can have a direct impact upon their mechanical behavior in health and disease. Thus, mechanical analysis requires the accurate quantification of three-dimensional in vivo surface geometry. We present a fully generalized surface fitting method for surface geometric analysis that uses finite element based hermite biquintic polynomial interpolation functions. The method generates a contiguous surface of C² continuity, allowing computation of the finite strain and curvature tensors over the entire surface with respect to a single in-surface coordinate system. The Sobolev norm, which restricts element length and curvature, was utilized to stabilize the interpolating polynomial at boundaries and in regions of sparse data. A major advantage of the current method is its ability to fully quantify surface deformation from an unstructured grid of data points using a single interpolation scheme. The method was validated by computing both the principal curvature distributions for phantoms of known curvatures and the principal stretch and principal change of curvature distributions for a synthetic spherical patch warping into an ellipsoidal shape. To demonstrate the applicability to biomedical problems, the method was applied to quantify surface curvatures of an abdominal aortic aneurysm and the principal strains and change of curvatures of a deforming bioprosthetic heart valve leaflet. The method proved accurate for the computation of surface curvatures, as well as for strains and curvature change for a surface undergoing large deformations. © 2000 Biomedical Engineering Society. PAC00: 8719Rr, 8719Hh, 8768+z, 0260Ed, 0210Sp     

Estimation of the Shear Stress on the Surface of an Aortic Valve Leaflet

The limited durability of xenograft heart valves and the limited supply of allografts have sparked interest in tissue engineered replacement valves. A bioreactor for tissue engineered valves must operate at conditions that optimize the biosynthetic abilities of seeded cells while promoting their adherence to the leaflet matrix. An important parameter is shear stress, which is known to influence cellular behavior and may thus be crucial in bioreactor optimization. Therefore, an accurate estimate of the shear stress on the leaflet surface would not only improve our understanding of the mechanical environment of aortic valve leaflets, but it would also aid in bioreactor design. To estimate the shear stress on the leaflet surface, two-component laser-Doppler velocimetry measurements have been conducted inside a transparent polyurethane valve with a trileaflet structure similar to the native aortic valve. Steady flow rates of 7.5, 15.0, and 22.5 L/min were examined to cover the complete range possible during the cardiac cycle. The laminar shear stresses were calculated by linear regression of four axial velocity measurements near the surface of the leaflet. The maximum shear stress recorded was 79 dyne/cm², in agreement with boundary layer theory and previous experimental and computational studies. This study has provided a range of shear stresses to be explored in bioreactor design and has defined a maximum shear stress at which cells must remain adherent upon a tissue engineered construct. © 1999 Biomedical Engineering Society. PAC99: 8719Rr, 8768+z, 8719Hh, 4262Be, 4727Nz, 0630Gv     

Numerical simulation of mechanical mitral heart valve closure

A computational fluid dynamic simulation of a mechanical heart valve closing dynamics in the mitral position was performed in order to delineate the fluid induced stresses in the closing phase. The pressure and shear stress fields in the clearance region and near the inflow (atrial) side of the valve were computed during the mitral heart valve closure. Three separate numerical simulations were performed. The atrial chamber pressure was assumed to be zero in all the simulations. The first simulation was steady flow through a closed mitral valve with a ventricular pressure of 100 mm Hg (1.3 kPa). In the second simulation, the leaflet remained in the closed position while the ventricular pressure increased from 0 to 100 mm Hg at a rate of 2000 mm Hg/s (simulating leaflet closure by gravity before the ventricular pressure rise – gravity closure). In the third case, the leaflet motion from the fully open position to the fully closed position was simulated for the same ventricular pressure rise (simulating the normal closure of the mechanical valve). Normal closure (including leaflet motion towards closure, and sudden stop in the closed position) resulted in a relatively large negative pressure transient which was not present in the gravity closure simulation. The wall shear stresses near the housing and the leaflet edge close to the inflow side were around 4000 Pa with normal closure compared to about 725 Pa with gravity closure. The large negative pressure transients and significant increase in wall shear stresses due to the simulation of normal closure of the mechanical valve is consistent with the previously reported increased blood damage during the closing phase. © 2001 Biomedical Engineering Society. PAC01: 8719Hh, 8780-y, 8719Uv, 8710+e     

Surface strains in the anterior leaflet of the functioning mitral valve

The mitral valve (MV) is a complex anatomical structure whose function involves a delicate force balance and synchronized function of each of its components. Elucidation of the role of each component and their interactions is critical to improving our understanding of MV function, and to form the basis for rational surgical repair. In the present study, we present the first known detailed study of the surface strains in the anterior leaflet in the functioning MV. The three-dimensional spatial positions of markers placed in the central region of the MV anterior leaflet in a left ventricle-simulating flow loop over the cardiac cycle were determined. The resulting two-dimensional in-surface strain tensor was computed from the marker positions using a C ⁰ Lagrangian quadratic finite element. Results demonstrated that during valve closure the anterior leaflet experienced large, anisotropic strains with peak stretch rates of 500%–1000%/s. This rapid stretching was followed by a plateau phase characterized by relatively constant strain state. We hypothesized that the presence of this plateau phase was a result of full straightening of the leaflet collagen fibers upon valve closure. This hypothesis suggests that the MV collagen fibers are designed to allow leaflet coaptation followed by a dramatic increase in stiffness to prevent further leaflet deformation, which would lead to valvular regurgitation. These studies represent a first step in improving our understanding of normal MV function and to help establish the principles for repair and replacement. © 2002 Biomedical Engineering Society. PAC2002: 8719Hh, 8719Uv, 8719Rr     

Biosynthetic activity in heart valve leaflets in response to in vitro flow environments

The development of bioreactors for tissue engineered heart valves would be aided by a thorough understanding of how mechanical forces impact cells within valve leaflets. The hypothesis of the present study is that flow may influence the biosynthetic activity of aortic valve leaflet cells. Porcine leaflets were exposed to one of several conditions for 48 h, including steady or pulsatile flow in a tubular flow system at 10 or 20 l/min, and steady shear stress in a parallel plate flow system at 1, 6, or 22 dyne/cm². Protein, glycosaminoglycan, and DNA synthesis increased during static incubation but remained at basal levels after exposure to flow. The modulation of synthetic activity was attributed to the presence of a shear stress on the leaflet surface, which may be transmitted to cells within the leaflet matrix through tensile forces. The -smooth muscle (-SM) actin distribution observed in fresh leaflets was proportionately decreased after exposure to antibiotics and not recovered by either static incubation or exposure to flow. These results indicate that exposure to flow maintains leaflet synthetic activity near normal levels, but that the inclusion of another force, such as bending or backpressure, may be necessary to preserve -SM actin immunoreactive cells. © 2001 Biomedical Engineering Society. PAC01: 8780Rb, 8719Hh, 8719Uv, 8715Rn, 8768+z, 8719Ff, 8714Gg, 8714Ee     

Computational Flow Modeling of the Left Ventricle Based on In Vivo MRI Data: Initial Experience

A combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in heart chambers, with specific application in the present study to the human left ventricle. The proposed framework employs MRI scans of a human heart to obtain geometric data, which are then used for the CFD simulations. These latter are accomplished by geometrical modeling of the ventricle using time-resolved anatomical slices of the ventricular geometry and imposition of inflow/outflow conditions at orifices notionally representing the mitral and aortic valves. The predicted flow structure evolution and physiologically relevant flow characteristics were examined and compared to existing information. The CFD model convincingly captures the three-dimensional contraction and expansion phases of endocardial motion in the left ventricle, allowing simulation of dominant flow features, such as the vortices and swirling structures. These results were qualitatively consistent with previous physiological and clinical experiments on in vivo ventricular chambers, but the accuracy of the simulated velocities was limited largely by the anatomical shortcomings in the valve region. The study also indicated areas in which the methodology requires improvement and extension. © 2001 Biomedical Engineering Society. PAC01: 8719Hh, 4711+j, 8761Lh, 8719Uv     

Measurement and reconstruction of the leaflet geometry for a pericardial artificial heart valve

This paper describes the measurement and reconstruction of the leaflet geometry for a pericardial heart valve. Tasks involved include mapping the leaflet geometries by laser digitizing and reconstructing the 3D freeform leaflet surface based on a laser scanned profile. The challenge is to design a prosthetic valve that maximizes the benefits offered to the recipient as compared to the normally operating naturally-occurring valve. This research was prompted by the fact that artificial heart valve bioprostheses do not provide long life durability comparable to the natural heart valve, together with the anticipated benefits associated with defining the valve geometries, especially the leaflet geometries for the bioprosthetic and human valves, in order to create a replicate valve fabricated from synthetic materials. Our method applies the concept of reverse engineering in order to reconstruct the freeform surface geometry. A Brown & Shape coordinate measuring machine (CMM) equipped with a HyMARC laser-digitizing system was used to measure the leaflet profiles of a Baxter Carpentier-Edwards pericardial heart valve. The computer software, Polyworks was used to pre-process the raw data obtained from the scanning, which included merging images, eliminating duplicate points, and adding interpolated points. Three methods, creating a mesh model from cloud points, creating a freeform surface from cloud points, and generating a freeform surface by B-splines are presented in this paper to reconstruct the freeform leaflet surface. The mesh model created using Polyworks can be used for rapid prototyping and visualization. To fit a freeform surface to cloud points is straightforward but the rendering of a smooth surface is usually unpredictable. A surface fitted by a group of B-splines fitted to cloud points was found to be much smoother. This method offers the possibility of manually adjusting the surface curvature, locally. However, the process is complex and requires additional manipulation. Finally, this paper presents a reverse engineered design for the pericardial heart valve which contains three identical leaflets with reconstructed geometry.     

Observation of cavitation in a mechanical heart valve in a total artificial heart

Recently, cavitation on the surface of mechanical heart valves has been studied as a cause of fractures occurring in implanted mechanical heart valves. The cause of cavitation in mechanical heart valves was investigated using the 25 mm Medtronic Hall valve and the 23 mm Omnicarbon valve. Closing of these valves in the mitral position was simulated in an electrohydraulic totally artificial heart. Tests were conducted under physiologic pressures at heart rates from 60 to 100 beats per minute with cardiac outputs from 4.8 to 7.7 L/min. The disk closing motion was measured by a laser displacement sensor. A high-speed video camera was used to observe the cavitation bubbles in the mechanical heart valves. The maximum closing velocity of the Omnicarbon valve was faster than that of the Medtronic Hall valve. In both valves, the closing velocity of the leaflet, used as the cavitation threshold, was approximately 1.3-1.5 m/s. In the case of the Medtronic Hall valve, cavitation bubbles were generated by the squeeze flow and by the effects of the venturi and the water hammer. With the Omnicarbon valve, the cavitation bubbles were generated by the squeeze flow and the water hammer. The mechanism leading to the development of cavitation bubbles depended on the valve closing velocity and the valve stop geometry. Most of the cavitation bubbles were observed around the valve stop and were generated by the squeeze flow.     

A three-dimensional analysis of flow in the pivot regions of an ATS bileaflet valve

Bileaflet heart valves are currently the most commonly implanted type of mechanical prosthetic valve, because of their low transvalvular pressure drop, centralised flow and durability. However, in common with all mechanical heart valves, implanted bileaflet valves show an inherent tendency for blood clot formation at the valve site. Fluid dynamical phenomena associated with blood clotting are elevated blood shear stresses and regions of persistent blood recirculation, particularly when both occur together. Using three-dimensional CFD modelling, combined with enlarged scale experimental modelling, we investigated the blood flow through the ATS bileaflet valve during forward flow, with particular attention to the leaflet pivot regions. Recirculating regions were found both within and downstream of the valve housing ring. Qualitative assessment of the entire cardiac cycle suggested that recirculating blood within the housing ring will be washed away whilst the valve is closed, but as with all bileaflet valve designs recirculating blood downstream of the valve may have a residence time much longer than one cardiac cycle.     

Fluid Dynamic Assessment of Three Polymeric Heart Valves Using Particle Image Velocimetry

Polymeric heart valves have the potential to reduce thrombogenic complications associated with current mechanical valves and overcome fatigue-related problems experienced by bioprosthetic valves. In this paper we characterize the in vitro velocity and Reynolds Shear Stress (RSS) fields inside and downstream of three different prototype trileaflet polymeric heart valves. The fluid dynamic differences are then correlated with variations in valve design parameters. The three valves differ in leaflet thickness, ranging from 80 to 120 μm, and commisural design, either closed, opened, or semi-opened. The valves were subjected to aortic flow conditions and the velocity measured using three-dimensional stereo Particle Image Velocimetry. The peak forward flow phase in the three valves was characterized by a strong central orifice jet of approximately 2 m/s with a flat profile along the trailing edge of the leaflets. Leakage jets, with principle RSS magnitudes exceeding 4,500 dyn/cm², were observed in all valves with larger leaflet thicknesses and also corresponded to larger leakage volumes. Additional leakage jets were observed at the commissural region of valves with the open and the semi-open commissural designs. The results of the present study indicate that commissural design and leaflet thickness influence valve fluid dynamics and thus the thrombogenic potential of trileaflet polymeric valves.     

Experimental Investigation of the Steady Flow Downstream of the St. Jude Bileaflet Heart Valve: A Comparison Between Laser Doppler Velocimetry and Particle Image Velocimetry Techniques

This study investigates turbulent flow, based on high Reynolds number, downstream of a prosthetic heart valve using both laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). Until now, LDV has been the more commonly used tool in investigating the flow characteristics associated with mechanical heart valves. The LDV technique allows point by point velocity measurements and provides enough statistical information to quantify turbulent structure. The main drawback of this technique is the time consuming nature of the data acquisition process in order to assess an entire flow field area. Another technique now used in fluid dynamics studies is the PIV measurement technique. This technique allows spatial and temporal measurement of the entire flow field. Using this technique, the instantaneous and average velocity flow fields can be investigated for different positions. This paper presents a comparison of PIV two-dimensional measurements to LDV measurements, performed under steady flow conditions, for a measurement plane parallel to the leaflets of a St. Jude Medical (SJM) bileaflet valve. Comparisons of mean velocity obtained by the two techniques are in good agreement except for where there is instability in the flow. For second moment quantities the comparisons were less agreeable. This suggests that the PIV technique has sufficient temporal and spatial resolution to estimate mean velocity depending on the degree of instability in the flow and also provides sufficient images needed to duplicate mean flow but not for higher moment turbulence quantities such as maximum turbulent shear stress. © 2000 Biomedical Engineering Society. PAC00: 8719Uv, 4262Be, 8780-y     

Bileaflet Aortic Valve Prosthesis Pivot Geometry Influences Platelet Secretion and Anionic Phospholipid Exposure

The clinical histories of the Medtronic Parallel (MP) and St. Jude Medical (SJM) Standard valves suggest pivot geometry influences the thrombogenic characteristics of bileaflet prostheses. This work studied the effects of various pivot geometries on markers of platelet damage in a controlled, in vitro apparatus. The Medtronic Parallel valve, two St. Jude Medical valves, and two demonstration prostheses were used to study the effects of bileaflet pivot design, gap width, and size on platelet secretion and anionic phospholipid expression during leakage flow. A centrifugal pump was used to drive blood through a circuit containing a bileaflet prosthesis. Samples were taken at set time intervals after the start of the pump. These samples were analyzed by cell counting, flow cytometry, and enzyme-linked immunosorbant assay. No significant differences were observed in platelet secretion or anionic phospholipid expression between experiments with the SJM 27 Standard regular leaker, the SJM 20 regular leaker, and the MP 27 valves. Significant differences in platelet secretion and anionic phospholipid expression were observed between a SJM 27 Standard regular leaker and a SJM 27 high leaker valve. These studies suggest that leakage gap width within bileaflet valve pivots has a significant effect on platelet damage initiated by leakage flow. © 2001 Biomedical Engineering Society. PAC01: 8719Uv, 8719Tt, 8380Lz, 8768+z     

Mechanical valve closing dynamics: Relationship between velocity of closing, pressure transients, and cavitation initiation

In this study, the closing dynamics of mechanical heart valves was experimentally analyzed with the valves mounted in the mitral position of anin vitro flow chamber simulating a single closing event. The average linear velocity of the edge of the leaflet during the final 2.065° of the traverse before closing was measured using a laser sweeping technique, and the negative pressure transients at 2 mm from the leaflet inflow surface in the fully closed position was recorded at the instant of valve closure. The cavitation number was computed for the various mechanical valves at a range of load at valve closure. The data were correlated with cavitation bubble visualization previously obtained with the same experimental set up. Cavitation incipience with mechanical valves was found to be independent of the flexibility of the valve holder. For the same loading rate at valve closure, valves with flexible (polyethylene) leaflets were found to close with comparable velocity to those with rigid (pyrolytic carbon) leaflets, but the negative pressure transients did not reach magnitudes close to the vapor pressure for the fluid with flexible leaflets. For the same leaflet closing velocity (and hence the cavitation number), valves with a seat stop or a seating lip in the region of maximum leaflet velocity were observed to cavitate earlier, suggesting that the effect of “squeeze flow” may be an important factor in cavitation incipience. This study was presented at the Biomedical Engineering Society's 1996 Annual Fall Meeting, October 1996.     

Examination of cavitation-induced surface erosion pitting of a mechanical heart valve using closing velocities

 Recently, cavitation on the surface of mechanical heart valves has been studied as a cause of fractures that occur in implanted mechanical heart valves. Several factors, including peak dp/dt of the ventricular pressure, maximum closing velocity of the leaflet, and squeeze flow, have been studied as indices of the cavitation threshold. In the present study, cavitation erosion on the surface of a mechanical valve was examined by focusing on squeeze flow and the water-hammer phenomenon during the closing period of the valve. A simple solenoid-actuated test device that can directly control the valve closing velocity was developed, and opening–closing tests of 3000 and 40 000 cycles were performed at various closing velocities. The results showed that there was a closing velocity threshold above which erosion pitting was induced and that the threshold was about 0.4 m/s in the valves used in this study. Cavitation-induced erosion pits were observed only in regions where squeeze flow occurred immediately before valve closure. On the other hand, the number of the pits was found to be closely related to the area of the water hammer-induced pressure were below the critical pressure defined by water vapor pressure. Therefore, it was concluded that cavitation is initiated and augmented by the two pressure drops due to squeeze flow and the water-hammer phenomenon, respectively. Received: January 15, 2002 / Accepted: May 30, 2002 Correspondence to:H. Lee     

Cardiac fluid dynamics.

The heart is modeled as a system of elastic and/or contractile fibers immersed in a viscous incompressible fluid. Simulated heart walls and valves are constructed by arranging the fibers according to an idealized version of the actual distribution of muscle fibers in the heart walls and collagen fibers in the valve leaflets. Then the combined motion of the fluid-fiber system is predicted through the numerical solution of its coupled equations of motion. Fluid equations are solved by a finite difference method on a fixed, regular computational lattice. Fiber points move freely through this lattice without being constrained to lie at the lattice intersections. Communication between fibers and fluid involves interpolation of the fluid velocity to the fiber points and the spreading of the fiber forces to the computational lattice of the fluid. Both of these operations make use of a smoothed approximation to the Dirac delta function. The entire method is suitable for implementation on vector, parallel, or parallel-vector hardware. Applications include the investigation of normal cardiac function, the simulation of disease processes affecting the mechanical function of the heart or its valves, and the computer-assisted design of prosthetic cardiac valves.     

Improved In Vitro Quantification of the Force Exerted by the Papillary Muscle on the Left Ventricular Wall: Three-Dimensional Force Vector Measurement System

Recent developments indicate that the forces acting on the papillary muscles can be a measure of the severity of mitral valve regurgitation. Pathological conditions, such as ischemic heart disease, cause changes in the geometry of the left ventricle and the mitral valve annulus, often resulting in displacement of the papillary muscles relative to the annulus. This can lead to increased tension in the chordae tendineae. This increased tension is transferred to the leaflets, and can disturb the coaptation pattern of the mitral valve. The force balance on the individual components governs the function of the mitral valve. The ability to measure changes in the force distribution from normal to pathological conditions may give insight into the mechanisms of mitral valve insufficiency. A unique in vitro model has been developed that allows quantification of the papillary muscle spatial position and quantification of the three-dimensional force vector applied to the left ventricular wall by the papillary muscles. This system allows for the quantification of the global force exerted on the posterior left ventricular wall from the papillary muscles during simulation of normal and diseased conditions. © 2001 Biomedical Engineering Society. PAC01: 8719Rr, 8719Ff, 8719Hh, 8719Xx, 8710+e     

Finite Element Investigation of Stentless Pericardial Aortic Valves: Relevance of Leaflet Geometry

Recent developments in aortic valve replacement include the truly stentless pericardial bioprostheses with single point attached commissures (SPAC) implantation technique. The leaflet geometry available for the SPAC valves can either be a simple tubular or a complex three-dimensional structure molded using specially designed molds. Our main objective was to compare these two leaflet designs, the tubular vs. the molded, by dynamic finite element simulation. Time-varying physiological pressure loadings over a full cardiac cycle were simulated using ABAQUS. Dynamic leaflet behavior, leaflet coaptation parameters, and stress distribution were compared. The maximum effective valve orifice area during systole is 633.5 mm² in the molded valve vs. 400.6 mm² in the tubular valve, and the leaflet coaptation height during diastole is 4.5 mm in the former, in contrast to 1.6 mm in the latter. Computed compressive stress indicates high magnitudes at the commissures and inter-leaflet margins of the tubular valve, the highest being 3.83 MPa, more than twice greater than 1.80 MPa in the molded valve. The molded leaflet design which resembles the native valve exerts a positive influence on the mechanical performance of the SPAC pericardial valves compared with the simple tubular design. This may suggest enhanced valve efficacy and durability.     

Cavitation phenomenon in monoleaflet mechanical heart valves with electrohydraulic total artificial heart

Recently, cavitation on the surface of mechanical heart valves has been studied as a cause of fractures occurring in implanted mechanical heart valves. In this study, to investigate the mechanism of cavitation bubbles associated with monoleaflet mitral valves in an electrohydraulic total artificial heart (EHTAH), and to select the best valves for our EHTAH system, we measured three parameters. First, an image was created of the cavitation bubbles using a high-speed camera. Second, pressure drop in the vicinity of the valve surface was measured using mini pressure sensor. Then, the closing of the valve was observed using a Laser displacement sensor. Most of the cavitation bubbles in the Medtronic Hall valve were observed at the edge of the valve stop. With the Omnicarbon valve, the cavitation bubbles were observed at the edge of the valve and on the inner side of the leaflet. On the other hand, cavitation bubbles were observed only on the inner side of the leaflet in Bj?rk-Shiley valve. Cavitation bubbles concentrated on the edge of the valve stop; the major cause of these cavitation bubbles was determined to be the squeeze flow. The formation of cavitation bubbles depended on the valve closing velocity and the valve leaflet geometry. From a viewpoint of squeeze flow, a low closing velocity and a small size of the valve stop could minimize cavitation.     

Calcification and stress distribution in bovine pericardial heart valves.

There is a strong relationship between mechanical stress and calcification in biological prosthetic heart valves. A dynamic in vitro calcification test has been used to study the relationship between stress distributions in the leaflets of bovine pericardial valves and the deposition of calcium over the leaflet surfaces. Intuitive stress regions have been defined over the leaflet surfaces. Calcium uptake by the leaflets has been assayed directly by ashing of leaflet material and analysis of the ash by atomic absorption spectrophotometry. Calcium and phosphorus distribution over the leaflet surface has been analyzed using energy-dispersive x-ray analysis by scanning electron microscope and data points assigned to the appropriate stress region. The uptake of calcium is assessed by comparing stress regions, surfaces, and the degree of calcification of the valve. Differences between stress regions and surfaces are significant. Uptake of calcium in these valves appears to be strongly related to the degree and type of stress present in the valve leaflets.