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Comparison of the in vivo and in vitro mechanical properties of aortic valve leaflets
J
THoRAc CARDIOVASC SURG
92:29-36, 1986
Comparison of the in vivo and in vitro mechanical properties of aortic valve leaflets The mechanical properties of aortic valve leaflets are responsible for the efficiency and longevity of the valve. These properties in the radial direction were investigated in vivo in dogs. During cardiopulmonary bypass, radiopaque markers were placed on the leaflets. Later, from a normally functioning valve, the marker positions were recorded on videotape during fluoroscopy, and the leaflet length was determined. I.eaftet length in the radial direction increased 31 % from systole to diastole. During diastole, leaflet length increased by 3.9 % as the pressure gradient increased from 60 to 200 mm Hg, During systole, the leaflet had a low elastic modulus. In vitro, the stress-strain properties of the leaflets were studied. For an increase in stress in vitro that corresponded to an increase in pressure gradient from 60 to 200 mm Hg, the leaflet length increased 8.7%. This increase was more than twice that measured in vivo, which indicates that during diastole the leaflet is much stiffer in vivo than in vitro. This stiffening appears to be due to stress in the circumferentiaUy oriented coUagen fibers of the leaflet, which prevents stretching in the radial direction. In systole, the lower elastic modulus reduces the flexion stresses, and in diastole, stiffening prevents the leaflet from prolapsing under pressure.
Mano J. Thubrikar, Ph.D., Jaafar Aouad, D.V.M., and Stanton P. Nolan, M.D.,
Charlottesville, Va.
firing each cardiac cycle, the opening and closing of the aortic valve causes the leaflets of the valve to undergo loading and unloading, reversal of their curvature, and a great deal of flexion in the region of the leaflet attachments. In this process, the leaflets are subjected to complex stresses and strains that are potentially damaging, yet the leaflets survive billions of cardiac cycles. To understand their remarkable durability, one must analyze their mechanics in vivo. We have measured and analyzed the changes in leaflet length in the radial direction and have integrated this information with our knowledge of the behavior of the leaflet in the circumferential direction. We have further compared the behavior of the leaflet in vivo and in vitro. Materials and methods The length of the aortic valve leaflet was measured in vivo by the marker-fluoroscopy technique developed in From the Department of Surgery, University of Virginia Medical Center, Charlottesville, Va. Received for publication May 13, 1985. Accepted for publication Aug. 8, 1985. Address for reprints: Mano J. Thubrikar, Ph.D., Box 263, Department of Surgery, University of Virginia Medical Center, Charlottesville, Va. 22908.
our laboratory and described previously.' The same leaflets were then studied in vitro for their stress-strain properties and the results of these two studies were compared. In 10 dogs 13 aortic valve leaflets were studied in vivo. For the implantation of radiopaque markers on the aortic valve, the dogs were placed on total cardiopulmonary bypass. The aorta was opened and the aortic valve exposed. Small platinum markers, 1 by I mm and weighing 10 mg, were then sutured to the leaflets in the desired positions. Most frequently, two markers were attached to a single leaflet, one at the base and the other near the line of coaptation, both in the radial direction of the leaflet. The distance between these two markers indicated the length of that segment of the leaflet. On six leaflets the markers were attached to the aortic side and on seven leaflets, to the ventricular side. This was done to explore whether there was any difference in the length change of the two surfaces of the leaflet. A third marker was placed on the free edge of the leaflet. Three additional markers were attached to the aortic wall at the valve commissures. The typical position of the six markers is depicted in Fig. I. Two leaflets were marked in each of three dogs. After marker placement, the aorta was repaired and cardiopulmonary bypass discontinued. The dogs were allowed to recover for at least 15 days 29
30
Thubrikar, Aouad, Nolan
The Journal of Thoracic and Cardiovascular Surgery
Fig. 1. Schematic drawing of the aortic valve showing placement of radiopaquemarkers. Markers A, B, and C wereplaced on the leafletin the radial direction. Markers D, E, and F were placedat the three commissures of the valve. Distance BC was used to determine the change in leaflet length in the loadbearing portion.
before study. They were studied several times, and intervals between any two studies ranged from 15 days to 2 months. During each study the dogs were anesthetized with pentobarbitol (25 mg/kg, intravenously) and subjected to roentgenography, The markers were visualized on a normally functioning valve, and the position of the markers was recorded on videotape during fluoroscopy. For the length of the leaflet to be measured, the leaflet had to be seen in a perfect side view. This was achieved by rotating the dog to superimpose the two commissural markers placed at two ends of the marked leaflet. Fig. 2 shows such a projection of the valve. The blood pressure in the ascending aorta was recorded simultaneously with the videotaping of leaflet motion. In some dogs ventricular pressure was recorded by passing the catheter across the aortic valve, Recordings were made at increased and decreased pressures, which were achieved by the intravenous infusion of angiotensin or nitroprusside, respectively. All pressure recordings were made with a pressure transducer (Statham P23 10) via a 7F fluid-filled catheter having side holes and an end hole. The recordings were repeated after the dog had been rotated 180 degrees on its spinal axis to allow for correction of any error that may occur by movement of the valve toward or away from the x-ray source during the cardiac cycle. I To correlate the videotape recording with the pressure recording, a separate electrical circuit was used that triggered a solenoid in the videofield and simultaneously activated an event marker on the pressure recording. Data were analyzed by displaying the videotape on a television screen in a stop-motion mode and recording the positions of the markers on acetate paper. The videotape was advanced one field at a time and the positions recorded. Since the rate of recording
Fig. 2. The two upperdrawings showa perfectside view of a marked leaflet when the aortic valve is closed (left) and open (right). In this view, two commissure markers D and E are superimposed. A, B, and C are the markers on the leaflet. The two lower photographs show the actual fluoroscopic images of the markerson the aortic valve of a dog that correspond to the views in the upper drawings.
was 60 videofields per second, we obtained 60 data points in I second. The data gathering was performed for at least three cardiac cycles at any given pressure. Videofields were deliberately ignored where the markers could not be seen clearly or where the commissure markers were not superimposed. The distance between the two leaflet markers was measured to determine the length of the leaflet during systole and diastole. For these studies, systole is defined as a time period when the valve is open, as indicated by the position of the leaflet marker, and diastole as a time period when the valve is closed, also as indicated by the position of the leaflet marker (Fig. 2). After the studies were completed, the dogs were killed and the leaflets excised. Nine leaflets were removed from six dogs for analysis in vitro. A rectangular strip in the radial direction of the leaflet was cut from each of the leaflets using parallel blades. Some strips contained the previously implanted markers and others had no markers. The thickness of each strip was measured with a micrometer equipped with an electrical circuit to produce a signal when the two tips of the micrometer contacted the opposing surfaces of the strip, The width and length of these strips were also measured. The strips were subjected to a uniaxial stress-strain experiment in an Instron tensiletesting machine. In these experiments, the strips were elongated at a rate of 5 mm/rnin, and the force
Volume 92 Number 1 July, 1986
Mechanical properties of aortic valve leaflets
31
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developed in them was recorded continuously. From the force-length relationship, an engineering stress-strain curve was obtained. Stress in the leaflet was determined based on the consideration that the leaflet is a thin cylindrical shell. Hence, stress in the radial direction = (PR/2t), where P isthe pressure gradient across the leaflet, R is the radius of the cylinder formed by the leaflet, and t is the thickness of the leaflet. The pressure gradient P was measured in vivo during fluoroscopy. Thickness twas measured in vitro. The radius R was also determined in vitroas follows. In four dogs the entire aortic valve was removed. A silicone rubber cast of the closed valve was made at an intra-aortic pressure of 80 to 100 mm Hg. The radius of the leaflet in diastole was measured from these casts. During the bypass operation on the dogs, during the multiple studies that followed, and when the dogs were killed, humane treatment was provided as set forth in the guidelines published by the National Institutes of Health.
Results In vivo, the leaflet length in the radial direction changed during each cardiac cycle (Fig. 3). The leaflet was shorter in systole and longer in diastole. The length did not change appreciably during systole or during diastole; the major change occurred during the transition between systole and diastole. This was true for all dogs and for all leaflets studied. Table I shows the change in leaflet length obtained from several studies on 13 leaflets from 10 dogs. The increase in leaflet length is expressed as follows: LD - Ls AL% = - - -
Ls
x 100%
Table I. Increase in the leaflet length (IlL %) from systole to diastole Dog No.
Leaflet
No. of studies
AL%
R R R R R R
3 8 4 9 6 6 2 5 5 6 2 6 2 8 4 10 7 6 2 3 5
31.1 35.9 30.7 25.9 56.7 23.8 58.6 24.0 19.8 30.5 17.6 33.9 15.6 16.2 20.6 24.2 36.8 44.9 19.2 58.9 21.2
2 3
L L 4
R R
N N 5 6 7 8 9 10 Mean ± SE
R R R R R
L L L R
30.8 ± 3
Legend: R. Leaflet corresponding (0 the right coronary aortic sinus. L. Leaflet corresponding to the left coronary aortic sinus. N. Leaflet corresponding to noncoronary aortic sinus. SE. Standard error.
where L, and L D represent the length in systole and in diastole, respectively. In Table I each value of &% represents an average of several cardiac cycles from multiple studies. The leaflet length increased by an average of 30.8% ± 3% (mean ± standard error). In determining this average, we used data not only from the control systemic pressure, but also from the pharma-
32
The Journal of Thoracic and Cardiovascular Surgery
Thubrikar, Aouad, No/an
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cologicaUy increased and decreased systemic pressures. There were no differences between the data obtained with markers on the aortic surface of the leaflet and the data obtained with markers on the ventricular surface. In exploring the effect of systemic pressure on changes in the leaflet length, we found that the increase in leaflet length remained constant as systemic pressure increased. Similar results, for three different leaflets from three dogs, are presented in Fig. 4. which shows that the increase in leaflet length does not change appreciably as the diastolic pressure is increased. Even more interesting results were seen when leaflet length was plotted against peak systolic pressure or pressure gradient. When systolic pressure was increased, systolic leaflet length either increased slightly or remained the same, perhaps because there was little or no increase in the pressure gradient across the leaflet (Fig. 5). This was true in all 12 studies on 10 leaflets of seven dogs. When the leaflet length was plotted against pressure gradient across the leaflet, a graph was obtained that essentially represented the stress-strain properties of the leaflet in vivo (Fig. 6). In diastole, the pressure gradient across the leaflet was measured as the difference between the aortic and ventricular pressures in mid-diastole. In systole, the pressure gradient across the leaflet, which is small and difficult to determine accurately, was not measured but was assumed to vary between 0 and 10 mm Hg. Usually it varies from 0 mm Hg to + 10 mm Hg to a negative value as reported in the literature.s ' Graphs like that shown in Fig. 6 were obtained from 12 studies on 10 leaflets of seven dogs and demonstrated a similar behavior of all leaflets. The graph (Fig. 6) indicates that, during systole, the leaflet
goes through a large change in length for a small change in pressure gradient, whereas, during diastole, the leaflet goes through a small change in length for a large change in pressure gradient. The leaflet, therefore, is in an "elastic phase" (less stiffness) in systole and in an "inelastic phase" (more stiffness) in diastole. The graph (Fig. 6) represents the overall behavior of the leaflet in vivo over a large range of systemic pressure, where the pressure across the leaflet varies from 0 mm Hg to more than 200 mm Hg. This overall behavior of the leaflet, however, may not be detected in individual cardiac cycles because the changes involved may be too small to measure. It is therefore not surprising that during a single cardiac cycle, the leaflet length change from systole to diastole was detected, but changes during systole or diastole were not (Fig. 3). In vivo, the pressure gradient across the leaflet represents stress on the leaflet and the change in the leaflet length represents strain. Therefore, Fig. 6 defines the segments of the stress-strain curve in which the leaflet functions during systole and diastole. Hence, a smooth curve was drawn through all the data points (Fig. 6) so that the curve characteristically resembled the stress-strain curve obtained in vitro (Fig. 7). In vitro, stress-strain curves were determined for nine leaflets from six dogs, and all of the curves showed a characteristic nonlinear behavior (Fig. 7). For the stress-strain curves obtained both in vivo and in vitro, we determined the stresses, strains, and moduli of elasticity in systole and diastole. We obtained an incremental modulus that was calculated from incremental stress and incremental strain. To obtain the stress in the leaflet in vivo, we considered the leaflet to
Volume 92
Mechanical properties of aortic valve leaflets 33
Number 1
July, 1986
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be a thin cylindrical shell. Our previous studies' and those of others' have shown that the leaflet is cylindrical in its load-bearing portion. Hence, stress in the radial direction of the leaflet (oR) is equal to (PR/2t). In systole, oR was determined for pressure gradients of 0 and 10 rom Hg. These two stresses were plotted on the stress-strain curve in vitro, and the corresponding strains 10 and 1 were determined (Fig. 7). In vivo, 10 and I represent the two limits of the length measurement in systole, wherein the minimum length corresponds to a pressure gradient of zero, and the maximum length corresponds to a pressure gradient of 10 mm Hg (Fig. 6). The incremental strain in systole is given by the equation: .6.L% = ES% =
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This is shown in Table II. The average incremental strain was 14.9% in vivo and 9.6% in vitro. Modulus of elasticity = (incremental stress/incremental strain) is also indicated in Table II. In diastole, oR was determined for pressure gradients of 60 mm Hg and 200 mm
Hg. These two stresses were plotted on the stress-strain
Fig. 6. Typical plot of leaflet length versus pressure gradient across the leaflet in vivo in a single dog. The circles represent measured leaflet length and measured pressure gradient in diastole. The bars represent measured leaflet length and assumed pressure gradient of 0 to 10 mm Hg in systole. The lengths I." I, I" and 12 correspond to the gradients of 0, 10, 60, and 200 mm Hg, respectively. Eo and ES represent strains. The origin (12,0) is arbitrarily chosen for convenience, since minimum leaflet length measured in this case was 13 mm during systole when the gradient was not measured.
curve and the corresponding strains II and 11 were determined from the curve. The incremental strain (Figs. 6 and 7) is given by the formula. .6.L% = Eo% =
1 -I,
2 -x
II
100%
The average incremental strain was 3.9% in vivo and 8.7% in vitro (Table 11). The modulus of elasticity is also indicated in Table II. It is worth emphasizing that the modulus of elasticity is normally determined only for unidirectional stress conditions, that is, in these studies for in vitro experiments; however, we have reported values obtained in vivo for a purpose of comparison. In these calculations, the radius of the leaflet was that measured in diastole and taken to be the same in systole, as had been observed in our previous experiments." Discussion In each cardiac cycle, the length of the leaflet in the radial direction increased by 30.8% from systole to
The Journal 01
3 4 Thubrikar, Aouad, Nolan
Thoracic and Cardiovascular Surgery
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Fig. 7. Typical engineering stress-strain curve of a single leaflet in the radial direction obtained under in vitro uniaxial loading conditions. Stresses corresponding to the pressure gradients of 0, 10, 60, and 200 mm Hg are shown; corresponding lengths 10 , I, II, and 12 are also indicated. fo and fs represent strains in diastole and in systole, respectively.
----- ------t
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Fig. 8. Schematic representation of the leaflet structure showing circumferentially oriented collagen cords as the dominant structural component. When the leaflet is pulled only radially, the collagen cords can separate and do not offer resistance to stretching. When the leaflet is pulled both radially and circumferentially, then tension in the collagen cords in the circumferential direction prevents them from separating. Consequently, they resist stretching in the radial direction.
diastole. Our previous studies? have shown that the leaflet length in the circumferential direction increased by 11.9% from systole to diastole (the same as a decrease of 10.6% from diastole to systole). This length change is large and could damage the leaflet by fatigue; however, it occurred in response to a change of the pressure gradient (stress) on the leaflet. It would appear either that the leaflet is less susceptible to fatigue failure or that the damage is reparable, since the length change occurs in normal valves, which survive for a hundred years. The advantages of length change are two: (I) The
leaflet functions in the low modulus region in systole, and this reduces flexion stresses on the leaflet," since flexion rigidity is proportional to elastic modulus X (thickness)'. (2) The leaflet is relaxed in systole and therefore not subjected to creep from constant stress. In other words, the leaflet minimizes flexion stresses and creep at the expense of fatigue. The strain of 30.8% in the leaflet in vivo can be compared with strains measured in vitro by others. Clark? measured transition strains of 24% ± 8% in human leaflets, and his results agree fairly well with those reported here. Transition strain is the strain at which transition from low modulus to high modulus takes place, that is, where the "knee" in the stress-strain curve occurs. Although we did not determine transition strains in vitro, they were close to 30%, as may be noted from Fig. 7. Strains in excess of 70% in fresh porcine aortic leaflets were reported by Broom and Christie, 10 but they are higher than those observed in the present study. The reason may be that porcine leaflets show higher strains than do canine leaflets. Also, our measurements were made in vivo and theirs in vitro under uniaxial loading conditions. Missirlis and Chong " measured strains in the radial direction of the leaflets of fresh porcine aortic valves in vitro. In these experiments, the closed valve was subjected to increasing pressure, and measurements were made locally in various parts of the leaflets. They reported strains ranging from 10% in some areas to 100% in others; the strains increased from the base of the leaflet to the coaptation edge. In an
Volume 92 Number 1
Mechanical properties of aortic valve leaflets
July, 1986
35
Table II. Strains in the leaflet in the radial direction Diastole (60-200 mm Hg) DogNo.
Leaflet
ilL% in vivo
1 2 3
R R
6.2 4.4 2.0 4.0 1.9 I.7 7.9 3.4 0.7 1.9 8.2
4
5 6 7
R R L R R N R
R R L L N
I
ilL % in vitro
Systole (0-10 mm Hg)
ilL% in vivo
11.5
I
ilL % in vitro
13.0
9.2 9.7
9.0
10.0
7.2
8.7
5.6 5.8 6.0 9.7 9.1
25.0 15.0 24.0 12.5 17.0
8.2 8.6 9.0
13.7 8.0
4.3 9.6 13.6
11.0
8.8
Mean ± SD
3.9 ± 2.5
8.7 ± 2.5
14.9 ± 6
Modulus of elasticity (dynes/em')
24.4 X 10'
11.6 X 10'
0.50
x 10'
9.6 ± 1.8 0.75
x 10'
For legend see Table I. SD, Standard deviation.
"inelastic phase" (i.e., in diastole), their data and ours are comparable. There have been other studies that investigated pressure deformation behavior of the leaflets invitro," 13 and there have been studies in vivo of length change in the circumferential direction of the leaflet ' 4, 15; however, there are no reported in vivo studies in the radial direction of the leaflet for comparison to our results. The observation that the length change does not vary with systemic pressure (Fig. 4) is interesting, because we? had found the same results for the leaflet in the circumferential direction. In determining the stresses in the leaflet, we used an approximation of a thin cylindrical shell under pressure. Such an approximation is valid for the leafletwhere R/t Is 25 or more. This approach was used successfully in our previous analysis." The modulus of elasticityin vitro was 118 gm/mm' in the post-transition state and 7 gm/mm 2 in the pretransition state. Clark? reported values for human leaflets to be 174 gm/rnm- and 1.13 gm/mm2, which compare favorably with ours, considering that our values are for large incrementsof stress and theirs are for small. Comparison of strains in vivo and in vitro. In systole, the incremental strains in vivo were 14.9% and b in vitro were 9.6%, for an increase in pressure gradient of10mm Hg (Table 11). Since some amount of leaflet folding can occur in systole, the length change is most likely exaggerated in that phase. As can be seen from Fig. 6,only one reading underestimatingthe leaflet
length will result in overestimation of strain. In vivo the leaflet is under biaxial load and in vitro it is under uniaxial load; therefore, the leaflet is not likely to be longer in vivo than in vitro. For these reasons,we believe that the true strains in vivo are quite close to those observed in vitro. In diastole, the incremental strains in vivo were 3.9% and those in vitro were 8.7%, for an increase of the pressure gradient of 140 mm Hg (the difference between 200 and 60 mm Hg). Since the leaflet does not fold in the load-bearing portion in diastole, these measurements are accurate. They suggest that the leaflet is much more stretchable in vitro than in vivo. This is an important observation, because several studies performed in vitro have implied that the results can be extrapolated to in vivo performance. Broom's and Christie's report,'? for example, showed 70% strains in porcine leaflets in vitro. Such high strains in vivo are unlikely even in porcine leaflets, because if they did occur, the leaflets would prolapse into the ventricle, and the valve would be incompetent. The reasons that strains are lower in vivo can be seen from Fig. 8. In vitro, when force is applied in the radial direction, it stretches the leaflet with little resistance. In vivo, when force is present in both the circumferential and radial directions of the leaflet, then the circumferential stress in the collagen cords of the leaflet prevents the cords from separating. In vivo, therefore, major resistance to excessive stretching in the radial direction comes from the stress in the circumferentialfibers. Broom and Christie'?
The Journal of
36
Thubrikar, Aouad, Nolan
mentioned that the major leaflet strength in the radial direction comes from the radially oriented collagen and elastin fibers, and that the circumferentially oriented fibrosa does not play a significant role. Our in vivo observations indicate that it is the fibrosa that prevents excessive radial stretching of the leaflet. This observation further indicates that the interaction between the circumferential and radial forces on the leaflet is important for maintaining its longevity. The absence of this interaction would cause the leaflet to deteriorate from excessive shear or cause leaflet prolapse from excessive stretching.
Conclusions Cyclic changes in aortic leaflet length are important for longevity, because they reduce flexion stress and creep in the leaflet. Stiffening of the leaflet in diastole from the interaction between the circumferential and radial forces is important for the prevention of leaflet prolapse. The absence of either of these phenomena, which may occur in bioprosthetic or congenitally malformed valves, will compromise the function of the valve. REFERENCES Thubrikar M, Harry R, Nolan SP: Normal aortic valve function in dogs. Am J Cardiol 40:563-568, 1977 2 Driscol TE, Eckstein RW: Systolic pressure gradients across the aortic valve and in the ascending aorta. Am J Physiol 209:557-563, 1965 3 McDonald A: Blood Flow in Arteries, Baltimore, 1974, The Williams & Wilkins Company, p 121 4 Thubrikar M, Piepgrass WC, Shaner TW, Nolan SP: The
Thoracic and Cardiovascular Surgery
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IO
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12 13
14
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design of the normal aortic valve. Am J Physiol 241:H795-H801, 1981 Swanson WM, Clark RE: Dimensions and geometric relationships of the human aortic valve as a function of pressure. Circ Res 35:871-882, 1974 Thubrikar M, Piepgrass WC, Deck JD, Nolan SP: Stresses of natural vs prosthetic aortic valve leaflets in vivo. Ann Thorac Surg 30:230-239, 1980 Thubrikar M, Piepgrass WC, Bosher LP, Nolan SP: The elastic modulus of canine aortic valve leaflets in vivoand in vitro. Circ Res 47:792-800, 1980 Harvey JF: Theory and design of modern pressure vessels. New York, 1974, von Nostrand Reinhold, p 95 Clark RE: Stress-strain characteristics of fresh and frozen human aortic and mitral leaflets and chordae tendineae. J THoRAc CARDIOVASC SURG 66:202-208, 1973 Broom NO, Christie GW: The structure/function relationship of fresh and glutaraldehyde-fixed aortic valve leaflets, Cardiac Bioprostheses: Proceedings of the Second International Symposium, LH Cohn, V Gallucci, OOs., New York, 1982, Yorke Medical Books, pp 476-491 Missirlis YF, Chong M: Aortic valve mechanics-Part I: Material properties of natural porcine aortic valves. J Bioenerg Biomembr 2:287-300, 1978 Wright JEC, Ng YL: Elasticity of human aortic valve cusps. Cardiovasc Res 8:384-390, 1974 Broom NO: The observation of collagen and elastin structures in wet whole mounts of pulmonary and aortic leaflets. J THORAC CARDIOVASC SURG 75:121-130, 1978 Brewer RJ, Mentzer RM, Deck JD, Ritter RC, Trefil JS, Nolan SP: An in vivo study of the dimensional changes of the aortic valve leaflets during the cardiac cycle. J THoRAe CARDIOVASC SURG 74:645-650, 1977 Brewer RJ, Deck JD, Capati B, Nolan SP: The dynamic aortic root. J THoRAc CARDIOVASC SURG 72:413-417, 1976
THoRAc CARDIOVASC SURG
92:29-36, 1986
Comparison of the in vivo and in vitro mechanical properties of aortic valve leaflets The mechanical properties of aortic valve leaflets are responsible for the efficiency and longevity of the valve. These properties in the radial direction were investigated in vivo in dogs. During cardiopulmonary bypass, radiopaque markers were placed on the leaflets. Later, from a normally functioning valve, the marker positions were recorded on videotape during fluoroscopy, and the leaflet length was determined. I.eaftet length in the radial direction increased 31 % from systole to diastole. During diastole, leaflet length increased by 3.9 % as the pressure gradient increased from 60 to 200 mm Hg, During systole, the leaflet had a low elastic modulus. In vitro, the stress-strain properties of the leaflets were studied. For an increase in stress in vitro that corresponded to an increase in pressure gradient from 60 to 200 mm Hg, the leaflet length increased 8.7%. This increase was more than twice that measured in vivo, which indicates that during diastole the leaflet is much stiffer in vivo than in vitro. This stiffening appears to be due to stress in the circumferentiaUy oriented coUagen fibers of the leaflet, which prevents stretching in the radial direction. In systole, the lower elastic modulus reduces the flexion stresses, and in diastole, stiffening prevents the leaflet from prolapsing under pressure.
Mano J. Thubrikar, Ph.D., Jaafar Aouad, D.V.M., and Stanton P. Nolan, M.D.,
Charlottesville, Va.
firing each cardiac cycle, the opening and closing of the aortic valve causes the leaflets of the valve to undergo loading and unloading, reversal of their curvature, and a great deal of flexion in the region of the leaflet attachments. In this process, the leaflets are subjected to complex stresses and strains that are potentially damaging, yet the leaflets survive billions of cardiac cycles. To understand their remarkable durability, one must analyze their mechanics in vivo. We have measured and analyzed the changes in leaflet length in the radial direction and have integrated this information with our knowledge of the behavior of the leaflet in the circumferential direction. We have further compared the behavior of the leaflet in vivo and in vitro. Materials and methods The length of the aortic valve leaflet was measured in vivo by the marker-fluoroscopy technique developed in From the Department of Surgery, University of Virginia Medical Center, Charlottesville, Va. Received for publication May 13, 1985. Accepted for publication Aug. 8, 1985. Address for reprints: Mano J. Thubrikar, Ph.D., Box 263, Department of Surgery, University of Virginia Medical Center, Charlottesville, Va. 22908.
our laboratory and described previously.' The same leaflets were then studied in vitro for their stress-strain properties and the results of these two studies were compared. In 10 dogs 13 aortic valve leaflets were studied in vivo. For the implantation of radiopaque markers on the aortic valve, the dogs were placed on total cardiopulmonary bypass. The aorta was opened and the aortic valve exposed. Small platinum markers, 1 by I mm and weighing 10 mg, were then sutured to the leaflets in the desired positions. Most frequently, two markers were attached to a single leaflet, one at the base and the other near the line of coaptation, both in the radial direction of the leaflet. The distance between these two markers indicated the length of that segment of the leaflet. On six leaflets the markers were attached to the aortic side and on seven leaflets, to the ventricular side. This was done to explore whether there was any difference in the length change of the two surfaces of the leaflet. A third marker was placed on the free edge of the leaflet. Three additional markers were attached to the aortic wall at the valve commissures. The typical position of the six markers is depicted in Fig. I. Two leaflets were marked in each of three dogs. After marker placement, the aorta was repaired and cardiopulmonary bypass discontinued. The dogs were allowed to recover for at least 15 days 29
30
Thubrikar, Aouad, Nolan
The Journal of Thoracic and Cardiovascular Surgery
Fig. 1. Schematic drawing of the aortic valve showing placement of radiopaquemarkers. Markers A, B, and C wereplaced on the leafletin the radial direction. Markers D, E, and F were placedat the three commissures of the valve. Distance BC was used to determine the change in leaflet length in the loadbearing portion.
before study. They were studied several times, and intervals between any two studies ranged from 15 days to 2 months. During each study the dogs were anesthetized with pentobarbitol (25 mg/kg, intravenously) and subjected to roentgenography, The markers were visualized on a normally functioning valve, and the position of the markers was recorded on videotape during fluoroscopy. For the length of the leaflet to be measured, the leaflet had to be seen in a perfect side view. This was achieved by rotating the dog to superimpose the two commissural markers placed at two ends of the marked leaflet. Fig. 2 shows such a projection of the valve. The blood pressure in the ascending aorta was recorded simultaneously with the videotaping of leaflet motion. In some dogs ventricular pressure was recorded by passing the catheter across the aortic valve, Recordings were made at increased and decreased pressures, which were achieved by the intravenous infusion of angiotensin or nitroprusside, respectively. All pressure recordings were made with a pressure transducer (Statham P23 10) via a 7F fluid-filled catheter having side holes and an end hole. The recordings were repeated after the dog had been rotated 180 degrees on its spinal axis to allow for correction of any error that may occur by movement of the valve toward or away from the x-ray source during the cardiac cycle. I To correlate the videotape recording with the pressure recording, a separate electrical circuit was used that triggered a solenoid in the videofield and simultaneously activated an event marker on the pressure recording. Data were analyzed by displaying the videotape on a television screen in a stop-motion mode and recording the positions of the markers on acetate paper. The videotape was advanced one field at a time and the positions recorded. Since the rate of recording
Fig. 2. The two upperdrawings showa perfectside view of a marked leaflet when the aortic valve is closed (left) and open (right). In this view, two commissure markers D and E are superimposed. A, B, and C are the markers on the leaflet. The two lower photographs show the actual fluoroscopic images of the markerson the aortic valve of a dog that correspond to the views in the upper drawings.
was 60 videofields per second, we obtained 60 data points in I second. The data gathering was performed for at least three cardiac cycles at any given pressure. Videofields were deliberately ignored where the markers could not be seen clearly or where the commissure markers were not superimposed. The distance between the two leaflet markers was measured to determine the length of the leaflet during systole and diastole. For these studies, systole is defined as a time period when the valve is open, as indicated by the position of the leaflet marker, and diastole as a time period when the valve is closed, also as indicated by the position of the leaflet marker (Fig. 2). After the studies were completed, the dogs were killed and the leaflets excised. Nine leaflets were removed from six dogs for analysis in vitro. A rectangular strip in the radial direction of the leaflet was cut from each of the leaflets using parallel blades. Some strips contained the previously implanted markers and others had no markers. The thickness of each strip was measured with a micrometer equipped with an electrical circuit to produce a signal when the two tips of the micrometer contacted the opposing surfaces of the strip, The width and length of these strips were also measured. The strips were subjected to a uniaxial stress-strain experiment in an Instron tensiletesting machine. In these experiments, the strips were elongated at a rate of 5 mm/rnin, and the force
Volume 92 Number 1 July, 1986
Mechanical properties of aortic valve leaflets
31
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developed in them was recorded continuously. From the force-length relationship, an engineering stress-strain curve was obtained. Stress in the leaflet was determined based on the consideration that the leaflet is a thin cylindrical shell. Hence, stress in the radial direction = (PR/2t), where P isthe pressure gradient across the leaflet, R is the radius of the cylinder formed by the leaflet, and t is the thickness of the leaflet. The pressure gradient P was measured in vivo during fluoroscopy. Thickness twas measured in vitro. The radius R was also determined in vitroas follows. In four dogs the entire aortic valve was removed. A silicone rubber cast of the closed valve was made at an intra-aortic pressure of 80 to 100 mm Hg. The radius of the leaflet in diastole was measured from these casts. During the bypass operation on the dogs, during the multiple studies that followed, and when the dogs were killed, humane treatment was provided as set forth in the guidelines published by the National Institutes of Health.
Results In vivo, the leaflet length in the radial direction changed during each cardiac cycle (Fig. 3). The leaflet was shorter in systole and longer in diastole. The length did not change appreciably during systole or during diastole; the major change occurred during the transition between systole and diastole. This was true for all dogs and for all leaflets studied. Table I shows the change in leaflet length obtained from several studies on 13 leaflets from 10 dogs. The increase in leaflet length is expressed as follows: LD - Ls AL% = - - -
Ls
x 100%
Table I. Increase in the leaflet length (IlL %) from systole to diastole Dog No.
Leaflet
No. of studies
AL%
R R R R R R
3 8 4 9 6 6 2 5 5 6 2 6 2 8 4 10 7 6 2 3 5
31.1 35.9 30.7 25.9 56.7 23.8 58.6 24.0 19.8 30.5 17.6 33.9 15.6 16.2 20.6 24.2 36.8 44.9 19.2 58.9 21.2
2 3
L L 4
R R
N N 5 6 7 8 9 10 Mean ± SE
R R R R R
L L L R
30.8 ± 3
Legend: R. Leaflet corresponding (0 the right coronary aortic sinus. L. Leaflet corresponding to the left coronary aortic sinus. N. Leaflet corresponding to noncoronary aortic sinus. SE. Standard error.
where L, and L D represent the length in systole and in diastole, respectively. In Table I each value of &% represents an average of several cardiac cycles from multiple studies. The leaflet length increased by an average of 30.8% ± 3% (mean ± standard error). In determining this average, we used data not only from the control systemic pressure, but also from the pharma-
32
The Journal of Thoracic and Cardiovascular Surgery
Thubrikar, Aouad, No/an
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cologicaUy increased and decreased systemic pressures. There were no differences between the data obtained with markers on the aortic surface of the leaflet and the data obtained with markers on the ventricular surface. In exploring the effect of systemic pressure on changes in the leaflet length, we found that the increase in leaflet length remained constant as systemic pressure increased. Similar results, for three different leaflets from three dogs, are presented in Fig. 4. which shows that the increase in leaflet length does not change appreciably as the diastolic pressure is increased. Even more interesting results were seen when leaflet length was plotted against peak systolic pressure or pressure gradient. When systolic pressure was increased, systolic leaflet length either increased slightly or remained the same, perhaps because there was little or no increase in the pressure gradient across the leaflet (Fig. 5). This was true in all 12 studies on 10 leaflets of seven dogs. When the leaflet length was plotted against pressure gradient across the leaflet, a graph was obtained that essentially represented the stress-strain properties of the leaflet in vivo (Fig. 6). In diastole, the pressure gradient across the leaflet was measured as the difference between the aortic and ventricular pressures in mid-diastole. In systole, the pressure gradient across the leaflet, which is small and difficult to determine accurately, was not measured but was assumed to vary between 0 and 10 mm Hg. Usually it varies from 0 mm Hg to + 10 mm Hg to a negative value as reported in the literature.s ' Graphs like that shown in Fig. 6 were obtained from 12 studies on 10 leaflets of seven dogs and demonstrated a similar behavior of all leaflets. The graph (Fig. 6) indicates that, during systole, the leaflet
goes through a large change in length for a small change in pressure gradient, whereas, during diastole, the leaflet goes through a small change in length for a large change in pressure gradient. The leaflet, therefore, is in an "elastic phase" (less stiffness) in systole and in an "inelastic phase" (more stiffness) in diastole. The graph (Fig. 6) represents the overall behavior of the leaflet in vivo over a large range of systemic pressure, where the pressure across the leaflet varies from 0 mm Hg to more than 200 mm Hg. This overall behavior of the leaflet, however, may not be detected in individual cardiac cycles because the changes involved may be too small to measure. It is therefore not surprising that during a single cardiac cycle, the leaflet length change from systole to diastole was detected, but changes during systole or diastole were not (Fig. 3). In vivo, the pressure gradient across the leaflet represents stress on the leaflet and the change in the leaflet length represents strain. Therefore, Fig. 6 defines the segments of the stress-strain curve in which the leaflet functions during systole and diastole. Hence, a smooth curve was drawn through all the data points (Fig. 6) so that the curve characteristically resembled the stress-strain curve obtained in vitro (Fig. 7). In vitro, stress-strain curves were determined for nine leaflets from six dogs, and all of the curves showed a characteristic nonlinear behavior (Fig. 7). For the stress-strain curves obtained both in vivo and in vitro, we determined the stresses, strains, and moduli of elasticity in systole and diastole. We obtained an incremental modulus that was calculated from incremental stress and incremental strain. To obtain the stress in the leaflet in vivo, we considered the leaflet to
Volume 92
Mechanical properties of aortic valve leaflets 33
Number 1
July, 1986
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be a thin cylindrical shell. Our previous studies' and those of others' have shown that the leaflet is cylindrical in its load-bearing portion. Hence, stress in the radial direction of the leaflet (oR) is equal to (PR/2t). In systole, oR was determined for pressure gradients of 0 and 10 rom Hg. These two stresses were plotted on the stress-strain curve in vitro, and the corresponding strains 10 and 1 were determined (Fig. 7). In vivo, 10 and I represent the two limits of the length measurement in systole, wherein the minimum length corresponds to a pressure gradient of zero, and the maximum length corresponds to a pressure gradient of 10 mm Hg (Fig. 6). The incremental strain in systole is given by the equation: .6.L% = ES% =
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0
0
This is shown in Table II. The average incremental strain was 14.9% in vivo and 9.6% in vitro. Modulus of elasticity = (incremental stress/incremental strain) is also indicated in Table II. In diastole, oR was determined for pressure gradients of 60 mm Hg and 200 mm
Hg. These two stresses were plotted on the stress-strain
Fig. 6. Typical plot of leaflet length versus pressure gradient across the leaflet in vivo in a single dog. The circles represent measured leaflet length and measured pressure gradient in diastole. The bars represent measured leaflet length and assumed pressure gradient of 0 to 10 mm Hg in systole. The lengths I." I, I" and 12 correspond to the gradients of 0, 10, 60, and 200 mm Hg, respectively. Eo and ES represent strains. The origin (12,0) is arbitrarily chosen for convenience, since minimum leaflet length measured in this case was 13 mm during systole when the gradient was not measured.
curve and the corresponding strains II and 11 were determined from the curve. The incremental strain (Figs. 6 and 7) is given by the formula. .6.L% = Eo% =
1 -I,
2 -x
II
100%
The average incremental strain was 3.9% in vivo and 8.7% in vitro (Table 11). The modulus of elasticity is also indicated in Table II. It is worth emphasizing that the modulus of elasticity is normally determined only for unidirectional stress conditions, that is, in these studies for in vitro experiments; however, we have reported values obtained in vivo for a purpose of comparison. In these calculations, the radius of the leaflet was that measured in diastole and taken to be the same in systole, as had been observed in our previous experiments." Discussion In each cardiac cycle, the length of the leaflet in the radial direction increased by 30.8% from systole to
The Journal 01
3 4 Thubrikar, Aouad, Nolan
Thoracic and Cardiovascular Surgery
12
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Fig. 7. Typical engineering stress-strain curve of a single leaflet in the radial direction obtained under in vitro uniaxial loading conditions. Stresses corresponding to the pressure gradients of 0, 10, 60, and 200 mm Hg are shown; corresponding lengths 10 , I, II, and 12 are also indicated. fo and fs represent strains in diastole and in systole, respectively.
----- ------t
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Fig. 8. Schematic representation of the leaflet structure showing circumferentially oriented collagen cords as the dominant structural component. When the leaflet is pulled only radially, the collagen cords can separate and do not offer resistance to stretching. When the leaflet is pulled both radially and circumferentially, then tension in the collagen cords in the circumferential direction prevents them from separating. Consequently, they resist stretching in the radial direction.
diastole. Our previous studies? have shown that the leaflet length in the circumferential direction increased by 11.9% from systole to diastole (the same as a decrease of 10.6% from diastole to systole). This length change is large and could damage the leaflet by fatigue; however, it occurred in response to a change of the pressure gradient (stress) on the leaflet. It would appear either that the leaflet is less susceptible to fatigue failure or that the damage is reparable, since the length change occurs in normal valves, which survive for a hundred years. The advantages of length change are two: (I) The
leaflet functions in the low modulus region in systole, and this reduces flexion stresses on the leaflet," since flexion rigidity is proportional to elastic modulus X (thickness)'. (2) The leaflet is relaxed in systole and therefore not subjected to creep from constant stress. In other words, the leaflet minimizes flexion stresses and creep at the expense of fatigue. The strain of 30.8% in the leaflet in vivo can be compared with strains measured in vitro by others. Clark? measured transition strains of 24% ± 8% in human leaflets, and his results agree fairly well with those reported here. Transition strain is the strain at which transition from low modulus to high modulus takes place, that is, where the "knee" in the stress-strain curve occurs. Although we did not determine transition strains in vitro, they were close to 30%, as may be noted from Fig. 7. Strains in excess of 70% in fresh porcine aortic leaflets were reported by Broom and Christie, 10 but they are higher than those observed in the present study. The reason may be that porcine leaflets show higher strains than do canine leaflets. Also, our measurements were made in vivo and theirs in vitro under uniaxial loading conditions. Missirlis and Chong " measured strains in the radial direction of the leaflets of fresh porcine aortic valves in vitro. In these experiments, the closed valve was subjected to increasing pressure, and measurements were made locally in various parts of the leaflets. They reported strains ranging from 10% in some areas to 100% in others; the strains increased from the base of the leaflet to the coaptation edge. In an
Volume 92 Number 1
Mechanical properties of aortic valve leaflets
July, 1986
35
Table II. Strains in the leaflet in the radial direction Diastole (60-200 mm Hg) DogNo.
Leaflet
ilL% in vivo
1 2 3
R R
6.2 4.4 2.0 4.0 1.9 I.7 7.9 3.4 0.7 1.9 8.2
4
5 6 7
R R L R R N R
R R L L N
I
ilL % in vitro
Systole (0-10 mm Hg)
ilL% in vivo
11.5
I
ilL % in vitro
13.0
9.2 9.7
9.0
10.0
7.2
8.7
5.6 5.8 6.0 9.7 9.1
25.0 15.0 24.0 12.5 17.0
8.2 8.6 9.0
13.7 8.0
4.3 9.6 13.6
11.0
8.8
Mean ± SD
3.9 ± 2.5
8.7 ± 2.5
14.9 ± 6
Modulus of elasticity (dynes/em')
24.4 X 10'
11.6 X 10'
0.50
x 10'
9.6 ± 1.8 0.75
x 10'
For legend see Table I. SD, Standard deviation.
"inelastic phase" (i.e., in diastole), their data and ours are comparable. There have been other studies that investigated pressure deformation behavior of the leaflets invitro," 13 and there have been studies in vivo of length change in the circumferential direction of the leaflet ' 4, 15; however, there are no reported in vivo studies in the radial direction of the leaflet for comparison to our results. The observation that the length change does not vary with systemic pressure (Fig. 4) is interesting, because we? had found the same results for the leaflet in the circumferential direction. In determining the stresses in the leaflet, we used an approximation of a thin cylindrical shell under pressure. Such an approximation is valid for the leafletwhere R/t Is 25 or more. This approach was used successfully in our previous analysis." The modulus of elasticityin vitro was 118 gm/mm' in the post-transition state and 7 gm/mm 2 in the pretransition state. Clark? reported values for human leaflets to be 174 gm/rnm- and 1.13 gm/mm2, which compare favorably with ours, considering that our values are for large incrementsof stress and theirs are for small. Comparison of strains in vivo and in vitro. In systole, the incremental strains in vivo were 14.9% and b in vitro were 9.6%, for an increase in pressure gradient of10mm Hg (Table 11). Since some amount of leaflet folding can occur in systole, the length change is most likely exaggerated in that phase. As can be seen from Fig. 6,only one reading underestimatingthe leaflet
length will result in overestimation of strain. In vivo the leaflet is under biaxial load and in vitro it is under uniaxial load; therefore, the leaflet is not likely to be longer in vivo than in vitro. For these reasons,we believe that the true strains in vivo are quite close to those observed in vitro. In diastole, the incremental strains in vivo were 3.9% and those in vitro were 8.7%, for an increase of the pressure gradient of 140 mm Hg (the difference between 200 and 60 mm Hg). Since the leaflet does not fold in the load-bearing portion in diastole, these measurements are accurate. They suggest that the leaflet is much more stretchable in vitro than in vivo. This is an important observation, because several studies performed in vitro have implied that the results can be extrapolated to in vivo performance. Broom's and Christie's report,'? for example, showed 70% strains in porcine leaflets in vitro. Such high strains in vivo are unlikely even in porcine leaflets, because if they did occur, the leaflets would prolapse into the ventricle, and the valve would be incompetent. The reasons that strains are lower in vivo can be seen from Fig. 8. In vitro, when force is applied in the radial direction, it stretches the leaflet with little resistance. In vivo, when force is present in both the circumferential and radial directions of the leaflet, then the circumferential stress in the collagen cords of the leaflet prevents the cords from separating. In vivo, therefore, major resistance to excessive stretching in the radial direction comes from the stress in the circumferentialfibers. Broom and Christie'?
The Journal of
36
Thubrikar, Aouad, Nolan
mentioned that the major leaflet strength in the radial direction comes from the radially oriented collagen and elastin fibers, and that the circumferentially oriented fibrosa does not play a significant role. Our in vivo observations indicate that it is the fibrosa that prevents excessive radial stretching of the leaflet. This observation further indicates that the interaction between the circumferential and radial forces on the leaflet is important for maintaining its longevity. The absence of this interaction would cause the leaflet to deteriorate from excessive shear or cause leaflet prolapse from excessive stretching.
Conclusions Cyclic changes in aortic leaflet length are important for longevity, because they reduce flexion stress and creep in the leaflet. Stiffening of the leaflet in diastole from the interaction between the circumferential and radial forces is important for the prevention of leaflet prolapse. The absence of either of these phenomena, which may occur in bioprosthetic or congenitally malformed valves, will compromise the function of the valve. REFERENCES Thubrikar M, Harry R, Nolan SP: Normal aortic valve function in dogs. Am J Cardiol 40:563-568, 1977 2 Driscol TE, Eckstein RW: Systolic pressure gradients across the aortic valve and in the ascending aorta. Am J Physiol 209:557-563, 1965 3 McDonald A: Blood Flow in Arteries, Baltimore, 1974, The Williams & Wilkins Company, p 121 4 Thubrikar M, Piepgrass WC, Shaner TW, Nolan SP: The
Thoracic and Cardiovascular Surgery
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6
7
8 9
IO
11
12 13
14
15
design of the normal aortic valve. Am J Physiol 241:H795-H801, 1981 Swanson WM, Clark RE: Dimensions and geometric relationships of the human aortic valve as a function of pressure. Circ Res 35:871-882, 1974 Thubrikar M, Piepgrass WC, Deck JD, Nolan SP: Stresses of natural vs prosthetic aortic valve leaflets in vivo. Ann Thorac Surg 30:230-239, 1980 Thubrikar M, Piepgrass WC, Bosher LP, Nolan SP: The elastic modulus of canine aortic valve leaflets in vivoand in vitro. Circ Res 47:792-800, 1980 Harvey JF: Theory and design of modern pressure vessels. New York, 1974, von Nostrand Reinhold, p 95 Clark RE: Stress-strain characteristics of fresh and frozen human aortic and mitral leaflets and chordae tendineae. J THoRAc CARDIOVASC SURG 66:202-208, 1973 Broom NO, Christie GW: The structure/function relationship of fresh and glutaraldehyde-fixed aortic valve leaflets, Cardiac Bioprostheses: Proceedings of the Second International Symposium, LH Cohn, V Gallucci, OOs., New York, 1982, Yorke Medical Books, pp 476-491 Missirlis YF, Chong M: Aortic valve mechanics-Part I: Material properties of natural porcine aortic valves. J Bioenerg Biomembr 2:287-300, 1978 Wright JEC, Ng YL: Elasticity of human aortic valve cusps. Cardiovasc Res 8:384-390, 1974 Broom NO: The observation of collagen and elastin structures in wet whole mounts of pulmonary and aortic leaflets. J THORAC CARDIOVASC SURG 75:121-130, 1978 Brewer RJ, Mentzer RM, Deck JD, Ritter RC, Trefil JS, Nolan SP: An in vivo study of the dimensional changes of the aortic valve leaflets during the cardiac cycle. J THoRAe CARDIOVASC SURG 74:645-650, 1977 Brewer RJ, Deck JD, Capati B, Nolan SP: The dynamic aortic root. J THoRAc CARDIOVASC SURG 72:413-417, 1976