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Ann Thorac Surg 2004;77:844-851
© 2004 The Society of Thoracic Surgeons
a Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India
b Department of Cardiothoracic Surgery, Ramachandra Medical College, Chennai, India
Accepted for publication June 23, 2003.
* Address reprint requests to Dr Balakrishnan, Department of Cardiothoracic Surgery, Ramachandra Medical College, Porur, Chennai–600 116, India
e-mail: cvskrb{at}giasmd01.vsnl.net.in
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Abstract |
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METHODS: A dynamic, finite element model with time varying pressure was used in this study. Shell elements with linear elastic properties for the leaflet and root were used. Two different cases were analyzed: (1) normal leaflets inside a compliant root, and (2) normal leaflets inside a stiff root.
RESULTS: A compliant aortic root contributes substantially to the smooth and symmetrical leaflet opening with minimal gradients. In contrast, the leaflet opening inside a stiff root is delayed, asymmetric, and wrinkled. However, this wrinkling is not associated with increased leaflet stresses. In compliant roots, the effective valve orifice area can substantially increase because of increased root pressure and transvalvular gradients. In stiff roots this effect is strikingly absent.
CONCLUSIONS: A compliant aortic root contributes substantially to smooth and symmetrical leaflet opening with minimal gradients. The compliance also contributes much to the ability of the normal aortic valve to increase its effective valve orifice in response to physiologic demands of exercise. This effect is strikingly absent in stiff roots.
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Introduction |
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TopAbstractIntroductionMaterial and methodsResultsCommentConclusionsReferences |
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Material and methods |
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TopAbstractIntroductionMaterial and methodsResultsCommentConclusionsReferences |
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The surface model generated was used to develop a finite element model using shell elements with four nodes. A total of 5,600 elements and 5,870 nodes were used in this study. Mesh quality checks were done to ensure minimum warping and distortions. No symmetry was exploited as was done in the previous analysis [3], because of the nature of analysis, which is dynamic in the current case. Contact conditions were defined between the leaflets, and also between the leaflets and the root. The analysis is geometric and nonlinear due to the large displacements of the leaflets.
As pointed out in [3], one of the major issues in the analysis of the valve is the definition of the stress-free state. In most of the other studies on the aortic valve, the closed position of the valve was taken as the standard stress-free state [4, 5]. These models are static; the analysis started from the closed position and an equilibrium position determined for the diastolic pressure. In this model, starting from the open position, a ramp of 100 mm Hg is applied to close the valve, followed by the application of the pressure cycle in the aortic and ventricular side. A typical pressure–time relationship used in this work is shown in Figure 2b. The surfaces formed in the model are classified as a part of the ventricle, aorta, or the leaflet. The three pressure–time relationship used for these surfaces are shown in this figure.
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A linear elastic material was used in this study. The material model may not mimic the material behavior accurately, but the main purpose of this work is to study the effect of leaflet thickness, root and sinus thickness, and their stiffness on the aortic valve performance. The model acts as a base to vary the properties. Basically two conditions were considered. The first condition was a normal valve with a leaflet thickness of 0.6 mm and a Young's Modulus of 1 Mpa and root and sinus modulus of 2 Mpa [3]. The second condition considered was a normal leaflet in a stiff root of 10 Mpa. A normal leaflet in a stiff root, as may happen in valve sparing root replacements or stented valves was thus mimicked. The Poisson's ratio was maintained at 0.45 to mimic near incompressibility conditions. The model was fixed at the upper end and lower end.
The analysis was performed in ABAQUS/EXPLICIT code (Hibbit, Karlsson and Sorensen Inc, Pawtucket, RI). Because the code uses a reduced integration procedure, hour-glassing is a serious issue. Hour-glass control was applied, and the artificial strain energy was monitored to ensure that this remains low.
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Results |
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Opening and closing of leaflet
Figure 1 shows the opening and closing of the aortic leaflets inside a normal and a stiff root. The frames are captured in the same phase of one cardiac cycle. As can be seen from the figures, the opening and closing of the leaflets inside a normal root is smooth and symmetrical. On the other hand, inside a stiff root the leaflet opening tends to be asymmetric with considerable wrinkling. Both these phenomena are a consequence of the effect of aortic root compliance on the leaflet opening as explained below.
In a normally compliant root, aortic root dilatation precedes and, in fact, aids in the opening of the leaflets [3, 7]. This aortic root dilatation pulls the closed leaflets apart, reducing the frictional forces at the commissure. A minimal pressure gradient of 
2 mm Hg is then enough to spring open the closed aortic valve. Inside a stiff root this "pull-release" mechanism is absent, which is graphically shown in Figure 2. Figure 2 tracks the displacement of a point in the commissure (referred to as root node displacement) and nodule of Arantius (referred to as leaf node displacement) with time. As can be seen, aortic root dilatation, seen as commissural displacement, precedes the separation of the aortic leaflets. By the time the aortic leaflet separation starts at point "A," the root dilatation is about 65% of its final diameter. This aortic leaflet separation point is clearly before a gradient between the left ventricle and the aorta is achieved and the slope of the curve rises sharply until a maximum displacement is reached at point "B" at which the aortic opening is circular (Fig 3a). This is followed by a drop to point "C" at which the opening of the aortic valve becomes more triangular (Fig 3b). The corresponding echocardiogram figures clearly bring out this phenomenon and are shown in Figure 2. Finally, the valve returns to the closed position at point "D." To understand this phenomenon, we need to look at the graph of commissural displacement signifying aortic root dilatation. As can be seen, the commissures continue to separate and the root continues to expand until position "F" though the pressure in the aorta has started to drop. This is due to the velocity of the commissure, which does not change directions immediately with the drop in aortic pressure, and consequently it continues an outward motion. As a result of this phenomenon, compared to position "B," the aortic root continues to dilate and straightens the free edge of the leaflets to assume a final triangular shape at "C," incidentally decreasing the final EVOA as compared with a circular orifice at position "B." Interestingly similar experimental observations have been made by other investigators [1].
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Therefore, the leaflets inside a stiff root show a lot of inertia and begin to open later (almost lazily), and they are also asymmetric in their opening. The wrinkling of the leaflets inside a stiff aortic root is due to the absence of aortic root dilatation, which is therefore unable to accommodate the excess slack of the free edge of the leaflets, as in a normal, compliant root, which experiences a tensile pull and expands in systole.
Aortic valve area in normal and stiff root
The contribution of aortic root compliance to the final EVOA was also examined in this study. In this work, the EVOA is defined as the projected area available for blood flow. The area is calculated by projecting the opening perpendicular to the aorta. The figure is captured and the area is calculated in terms of pixel area. Calibration of the pixel area is carried out with the known area of the undeformed root. Aortic root area is defined as the area confined by the aortic annulus without the leaflets.
The effect of two measurements, namely, the aortic pressure and the gradient across the leaflet on the valve orifice area were studied. First, the effect of increasing root pressure on the aortic root area was studied (Fig 4). As can be expected in a compliant root, the root area increases with pressure compared with a stiff root in which the root area remains constant.
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2 mm Hg inside a compliant root, the pull of aortic root dilatation straightens the free edges of the aortic leaflet. As a consequence, the valve opening is triangular (Fig 3b) and a gap may be noted between the aortic wall and the body of the leaflet (Fig 7a). This triangulation of the valve orifice through an inward movement of the leaflet compensates for the increase in root area leading to an unchanged EVOA, regardless of the aortic root pressure as long as the gradient is 2 mm Hg.
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Comment |
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TopAbstractIntroductionMaterial and methodsResultsCommentConclusionsReferences |
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Though there are several methods of studying aortic valve function, such as animal studies [8] and work bench situations [9], finite element modeling was used in this study as it provides parametric "what if" testing rather easily. Also the observed phenomenon can very clearly be explained using this technique. In this work, the objective was to investigate the effect of a compliant versus stiff aortic root on two main phenomena: (1) the effect of root compliance on leaflet opening and closing, and (2) the effect of root compliance on EVOA.
There has been a lot of debate in the surgical literature on the importance of a compliant aortic root, and it is obvious from several studies [4, 5] that in a normal compliant aortic root, root dilatation preceeds leaflet opening and may in fact aid it by a "pull-release" mechanism. It has been shown here that a compliant aortic root aids considerably in leaflet opening, resulting in a smooth and symmetrical orifice that assumes a characteristic triangular shape, which is commonly seen in short axis cuts of the aortic valve on echocardiograms.
In contrast, inside a stiff root the leaflet opening is delayed, it shows a lot of inertia, and it is wrinkled and asymmetric. It is also unaided by aortic root dilatation. Robicsek and Thubrikar [9], using a work bench model of the aortic root, demonstrated fundamental differences in the way the leaflets opened and closed in normal and stiff roots. The smooth and symmetric opening of the leaflets inside a normal root, and the wrinkled, asymmetric opening of the leaflets in a stiff root were well brought out in this article, and they appear to be very similar to the results presented in Figure 1. They have speculated that the wrinkling of the leaflets inside a stiff root would increase the leaflet stresses and may in fact be responsible for their eventual calcification. There seems to be no significant increase in the maximum principal stresses (tensile stress) in the leaflets due to wrinkling, as depicted in Figure 8. This figure represents the maximum total stress (including bending and membrane for compression and tension) across the section of the leaflet. There are, however, larger regions in the leaflets inside the stiff root, where the compressive stresses (minimum principle stresses) are higher (Fig 8c and 8d). A detailed stress analysis will be reported in a future publication.
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The second major phenomenon studied in this work is the effect of a stiff versus a compliant root on EVOA. As expected, the aortic ring area increases in a linear fashion in a compliant root compared to a stiff root. However, surprisingly, this did not translate into higher EVOA in a compliant root with higher blood pressures alone. In fact, across a range of blood pressures, the EVOA is constant in both compliant and stiff roots for a gradient of 2 mm Hg. The EVOA increases inside a compliant root only when small gradients of up to 8 mm Hg are introduced. This increase, of about 25%, is one of the most important findings of this study. This is strikingly absent in stiff roots.
Stiff roots seem to function at the maximum level of efficiency and do not seem capable of increasing the valve area by any mechanism. A several fold increase in cardiac output is seen in many physiologic situations (eg, in marathon runners and race horses), and it is obvious that the normal aortic valve needs to cope with this increase in output without being obstructive; a compliant aortic root makes this possible. It is also evident that though the valve area increases with increasing gradient, the slope seems to become flatter as the transvalvular gradient approaches 8 mm Hg, because at increased gradients the leaflet bends backwards and moves further toward the aortic wall, as far as it can go. In published studies of healthy volunteers during exercise, peak gradients across a normal aortic valve have been in the range of 6 to 10 mm Hg [11]. Therefore, the effect of transvalvular gradients up to 8 mm Hg on the EVOA was studied. It is obvious from this study that a small gradient of 8 mm Hg helps increase the EVOA by pushing and bending the leaflets towards the aortic wall. Higashidate and colleagues [12] have made real time measurements of EVOA using the principle of electromagnetic induction. Interestingly, the aortic valve orifice area is measured very similarly to that obtained in the present work. The initial slow increase even before a significant increase in aortic pressure, followed by a rapid increase in the area, and a slow decrease followed by rapid closure were observed by this group in anesthetized dogs.
Granted that a compliant aortic root aids in leaflet opening, resulting in a smooth and symmetric aortic orifice, and in contrast, a stiff root has a leaflet that opens late, is asymmetric, and is wrinkled. But what harm does this do? This is unclear. Further investigations are required to understand the damage to the leaflet if any due to wrinkling. It has been speculated that the stresses in a wrinkled leaflet inside a stiff root may be high, and in fact, a hypothesis on calcification of these leaflets has been proposed [7]. The current study showed larger regions of higher compressive stresses in a wrinkled leaflet inside a stiff root than the leaflets inside a normal root, but no difference in the tensile stresses. However, further investigations are required to determine the effect, if any, of such stresses and wrinkling.
This work uses a dynamic model to study wrinkling and is fundamentally different from many other studies based on static analysis. A dynamic model of the aortic valve used here is a more physiologic way of looking at the valve function. All the models used so far to carry out a detailed stress analysis are static in nature. This means that the stresses are determined by applying maximum leaflet pressure on a closed valve. The pressure is not varied with time; hence the valves are not made to open and close as is done in this study.
When the EVOA is compared between compliant and stiff roots; it is clearly an advantage to have a compliant root as the valve area can increase substantially with increasing root pressure and gradient. This advantage is strikingly absent in stiff roots. However, under normal resting conditions, the EVOA inside a stiff and compliant root is not very different, and in fact, inside a stiff root it may be slightly higher because of the absence of triangulation of the orifice.
The best hemodynamics in terms of gradients and valve areas during exercise are in normal aortic valves, pulmonary autografts, and cryopreserved homografts, followed by stentless valves (in that order) [12]. The least efficient valves in terms of exercise gradients are stented valves [13]. The reasons are obvious from this study.
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Conclusions |
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References |
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