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J Thorac Cardiovasc Surg 2000;119:753-762
© 2000 The American Association for Thoracic Surgery
SURGERY FOR ACQUIRED CARDIOVASCULAR DISEASE |
From the Department of Biomedical Engineering, Cleveland Clinic Foundation, Cleveland, Ohioa; Division of Cardiothoracic Surgery, University of Wisconsin, Madison, Wisb; and Department of Mechanical Engineering, University of Washington, Seattle, Wash.c
Supported by the Whitaker Foundation and the National Partnership for Advanced Computational Infrastructure.
Address for reprints: Karyn S. Kunzelman, PhD, University of Wisconsin, CSC H4/368, 600 Highland Ave, Madison, WI 53792-3236 (E-mail: karynk{at}surgery.wisc.edu ).
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Abstract |
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Introduction |
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1,2 or above the leaflet attachments. 3,4 The goal of these procedures is to preserve the native valve, avoid life-long anticoagulation, and restore normal valve function by recreating the normal anatomic root environment.
Although early and midterm results of such procedures have been reported favorably, 4 true long-term results are not yet available; thus the durability of these procedures is not known. This durability is likely dependent on the stress state of the aortic valve leaflets and their ability to function normally within the artificial root environment. Because the compliant tissue properties and rounded shape of the native aortic root promote the normal function of valve, 5,6 root replacement with a cylindrically shaped and relatively stiffer 7 polyester graft would affect the resulting levels of stress and strain in the spared aortic valve leaflets. Furthermore, we suspect that the combined function of the native valve and the root graft may be different from the combined function of the native valve and the normal root.
Although the theoretical advantages and disadvantages of differing valve-sparing procedures have been examined, 8 no systematic study of the resulting influence on the stresses of the spared valve has yet been conducted. To perform such a study, we have developed a fully 3-dimensional, anatomically realistic finite element mathematical model of the aortic root and valve. As opposed to prior finite element models of the aortic valve, 9,10 our model does not presume any a priori symmetry, and it includes the root walls with their sinuses of Valsalva and their respective coronary ostia. The objective of this investigation was to model and evaluate three potential surgical options for restoring valve competence via aortic root replacement by analyzing the functional and closing characteristics of the simulated spared aortic valve.
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Methods |
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1 The second model (tailored) simulated a "neo-sinus" procedure (Fig 2) in which the graft was tailored and sutured above the leaflet attachments, 3,4 with the potential for sinus accommodation. The third model (pseudosinus) simulated a procedure (Fig 3) in which the graft was "scalloped" and then sutured in a plane below the anulus, 2 so that the resulting bulging of the graft recreated the sinuses. The results of these models were compared to that of our normal model of the aortic root and valve. The primary methods have been described in detail previously 11 and are summarized here.
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12
Our finite element model was developed with the use of ANSYS software (version 5.3, ANSYS Inc, Canonsburg, Pa) run on a DEC Alphastation 400 4/233 workstation (Digital Equipment Corporation, Maynard, Mass). Magnetic resonance imaging of normal human aortic valve and root specimens was used to establish the geometry for the model. Because assemblies of triangular shell elements are well suited to reproduce curved geometries, we selected the six-noded triangular shell element to take advantage of its capacity for linearly varying stress and strain. 12 Preliminary benchmark models (simple structural analysis problems in which the solution is known) using these same elements at the same density as in our root/valve model had stresses, strains, and displacements with a numerical accuracy within less than 0.5%. We created 5000 elements to represent the aortic root and 1815 elements for the three valve leaflets.
Element thicknesses and material properties
The normal aortic root thickness values were measured directly from the magnetic resonance images of the root wall. The thicknesses of the unpressurized valve leaflets were determined from published data. 13,14 The anisotropic material properties of both tissues were also calculated from published stress-strain data, 15-17 including a Poisson ratio of 0.45 to account for tissue incompressibility. 18 To represent the pliability of the aortic valve leaflets, 19 the bending stiffness of the shell elements in the valve was reduced by 98.5% (method detailed previously in an appendix 11). The polyester material (polyethylene terephthalate) was assumed to be isotropic with a Poisson ratio of 0.3, 20 an elastic modulus of 7840 kPa (based on the range of stiffnesses reported in the literature 21-23), fabric thickness 24 of 0.305 mm, and a crimp angle of 40°.
Modifications for graft models
Each graft model required modification of our established model, 11 which incorporates normal aortic root shape and element properties. First, the cylindrical graft model was created by removing the root elements located above the valve attachment edge from the normal root geometry, then simulating a 24-mm diameter graft cylinder with inclusion of the remnant aortic wall (Fig 4, a and b ). The effective material properties of a crimped, woven polyester graft were assigned to the cylinder. In the areas where the remnant aortic wall was present within the graft (in yellow, Fig 4, b ), the elements were assigned material properties of the combined graft and aortic wall.
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, c and d ) in an edge-to-edge fashion. Thus, in remnant aortic wall areas (in yellow, Fig 4, d ), the elements were assigned material properties of the aortic wall alone.
Finally, to represent the sinus shape that would optimally be attained by a pseudosinus model, the same root elements were again removed and replaced by a polyester cylinder above the sinotubular junction (Fig 4, e and f ). Below the sinotubular junction, sinus-shaped polyester root walls were simulated, with inclusion of the remnant aortic wall. The elements representing the remnant aortic wall within the graft (in yellow, Fig 4, f ) were assigned material properties of the combined graft and aortic wall. The curved shape of the sinus walls in the model is described by the following logistic function:
To simulate the anastomosis of the coronary ostia "buttons" to the root graft, we repositioned the right and left coronary ostia at the center of their respective sinuses. In addition, the thickness and stiffness of the graft were added to the ostia elements closest to the root to simulate the suturing of the ostial button to the graft.
Boundary conditions
Geometric boundary constraints were assigned to all models in exactly the same manner. First, contact elements were incorporated into the coapting leaflet surface to allow for the free sliding of leaflet surfaces and to prevent the leaflets from passing through each other or through the root wall. Second, the lowest layer of the aortic root base was restricted to in-plane displacement. Third, the physiologic longitudinal stretch found normally in the aorta and other arteries 25 was imposed by applying a tension boundary condition at the top of the simulated ascending aorta and at the distal ends of the coronary ostia.
Pressure loading pattern
To model the early diastolic loading of the aortic valve and root/graft, we applied simulated physiologic pressures to the valve and root/graft structure in two phases. In the first phase, the aortic root (or root graft) alone was pressurized in a linearly increasing manner until it reached the end-systolic aortic pressure level. In the second phase, physiologic pressures were applied to the aortic valve, to the root or root graft, and to the region of the root underneath the valve. These pressures were calculated from aortic and left ventricular pressures and an assumed average negative chest pressure of 5 mm Hg. Loading started at end-systole, just after valve closure, and finished at the end of left ventricular isovolumic relaxation, when peak pressure across the valve was reached.
Solution method
The models were solved on the DEC Alphastation workstation or on the Cray J90 supercomputer system (Silicon Graphics, Inc, Mountain View, Calif) at the Texas Advanced Computing Center. The solution was performed iteratively by dividing the pressure loading phases into a number of equal steps (81 aortic root preliminary steps + 118 physiologic root/valve steps = 199 total).
Output analysis
Stress and strain in the valve and root or root graft were examined at the end of physiologic loading. (Stress [
] is defined as the force [F] applied to the tissue divided by cross-sectional area [A], ie, = F/A. Strain [
] is defined as percent extension of the tissue, ie, = 
L/Lo, where L is change in length and Lo is original length.) For both the leaflets and root sinuses, the magnitude and location of the principal tensile stresses and strains were recorded. Regional magnitudes were calculated by grouping sets of elements to define specific model components (belly, coaptation area, free margin, attachment edge, annular sinus wall, sinotubular junction sinus wall) and then analyzing those components to determine the average, standard deviation, maximum, and minimum values. In addition, the "peak average" was calculated, which was the average value of the 5% of elements with the highest values (the peak standard deviation was calculated similarly). The coaptation area, defined as the percentage of leaflet area contacting the adjacent leaflet surfaces, was also examined throughout the preliminary root loading and subsequent physiologic root/valve loading phases. The stress and strain results were compared by means of analysis of variance to determine significant differences with respect to the graft type.
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Results |
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An analysis of average directional strains in these graft model leaflets demonstrated that the valve was displaced downward toward the left ventricular outflow tract to a greater extent than in the normal model. In all the graft models, there was much less leaflet strain in the radial direction than in the longitudinal direction, with radial/longitudinal strain ratios of 0.29:1, 0.18:1, and 0.29:1, respectively, in the cylindrical, tailored, and pseudosinus models. This situation is opposite that found in the normal root model, in which there was more leaflet radial strain than longitudinal strain, with a ratio of 1.94:1.
Graft stress and strain
For all models, the grafts maintained their approximate original shapes even at the peak aortic pressure (as shown in Fig 5). In the cylindrical graft model, the graft had 1081% higher stress (P = .0001) and 86% lower strains (P = .0001) as compared with the normal aortic root (Fig 8). In the tailored graft model, the graft had 517% higher stress (P = .0001) and 90% lower strain (P = .0001). The pseudosinus graft had 191% higher stress (P = .0001) and 96% lower strain (P = .0001).
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Discussion |
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11 First, we chose to model only the rapid final closing phase of the valve leaflets, as tensile stresses are highest during this period. Second, the model material properties were assumed to be constant in the physiologic range of the stress-strain curve. This choice was partly software-dependent: ANSYS finite element software does not permit both anisotropic and nonlinear material behavior. Therefore the stress and strain results in the model may be lower than in the actual tissues. However, we are simulating diastolic function only, where the valve and aortic tissue has been reported to function in the linear, higher stiffness region of its stress-strain function. 15,26 Third, the stress analysis was based on the assumption that the zero-pressure state in the root and valve at the start of model solution was equivalent to a zero-stress state. Because of residual stresses caused by the differential makeup of the valve and aortic wall layers 17,27 and dynamic motion throughout the cardiac cycle, a zero-stress state may not exist in vivo. We assumed that the magnitude of these residual stresses would be negligible in comparison with the valve and root stresses at peak valve pressure. Fourth, a small-deformation analysis, rather than large-deformation analysis, was used. Our rationale for this approach was that the applied simulated pressures did not lead to significant changes in the model geometry. We therefore assumed that any incrementally increased deformations that could be gained from a large deformation analysis would not be large enough to justify the extra computational burden. Despite these limitations, the different graft models used identical physiologic loading conditions; only specific material properties and root geometry were altered. Therefore comparison between models provides a relative estimate of the stress and strain differences that could be expected in vivo due to aortic root replacement with a vascular graft.
Graft influence on leaflet stress, strain, and coaptation
All three graft models altered the normal stress, strain, and coaptation patterns as compared with the normal model. In the cylindrical model, diastolic leaflet stresses and strains were predominantly increased at the attachment edge and belly, the two leaflet regions closest to the graft. These regions are already subject to high bending and flexural stresses during leaflet opening, 26 and further increases in stress during closure could be damaging. Stresses in the leaflet coaptation area and free margins were less affected because of the increased leaflet coaptation, which provided those regions with compressive stress relief. However, this increased coaptation is a result of the simulated valve functioning within a smaller space than normal (the stiff polyester graft). The resultant potential for leaflet folding and buckling would likely cause leaflet damage in the clinical setting and may significantly reduce the durability of the procedure. The incremental improvement in leaflet stresses, strain, and coaptation in the tailored graft model as compared with the original cylindrical model is related to the graft having been "trimmed" to have a simulated attachment above the crown-shaped valve anulus. The lack of circumferential restriction around the remaining aortic root provided an increased freedom of movement at the commissures. The pseudosinus graft model resulted in the lowest stress levels in the valve and sinus walls of all the graft models. Although leaflet stresses were still increased at the attachment edge, the relatively normal stresses in the central leaflet areas in this graft model reflect the more normal coaptation as a result of the narrowed upper sinus diameter. Overall, these models suggest that although selected graft tailoring styles may perform relatively better than the original cylindrical graft, the rounded shape of the root wall (as created by the pseudosinus graft procedure) is more suitable to share the pressure-induced load with the leaflets than the cylindrical or tailored graft.
Graft influence on root-valve relationship
These changes in leaflet stress, strain, and coaptation indicate a departure from the normal aortic root–valve relationship, in that the definitive shape of the valve-root sinus functional unit has been changed. As described by Thubrikar and associates 5 each leaflet and corresponding sinus wall comprise a cylindrically shaped functional "unit" with continuity between the leaflets and root to distribute the diastolic pressure load. In this manner, the aortic valve transfers the high attachment edge stresses from the leaflet to the lower-stiffness root wall. This stress transfer appeared to be reversed in the graft models, where high stresses in the grafts were transferred to the valve, thereby increasing the overall leaflet stresses. Additionally, the functional unit represented by the sinus wall and leaflet together in these models was not cylindrically shaped (Fig 9). The changes to the root-valve relationship in the pseudosinus model were not as pronounced as that in the cylindrical and tailored models.
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16,28 concern has been expressed that the use of this material might transfer high stresses to the spared aortic valve, perhaps reducing the durability of a surgical valve repair. In our finite element models of valve sparing, the woven polyester graft did not fully restore the normal aortic valve environment. However, optimization of vascular graft design involves a greater number of variables than simply shape and material properties (ie, biocompatibility considerations). Future finite element modeling may provide additional evaluation of alternative material choices and may contribute to the eventual design of a "mechanically biocompatible" aortic root graft. |
Conclusion |
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Footnotes |
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References |
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P = .0005 indicate significant difference as compared with the normal root model. b, Schematics of altered leaflet stress patterns in the graft models as compared with normal.
