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Ann Thorac Surg 2005;79:1268-1275
© 2005 The Society of Thoracic Surgeons
a Cardiac Surgery Division, IRCCS San Raffaele Hospital, Milan, Italy
b Politecnico di Milano, Bioengineering Department, Milan, Italy
Accepted for publication April 5, 2004.
* Address reprint requests to Dr Maisano, Cardiochirurgia, Ospedale San Raffaele, Via Olgettina 60, 20132, Milan, Italy
francesco.maisano{at}hsr.it
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Abstract |
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METHODS: Using finite element model simulations, we tested valve competence after the implantation of conventional D-shaped versus dog bone–shaped annuloplasty rings, the latter of which was designed to selectively reduce the septolateral dimension of the annulus. Three models were compared: model A, simulating the native mitral valve; model B, simulating the same valve after annuloplasty with a conventional D-shaped annuloplasty; and model C, simulating a dog-bone annuloplasty ring implantation. Each model was then challenged by progressively pulling the tip of the papillary muscles away from the annulus plane to simulate ventricular remodeling and leaflet tethering. Valve competence was compared in each model for each degree of leaflet tethering.
RESULTS: After maximal leaflet tethering simulation (4-mm apical displacement of the papillary tips), the regurgitant area increase was 70.4 mm2 for model A and 52.9 mm2 for model B. In model C, the regurgitant area was only negligibly affected by papillary displacement, increasing to 3.9 mm2.
CONCLUSIONS: An annular prosthesis with selective reduction in the septolateral dimension is more effective than a conventional prosthesis for treating leaflet tethering in functional mitral regurgitation. Use of disease-specific annular prostheses is needed to improve the results of valve reconstruction.
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Introduction |
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TopAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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| Drs Maisano, Redaelli, and Alfieri disclose that they have a financial relationship with Edwards Lifesciences.
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My colleagues and I hypothesized that the use of a specifically designed annular prosthesis with a modified shape could improve the capability of annuloplasty to force coaptation in the presence of leaflet tethering and apical displacement of the mitral leaflets. More specifically, we designed an annular prosthesis with a deep reduction in the anteroposterior dimension (corresponding to the septolateral dimension of the native annulus) by creating an indentation in the middle portion of the posterior and anterior curvature of the annular prosthesis.
To test this hypothesis, we used the computational tools of structural mechanics to evaluate the effects of annuloplasty performed with conventional versus modified-shape prostheses in a simulated mitral valve affected by progressive degrees of leaflet tethering.
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Material and Methods |
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Three different annular configurations were analyzed (Fig 1): a natural valve with a round annulus was modeled as a base line (model A); a D-shaped annulus simulated the implantation of an undersized conventional ring with the typical D shape (model B), and a modified-shape prosthesis was configured in the shape of a dog bone (model C). The dog-bone prosthesis had a reduced septolateral dimension (halved in comparison to the conventional D-shaped ring) but maintained the natural length of the anterior tract of the annulus.
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Valve Geometry and Mechanical Properties
THE ANNULUS
Figure 1 shows models A, B, and C, corresponding to the base line valve configuration and to the 2 different annuloplasty implants. All models were developed on the basis of the following common assumptions: first, the valve was symmetrical to the plane that was perpendicular to the valve orifice and passed through the highest point of the profile of each leaflet, and second, the completely open valve configuration was considered the initial (ie, undeformed) one. In this configuration the leaflets lay on the lateral surface of a cylinder whose cross-sectional plane corresponded to the valve orifice. Third, in each model the valve annulus length was modified to adapt to the simulated annuloplasty prosthetic ring.
In the base line mitral valve (model A), the annulus was assumed to be circular, and its diameter was set as equal to 32 mm, so that the orifice area was 8.04 mm2 and the entire annular circumferential length was 100.5 mm. In accordance with data reported by Kunzelman and colleagues [13], the annulus was divided into 2 parts that corresponded to the insertions of the anterior and posterior leaflets, which were 41.9 and 58.6 mm long, respectively.
Model B simulated the implantation of an undersized conventional prosthesis (Seguin Ring; St. Jude Medical, St. Paul, MN) characterized by an intercommissural distance of 30 mm. The anteroposterior distance was set at 21.7 mm in accordance with the 3:4 ratio shape of commercially available prostheses. Hence, the length of the anterior portion of the annulus was reduced from 41.9 to 34.5 mm. The resulting orifice area at the annular level was 5.1 cm2.
Model C simulates the implantation of a modified-shape annuloplasty prosthesis in the same valve. Compared with model B annular geometry, in model C, the anteroposterior distance was halved by deflecting the middle portion of the "anterior" and "posterior" hemiannulus and simulating the implantation of an annuloplasty prosthesis with a dog-bone shape. Notably, in model C the anterior tract of the annulus was almost as long as in the base line model (anterior annular length, 39.3 mm). The orifice area was the same for models B and C, for better comparison of the results.
THE LEAFLETS
The leaflet profile did not differ among the 3 simulations. The mitral valve leaflet profile (Fig 1a) was generated according to the data reported by Kunzelman and colleagues [13]. The anterior and posterior leaflet heights—that is the distance of the points of the leaflets' free edges from the annulus—were assumed to be 24 and 13.7 mm, respectively, whereas the anterolateral and posteromedial commissural heights were set as equal to 6.8 mm. The surface of the anterior leaflet was 678 mm2 in the base line model and was kept almost constant in models B and C. The thickness of the leaflets was assumed to be uniform and equal to 0.8 mm. In model A the anterior and posterior annular lengths were assumed to be 41.9 and 58.6 mm, respectively; in models B and C the overall annular length was reduced to fit the ring contour, whereas the anteroposterior length ratio was fixed. Leaflets were meshed by means of ABAQUS (ABAQUS, Inc, Hibbitt, Karlsson & Sorensen, Pawtucket, RI, version 6.2) S4R (4 nodes, reduced integration, and shell elements). The mechanical properties of the leaflets were chosen according to the model of Kunzelman and associates [14].
THE CHORDAE
Forty chordae tendineae with a constant section of 0.4 mm2 were modeled. The mechanical behavior of the chordae was assumed to be nonlinear and elastic according to Kunzelman and associates' data [14]. To simplify the model only the marginal chordae, inserted directly into the free edge of the leaflets, were considered, because they support the main part of the load when the valve closes and because, as demonstrated by in vitro and in vivo studies, basal (second-order) chordae only slightly influence leaflet coaptation and leaflet shape [15–17] in healthy hearts. However, secondary chordae can be involved in leaflet malcoaptation in the case of functional MR [9].
THE PAPILLARY MUSCLES
The position of the papillary muscle tips was set as fixed, because in the absence of papillary muscle dysfunction, papillary muscle contraction and PMD offset each other during the systolic phase [12]. In this study, the papillary muscle tips were located 29 mm below the valve annulus at base line; subsequently they were progressively translated away from the annulus to simulate PMD and mitral valve tethering. Both papillary muscles were displaced at the same time. Papillary translation occurred along the direction perpendicular to the annular plane. No transversal (ie, lateral) displacement or interpapillary distance modifications were introduced into the model, although these alterations may be part of the clinical presentation of functional MR [18].
Annuloplasty Effects at Baseline and Subsequent PMD Simulations
For each model, 4 simulations were performed to test coaptation at baseline and after 3 progressive degrees of PMD, as seen in functional MR. In the first simulation, a uniform ventricular pressure up to 120 mm Hg was applied as a distributed load to the ventricular surface of the leaflets to obtain valve closure and to simulate the effect of blood on the mitral leaflets at the base line (no leaflet tethering).
In the following simulations, the nodes representing papillary muscle tips were progressively displaced (2, 3, and 4 mm) from the annular plane to simulate 3 incremental degrees of mitral valve tethering. Regurgitant area was estimated as a function of the PMD. To obtain a reliable evaluation of the regurgitant area through the valve, the orifice area was projected onto the plane in which the annuloplasty ring lays; the contour of the projected area was then used to calculate the area according to a triangulation scheme.
Numeric analyses were performed by means of the ABAQUS code. Regurgitation areas were meshed by means of 4-node and shell elements by using the GAMBIT preprocessor (Fluent, Inc, Lebanon, IL), and they were evaluated with Fluent software (Fluent, Inc).
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Results |
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TopAbstractIntroductionMaterial and MethodsResultsCommentReferences |
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Because the lack of coaptation is due to a characteristic of shell elements rather than to an effective valve malfunction, the area values at 0 PMD were set as reference 0 values, and results were reported as the differential value from base line. Figure 3 reports the differential regurgitation area values as a function of progressive PMD.
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Leaflet Stress Distributions
Maximum in-plane stress values in the leaflets are reported in Table 1. An overview of our results indicates that the implantation of the 2 rings analyzed here (models B and C) causes comparable stress values in the area close to the free edge, whereas they have quite different consequences in the annular region of the leaflets. Regarding the free edge area, a comparison between the base line configuration (model A) and the 2 annuloplasty configurations (models B and C) shows that both rings increased the stresses in the subcommissural (posterior leaflet clefts) and commissural regions (31% and 52%, respectively), whereas they decreased (–36%) elsewhere. With respect to the annular region, the classic D-shaped ring implies a sensible reduction in the stresses in the midanterior zone (–57%) and a slight increase in the midposterior part (+13%) with respect to the base line configuration. However, the dog-bone ring reduced stresses in both the midanterior and midposterior regions (–25% and –38%, respectively). Nonetheless, no marked change occurred in the commissural regions when comparing the 3 models.
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Comment |
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We hypothesized that failure of undersized annuloplasty in these patients could be related to the inadequacy of the design of currently available ring devices to treat functional MR. In this study, modifying the shape of the annuloplasty ring so that it was specifically designed for the correction of functional MR was more efficient in preserving coaptation in the presence of leaflet tethering as compared with a conventional ring with the same effective orifice area.
Commercially available rigid ring prostheses commonly have a D shape, with the anterior portion of the annulus almost straight and the posterior portion curved to reproduce the shape of the anterior leaflet. The ratio between the anteroposterior and the intercommissural dimension is approximately 3:4 for all prostheses. The implantation of such prostheses has had excellent results in rheumatic and degenerative diseases.
The design of the Carpentier Classic ring (Edwards Lifesciences Inc, Irvine, CA), the progenitor of all annuloplasty prostheses, was originally intended to correct rheumatic MR [19]. This shape is sometimes inadequate to treat other forms of MR, such as Barlow's disease. As a consequence, it is an accepted practice to modify the shape of the Carpentier Classic ring by bending the 2 short anterior segments to make the annular prosthesis rounder, to avoid postoperative systolic anterior leaflet motion.
In the case of functional mitral valve regurgitation, the rationale for modifying the shape of the annular prostheses is to encourage leaflet coaptation by selective septolateral reduction in the annulus. However, intercommissural distance (or anterior annular length) reduction is not necessary and is potentially detrimental because it may induce distortion and bending at the base of the anterior leaflet.
Moreover, because functional MR often results in a central jet, we postulated that selectively reducing the central septolateral dimension could better correct functional MR by concomitantly minimizing the annular surface area reduction. On the basis of these concepts, an annular prosthesis in the shape of a dog bone was designed to push the central portion of the posterior annulus toward the anterior portion.
A similar concept was advocated by Timek and associates [10], who demonstrated that septolateral cinching of the mitral annulus with a suture effectively prevented MR in an acute model of ischemic MR in sheep. We clinically tested the concept of selective septolateral annular reduction in the annular dimensions by manually modifying the shape of the Carpentier Classic ring in a group of 14 patients with functional MR. In this yet-unpublished series of patients, functional MR was successfully treated by implanting the prosthesis compressed in the so-called anteroposterior dimension, leaving the intercommissural distance—and hence the length of the anterior portion of the annulus—untouched. (In doing so, the prosthesis maintained the D shape, but with appreciable reduction in the septolateral distance of the ring). The choice of the prosthesis was based on the fact that the Carpentier Classic rigid ring is built with a malleable internal metal structure that allows modifications of the original shape of the prosthesis before implantation.
In this study, we tested the behavior of a standard undersized ring prosthesis in comparison with a prosthesis with a modified shape, and we simulated their implantation on a tethered mitral valve. On the basis of the numeric findings, we discovered, first, that when compared with the standard prosthesis, the dog bone–shaped ring improved coaptation, as confirmed by the constancy of the regurgitation area during PMD. Second, the larger perimeter to area ratio of the dog bone–shaped ring with respect to the D-shaped ring is likely to inhibit or minimize the occurrence of wrinkles on the leaflet tissue immediately adjacent to the annulus.
However, the dog bone–shaped ring profile used in these simulations was associated with suboptimal coaptation at the commissures, and this requires further investigation. As shown in the Results section, for PMD equal to 0, the regurgitant area in the commissural region was greater when compared with the D-shaped configurations. Although this outcome was emphasized by the intrinsic unnatural bending stiffness of the finite element models used for the simulation, a ring design promoting the commissural leaflet coaptation could improve the valve continence in this region.
Stresses acutely induced on the leaflets by implantation of the 2 prosthetic rings are a main issue. The use of a rigid or semirigid prosthetic ring alters annular geometry and inhibits annular motion during the cardiac cycle. Nonetheless, ring rigidity is mandatory, because the prosthesis has to reduce annular dimensions and, as in the case of the dog bone–shaped ring, enforce and maintain the desired shape for the annulus. The results obtained in this study lead to the conclusion that stresses induced by the dog bone–shaped ring (model C) and the D-shaped ring (model B) are mostly the same in the free edge area close to chordae insertions on the leaflets. Stress values in the annular region of the leaflets were higher for the dog-bone ring in comparison to the D-shaped ring, even if stresses were decreased in comparison to the base line model. Conversely, the dog bone–shaped ring was associated with lower stresses in the midposterior region (120 vs 220 kPa).
Nevertheless, stress values obtained for the models discussed here need careful interpretation; the 3 implemented models cannot include the effects of long-term tissue remodeling, which might offset stress increase. Moreover, as previously stated, models B and C do not take into account the distortion induced by rigid prosthesis implantations on the leaflets and on the annulus. Further studies should include this feature to obtain more reliable results.
Limitations
The results reported in this work demand careful interpretation. In particular, several factors have to be considered when they are applied to clinical practice.
First, the model analyzes acute changes of annular geometry and valve tethering on the native mitral valve and the effects of their correction by means of an annuloplasty ring. It does not account for preexistent regional tissue alteration, possible valve remodeling, or pathologic fibrotic tissue formation. In chronic functional MR, left ventricular geometry is frequently more corrupted with higher degrees of PMD. In this simulation, mild degrees of PMD (eg, a 2-mm increase of the annular to the papillary dimension) were associated with a sensible increase of the mitral regurgitant area in models A and B. These results are comparable to the observations obtained during acute ischemia in a sheep model of acute functional MR, in which minimal changes of left ventricular geometry were associated with marked leaflet tethering and malcoaptation [20]. PMD was simulated as pure apical displacement (increased papilloannular distance). This is a simplification of the scenario observed in chronic functional MR, in which lateral and apical displacement are present. However, lateral displacement is considered to be less important than apical displacement in the pathogenesis of leaflet tethering [18].
Second, as far as base line valve geometry is concerned, a simplified assumption consists of the circumferential shape of the annulus; in systole, the shape of the annulus is ellipsoidal because of muscle contraction. However, in the case of pathologic dilation of the left ventricle, the systolic eccentricity is critically reduced [21]. In these models, the annulus was modeled as a planar structure, and its contraction was not taken into consideration. This assumption might be restrictive when the native mitral valve (model A) is modeled, but it is not critical when the implantation of a rigid or semirigid annuloplasty ring is simulated (models B and C). In this case, rigidity (and, for the modeled prostheses, planarity) is the desired consequence of annuloplasty prosthesis implantation.
Third, the choice of the input values for valve modeling was the result of a compromise to obtain data for comparison, rather than to reproduce a real clinical scenario. First, the undersizing of model B was not as aggressive as in clinical practice, where the annulus is usually reduced to a minimum. We decided to maintain the same orifice area at the annular plane for models B and C to focus on the effects of shape modifications on valve competence. The results obtained with this setup demonstrate that the annular shape of model C is more resistant to valve tethering than the conventional shape of model B of the same surface area. The only way to compare the 2 models in a real-world setting would be a clinical study comparing markedly undersized annuloplasty (with prostheses as small as 26 mm) with modified-shape annuloplasty prostheses.
Fourth, the heights of the characteristic points of the open-valve leaflets' free profile were the same in the 3 models. Nonetheless, the annular length changed from model to model, because it was assumed that leaflets adapt to the annuloplasty ring. This has a twofold consequence: on the one hand, the ratio between the leaflet area and the valve orifice area changes, and this detrimental effect is more pronounced for the D-shaped ring; on the other hand, the formation of wrinkles mainly affects the D-shaped ring because of the insertion of the valve into a smaller ring was not taken into account. In particular, the second aspect should be considered when results are interpreted in terms of stress acting on the leaflets. In this study, stress values were due to the concurrent action of blood pressure and chordae tendineae traction on the leaflets and not to annular distortion induced by the insertion of prosthetic rings.
Fifth, as previously mentioned, the model does not include structural (second-order) chordae, in accordance with their negligible influence on leaflet coaptation and on leaflet shape [15–17]. However, the correct quantification of this influence through a finite-element model could be a new and interesting task, because the absence of perturbed leaflet geometry after second-order chordae removal observed in these studies does not exclude abnormal stress distribution on the first-order chordae, which could lead to altered leaflet shape or mitral insufficiency over the long term [17].
Sixth, in this study, the hemodynamic effects due to blood regurgitation were not taken into consideration. Another prospect is that the fluid structure interaction approach may be of great interest for modeling the mitral valve/annuloplasty prosthesis interactions, because this would also make it possible to estimate the effects of the valve orifice modifications on local hemodynamics. The authors have been involved in work on fluid structure interaction in the cardiovascular system [22–25]. Their work is based on arbitrary lagrangian eulerian (ALE) algorithms that require grid deformation. Regarding mitral valve mechanics, the ALE-based fluid structure approach is very complex because of the large rotation involved. Our current studies are focused on solving this limitation by coupling mesh deformation and remeshing algorithms. Alternatively, 2 articles dealing with 3-dimensional fluid structure interaction phenomena in the stented [26] and natural [27] aortic valve were published in 2003. They are based on algorithms that treat the blood as eulerian and overcome the problem of deforming the computational grid typical of ALE-based methods, thus very effectively managing the leaflet motion. The drawback is a slight inaccuracy of the calculations at the leaflet boundary. These are truly pioneering works, but they are still being tested because they focus on the method itself rather than on its applications.
Finally, valve leaflets were meshed with an S4R shell element. They are 4-node reduced-integration elements with a lower element rigidity and bending stiffness in comparison with the corresponding fully integrated element. Nonetheless, they are less flexible than the real continuum they simulate. In fact, they can transmit momentum, whereas real valve leaflets can be inflected with almost no momentum applied. As a consequence, simulated leaflets do not fold as much as real ones; hence, in the models presented here, the valve cannot close perfectly, even when papillary muscles are kept in their physiologic position. Further simulations should account for this critical aspect and solve it by properly scaling material properties and element thickness to reduce their bending stiffness while maintaining their traction stiffness unchanged [14, 27, 28].
Conclusions
These results introduce a new perspective for mitral annuloplasty. Currently available annuloplasty devices are not specific and are not purposely designed to treat individual diseases. However, annular dysfunction may be disease specific, and specialized devices may improve the efficacy of annuloplasty, particularly in the case of functional mitral valve regurgitation. The introduction of functional MR-dedicated prostheses with selective reduction in the septolateral dimension may improve the results of conventional undersized annuloplasty, particularly in the presence of severe leaflet tethering.
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Appendix |
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is 0.0356999, K is 6.0, a1 is 5.40814, a2 is 4.2918, a3 is 5.30630, a4 is 3.06855, a5 is –0.09161, a6 is –0.5986, a7 is –0.30913, a8 is –1.15527, a9 is 1.0269, a10 is 0.25297, a11 is –0.64712, and a12 is 0.11715. The 3-dimensional leaflet profile and the 3-dimensional model of the valve leaflets were generated with GAMBIT (Fluent Inc). To apply the finite element computational technique, the model was meshed into 2280 four-node reduced-integration shell elements (900 for the anterior leaflet and 1380 for the posterior leaflet), defined as S4R elements in the ABAQUS code.
Chordae Model Generation
Chordae tendineae were modeled by means of forty 2-node truss elements. The truss elements were placed between the nodes of the leaflet profile and the papillary muscle ends (which were assumed to be symmetrical and separated by a distance of 10.7 mm) 29 mm below the valve annulus. The papillary muscle position was chosen on the basis of the experimental data of Green and colleagues [18]. In fact, in this study, an important asymmetry between the positions of the 2 papillary muscles was highlighted, because the anterior one was closer to the valve orifice with respect to the posterior one (24.1 ± 1.2 mm vs 32.1 ± 2.4 mm for ovine mitral valves). According to the symmetry hypothesis that characterizes the models implemented in this study, the distance of the papillary muscles from the valve orifice was chosen as the average value of the entire range.
Leaflet Mechanical Properties Setup
Valve leaflet tissue consists of an elastin matrix and collagen fibers. In the central region of both leaflets, the fibers are oriented along the circumferential axis, parallel to the annulus. Because of this structure, the valve leaflet tissue behaves as a fiber-reinforced composite material. However, only in the anterior leaflet is there a notable difference between the stiffness values in the longitudinal (that is, the direction perpendicular to the annulus) and circumferential direction [29, 30]. Therefore, in this model and in that published by Kunzelman and colleagues [14], both leaflets were assumed to be homogeneous and to have a linear, elastic, orthotropic mechanical behavior defined by the *ELASTIC, TYPE=LAMINA option, available in ABAQUS for shell elements. The anterior leaflets are characterized by a circumferential and longitudinal elastic modulus of 6.230 and 2.09 MPa, respectively; a shear modulus of 1.370 MPa; and a Poisson ratio of 0.488 to simulate the near-incompressibility of the tissue. In turn, the posterior leaflet's elastic modulus is 2.350 and 1.887 MPa in the circumferential and longitudinal directions, respectively, whereas its shear modulus is 0.690 MPa and its Poisson ratio is 0.480 [15]. Hence, only the anisotropy of the stress-strain characteristic of the leaflet tissue, and not its fiber-reinforced nature and the possible nonlinearity related to it, was accounted for.
Chordae Mechanical Properties Setup
The mechanical behavior of the chordae tendineae was consistent with the behavior of many other collagenous structures. It was characterized by an initial low pretransition modulus at low strains (< 2.5%). When the strain increased, a considerable increase in stiffness occurred, and the stress-strain behavior became almost linear (posttransition modulus) [15]. In a previous study [12] chorda tissue was modeled as a linear material with an elastic modulus equal to the posttransition modulus [15]. Such a solution could limit valve leaflet movement, because it is equivalent to simulate pretensioned chordae. On the basis of this consideration and given the objective of this study, a different and more accurate material model was adopted. A quadratic polynomial strain energy function was applied to simulate the nonlinear elastic behavior. Once a set of experimental data by Kunzelman and Cochran [15] was provided as input, the strain energy function was assigned by the computational code as follows:
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1 and 2 are the first and second deviatory strain invariants, defined as follows:
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i as the deviatory stretches calculated from the principal stretches 
i and the total volume ratio J by the formula
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Annulus Constraints and Leaflet Coaptation Simulations
Because only leaflet rotation with respect to the annulus, but not annular contraction, was accounted for, the nodes belonging to the annulus were fully constrained with respect to translations. However, they were allowed to rotate with respect to each of the cartesian axes. During systole, leaflet coaptation was modeled through finite sliding contact between 2 element-based surfaces, each one corresponding to the atrial side of 1 leaflet. Interaction between the leaflets in the direction normal to their surface was simulated without any penalty algorithm. Tangential contact interaction was characterized by a friction coefficient of 0.9 between the leaflet surfaces. Although presumably higher than the real one, this value was adopted to avoid complete slipping of 1 leaflet onto the other and, hence, leaflet prolapse.
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- = values calculated for model A (no ring implanted); -
- = values obtained for model B (classic D-shaped ring); -
- = values determined for model C (dog bone–shaped ring implanted).