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Ann Thorac Surg 2007;84:92-101
© 2007 The Society of Thoracic Surgeons
a Politecnico di Milano, Bioengineering Department, Milan, Italy
b Cardiac Surgery Division, IRCCS San Raffaele Hospital, Milan, Italy
c University of Michigan Hospital, Ann Arbor, Michigan
d Politecnico di Torino, Mechanics Department, Torino, Italy
Accepted for publication March 5, 2007.
* Address correspondence to Dr Votta, Dipartimento di Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milan, 20133, Italy (Email: emiliano.votta{at}polimi.it).
| Drs Maisano, Bolling, Alfieri, and Redaelli disclose that they have a financial relationship with Edwards LifeSciences.
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Abstract |
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 Top Abstract IntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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Methods: The performance of the Geoform ring, a recently designed FMR-specific prosthesis, was compared with that of a standard Physio annuloplasty ring. Finite element modeling was used to simulate dilated cordiomyopathy-related FMR and compare, at the systolic peak, the valve’s pathologic condition with the postoperative scenario corresponding to both devices. Three degrees of the pathology were simulated by progressively displacing papillary muscles apically, up to 5 mm. Three ring sizes were modeled.
Results: Regurgitant area, coaptation length, and stresses acting on valve structures were assessed. When the use of the Geoform was modeled, coaptation length was always longer than 7 mm. In the most unfavorable case, the regurgitant area reduction was 74% with respect to baseline, and leaflets stresses were reduced by 20% when undersizing was simulated. When Physio ring implantation was simulated, coaptation length maximum extent was equal to 4.3 mm, the maximum regurgitant area reduction was equal to 60%, and leaflet stress reduction was observed.
Conclusions: Disease-specific prostheses may allow for restoration of valve competence even for significant degrees of leaflets tethering and avoid the need for aggressive undersizing, thus leading to more durable results.
Undersized annuloplasty is the usual method to treat functional mitral regurgitation (FMR) [1–3]. It is aimed at promoting coaptation of tethered leaflets by reducing the anteroposterior distance at the annular level. Using conventional prostheses, however, all dimensions of the mitral valve are reduced. In some occasions, very small prostheses have to be implanted to obtain an anteroposterior dimension reduction sufficient to correct FMR. Although in general, early results of annuloplasty repair are satisfactory, late recurrence of FMR can be observed in a significant number of patients [4–7]. It is hypothesized that a remodeling repair resulting in increased coaptation lengths will be associated with more durable long-term results [8].
In a previous paper [9], we formulated the hypothesis that long-term annuloplasty durability could be improved by the adoption of prostheses with a highly reduced anteroposterior dimension of the ring in its central portion, supporting this statement with some preliminary mathematical modeling evidences. Recently, the Geoform ring (Edwards Lifesciences, Irvine, California) has been introduced into the market specifically for the correction of FMR characterized by symmetric papillary muscles dislocation and by regurgitant jets in the central portion of the valvular orifice. When compared with a traditional annuloplasty ring, the intercommissural (IC) dimension is equivalent; however, the anteroposterior distance is reduced by 41%. In addition, the ring has a three-dimensional shape with an elevated posterior (P2) segment, designed to pull the posterior leaflet and lateral ventricular wall upward (atrially) and inward (toward A2), to enhance A2-P2 coaptation (Fig 1).
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Material and Methods |
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TopAbstractIntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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Starting from the valve open geometry, valve closure in the three configurations was simulated adopting a consistent procedure, exemplified in Figure 2. In step 1, papillary muscles tips were pulled apically, in other words, away from the valve orifice and perpendicularly to it, to simulate FMR. In step 2, to obtain configurations B and C, the annulus was deformed by imposing proper nodal displacements, to fit with the profile of the tested rings, as taken from technical drawings provided by the manufacturer. In step 2, annular shape was modified hypothesising that the fibrous, namely, intertrigonal, and muscular tracts of the native annulus had to fit with the corresponding geometry of the prosthesis. In step 3, a pressure load linearly rising up to 120 mm Hg was applied to the ventricular face of the leaflets to simulate valve closure during systole. During valve closure, no further displacements were allowed to the nodes belonging to the valve annulus, namely, no annular contraction was included into the simulation. This assumption is well suited to the Geoform ring, given its high rigidity, whereas it is a simplification of the clinical scenario as far as the Physio ring is concerned. In the second case, the simulated prosthetic device is a complete flexible ring, which should allow some residual annular motion due to active contraction. However, no quantitative data are available specifically for the Physio ring, and in vivo studies on sheep have shown that all of the geometrical changes of the annulus are nearly absent after annuloplasty with complete flexible rings [10].
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Disease Model
In all configurations, to simulate mitral valve leaflets tethering, papillary muscle tips were displaced apically from the annular plane. Both papillary muscles were symmetrically displaced, as it is the case in dilated cardiomyopathy and in end-stage ischemic cardiomyopaty. No lateral displacement was imposed to simulate increase of the distance between the papillary muscles, as a simplification and because of the uncertainty of the role of the interpapillary distance in the pathogenesis of FMR [11]. Three different degrees of leaflet tethering were simulated, respectively corresponding to a papillary muscles apical displacement (PMD) equal to 1, 3, and 5 mm. For each kind of prosthesis, three different sizes were simulated, characterized by an intertrigonal distance of 28, 30, and 32 mm, respectively. Simulations were run under ABAQUS/Explicit, version 6.5-1 (ABAQUS, Providence, Rhode Island).
Mitral Valve Geometry
The baseline model of the mitral valve was developed to reproduce an average mitral valve. It was defined on the basis of experimental data from literature under the simplifying hypothesis of valve symmetry [12].
Annulus and leaflets
The annulus was modeled as a planar line, with no physical properties, that provides insertion for the leaflets. Its relevant geometrical data, attained through the procedure described in Appendix 1, are provided in Table 1. Leaflet free edge profile was generated from experimental data reported by Kunzelman and colleagues [13], accounting for all of the three cusps of the posterior leaflet: P1, P2, and P3. Both leaflets were assumed 0.8 mm thick all over their extent, with the exception of the area adjacent to their free edge (corresponding to the rough zone), where leaflet thickness was set equal to 1.1 mm, owing to the thickening associated with the presence of chordae tendineae insertions.
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Chordae tendineae
Only marginal chordae were modeled, these being mainly responsible for counteracting the action of systolic ventricular pressure on the leaflets [14–16]. Fifty-two chordae were assumed initially straight and with a constant cross-sectional area of 0.4 mm2. Their average length was equal to 19.4 mm, having a standard deviation of 2.0 mm. Each chorda was discretized using six first-order truss elements.
Material Properties
All tissues were modeled as homogeneous and elastic, neglecting viscoelastic effects.
Leaflets
Leaflets tissue was assumed linear and orthotropic, thus neglecting its nonlinear response [17, 18]. Values of Young modulus, shear modulus, and Poisson ratio of each of the two leaflets, reported in Table 2, were set according to literature [16].
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Contact interactions
Leaflets contact was modeled adopting a 0.05 friction coefficient for their tangential interaction. This value was chosen since it characterizes the contact between soft and wet surfaces, such as hydrogels or low-friction lubricated Teflon, whose surface behavior may be considered as a good approximation of that of the leaflets in absence of more specific experimental data. Moreover, leaflet interaction normal to their surface area was described through a penalty contact algorithm, which implies that leaflets start interacting just before actually touching each other and, in the contact process, a small viscous energy dissipation phenomena occurs. The rationale for this choice is twofold; first, it allows smoothing of abrupt contacts, avoiding potential convergence problems in the numerical simulations; second, it is justified in that in-vivo leaflets do actually start to interact before actually coapting, since just before actual contact a blood film is trapped between them and is moved away by the leaflets.
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Results |
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TopAbstractIntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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Valve Competence
Regurgitant area (RA) as a function of PMD was estimated by means of a planar measure, as the one detectable in an echographic top view of the valve. For this purpose, the leaflets’ free edge was extracted at the systolic peak, by calculating the current position of the nodes belonging to it. It was then projected on the plane where the native annulus lies to obtain a planar contour, and finally, RA was estimated as the extent of the areas within the contour that were surrounded by tracts of the leaflets that did not coapt. An example is depicted in Figure 3, which shows the areas obtained for the baseline configuration (top panel, IC = 32) and for the postoperative one with a Geoform (middle panel) and a Physio (bottom panel) ring, both characterized by an IC distance of 30 mm. A qualitative analysis of the RA contours shows that Geoform ring enhances leaflets competence in the valve mid portion and in the subcommissural regions.
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When a mild undersizing (30-mm prostheses) was simulated, the reduction of RA with the Physio ring was equal to 26%, 43%, and 33% for PMD equal to 1, 3, and 5 mm with respect to the baseline model, respectively. It was equal to 68%, 79%, and 84% for PMD equal to 1, 3, and 5 mm, respectively, when the implantation of the Geoform ring was simulated.
When a more aggressive undersizing (28-mm prostheses) was considered, RA reduction associated with Physio ring implantation was equal to 43%, 60%, and 57% for PMD equal to 1, 3, and 5 mm, respectively, as compared with the baseline model. It was equal to 77%, 81%, and 89% for PMD equal to 1, 3, and 5 mm, respectively, when the implantation of the Geoform ring was simulated.
Moreover, maximum coaptation length (Lmeasure) in the valve mid portion was measured as in clinical practice; in a view along the IC axis, the valve’s cross section at the SL diameter was considered (Fig 5, top panel), and Lmeasure was defined as the length of the line from the beginning of the coapting tract to the leaflet free edge (Fig 5, mid panel). Moreover, the measure was divided into two terms, usually indistinguishable in echocardiographic images (Fig 5, mid panel): the length of the tract where leaflets are actually in contact (Lcoapt) and the mismatch between the free margins of the two coapting leaflets (Lfm). Calculated values are plotted in the bottom panel of Figure 5. In pathologic conditions, no coaptation was obtained when the maximum PMD (5 mm) was simulated. For PMD equal to 1 and 3 mm, Lmeasure was 4.1 and 3.0 mm for PMD, respectively, but Lcoapt was always smaller than 1 mm.
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When the implantation of a Geoform annuloplasty ring was assumed, for every considered PMD value, Lcoapt ranged from 7.0 mm (28-mm ring, PMD = 5 mm) to 9.1 (28-mm ring, PMD = 1 mm). The Lmeasure was always greater than 8.9 mm.
Leaflets Stress Distributions
Stress data were gathered with reference to two aspects: first, location and entity of peak stresses on the leaflets; second, maximum stresses acting on the annular region of the leaflets. As far as the first aspect is concerned, Figure 6
reports an example of the obtained contours of maximum principal stresses (SI) acting on the leaflets for every considered degree of pathology, the value of PMD increasing from left to right. The pathologic configuration (top panel) and the postoperative configurations obtained with 30-mm prostheses (mid and bottom panels) are depicted. The most stressed areas are located close to the leaflet free edge, consistently with the fact that they experience abnormal stresses due to the transfer of concentrated loads from pretensioned chordae. These areas are in the fessural region when the lowest PMD value (1 mm) is considered and move to the commissural one when higher PMD values (3 and 5 mm) are simulated.
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18%) is obtained with the biggest ring’s size (32 mm); when PMD is equal to 3 mm, the highest reduction (25%) is obtained with the intermediate ring’s size (30 mm); and when PMD is set to 5 mm, the highest reduction (20%) is obtained with the smallest ring’s size (28 mm).
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As far as the maximum principal stresses SI acting on the leaflets annular region are concerned, for each simulated condition, four areas were analyzed, defined on the basis of the leaflet therein inserted: midanterior (anterior leaflet, A2 region), commissural, midposterior (P2 scallop), and lateral (P1 and P3 scallops). From a qualitative point of view, the peak values patterns were similar: the highest values were always observed in the commissural tract of the annulus, the lowest values were observed in the insertion of the midportion of the anterior leaflet and of the P1 and P3 scallops, while intermediate values were assessed at the insertion of the P2 scallop on the annulus. In any case, stresses are much lower than the ones calculated close to the leaflet free margin. However, the way the two prosthetic rings affect stresses in the different tracts is significantly different, as indicated by the quantitative data reported in Table 4 for the most severe simulated pathologic condition (PMD = 5 mm). In this pathologic condition, when the implantation of a Geoform ring was modeled, SI stresses in the midanterior tract were increased by 11% with respect to the preoperative condition when a 32-mm ring was considered, but were reduced by 22% and 28%, respectively, for a 30-mm and a 28-mm ring. The SI peak values increased by 12% to 19% in the commissural tract and by 5% to 11% at the annular insertion of the P1 and P3 scallops, depending on the ring’s size. At the annular insertion of the P2 posterior scallop, a relevant stress increase (from 53% to 121%) was assessed, the increase becoming more and more significant when progressively smaller rings were considered.
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Comment |
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TopAbstractIntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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As far as the rings’ capability to enhance leaflets coaptation is concerned, the following considerations might be pointed out. First, the Geoform ring, compared with the standard prosthesis, improves coaptation in FMR, and its effectiveness is resistant to papillary muscle displacement; in fact, RA only slightly increased when the maximum PMD (5 mm) was simulated.
Second, the Physio ring needs undersizing to induce coaptation; to halve RA extension with respect to the baseline model, a two-size undersizing was needed when the worst pathologic condition was simulated (PMD = 5 mm). On the contrary, the Geoform ring did not seem to require aggressive undersizing, at least for the degree of pathology herein considered. This result could have interesting implications with respect to the interaction between the mitral and the aortic valves through the fibrous part of the annulus. Current annuloplasty rings require aggressive undersizing; therefore, their insertion on the native mitral annulus implies an important shortening and distortion of its intertrigonal tract, potentially influencing the normal aortic valve mechanics. On the contrary, a prosthetic ring capable to enhance leaflet coaptation without aggressive shrinking is likely to be able to preserve it.
Third, when the implantation of the Geoform ring was simulated, the maximum extent of the actual coaptation length Lcoapt was at least doubled with respect to the one obtained for the corresponding Physio ring size for any analyzed configuration. Moreover, for every considered PMD value, a coaptation length (Lcoapt) of 7 mm or longer was observed in all cases. On the contrary, this value was never achieved when the presence of a Physio prosthesis was modeled.
Regarding the capability of the two rings to limit stresses induced on the leaflets by tethering, the stress distribution on the leaflets was similar in the pathologic valve configuration and in the postoperative ones. However, the two rings showed rather different characteristics in terms of peak stress reduction at the leaflet free edge and in terms of stresses induced by the annuloplasty procedure on the annular region of the leaflets and thus, likely, on the surrounding annulus fibrosus. As far as the first aspect is concerned, when the presence of Geoform prostheses was modeled, peak stresses were mainly reduced with respect to those observed when no ring was included in the model; only with severe FMR (5 mm PMD) and no undersizing, stresses were higher than those observed in the baseline model. On the other hand, the Physio ring becomes less and less effective in reducing stresses with the increase of FMR and, with the exception of the lowest degree of FMR (1 mm PMD), stresses were always higher than those attained with the Geoform ring. In general, for every combination of PMD value and ring size, stress reduction was suboptimal if compared with the one obtained by the Geoform ring.
When the stress analysis is focused on the leaflet annular region, the insertion of the two prosthetic devices has remarkably different mechanical effects. The Physio ring induces only slight increases of the stress peak values in this region; increases become significant, at the insertion of the anterior leaflet and of the P1 and P3 scallops, only when aggressive undersizing is performed. On the other hand, the Geoform ring highly augments stresses at the insertion of the P2 posterior scallop, their rise becoming more and more significant when progressively smaller rings are taken into consideration. Given the continuity between the abovementioned region and the surrounding structures, that is, the annulus and the myocardium, it is reasonable to presume that the observed stress increases reflect an increase of the tensions acting in the surrounding annulus and myocardium. This possibly detrimental effect of the Geoform ring is likely to be related to its narrowed and highly nonplanar profile in the midposterior tract, which induces a geometrical distortion of the corresponding part of the annulus and of the immediately adjacent anatomical structures.
In conclusion, the study herein discussed appears to confirm our previous computational findings concerning the possibility of obtaining better results in the correction of FMR by means of disease-specific annuloplasty devices [9], characterized by a narrowed profile in their midportion. However, the present work also highlights the potential drawback of such prostheses, related to the geometrical distortion they impose on the annulus and to the subsequent nonphysiologic tensile state of the adjacent tissues. This particular aspect could not be studied by means of the previous preliminary finite element model, which neglected the actual annular deformation associated with the annuloplasty procedure [9].
Limitations of the Study
The indications provided by the present study, although interesting, need to be carefully interpreted before any definitive conclusion with respect to clinical practice can be made. The adopted computational model is based on some assumptions that have to be stressed, although they are not likely to controvert the reliability of the obtained results:
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Appendix |
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The geometry of the resulting orifice area (OA) in the diastolic configuration was used to position the two trigones on the anterior portion of the annulus. According to the data reported by Timek and colleagues [27], the diastolic value of the intertrigonal length (ITL) for a sheep is equal to 33 mm, in valves with a 830 mm2 OA. This value was scaled by a
factor to obtain an ITL value (32.23 mm) feasible for the modeled valve and to position the trigones.
Leaflets
As in previous papers [9, 11], the profile of their free edge was generated according to data reported by Kunzelman and colleagues [13] for an excised porcine valve with an intercommissural distance of 28 mm, which were interpolated and scaled by a factor 32/28, according to the bigger dimensions of the modeled valve. The function adopted to interpolate the original data is:
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= 0.0356999, K = 6.0, a1 = 5.40814, a2 = 4.2918, a3 = 5.30630, a4 = 3.06855, a5 = –0.09161, a6 = –0.5986, a7 = –0.30913, a8 = –1.15527, a9 = 1.0269, a10 = 0.25297, a11 = –0.64712, and a12 = 0.11715. The area of the anterior and posterior leaflets is equal to 664.4 mm2 and 518.6 mm2, respectively. Consistently with actual mitral valve anatomy, the extent of the anterior leaflet alone is comparable with the one of the valve orifice in systole, when the annulus contracts and an approximately 25% valve orifice area reduction occurs [25, 28, 29].
Leaflets were discretized by means of 12120 S4R four-nodes shell elements with reduced integration. Element’s numerical thickness was defined after scaling by 0.3 the actual thickness values, to reduce, by 91%, their bending stiffness and better resemble the actual bending response of the valve leaflets. Owing to the thickness scaling procedure applied to leaflets shell elements, real values of elastic modulus were divided by a 0.3 scaling factor to obtain the values to be provided as input to the finite element solver [16, 30, 31].
Papillary Muscles Position
Dagum and coworkers [14] reported the distance (average value ± SD) of each papillary muscle from the mid point of the posterior portion of the annulus, from a commissure and from a trigone. Papillary muscles tips position was set in the center of mass of the volume containing the points whose distance from each reference point on the annulus differed from the experimental data by less than the corresponding standard deviation.
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Acknowledgments |
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TopAbstractIntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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References |
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TopAbstractIntroductionMaterial and MethodsResultsCommentAcknowledgmentsReferences |
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