Ann Thorac Surg 2006;82:1369-1377
© 2006 The Society of Thoracic Surgeons
Original Articles: Cardiovascular
In-Vivo Dynamic Deformation of the Mitral Valve Anterior Leaflet
Michael S. Sacks, PhDa,*,
Yoshiharu Enomoto, MDb,
Jeffrey R. Graybill, BSa,
W. David Merryman, MSa,
Ahmad Zeeshan, MDb,
Ajit P. Yoganathan, PhDc,
Robert J. Levy, MDd,
Robert C. Gorman, MDb,
Joseph H. Gorman, III, MDb
a Engineered Tissue Mechanics Laboratory, Department of Bioengineering, University of Pittsburgh, Pittsburgh, Pennsylvania
b Harrison Department of Surgical Research, University Pennsylvania School of Medicine, Philadelphia, Pennsylvania
c Cardiovascular Fluid Mechanics Laboratory, Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, Georgia
d Division of Cardiology, Children's Hospital of Philadelphia, Philadelphia, Pennsylvania
Accepted for publication March 21, 2006.
* Address correspondence to Dr Sacks, Engineered Tissue Mechanics Laboratory, McGowan Institute for Regenerative Medicine, 100 Technology Dr, Room 234, University of Pittsburgh, Pittsburgh, PA 15219 (Email: msacks{at}pitt.edu).
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Abstract
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BACKGROUND: Surgical techniques have been developed for mitral valve repair for a wide range of pathologies. However, excessive tissue stress and damage have been identified as etiologic factors limiting long-term durability. Before computational models to optimize valve repair can be realistically developed, in-vivo dynamic mitral valve leaflet strain data are required. However, these data do not presently exist. In the present study, a sheep model and sonomicrometry were used to compute the in-surface Eulerian strain tensor of the anterior leaflet over the cardiac cycle at varying afterloads.
METHODS: The anterior leaflet of nine Dorsett sheep (35 kg to 45 kg) was instrumented with nine 1-mm hemispherical piezoelectric transducers in a 15-mm square array. Three-dimensional crystal spatial positions were recorded at 250 Hz over several cardiac cycles, with peak left ventricular pressures varying from 90 mm Hg to 200 mm Hg. The in-surface Eulerian strain tensor was computed from the crystal displacements.
RESULTS: The mitral valve anterior leaflet experiences large anisotropic strains and peak strain rates of 400%/s, followed by an absolute cessation of any deformation during systole. Increasing left ventricular pressure also increased the effective leaflet stiffness but not the peak strains.
CONCLUSIONS: We report the first data on the dynamic in-vivo strain tensor of a functioning mitral valve anterior leaflet, which indicated large anisotropic strains and very high strain rates. Our observations also suggest that changes in left ventricular pressure and annular geometry result in altered effective leaflet stiffness, and may be an important factor in reducing leaflet stress and as such potentially affect mitral valve repair longevity.
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Introduction
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Over the past 30 years, surgical techniques have been developed and standardized that allow mitral valve repair to be attempted for all types of leaflet, chordal, and annular deformities [1–4]. Application of these techniques has now become ubiquitous. Early reports regarding the success of mitral valve repair [5, 6, 7] have spawned a trend toward prescribing surgery for patients with asymptomatic mitral regurgitation (MR) [8, 9]. Unfortunately, recent long-term studies using more rigorous definitions of failure have identified less optimistic results for repair durability; bringing into question such aggressive surgical practice and suggesting that repair techniques though mature can be improved upon [1, 10–12]. In most cases, failures were a result of disruption at the leaflet, chordal or annular suture lines. These failure modes suggest excessive tissue stress and the resulting strain induced tissue damage as an etiologic factor.
Recent modeling work has illustrated the potential importance in maintaining normal leaflet geometry as a way of minimizing stress distribution and improving repair durability [13, 14]. This work in association with improved three-dimensional imaging has piqued interest in developing computer models of the mitral valve that will allow evaluation of various new repair techniques and devices. However, before such models can be realistically developed a better understanding of the in-vivo leaflet stress–strain relationship will be necessary.
Our group has made substantial progress in quantifying the dynamic in-vitro mitral valve tissue strains under a variety of simulated hemodynamic and pathologic conditions [15, 16]. As is true for much of the valvular literature, the corresponding in-vivo dynamic data do not presently exist. That is because of the substantial experimental challenges in studying heart valve dynamics, which include complex anatomical geometries, large strains, and extremely rapid motions; all occurring within a blood contacting environment. This lack of data motivated the present study, wherein a sheep model and sonomicrometry array localization [17] were used to compute the in-surface Eulerian strain tensor of the anterior leaflet throughout the cardiac cycle at varying afterloads.
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Material and Methods
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Surgical Protocol
In compliance with guidelines for humane care (NIH Publication No. 85-23, revised 1985), 9 male Dorsett sheep (35 kg to 45 kg) were induced with sodium thiopental (10 to 15 mg/kg intravenously), intubated, anesthetized, and ventilated with isofluorane (1.5% to 2%) and oxygen. The surface electrocardiogram and arterial blood pressure were continuously monitored. Through a sterile left lateral thoracotomy, on cardiopulmonary bypass, nine 1-mm hemispherical PZT-5A piezoelectric transducers (Sonometrics, London, Ontario) were sutured with 6-0 polypropolene to the anterior mitral leaflet in a 15-mm square array (Fig 1). The array started 1 mm from the mitral annulus and extended to 3 mm of the coaptation line. A 1-mm transducer on the middle portion of the posterior mitral annulus and two 2-mm transducers on the left atrium were placed for orientation. With the leaflets placed in a coapted position by injecting saline into the left ventricle, the leaflet transducer wires were adjusted to allow a degree of slack that permitted free motion of the leaflets without letting the wires coil in the atrium. The atriotomy was then closed around the wires maintaining this relationship. After the animal was weaned from cardiopulmonary bypass and was hemodynamically stable, an epicardial echocardiogram was performed to assess valve competence. The chest was closed with the sonomicrometer skin bottoms fixed to the skin, and the animals were recovered from anesthesia.
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Fig 1. (a) A schematic of the mitral valve anterior leaflet showing the nine sonomicrometry transducer array. (b) An interoperative view of the anterior mitral leaflet as seen through a left atriotomy. The relationships of the leaflet, transducers, wires, and atrium are shown.
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Sonomicrometry Data Collection
Seven days after implantation the animals were again sedated with thiopental, placed supine, intubated, anesthetized with isoflurane, and mechanically ventilated. High-fidelity pressure transducers (SPC-350; Millar Instruments, Houston, Texas) for simultaneous measurements of left ventricular pressure and aortic root pressure were passed percutaneously into the left ventricle and ascending aorta via a femoral artery. Surface electrocardiogram, left ventricular pressure and aortic root pressure were monitored continuously (Hewlett-Packard 78534C monitor). Transducer wires were connected to a Sonometrics Series 5001 Digital Sonomicrometer (Sonometrics). A midline laparotomy was performed for transdiaphragmatic echocardiogram to assess valve competence at every hemodynamic condition. As described previously [17] sonomicrometry array localization was used to determine the three-dimensional coordinates of each transducer every 5 ms throughout the cardiac cycle using sonomicrometry distance data.
Three-dimensional sonomicrometry positional data were taken under the following conditions: (1) inhaled isoflurane concentration was titrated to a baseline systolic blood pressure of 90 mm Hg; (2) a neosynephrine infusion was then titrated to achieve systolic blood pressures of 150 and 200 mm Hg; (3) neosynephrine was discontinued and the animal allowed to return to a baseline systolic blood pressure of 90 mm Hg. Between each pharmacologic hemodynamic manipulation animals were allowed to stabilize for 15 minutes before sonomicrometry data were recorded. Ventilation was suspended during sonomicrometry measurements. Data were taken for approximately 15 contiguous cardiac cycles for every data set. Since cycle-to-cycle variations were extremely small, the last cycle was routinely chosen as representative.
Surface Strain Computations
Detailed methods for computing dynamic leaflet surface strains have been previously described [16]. Briefly, we adapted our previous approach to determine the two-dimensional in-surface Eulerian (ie, referenced to the deformed state configuration) strain tensor "e" at each time point using a finite element-based surface interpolation method. Eulerian strain tensor "e" was referred to a convective, in-surface coordinate system [18], which in the current study the axes were aligned to the local circumferential and radial directions of the leaflet (Fig 2a). The crystal configuration at the minimum left ventricular pressure was used as the reference state for all strain calculations, which represented the point of least deformation strain placed on the mitral valve anterior leaflet. The endpoint for data analysis was chosen to be the minimum left ventricular pressure after one heart cycle. Thus, the deformation for each valve is based from one full cardiac cycle, beginning and ending with the point of minimal left ventricular pressure. One benefit of the use of sonocrystals for strain determination is that the three-dimensional positional data from all frames are always available, as there is no need for straight optical pathways as required in the in-vitro studies [16].
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Fig 2. (A) A schematic of the nine sonocrystals placement on the mitral valve anterial leaflet surface, showing crystal positions in relation to valvular geometry, with c-circumferential and r-radial directions. (B) Two three-dimensional reconstructed views of the nine sonocrystals in the unloaded reference state (t = 0 ms) and the fully coapted state (t = 500 ms). Also shown below is a schematic showing the anatomic location of the nine crystals on the mitral valve anterior leaflet. Color fringes represent the relative change in area D = current area/original area. In the fully coapted state, homogeneity of the change in area was noticeable. However, most of the area delimited by the crystals was relatively homogenous and was represented by the value at the center crystal (no. 6). (Ao = aortic location; AC = anterior commissure; Co = coronary sinus location; PC = posterior commissure.)
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In preliminary analyses, we observed that the shear strains were very low and that the principal angles (corresponding to the direction of largest stretch with respect to the circumferential axes) were within approximately 10 degrees of the radial direction. Taken together, the parameters indicate a low amount of tissue shearing and that the major stretch direction was closely aligned to the radial axis. Thus, in the present study the principal strains corresponded to the radial (
radial, the major principal value) and circumferential (circ, the minor principal value) directions (Fig 2a), expressed as percent. The areal strain 
, representing the net local percent change in leaflet area, was computed using:
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The corresponding strain rates d(circ)/dt, d(radial)/dt, and d()/dt were computed using a 3-point numerical derivative algorithm [19] and expressed as percent per second.
Effects of Sonocrystal Implantation on Leaflet Biaxial Mechanical Properties
Suturing sonocrystals onto the mitral valve anterior leaflet surface introduces the possibility of local tethering effects, as well as tissue damage, both of which can affect strain measurement accuracy. To determine the extent that suturing of sonocrystals to the anterior mitral valve leaflet had on leaflet mechanical integrity, we utilized biaxial mechanical testing. Anterior mitral leaflets were prepared for biaxial testing as previously described [20]. Leaflets were first tested without the crystals to a peak tension of 90 N/m. Next, nine sonomicrometry transducers sutured to the leaflet while in the testing bath as done in the in-vivo study. The changes in the resulting strain measurements were used as an index if the affect of crystal placement on leaflet deformations. A total of six leaflets were so tested.
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Results
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General Observations
Transdiaphragmatic echocardiography revealed normal leaflet motion in animals (Fig 3). Seven animals had no MR and 2 animals had 1+ (both had 1+ MR before instrumentation). One of the animals with 1+ MR initially, increased to 2+ at an afterload of 200 mm Hg. Actual experimentally realized left ventricle peak pressures were within ± 1 mm Hg of the desired pressure peak for each group (Table 1). The strain measurement method was able to fit the displacement field of the nine marker sonocrystal array very well, with r2 for each displacement component approximately 0.98 or better over the entire cardiac cycle. Thus, the previous methods utilized for in-vitro data [16] were well suited to the present application.
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Fig 3. Echocardiographic image of a representative ovine mitral valve during systole (left) and diastole (right). The shape and motion of all instrumented valves was unchanged by placement of the sonomicrometry transducers as assessed by echocardiography. "Wi" marks the transducer wires as they pass through the left atrium. The triangles mark individual transducers on the anterior leaflet. (aMV = anterior mitral valve leaflet; AO = aorta; LA = left atrium; LV = left ventricle; pMV = posterior mitral valve leaflet.)
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Surface Strain Results
Surface strains were generally heterogeneous over the region delimited by the crystals (Fig 2b). However, the central region (near sonocrystal 6 in Fig 2) demonstrated generally homogeneous strains, and thus we elected to focus the present study on the results from this region. Note, too, that this approach was also chosen to allow for direct comparisons to the in-vitro data [16].
Peak stretch versus time responses demonstrated overall smooth deformations, with complete loading of the leaflet occurring in approximately 50 ms (Fig 4). Thus, as in our in-vitro investigations [16], we observed large anisotropic (ie, directionally dependent) strains. More importantly, the corresponding strain rates were quite high, on the order of 100%/s to 400%/s. This finding underscores the highly dynamic nature of the mitral valve (Fig 4). Peak strain rates typically occurred near full closure (or near full opening) consistently in all data.
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Fig 4. Representative time-stretch and time-areal strain traces, along with the corresponding strain rate data. We observed large anisotropic (ie, directionally dependent) strains. More importantly, the corresponding strain rates were quite high, on the order of 100%/s to 400%/s, underscoring the highly dynamic nature of the mitral valve.
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Mean peak circumferential strains ranged from peak 2.5% to 3.3%, and mean peak radial strains ranged from 16% to 22% (Fig 5). Corresponding areal strain ranged from 15% to 20%. Mean peak strain rates were approximately 300%/s to 400%/s in the radial direction, and 100%/s to 130%/s in the circumferential direction (Fig 6). Interestingly, there was comparatively little effect of maximum pressure level on either the peak stretches or the peak strain rates (Figures 5 and 6).
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Fig 5. Mean principal strains (a, b) and areal strain (c) for all three pressures levels for the current study, where in (a) the asterisk (*) indicates a statistically significant difference (p < 0.05) from the corresponding radial stretch at 90 mm Hg. Other than the differences between circumferential (circ) and mean radial peak strains, there were no significant differences with increasing LV pressure. In (d) are also shown for comparison the corresponding in-vitro data reproduced from [16], with substantially larger mean peak strains. **Statistically different from circumferential mean (p < 0.05).
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Fig 6. Mean principal peak strain rates for all three pressure level groups. While there were statistically significant differences between the radial group (black bars) and circumferential group (gray bars; p < 0.05), there were no differences due to increasing left ventricular pressure.
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Left Ventricular Pressure-Areal Strain Relation
To more closely investigate the effects of transvalvular pressure (ie, loading on the valve) during valve operation, we compared the left ventricular pressure to the areal strain (Fig 7). As in our in-vitro study [16], we observed a nonlinear relationship that bore a close resemblance to the stress-strain curve for collagenous tissues [21]. In particular, we noted that small left ventricular pressures were required to initially increase the anterior leaflet area, and then was followed by an extremely rapid increase in pressure to increase the leaflet area in the final closure phase. When examined more closely, the left ventricular pressure–areal strain relationship during the closed leaflet phase was found to be consistently linear (Fig 8a). Moreover, the slope of this linear relationship increased significantly with increased peak left ventricular pressure (Fig 8b).
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Fig 7. A representative left ventricular (LV) pressure–areal strain curve, which is analogous to a stress–strain curve for the leaflet and demonstrates the classic nonlinear soft tissue response. Note, too, the near-linear response for LV pressures above 20 mm Hg.
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Fig 8. (a) Representative linear regions from the left ventricular (LV) pressure–areal strain curves (others not shown for clarity), demonstrating the consistency of response. (b) Unlike the peak deformations results (Fig 4), the mean effective leaflet stiffness demonstrated statistically significant increases with peak LV pressure.
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Comparison of In-Vivo and In-Vitro Models
In comparing our current in-vivo results with our previous in-vitro studies, we noted that the magnitudes of the in-vivo deformations were consistently less than the in-vitro ones under comparable transvalvular pressure conditions (Fig 5). However, when normalized with respect to time and magnitude, the resulting deformation patterns were nearly identical (Fig 9). This result suggests that while there were inevitable differences between the porcine mitral valve tested under in-vitro conditions and the present in-vivo ovine mitral valve data, the overall scaled behavior patterns were remarkably similar.
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Fig 9. Principal stretch traces for both the current in-vivo data (open triangles [a, c, d]; open circles [b]) and the in-vitro data (solid circles) from our previous study [25]. Here, the peak stretches were normalized to unity, and the time normalized to one complete valve open/closed cycle. Of particular interest is the similarity in qualitative responses between the present ovine in-vivo and our previous porcine in-vitro responses.
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Effects of Sonocrystal Implantation on Leaflet Biaxial Mechanical Properties
Using our biaxial testing methods [21], the mean peak strains for the native leaflet at 90 N/m equibiaxial tension were (mean ± SEM) 20% ± 2.2% and 40% ± 4.8% in the circumferential and radial directions, respectively. After implanting the crystals, the peak stretches changed to 17% ± 2.8% (p = 0.386) and 33% ± 4.2% (p = 0.336), respectively. There were thus no significant changes in circumferential and radial stretches with the crystals attached. Not unexpectedly, additional tests performed with only sutures revealed the same results, suggesting that placements of the sonocrystals on the mitral valve anterior leaflet surface did not detectably alter the anterior leaflet tissue properties and hence the local deformation field.
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Comment
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Clinical Need for Improved Mitral Valve Repair
During the last 3 decades, starting with Carpentier's work, several surgical innovators have developed mitral valve repair techniques to the point of wide application throughout the world. Despite these successes, longer term follow-up has revealed that between 10% and 16% of patients undergoing mitral repair for myxomatous disease will require reoperation for severe MR within 10 years, even in the most experienced hands [2, 4, 5, 7]. Considering that patients with even mild residual MR after valve repair have decreased exercise tolerance compared with patients with a competent repair, the definition of repair failure as reoperation for severe MR may not be strict enough [22]. This is particularly true as more asymptomatic patients are being sent for valve repair.
Three recent studies from experienced mitral valve repair centers showed unexpectedly high incidence of recurrent MR after mitral valve repair. In one study, patients were followed for a mean of 18 months after repair. Forty-four percent of patients had 1+ or greater MR, whereas 18% had MR of 2+ or greater [12]. It is yet to be established if this rate of recurrent 2+ or greater MR is linear in this cohort, but if so it represents a failure rate of 12% per year. In a second study with longer follow-up, recurrent MR of greater than 1+ occurred at a rate of 8.3% per year and the rate of recurrent MR of greater than 2+ was 3.7% per year [11]. These rates were quite linear with a 7-year follow-up. A third study with 3-year follow-up corroborates the finding of the other two studies. This report demonstrated failure rates of between 3% and 4% per year (failure being defined as reoperation or recurrent MR of 2+ or greater) [1].
These clinical results have motivated our group to undertake novel experimental studies coupled with computational methods to develop quantitatively rigorous methods for evaluating both repair techniques and devices with the goal of improving mitral valve repair durability. To make the models realistic, a better understanding of both in-vivo leaflet geometry and in-vivo stress–strain relationship is necessary. This study represents a first step toward that goal.
Limitations
While this study is a first step toward that goal, it also highlights just how complicated the task may be. Because the techniques used may potentially alter leaflet dynamics, every attempt was made to attach the transducers atraumatically to the leaflets and to position the transducer wires within the atrium in a way that did not interfere with leaflet motion. That echocardiography demonstrated normal leaflet shape and motion and in-vitro testing demonstrated no effect of transducer placement on leaflet material properties lead us to believe the data presented are accurate in their description of dynamic mitral leaflet function.
Relation to Previous Studies
Our leaflet deformation results were qualitatively consistent with our previous in-vitro work (Fig 9). In particular, we noticed the key deformation patterns of the mitral valve leaflet were very consistent between the two studies (Fig 8). These include large, very rapid strains (as much as 400%/s, Fig 6) to the point of full coaptation, followed by an absolute cessation of any deformation during systolic ejection. The deformations during the final valve opening phase are basically a mirror reversal of the loading phase (Fig 8). This function is reflected in the overall behavior of the leaflet, where we observe an initial region with very large stiffness facilitating leaflet coaptation, followed by a rapidly stiffening region occurring once the leaflet coapts (Fig 7).
Despite the qualitative similarities with our previous in-vitro work, the magnitudes of peak stretches and stretch rates were found to be smaller in vivo compared with in vitro (Fig 5). Although differences in species studied (the in-vitro work was with porcine tissue) and strain measurement techniques used play a part, these differences more likely highlight the influence a functioning left ventricle (including a deformable annulus and contracting papillary muscles) has on leaflet geometry and function.
Biomechanical and Functional Implications
We observed that most of the mitral valve anterior leaflet experienced low shear strains, indicating that the principal directions were closely aligned to the local collagen fiber architecture [16]. This finding is at first not surprising given the highly aligned local collagen fiber structure [16]. Given that the mitral valve has complex attachments to the surrounding cardiac structures (eg, valve annulus, chordae tendinae), there is no a priori reason to assume that this would be the case in the functioning mitral valve. Thus, our current findings suggest that the central portion of the anterior leaflet behaves as a membranelike structure, with the greatest and least stretch directions aligned to the radial and circumferential directions, respectively.
Like all collagenous tissues [21, 23], the mitral valve anterior leaflet has been shown to be exhibit certain viscoelasticlike characteristics [24]. However, the constant deformation state during full closure (Fig 4) indicates that negligible creep (ie, increasing strain under a constant load) occurred while the valve was in the fully closed position. If creep occurred, then we would see increasing strain during the full closure period. This finding is not surprising since the total coaptation time is very short, only approximately 250 ms (Fig 4). Thus, any creep effects would have to be very rapid in order to be observed when the valve is closed; which did not occur in the present study. This result is consistent with our recent in-vitro mechanical testing [20] and in-vitro dynamic strain measurements (Fig 9). It further suggests that mitral valve leaflet collagen, unlike other dense collagenous tissue such as tendon [25, 26], is designed to reach a constant peak strain during coaptation and completely resist any further deformation. Additional research is under way in our laboratory to determine the underlying microstructural basis for this unique tissue behavior [27].
Another interesting finding of these experiments is the fact that increases in peak left ventricle pressure produced an increase in effective leaflet stiffness (ie, slope of the leaflet load versus areal strain relationship). Considering that for a given transvalvular pressure level, leaflet strain is a function of both leaflet geometry and mechanical properties, two explanations for this result are possible. The most obvious and straightforward is that the anterior leaflet stiffens with increases in peak left ventricular pressure. Another more subtle possibility is that at high left ventricular pressure, geometrical changes in left ventricle geometry (eg, papillary muscle position, annular geometry) occur to alter (reduce) peak leaflet strain. Understanding more completely each of these possibilities and their potential interaction may provide insights that help improve mitral valve repair techniques and devices in the future. It is our strong belief that a thorough knowledge of dynamic in-vivo mitral valve function will be required to achieve such insight.
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Acknowledgments
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This work was funded by National Institutes of Health grants HL-073021, HL-63954, P50 HL74731, and HL-52009. Michael S. Sacks, PhD, is an Established Investigator of the American Heart Association; W. David Merryman was supported by American Heart Association Predoctoral Fellowship 0515416U.
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Abstract
Introduction
