Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces

Tricuspid Valve Anterior Leaflet Strains in Ovine Functional Tricuspid Regurgitation

Functional tricuspid regurgitation (FTR) is thought to arise due to annular dilation and alteration of right ventricular (RV) geometry in the presence of normal leaflets, yet mitral leaflets have been shown to remodel significantly in functional mitral regurgitation. We set out to evaluate tricuspid valve anterior leaflet deformations in ovine FTR. Eleven animals (FTR group) underwent implantation of a pacemaker with high rate pacing to induce biventricular dysfunction and at least moderate TR. Subsequently, both FTR (n = 11) and Control (n = 12) animals underwent implantation of 6 sonomicrometry crystals around the tricuspid annulus, 4 on the anterior leaflet, and 14 on RV epicardium. Tricuspid valve geometry and anterior leaflet strains were calculated from crystal coordinates. Left ventricular ejection fraction and RV fractional area change were significantly lower in FTR animals versus Control. Tricuspid annular area, septo-lateral diameter, RV pressures were all significantly greater in the FTR group. Mean TR grade (+0-3) was 0.7 ± 0.5 in Control and 2.4 ± 0.5 in FTR (P = < 0.001). The anterior leaflet area and length increased significantly. Global radial leaflet strain was significantly lower in FTR mostly driven by decreased free edge leaflet strain. Global circumferential anterior leaflet strain was also significantly lower in FTR with more remarkable reduction in the belly region. Rapid ventricular pacing in sheep resulted in a clinically pertinent model of RV and annular dilation with FTR and leaflet enlargement. Both circumferential and radial anterior leaflet strains were significantly reduced with FTR. Functional TR may be associated with alteration of leaflet mechanical properties.

A computational model to predict cell traction-mediated prestretch in the mitral valve

Prestretch is observed in many soft biological tissues, directly influencing the mechanical behavior of the tissue in question. The development of this prestretch occurs through complex growth and remodeling phenomena, which yet remain to be elucidated. In the present study it was investigated whether local cell-mediated traction forces can explain the development of global anisotropic tissue prestretch in the mitral valve. Towards this end, a model predicting actin stress fiber-generated traction forces was implemented in a finite element framework of the mitral valve. The overall predicted magnitude of prestretch induced valvular contraction after release of in vivo boundary constraints was in good agreement with data reported on valvular retraction after excision from the heart. Next, by using a systematic variation of model parameters and structural properties, a more anisotropic prestretch development in the valve could be obtained, which was also similar to physiological values. In conclusion, this study shows that cell-generated traction forces could explain prestretch magnitude and anisotropy in the mitral valve.

Tricuspid valve leaflet strains in the beating ovine heart

The tricuspid leaflets coapt during systole to facilitate proper valve function and, thus, ensure efficient transport of deoxygenated blood to the lungs. Between their open state and closed state, the leaflets undergo large deformations. Quantification of these deformations is important for our basic scientific understanding of tricuspid valve function and for diagnostic or prognostic purposes. To date, tricuspid valve leaflet strains have never been directly quantified in vivo. To fill this gap in our knowledge, we implanted four sonomicrometry crystals per tricuspid leaflet and six crystals along the tricuspid annulus in a total of five sheep. In the beating ovine hearts, we recorded crystal coordinates alongside hemodynamic data. Once recorded, we used a finite strain kinematic framework to compute the temporal evolutions of area strain, radial strain, and circumferential strain for each leaflet. We found that leaflet strains were larger in the anterior leaflet than the posterior and septal leaflets. Additionally, we found that radial strains were larger than circumferential strains. Area strains were as large as 97% in the anterior leaflet, 31% in the posterior leaflet, and 31% in the septal leaflet. These data suggest that tricuspid valve leaflet strains are significantly larger than those in the mitral valve. Should our findings be confirmed they could suggest either that the mechanobiological equilibrium of tricuspid valve resident cells is different than that of mitral valve resident cells or that the mechanotransductive apparatus between the two varies. Either phenomenon may have important implications for the development of tricuspid valve-specific surgical techniques and medical devices.

Impact of tricuspid annular size reduction on right ventricular function, geometry and strain

OBJECTIVES

Restrictive tricuspid annuloplasty is a clinically accepted approach to treat functional tricuspid regurgitation. We set out to investigate the effect of varying degrees of tricuspid annular reduction on the right ventricular (RV) function, geometry and strain.

METHODS

Eight, healthy sheep (45 ± 4 kg) had 6 sonomicrometry crystals implanted around the tricuspid annulus and 20 onto the epicardium of the right ventricle defining 3 free wall regions: basal, mid and lower. A polypropylene annuloplasty suture was placed around the tricuspid annulus and externalized to an epicardial tourniquet. Simultaneous echocardiographic, haemodynamic and sonomicrometry data were acquired at baseline and during 5 consecutive annular reduction steps (TAR 1-5) with successive (5-7 mm) suture cinching. RV free wall circumferential, longitudinal and areal cardiac and interventional strains, RV radius of curvature (ROC), cross-sectional area and tricuspid annular dimensions were calculated from 3-dimensional crystal coordinates.

RESULTS

TAR 1-5 resulted in 19 ± 15%, 35 ± 15%, 51 ± 15%, 60 ± 15% and 68 ± 13% tricuspid annular area reduction, respectively. TAR 1 and 2 had minimal influence on the RV function, RV-ROC and strains. TAR 4 and 5 decreased RV-ROC in basal and mid-regions, but reduced the RV cross-sectional area change (from 19 ± 4% at baseline to 14 ± 3% and 13 ± 2%, respectively, P < 0.001) and circumferential and areal strains. TAR 3 significantly decreased free wall RV-ROC from 44.0 ± 1.5 to 42.6 ± 2.4 mm P < 0.001 at the RV base but maintained the regional ventricular function and strains.

CONCLUSIONS

In healthy ovine hearts, a tricuspid annular area reduction of ∼50% provides optimal conditions for reducing RV-ROC while maintaining regional RV function and strain patterns.

A fiduciary marker-based framework to assess heterogeneity and anisotropy of right ventricular epicardial strains in the beating ovine heart

Quantifying ventricular deformation in health and disease is critical to our understanding of normal heart function, heart disease mechanisms, and the effect of medical treatments. Imaging modalities have been developed that can measure ventricular deformation non-invasively. However, because of the small thickness, complex shape, and anatomic position of the right ventricle, using these technologies to determine its deformation remains challenging. Here we develop a first fiduciary marker-based method to assess heterogeneity and anisotropy of right ventricular epicardial strain across the entire free wall. To this end, we combine a high-density array of sonomicrometry crystals implanted across the entire right ventricular epicardial surface with a subdivision surface algorithm and a large deformation kinematics framework. We demonstrate our approach on four beating ovine hearts and present a preliminary regional analysis of circumferential, longitudinal, and areal strain. Moreover, we illustrate maps of the same strains across the entire right ventricular epicardial surface to highlight their spatial heterogeneity and anisotropy. We observe in these animals that RV epicardial strains vary throughout the cardiac cycle, are heterogeneous across the RV free wall, and are anisotropic with larger compressive strains, i.e., contraction, in the longitudinal direction than in the circumferential direction. Average peak compressive strains vary by region between -3.34% and -8.29% in circumferential direction, and -4.02% and -10.57% in longitudinal direction. In summary, we introduce an experimental framework that will allow us to study disease- and device-induced deformations, and long-term consequences of these deformations, including heterogeneous and anisotropic effects.

Contributions of prestrains, hyperelasticity, and muscle fiber activation on mitral valve systolic performance

The present study addresses the contributions of prestrains and muscle fiber activation to the global response of the mitral valve during systole. A finite element model of a porcine mitral valve is created using anatomical measurements and 3D echocardiographic recordings. The passive behavior of the leaflets is modeled using a transversely isotropic hyperelastic constitutive model, and we assume orthotropic muscle activations in the anterior leaflet. A simple approach to incorporate prestrains in the mitral valve apparatus is used by expanding the mitral annulus before applying the ventricular pressure to the mitral leaflets. Several finite element analyses are run with or without muscle activation and with or without prestrains. The analysis results are compared at peak systole with the echocardiograpic recordings. The case where prestrains and activation are accounted for simultaneously is the most efficient to approach the physiological flat shape of the closed valve observed in the echocardiograpic measurements. These results suggest that the active components present in the mitral leaflets and the presence of prestrains contribute to the physiological deformations of the mitral valve at peak systole and that material models based on in vitro mechanical testing are not sufficient for numerical studies of the mitral apparatus. Copyright © 2016 John Wiley & Sons, Ltd.

The impact of boundary conditions on surface curvature of polypropylene mesh in response to uniaxial loading

Exposure following pelvic organ prolapse repair has been observationally associated with wrinkling of the implanted mesh. The purpose of this study was to quantify the impact of variable boundary conditions on the out-of-plane deformations of mesh subjected to tensile loading. Using photogrammetry and surface curvature analyses, deformed geometries were accessed for two commercially available products. Relative to standard clamping methods, the amount of out-of-plane deformation significantly increased when point loads were introduced to simulate suture fixation in-vivo. These data support the hypothesis that regional increases in the concentration of mesh potentially enhance the host׳s foreign body response, leading to exposure.

Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin

Skin expansion delivers newly grown skin that maintains histological and mechanical features of the original tissue. Although it is the gold standard for cutaneous defect correction today, the underlying mechanisms remain poorly understood. Here we present a novel technique to quantify anisotropic prestrain, deformation, and growth in a porcine skin expansion model. Building on our recently proposed method, we combine two novel technologies, multi-view stereo and isogeometric analysis, to characterize skin kinematics: Upon explantation, a unit square retracts ex vivo to a square of average dimensions of [Formula: see text]. Upon expansion, the unit square deforms in vivo into a rectangle of average dimensions of [Formula: see text]. Deformations are larger parallel than perpendicular to the dorsal midline suggesting that skin responds anisotropically with smaller deformations along the skin tension lines. Upon expansion, the patch grows in vivo by [Formula: see text] with respect to the explanted, unexpanded state. Growth is larger parallel than perpendicular to the midline, suggesting that elevated stretch activates mechanotransduction pathways to stimulate tissue growth. The proposed method provides a powerful tool to characterize the kinematics of living skin. Our results shed light on the mechanobiology of skin and help us to better understand and optimize clinically relevant procedures in plastic and reconstructive surgery.

On the effect of prestrain and residual stress in thin biological membranes

Understanding the difference between ex vivo and in vivo measurements is critical to interpret the load carrying mechanisms of living biological systems. For the past four decades, the ex vivo stiffness of thin biological membranes has been characterized using uniaxial and biaxial tests with remarkably consistent stiffness parameters, even across different species. Recently, the in vivo stiffness was characterized using combined imaging techniques and inverse finite element analyses. Surprisingly, ex vivo and in vivo stiffness values differed by up to three orders of magnitude. Here, for the first time, we explain this tremendous discrepancy using the concept of prestrain. We illustrate the mathematical modeling of prestrain in nonlinear continuum mechanics through the multiplicative decomposition of the total elastic deformation into prestrain-induced and load-induced parts. Using in vivo measured membrane kinematics and associated pressure recordings, we perform an inverse finite element analysis for different prestrain levels and show that the resulting membrane stiffness may indeed differ by four orders of magnitude depending on the prestrain level. Our study motivates the hypothesis that prestrain is important to position thin biological membranes in vivo into their optimal operating range, right at the transition point of the stiffening regime. Understanding the effect of prestrain has direct clinical implications in regenerative medicine, medical device design, and and tissue engineering of replacement constructs for thin biological membranes.

Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain

Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore mitral valve physiology and pathology, and to classify the impact of novel treatment strategies. The selection of the appropriate constitutive model and the choice of its material parameters are paramount to the success of these models. However, the in vivo parameters values for these models are unknown. Here, we identify the in vivo material parameters for three common hyperelastic models for mitral valve tissue, an isotropic one and two anisotropic ones, using an inverse finite element approach. We demonstrate that the two anisotropic models provide an excellent fit to the in vivo data, with local displacement errors in the sub-millimeter range. In a complementary sensitivity analysis, we show that the identified parameter values are highly sensitive to prestrain, with some parameters varying up to four orders of magnitude. For the coupled anisotropic model, the stiffness varied from 119,021 kPa at 0 % prestrain via 36 kPa at 30 % prestrain to 9 kPa at 60 % prestrain. These results may, at least in part, explain the discrepancy between previously reported ex vivo and in vivo measurements of mitral leaflet stiffness. We believe that our study provides valuable guidelines for modeling mitral valve mechanics, selecting appropriate constitutive models, and choosing physiologically meaningful parameter values. Future studies will be necessary to experimentally and computationally investigate prestrain, to verify its existence, to quantify its magnitude, and to clarify its role in mitral valve mechanics.

Evidence of adaptive mitral leaflet growth

Ischemic mitral regurgitation is mitral insufficiency caused by myocardial infarction. Recent studies suggest that mitral leaflets have the potential to grow and reduce the degree of regurgitation. Leaflet growth has been associated with papillary muscle displacement, but role of annular dilation in leaflet growth is unclear. We tested the hypothesis that chronic leaflet stretch, induced by papillary muscle tethering and annular dilation, triggers chronic leaflet growth. To decipher the mechanisms that drive the growth process, we further quantified regional and directional variations of growth. Five adult sheep underwent coronary snare and marker placement on the left ventricle, papillary muscles, mitral annulus, and mitral leaflet. After eight days, we tightened the snares to create inferior myocardial infarction. We recorded marker coordinates at baseline, acutely (immediately post-infarction), and chronically (five weeks post-infarction). From these coordinates, we calculated acute and chronic changes in ventricular, papillary muscle, and annular geometry along with acute and chronic leaflet strains. Chronic left ventricular dilation of 17.15% (p<0.001) induced chronic posterior papillary muscle displacement of 13.49 mm (p=0.07). Chronic mitral annular area, commissural and septal-lateral distances increased by 32.50% (p=0.010), 14.11% (p=0.007), and 10.84% (p=0.010). Chronic area, circumferential, and radial growth were 15.57%, 5.91%, and 3.58%, with non-significant regional variations (p=0.868). Our study demonstrates that mechanical stretch, induced by annular dilation and papillary muscle tethering, triggers mitral leaflet growth. Understanding the mechanisms of leaflet adaptation may open new avenues to pharmacologically or surgically manipulate mechanotransduction pathways to augment mitral leaflet area and reduce the degree of regurgitation.

Development of a semi-automated method for mitral valve modeling with medial axis representation using 3D ultrasound

PURPOSE

Precise 3D modeling of the mitral valve has the potential to improve our understanding of valve morphology, particularly in the setting of mitral regurgitation (MR). Toward this goal, the authors have developed a user-initialized algorithm for reconstructing valve geometry from transesophageal 3D ultrasound (3D US) image data.

METHODS

Semi-automated image analysis was performed on transesophageal 3D US images obtained from 14 subjects with MR ranging from trace to severe. Image analysis of the mitral valve at midsystole had two stages: user-initialized segmentation and 3D deformable modeling with continuous medial representation (cm-rep). Semi-automated segmentation began with user-identification of valve location in 2D projection images generated from 3D US data. The mitral leaflets were then automatically segmented in 3D using the level set method. Second, a bileaflet deformable medial model was fitted to the binary valve segmentation by Bayesian optimization. The resulting cm-rep provided a visual reconstruction of the mitral valve, from which localized measurements of valve morphology were automatically derived. The features extracted from the fitted cm-rep included annular area, annular circumference, annular height, intercommissural width, septolateral length, total tenting volume, and percent anterior tenting volume. These measurements were compared to those obtained by expert manual tracing. Regurgitant orifice area (ROA) measurements were compared to qualitative assessments of MR severity. The accuracy of valve shape representation with cm-rep was evaluated in terms of the Dice overlap between the fitted cm-rep and its target segmentation.

RESULTS

The morphological features and anatomic ROA derived from semi-automated image analysis were consistent with manual tracing of 3D US image data and with qualitative assessments of MR severity made on clinical radiology. The fitted cm-reps accurately captured valve shape and demonstrated patient-specific differences in valve morphology among subjects with varying degrees of MR severity. Minimal variation in the Dice overlap and morphological measurements was observed when different cm-rep templates were used to initialize model fitting.

CONCLUSIONS

This study demonstrates the use of deformable medial modeling for semi-automated 3D reconstruction of mitral valve geometry using transesophageal 3D US. The proposed algorithm provides a parametric geometrical representation of the mitral leaflets, which can be used to evaluate valve morphology in clinical ultrasound images.

Mitral valve annuloplasty: a quantitative clinical and mechanical comparison of different annuloplasty devices

Mitral valve annuloplasty is a common surgical technique used in the repair of a leaking valve by implanting an annuloplasty device. To enhance repair durability, these devices are designed to increase leaflet coaptation, while preserving the native annular shape and motion; however, the precise impact of device implantation on annular deformation, strain, and curvature is unknown. In this article, we quantify how three frequently used devices significantly impair native annular dynamics. In controlled in vivo experiments, we surgically implanted 11 flexible-incomplete, 11 semi-rigid-complete, and 12 rigid-complete devices around the mitral annuli of 34 sheep, each tagged with 16 equally spaced tantalum markers. We recorded four-dimensional marker coordinates using biplane videofluoroscopy, first with device and then without, which were used to create mathematical models using piecewise cubic splines. Clinical metrics (characteristic anatomical distances) revealed significant global reduction in annular dynamics upon device implantation. Mechanical metrics (strain and curvature fields) explained this reduction via a local loss of anterior dilation and posterior contraction. Overall, all three devices unfavorably caused reduction in annular dynamics. The flexible-incomplete device, however, preserved native annular dynamics to a larger extent than the complete devices. Heterogeneous strain and curvature profiles suggest the need for heterogeneous support, which may spawn more rational design of annuloplasty devices using design concepts of functionally graded materials.

In vivo dynamic strains of the ovine anterior mitral valve leaflet

Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.

Saddle-shaped mitral valve annuloplasty rings improve leaflet coaptation geometry

OBJECTIVES

The mitral valve annulus naturally conforms to a saddle shape in systole. This configuration is believed to put the leaflets into a lower-energy equilibrium with the annulus and subvalvular apparatus. Conventional flat annuloplasty rings restrict posterior leaflet motion, which may result in a "monocusp" valve, affecting valvular stress distribution. It is hypothesized that saddle-shaped annuloplasty rings cause less distortion of the physiologic leaflet geometry than do flat rings.

METHODS

Twelve pigs were studied in an acute setting with 3-dimensional echocardiography and sonomicrometry before and after implantation of rigid flat (n = 5) and saddle-shaped (n = 7) annuloplasty rings. The rings were true sized to the annulus with equal anterior-posterior and commissure-commissure circumferential dimensions. The saddle-shaped rings had an annular height to commissural width ratio of 15%.

RESULTS

Saddle-shaped rings maintained both leaflets operational (P < .01). Flat rings made the posterior leaflet immobile and the anterior leaflet aligned flat along the annulus in systole, effectively resulting in monoleaflet function. The average distance from the papillary muscle tips to the posterior annulus decreased by 2.4 ± 0.4 mm after flat ring implantation (P < .01).

CONCLUSIONS

Saddle-shaped annuloplasty rings provide better leaflet coaptation geometry than do flat rings by not hoisting the papillary muscles toward the posterior annulus through the commissural chordae, allowing greater leaflet mobility. This entails a potentially beneficial impact on valvular stress distribution that could affect durability of the repaired valve.

Anterior mitral leaflet curvature during the cardiac cycle in the normal ovine heart

BACKGROUND

The dynamic changes of anterior mitral leaflet (AML) curvature are of primary importance for optimal left ventricular filling and emptying but are incompletely characterized.

METHODS AND RESULTS

Sixteen radiopaque markers were sutured to the AML in 11 sheep, and 4-dimensional marker coordinates were acquired with biplane videofluoroscopy. A surface subdivision algorithm was applied to compute the curvature across the AML at midsystole and at maximal valve opening. Septal-lateral (SL) and commissure-commissure (CC) curvature profiles were calculated along the SL AML meridian (M(SL))and CC AML meridian (M(CC)), respectively, with positive curvature being concave toward the left atrium. At midsystole, the M(SL) was concave near the mitral annulus, turned from concave to convex across the belly, and was convex along the free edge. At maximal valve opening, the M(SL) was flat near the annulus, turned from slightly concave to convex across the belly, and flattened toward the free edge. In contrast, the M(CC) was concave near both commissures and convex at the belly at midsystole but convex near both commissures and concave at the belly at maximal valve opening.

CONCLUSIONS

While the SL curvature of the AML along the M(SL) is similar across the belly region at midsystole and early diastole, the CC curvature of the AML along the M(CC) flips, with the belly being convex to the left atrium at midsystole and concave at maximal valve opening. These curvature orientations suggest optimal left ventricular inflow and outflow shapes of the AML and should be preserved during catheter or surgical interventions.