Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

An integrated framework for finite-element modeling of mitral valve biomechanics from medical images: application to MitralClip intervention planning

Treatment of mitral valve (MV) diseases requires comprehensive clinical evaluation and therapy personalization to optimize outcomes. Finite-element models (FEMs) of MV physiology have been proposed to study the biomechanical impact of MV repair, but their translation into the clinics remains challenging. As a step towards this goal, we present an integrated framework for finite-element modeling of the MV closure based on patient-specific anatomies and boundary conditions. Starting from temporal medical images, we estimate a comprehensive model of the MV apparatus dynamics, including papillary tips, using a machine-learning approach. A detailed model of the open MV at end-diastole is then computed, which is finally closed according to a FEM of MV biomechanics. The motion of the mitral annulus and papillary tips are constrained from the image data for increased accuracy. A sensitivity analysis of our system shows that chordae rest length and boundary conditions have a significant influence upon the simulation results. We quantitatively test the generalization of our framework on 25 consecutive patients. Comparisons between the simulated closed valve and ground truth show encouraging results (average point-to-mesh distance: 1.49 ± 0.62 mm) but also the need for personalization of tissue properties, as illustrated in three patients. Finally, the predictive power of our model is tested on one patient who underwent MitralClip by comparing the simulated intervention with the real outcome in terms of MV closure, yielding promising prediction. By providing an integrated way to perform MV simulation, our framework may constitute a surrogate tool for model validation and therapy planning.

Frontiers in growth and remodeling

Unlike common engineering materials, living matter can autonomously respond to environmental changes. Living structures can grow stronger, weaker, larger, or smaller within months, weeks, or days as a result of a continuous microstructural turnover and renewal. Hard tissues can adapt by increasing their density and grow strong. Soft tissues can adapt by increasing their volume and grow large. For more than three decades, the mechanics community has actively contributed to understand the phenomena of growth and remodeling from a mechanistic point of view. However, to date, there is no single, unified characterization of growth, which is equally accepted by all scientists in the field. Here we shed light on the continuum modeling of growth and remodeling of living matter, and give a comprehensive overview of historical developments and trends. We provide a state-of-the-art review of current research highlights, and discuss challenges and potential future directions. Using the example of volumetric growth, we illustrate how we can establish and utilize growth theories to characterize the functional adaptation of soft living matter. We anticipate this review to be the starting point for critical discussions and future research in growth and remodeling, with a potential impact on life science and medicine.

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.

The mechanobiology of mitral valve function, degeneration, and repair

In degenerative valve disease, the highly organized mitral valve leaflet matrix stratification is progressively destroyed and replaced with proteoglycan rich, mechanically inadequate tissue. This is driven by the actions of originally quiescent valve interstitial cells that become active contractile and migratory myofibroblasts. While treatment for myxomatous mitral valve disease in humans ranges from repair to total replacement, therapies in dogs focus on treating the consequences of the resulting mitral regurgitation. The fundamental gap in our understanding is how the resident valve cells respond to altered mechanical signals to drive tissue remodeling. Despite the pathological similarities and high clinical occurrence, surprisingly little mechanistic insight has been gleaned from the dog. This review presents what is known about mitral valve mechanobiology from clinical, in vivo, and in vitro data. There are a number of experimental strategies already available to pursue this significant opportunity, but success requires the collaboration between veterinary clinicians, scientists, and engineers.

On the in vivo deformation of the mitral valve anterior leaflet: effects of annular geometry and referential configuration

Alteration of the native mitral valve (MV) shape has been hypothesized to have a profound effect on the local tissue stress distribution, and is potentially linked to limitations in repair durability. The present study was undertaken to elucidate the relation between MV annular shape and central mitral valve anterior leaflet (MVAL) strain history, using flat annuloplasty in an ovine model. In addition, we report for the first time the presence of residual in vivo leaflet strains. In vivo leaflet deformations were measured using sonocrystal transducers sutured to the MVAL (n = 10), with the 3D positions acquired over the full cardiac cycle. In six animals a flat ring was sutured to the annulus and the transducer positions recorded, while in the remaining four the MV was excised from the exsanguinated heart and the stress-free transducer positions obtained. In the central region of the MVAL the peak stretch values, referenced to the minimum left ventricular pressure (LVP), were 1.10 ± 0.01 and 1.31 ± 0.03 (mean ± standard error) in the circumferential and radial directions, respectively. Following flat ring annuloplasty, the central MVAL contracted 28% circumferentially and elongated 16% radially at minimum LVP, and the circumferential direction was under a negative strain state during the entire cardiac cycle. After valve excision from the exsanguinated heart, the MVAL contracted significantly (18 and 30% in the circumferential and radial directions, respectively), indicating the presence of substantial in vivo residual strains. While the physiological function of the residual strains (and their associated stresses) are at present unknown, accounting for their presence is clearly necessary for accurate computational simulations of MV function. Moreover, we demonstrated that changes in annular geometry dramatically alter valvular functional strains in vivo. As levels of homeostatic strains are related to tissue remodeling and homeostasis, our results suggest that surgically introduced alterations in MV shape could lead to the long term MV mechanobiological and microstructural alterations that could ultimately affect MV repair durability.

Semi-automated mitral valve morphometry and computational stress analysis using 3D ultrasound

In vivo human mitral valves (MV) were imaged using real-time 3D transesophageal echocardiography (rt-3DTEE), and volumetric images of the MV at mid-systole were analyzed by user-initialized segmentation and 3D deformable modeling with continuous medial representation, a compact representation of shape. The resulting MV models were loaded with physiologic pressures using finite element analysis (FEA). We present the regional leaflet stress distributions predicted in normal and diseased (regurgitant) MVs. Rt-3DTEE, semi-automated leaflet segmentation, 3D deformable modeling, and FEA modeling of the in vivo human MV is tenable and useful for evaluation of MV pathology.

Mechanism of valvular regurgitation

PURPOSE OF REVIEW

Despite improvements in surgical techniques, valvular regurgitation results in major morbidity in children with heart disease. Functional anatomy, mechanisms of valve closure and adaptation to changing hemodynamic stress in normal mitral and tricuspid valves are complex and only partially understood. As well, pathology of atrioventricular valve regurgitation is further complicated by congenital valve abnormalities involving leaflet tissue, supporting chordal apparatus and displaced papillary muscles. This review provides a current understanding of the mechanisms that result in atrioventricular valve failure.

RECENT FINDINGS

Mitral valve leaflets have contractile elements, in addition to atrial muscle modulation of leaflet tension. When placed under mechanical tethering stress, the mitral valve adapts by leaflet expansion, which increases coaptation surface reserve and chordal thickening. Both pediatric and adult studies are increasingly reporting on the importance of subvalvar apparatus function in maintaining valve competency.

SUMMARY

The maintenance of efficient valve function is accomplished by a complex series of events involving atrial and annular contraction, annular deformation, active leaflet tension, chordal transmission of papillary muscle contractions and ventricular contraction.

Electromechanical coupling between the atria and mitral valve

Anterior leaflet (AL) stiffening during isovolumic contraction (IVC) may aid mitral valve closure. We tested the hypothesis that AL stiffening requires atrial depolarization. Ten sheep had radioopaque-marker arrays implanted in the left ventricle, mitral annulus, AL, and papillary muscle tips. Four-dimensional marker coordinates (x, y, z, and t) were obtained from biplane videofluoroscopy at baseline (control, CTRL) and during basal interventricular-septal pacing (no atrial contraction, NAC; 110-117 beats/min) to generate ventricular depolarization not preceded by atrial depolarization. Circumferential and radial stiffness values, reflecting force generation in three leaflet regions (annular, belly, and free-edge), were obtained from finite-element analysis of AL displacements in response to transleaflet pressure changes during both IVC and isovolumic relaxation (IVR). In CTRL, IVC circumferential and radial stiffness was 46 ± 6% greater than IVR stiffness in all regions (P < 0.001). In NAC, AL annular IVC stiffness decreased by 25% (P = 0.004) in the circumferential and 31% (P = 0.005) in the radial directions relative to CTRL, without affecting edge stiffness. Thus AL annular stiffening during IVC was abolished when atrial depolarization did not precede ventricular systole, in support of the hypothesis. The likely mechanism underlying AL annular stiffening during IVC is contraction of cardiac muscle that extends into the leaflet and requires atrial excitation. The AL edge has no cardiac muscle, and thus IVC AL edge stiffness was not affected by loss of atrial depolarization. These findings suggest one reason why heart block, atrial dysrhythmias, or ventricular pacing may be accompanied by mitral regurgitation or may worsen regurgitation when already present.

Multiple mitral leaflet contractile systems in the beating heart

Mitral valve closure may be aided by contraction of anterior leaflet (AL) cardiac myocytes located in the annular third of the leaflet. This contraction, observed as a stiffening of the annular region of the AL during isovolumic contraction (IVC), is abolished by beta-blockade (βB). Sub-threshold rapid pacing in the region of aorto-mitral continuity (STIM) also causes AL stiffening, although this increases the stiffness of the entire leaflet during both IVC and isovolumic relaxation (IVR). We investigated whether these contractile events share a common pathway or whether multiple AL contractile mechanisms may be present. Ten sheep had radiopaque-markers implanted: 13 silhouetting the LV, 16 on the mitral annulus, an array of 16 on the AL, and one on each papillary muscle tip. 4-D marker coordinates were obtained from biplane videofluoroscopy during control (C), βB (esmolol) and during βB+STIM. Circumferential and radial stiffness values for three AL regions (Annular, Belly, and free-Edge), were obtained from inverse finite element analysis of AL displacements in response to trans-leaflet pressure changes during IVC and IVR. βB+STIM increased stiffness values in all regions at both IVC and IVR by 35 ± 7% relative to βB (p<0.001). Thus, even when AL myocyte contraction was blocked by βB, STIM stiffened all regions of the AL during both IVC and IVR. This demonstrates the presence of at least two contractile systems in the AL; one being the AL annular cardiac muscle, involving a β-dependent pathway, others via a β-independent pathway, likely involving valvular interstitial cells and/or AL smooth muscle cells.

A novel approach to in vivo mitral valve stress analysis

Three-dimensional (3-D) echocardiography allows the generation of anatomically correct and time-resolved geometric mitral valve (MV) models. However, as imaged in vivo, the MV assumes its systolic geometric configuration only when loaded. Customarily, finite element analysis (FEA) is used to predict material stress and strain fields rendered by applying a load on an initially unloaded model. Therefore, this study endeavors to provide a framework for the application of in vivo MV geometry and FEA to MV physiology, pathophysiology, and surgical repair. We hypothesize that in vivo MV geometry can be reasonably used as a surrogate for the unloaded valve in computational (FEA) simulations, yielding reasonable and meaningful stress and strain magnitudes and distributions. Three experiments were undertaken to demonstrate that the MV leaflets are relatively nondeformed during systolic loading: 1) leaflet strain in vivo was measured using sonomicrometry in an ovine model, 2) hybrid models of normal human MVs as constructed using transesophageal real-time 3-D echocardiography (rt-3DE) were repeatedly loaded using FEA, and 3) serial rt-3DE images of normal human MVs were used to construct models at end diastole and end isovolumic contraction to detect any deformation during isovolumic contraction. The average linear strain associated with isovolumic contraction was 0.02 ± 0.01, measured in vivo with sonomicrometry. Repeated loading of the hybrid normal human MV demonstrated little change in stress or geometry: peak von Mises stress changed by <4% at all locations on the anterior and posterior leaflets. Finally, the in vivo human MV deformed minimally during isovolumic contraction, as measured by the mean absolute difference calculated over the surfaces of both leaflets between serial MV models: 0.53 ± 0.19 mm. FEA modeling of MV models derived from in vivo high-resolution truly 3-D imaging is reasonable and useful for stress prediction in MV pathologies and repairs.

Design and validation of a novel splashing bioreactor system for use in mitral valve organ culture

Previous research in our lab suggested that heart valve tissues cultured without mechanical stimulation do not retain their in vivo microstructure, i.e., cell density decreased within the deep tissue layers and increased at the periphery. In this study, a splashing rotating bioreactor was designed to apply mechanical stimulation to a mitral valve leaflet segment. Porcine valve segments (n = 9-10 per group) were cultured in the bioreactor for 2 weeks (dynamic culture), negative controls were cultured without mechanical stimulation (static culture), and baseline controls were fresh uncultured samples. Overall changes in cellularity and extracellular matrix (ECM) structure were assessed by H&E and Movat pentachrome stains. Tissues were also immunostained for multiple ECM components and turnover mediators. After 2 weeks of culture, proliferating cells were distributed throughout the tissue in segments cultured in the bioreactor, in contrast to segments cultured without mechanical stimulation. Most ECM components, especially collagen types I and III, better maintained normal expression patterns and magnitudes (as found in baseline controls) over 2 weeks of dynamic organ culture compared to static culture. Lack of mechanical stimulation changed several aspects of the tissue microstructure, including the cell distribution and ECM locations. In conclusion, mechanical stimulation by the bioreactor maintained tissue integrity, which will enable future in vitro investigation of mitral valve remodeling.

Transient stiffening of mitral valve leaflets in the beating heart

Anterior mitral leaflet stiffness during isovolumic contraction (IVC) is much greater than that during isovolumic relaxation (IVR). We have hypothesized that this stiffening is due to transient early systolic force development in the slip of cardiac myocytes in the annular third of the anterior leaflet. Because the atrium is excited before IVC and leaflet myocytes contract for < or = 250 ms, this hypothesis predicts that IVC leaflet stiffness will drop to near-IVR values in the latter half of ventricular systole. We tested this prediction using radiopaque markers and inverse finite element analysis of 30 beats in 10 ovine hearts. For each beat, circumferential (E(c)) and radial (E(r)) stiffness was determined during IVC (Deltat(1)), end IVC to midsystole (Deltat(2)), midsystole to IVR onset (Deltat(3)), and IVR (Deltat(4)). Group mean stiffness (E(c) + or - SD; E(r) + or - SD; in N/mm(2)) during Deltat(1) (44 + or - 16; 15 + or - 4) was 1.6-1.7 times that during Deltat(4) (28 + or - 11; 9 + or - 3); Deltat(2) stiffness (39 + or - 15; 14 + or - 4) was 1.3-1.5 times that of Deltat(4), but Deltat(3) stiffness (32 + or - 12; 11 + or - 3) was only 1.1-1.2 times that of Deltat(4). The stiffness drop during Deltat(3) supports the hypothesis that anterior leaflet stiffening during IVC arises primarily from transient force development in leaflet cardiac myocytes, with stiffness reduced as this leaflet muscle relaxes in the latter half of ventricular systole.

Mitral Valve Finite Element Modeling: Implications of Tissues’ Nonlinear Response and Annular Motion

Finite element modeling represents an established method for the comprehension of the mitral function and for the simulation of interesting clinical scenarios. However, current models still do not include all the key aspects of the real system. We implemented a new structural finite element model that considers (i) an accurate morphological description of the valve, (ii) a description of the tissues’ mechanical properties that accounts for anisotropy and nonlinearity, and (iii) dynamic boundary conditions that mimic annulus and papillary muscles’ contraction. The influence of such contraction on valve biomechanics was assessed by comparing the computed results with the ones obtained through an auxiliary model with fixed annulus and papillary muscles. At the systolic peak, the leaflets’ maximum principal stress contour showed peak values in the anterior leaflet at the strut chordae insertion zone (300 kPa) and near the annulus (200–250 kPa), while much lower values were detected in the posterior leaflet. Both leaflets underwent larger tensile strains in the longitudinal direction, while in the circumferential one the anterior leaflet experienced nominal tensile strains up to 18% and the posterior one experienced compressive strains up to 23% associated with the folding of commissures and paracommissures, consistently with tissue redundancy. The force exerted by papillary muscles at the systolic peak was equal to 4.11 N, mainly borne by marginal chordae (76% of the force). Local reaction forces up to 45 mN were calculated on the annulus, leading to tensions of 89 N/m and 54 N/m for its anterior and posterior tracts, respectively. The comparison with the results of the auxiliary model showed that annular contraction mainly affects the leaflets’ circumferential strains. When it was suppressed, no more compressive strains could be observed and peak strain values were located in the belly of the anterior leaflet. Computational results agree to a great extent with experimental data from literature. They provided insight into some of the features characterizing normal mitral function, such as annular contraction and leaflets’ tissue anisotropy and nonlinearity. Some of the computed results may be useful in the design of surgical devices and techniques. In particular, forces applied on the annulus by the surrounding tissues could be considered as an indication for annular prostheses design.

Regional stiffening of the mitral valve anterior leaflet in the beating ovine heart

Left atrial muscle extends into the proximal third of the mitral valve (MV) anterior leaflet and transient tensing of this muscle has been proposed as a mechanism aiding valve closure. If such tensing occurs, regional stiffness in the proximal anterior mitral leaflet will be greater during isovolumic contraction (IVC) than isovolumic relaxation (IVR) and this regional stiffness difference will be selectively abolished by beta-receptor blockade. We tested this hypothesis in the beating ovine heart. Radiopaque markers were sewn around the MV annulus and on the anterior MV leaflet in 10 sheep hearts. Four-dimensional marker coordinates were obtained from biplane videofluoroscopy before (CRTL) and after administration of esmolol (ESML). Heterogeneous finite element models of each anterior leaflet were developed using marker coordinates over matched pressures during IVC and IVR for CRTL and ESML. Leaflet displacements were simulated using measured left ventricular and atrial pressures and a response function was computed as the difference between simulated and measured displacements. Circumferential and radial elastic moduli for ANNULAR, BELLY and EDGE leaflet regions were iteratively varied until the response function reached a minimum. The stiffness values at this minimum were interpreted as the in vivo regional material properties of the anterior leaflet. For all regions and all CTRL beats IVC stiffness was 40-58% greater than IVR stiffness. ESML reduced ANNULAR IVC stiffness to ANNULAR IVR stiffness values. These results strongly implicate transient tensing of leaflet atrial muscle during IVC as the basis of the ANNULAR IVC-IVR stiffness difference.

Characterization of mitral valve anterior leaflet perfusion patterns

BACKGROUND AND AIM OF THE STUDY

Although previous histologic studies have demonstrated the presence of blood vessels in the anterior mitral leaflet (AML) and second-order chordae (SC), little is known of the pattern of leaflet perfusion. Hence, the pattern and source of AML perfusion was investigated in an ovine model.

METHODS

Fluorescein angiograms were obtained in 17 ovine hearts immediately after heparinization and cardioplegic arrest, using non-selective left coronary artery (LCA) and selective left anterior descending (LAD), proximal, mid- and distal left circumflex (LCx) perfusion. Serial photographs using a flash/filter system to optimize fluorescence were obtained through a left atriotomy.

RESULTS

The proximal half of the AML was seen to be richly vascularized. A loop of vessels was consistently observed in the mitral annulus and AML; these vessels ran along the annulus, extended to the sites of SC insertion, and created anastomoses between these insertions. The SC contributed to the AML perfusion and the anastomotic loop. Selective perfusion of the LAD or proximal LCx artery (ligated before the first obtuse marginal artery) did not perfuse the AML (n = 6). Perfusion of the mid- and distal LCx (n = 7) consistently supplied the AML via SC insertion sites and annular branches.

CONCLUSION

The ovine AML is perfused by vessels that run through the SC and annulus simultaneously, and then create a communicating arcade in the leaflet. These vessels originate from the mid- and distal portions of the LCx. A loss of perfusion as a result of microvascular disease could have adverse implications. Derangements in the extensive vascular component of the mitral valve could be an important contributing factor to valve disease.

Stress-strain behavior of mitral valve leaflets in the beating ovine heart

Excised anterior mitral leaflets exhibit anisotropic, non-linear material behavior with pre-transitional stiffness ranging from 0.06 to 0.09 N/mm(2) and post-transitional stiffness from 2 to 9 N/mm(2). We used inverse finite element (FE) analysis to test, for the first time, whether the anterior mitral leaflet (AML), in vivo, exhibits similar non-linear behavior during isovolumic relaxation (IVR). Miniature radiopaque markers were sewn to the mitral annulus, AML, and papillary muscles in 8 sheep. Four-dimensional marker coordinates were obtained using biplane videofluoroscopic imaging during three consecutive cardiac cycles. A FE model of the AML was developed using marker coordinates at the end of isovolumic relaxation (when pressure difference across the valve is approximately zero), as the reference state. AML displacements were simulated during IVR using measured left ventricular and atrial pressures. AML elastic moduli in the radial and circumferential directions were obtained for each heartbeat by inverse FEA, minimizing the difference between simulated and measured displacements. Stress-strain curves for each beat were obtained from the FE model at incrementally increasing transmitral pressure intervals during IVR. Linear regression of 24 individual stress-strain curves (8 hearts, 3 beats each) yielded a mean (+/-SD) linear correlation coefficient (r(2)) of 0.994+/-0.003 for the circumferential direction and 0.995+/-0.003 for the radial direction. Thus, unlike isolated leaflets, the AML, in vivo, operates linearly over a physiologic range of pressures in the closed mitral valve.

Active stiffening of mitral valve leaflets in the beating heart

The anterior leaflet of the mitral valve (MV), viewed traditionally as a passive membrane, is shown to be a highly active structure in the beating heart. Two types of leaflet contractile activity are demonstrated: 1) a brief twitch at the beginning of each beat (reflecting contraction of myocytes in the leaflet in communication with and excited by left atrial muscle) that is relaxed by midsystole and whose contractile activity is eliminated with beta-receptor blockade and 2) sustained tone during isovolumic relaxation, insensitive to beta-blockade, but doubled by stimulation of the neurally rich region of aortic-mitral continuity. These findings raise the possibility that these leaflets are neurally controlled tissues, with potentially adaptive capabilities to meet the changing physiological demands on the heart. They also provide a basis for a permanent paradigm shift from one viewing the leaflets as passive flaps to one viewing them as active tissues whose complex function and dysfunction must be taken into account when considering not only therapeutic approaches to MV disease, but even the definitions of MV disease itself.