Shape of the mitral annulus in normal individuals and dilated cardiomyopathies: computational modeling insights into leaflet stress distribution

Introduction: The mitral valve annulus naturally adopts a saddle shape in systole, likely concentrating systolic stress on the commissures where fibrous trigones are located. This study hypothesized that in patients with dilated cardiomyopathies, where the annulus is large and planar, the stress would be redirected. Methods: Computational modeling was employed to compare the stress distribution in saddle-shaped mitral valves (n.10 patients) with planar annuli seen in dilated cardiomyopathy (n.10 patients) using kinematics of the mitral valve annulus from systole to diastole extrapolated from computed tomography angiography. Results: Simulations revealed high stress near the anterolateral and posteromedial commissures in normal valves, in contrast to high leaflet stress in planar annuli. Significant differences in stress distribution were observed near the anterolateral (S = 0.427 ± 0.053 MPa in normal valves vs S = 0.211 ± 0.123 MPa in diseased valves, p < 0.001) and posterolateral commissures (S = 0.340 ± 0.008 MPa in normal valves vs S = 0.208 ± 0.060 MPa in diseased valves, p < 0.001). Additionally, mitral annulus disjunction was present in healthy patients but absent in those with annulus planarity due to dilated cardiomyopathy. Discussion: This study suggests that while the saddle-shaped annulus focuses leaflet stress on commissures, planar annuli distribute systolic stress over leaflet surfaces. This may trigger embryonic pathways and alter mitral leaflet collagen content, ultimately leading to valve remodeling. Identifying patients with early annular planarity prior to substantial leaflet remodeling may provide early treatments to prevent increasing mitral regurgitation.

Image-based simulation of mitral valve dynamic closure including anisotropy

Simulation of the dynamic behavior of mitral valve closure could improve clinical treatment by predicting surgical procedures outcome. We propose here a method to achieve this goal by using the immersed boundary method. In order to go towards patient-based simulation, we tailor our method to be adapted to a valve extracted from medical image data. It includes investigating segmentation process, smoothness of geometry, case setup and the shape of the left ventricle. We also study the influence of leaflet tissue anisotropy on the quality of the valve closure by comparing with an isotropic model. As part of the anisotropy analysis, we study the influence of the principal material direction by comparing methods to obtain them without dissection. Results show that our method can be scaled to various image-based data. We evaluate the mitral valve closure quality based on measuring bulging area, contact map, and flow rate. The results show also that the anisotropic material model more precisely represents the physiological characteristics of the valve tissue. Furthermore, results indicate that the orientation of the principal material direction plays a role in the effectiveness of the valve seal.

An In Silico Model for Predicting the Efficacy of Edge-to-Edge Repair for Mitral Regurgitation

In recent years, transcatheter edge-to-edge repair (TEER) has been widely adopted as an effective treatment for mitral regurgitation (MR). The aim of this study is to develop a personalized in silico model to predict the effect of edge-to-edge repair in advance to the procedure for each individual patient. For this purpose, we propose a combination of a valve deformation model for computing the mitral valve (MV) orifice area (MVOA) and a lumped parameter model for the hemodynamics, specifically mitral regurgitation volume (RVol). Although we cannot obtain detailed information on the three-dimensional flow field near the mitral valve, we can rapidly simulate the important medical parameters for the clinical decision support. In the present method, we construct the patient-specific pre-operative models by using the parameter optimization and then simulate the postoperative state by applying the additional clipping condition. The computed preclip MVOAs show good agreement with the clinical measurements, and the correlation coefficient takes 0.998. In addition, the MR grade in terms of RVol also has good correlation with the grade by ground truth MVOA. Finally, we try to investigate the applicability for the predicting the postclip state. The simulated valve shapes clearly show the well-known double orifice and the improvement of the MVOA, compared with the preclip state. Similarly, we confirmed the improved reverse flow and MR grade in terms of RVol. A total computational time is approximately 8 h by using general-purpose PC. These results obviously indicate that the present in silico model has good capability for the assessment of edge-to-edge repair.

A geometry-based finite element tool for evaluating mitral valve biomechanics

Mitral valve function depends on its complex geometry and tissue health, with alterations in shape and tissue response affecting the long-term restorarion of function. Previous computational frameworks for biomechanical assessment are mostly based on patient-specific geometries; however, these are not flexible enough to yield a variety of models and assess mitral closure for individually tuned morphological parameters or material property representations. This study details the finite element approach implemented in our previously developed toolbox to assess mitral valve biomechanics and showcases its flexibility through the generation and biomechanical evaluation of different models. A healthy valve geometry was generated and its computational predictions for biomechanics validated against data in the literature. Moreover, two mitral valve models including geometric alterations associated with disease were generated and analysed. The healthy mitral valve model yielded biomechanical predictions in terms of valve closure dynamics, leaflet stresses and papillary muscle and chordae forces comparable to previous computational and experimental studies. Mitral valve function was compromised in geometries representing disease, expressed by the presence of regurgitating areas, elevated stress on the leaflets and unbalanced subvalvular apparatus forces. This showcases the flexibility of the toolbox concerning the generation of a range of mitral valve models with varying geometric definitions and material properties and the evaluation of their biomechanics.

A toolbox for generating scalable mitral valve morphometric models

The mitral valve is a complex anatomical structure, whose shape is key to several traits of its function and disease, being crucial for the success of surgical repair and implantation of medical devices. The aim of this study was to develop a parametric, scalable, and clinically useful model of the mitral valve, enabling the biomechanical evaluation of mitral repair techniques through finite element simulations. MATLAB was used to parameterize the valve: the annular boundary was sampled from a porcine mitral valve mesh model and landmark points and relevant boundaries were selected for the parameterization of leaflets using polynomial fitting. Several geometric parameters describing the annulus, leaflet shape and papillary muscle position were implemented and used to scale the model according to patient dimensions. The developed model, available as a toolbox, allows for the generation of a population of models using patient-specific dimensions obtained from medical imaging or averaged dimensions evaluated from empirical equations based on the Golden Proportion. The average model developed using this framework accurately represents mitral valve shapes, associated with relative errors reaching less than 10% for annular and leaflet length dimensions, and less than 24% in comparison with clinical data. Moreover, model generation takes less than 5 min of computing time, and the toolbox can account for individual morphological variations and be employed to evaluate mitral valve biomechanics; following further development and validation, it will aid clinicians when choosing the best patient-specific clinical intervention and improve the design process of new medical devices.

Geometric description for the anatomy of the mitral valve: A review

The mitral valve is a complex anatomical structure whose physiological functioning relies on the biomechanical properties and structural integrity of its components. Their compromise can lead to mitral valve dysfunction, associated with morbidity and mortality. Therefore, a review on the morphometry of the mitral valve is crucial, more specifically on the importance of valve dimensions and shape for its function. This review initially provides a brief background on the anatomy and physiology of the mitral valve, followed by an analysis of the morphological information available. A characterisation of mathematical descriptions of several parts of the valve is performed and the impact of different dimensions and shape changes in disease is then outlined. Finally, a section regarding future directions and recommendations for the use of morphometric information in clinical analysis of the mitral valve is presented.

On the simulation of mitral valve function in health, disease, and treatment

The mitral valve (MV) is the heart valve that regulates blood ?ow between the left atrium and left ventricle (LV). In situations where the MV fails to fully cover the left atrioventricular ori?ce during systole, the resulting regurgitation causes pulmonary congestion, leading to heart failure and/or stroke. The causes of MV insuf?ciency can be either primary (e.g. myxomatous degeneration) where the valvular tissue is organically diseased, or secondary (typically inducded by ischemic cardiomyopathy) termed ischemic mitral regurgitation (IMR), is brought on by adverse LV remodeling. IMR is present in up to 40% of patients and more than doubles the probability of cardiovascular morbidity after 3.5 years. There is now agreement that adjunctive procedures are required to treat IMR caused by lea?et tethering. However, there is no consensus regarding the best procedure. Multicenter registries and randomized trials would be necessary to prove which procedure is superior. Given the number of proposed procedures and the complexity and duration of such studies, it is highly unlikely that IMR procedure optimization will be achieved by prospective clinical trials. There is thus an urgent need for cell and tissue physiologically based quantitative assessments of MV function to better design surgical solutions and associated therapies. Novel computational approaches directed towards optimized surgical repair procedures can substantially reduce the need for such trial-and-error approaches. We present the details of our MV modeling techniques, with an emphasis on what is known and investigated at various length scales.

On the chordae structure and dynamic behaviour of the mitral valve

We develop a fluid-structure interaction (FSI) model of the mitral valve (MV) that uses an anatomically and physiologically realistic description of the MV leaflets and chordae tendineae. Three different chordae models-complex, 'pseudo-fibre' and simplified chordae-are compared to determine how different chordae representations affect the dynamics of the MV. The leaflets and chordae are modelled as fibre-reinforced hyperelastic materials, and FSI is modelled using an immersed boundary-finite element method. The MV model is first verified under static boundary conditions against the commercial finite element software ABAQUS and then used to simulate MV dynamics under physiological pressure conditions. Interesting flow patterns and vortex formulation are observed in all three cases. To quantify the highly complex system behaviour resulting from FSI, an energy budget analysis of the coupled MV FSI model is performed. Results show that the complex and pseudo-fibre chordae models yield good valve closure during systole but that the simplified chordae model leads to poorer leaflet coaptation and an unrealistic bulge in the anterior leaflet belly. An energy budget analysis shows that the MV models with complex and pseudo-fibre chordae have similar energy distribution patterns but the MV model with the simplified chordae consumes more energy, especially during valve closing and opening. We find that the complex chordae and pseudo-fibre chordae have similar impact on the overall MV function but that the simplified chordae representation is less accurate. Because a pseudo-fibre chordal structure is easier to construct and less computationally intensive, it may be a good candidate for modelling MV dynamics or interaction between the MV and heart in patient-specific applications.

Modelling mitral valvular dynamics-current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed.

The geometric model of the human mitral valve

The mitral valve, which lies between the left atrium and the left ventricle, plays an important role in controlling the uniflux of blood from the left atrium to the left ventricle as one of the four human heart valves. A precise description of the shape of human mitral valve has vital significance in studying its physiological structure and periodic movement. Unsatisfyingly, there is almost no unified mathematical description of the same shape of human mitral valve in literature. In this paper, we present a geometric model for human mitral valve, as an elastic shell with a special shape. Parametric equations for the shape of human mitral valve are provided, including the anterior and the posterior parts, which can be thought as portions of two interfacing semi-elliptic cylindrical shells. The minor axis of one ellipse is equal to the major axis of the other. All the parameters are determined from the statistical data. Comparison of fitting results with existing examples validates the accuracy of our geometric model. Based on the fitting shape, one can further simulate the physiological function of the mitral valve using a suitable dynamic physical equation.

In vitro and in silico approaches to quantify the effects of the Mitraclip® system on mitral valve function

Mitraclip^® implantation is widely used as a valid alternative to conventional open-chest surgery in high-risk patients with severe mitral valve (MV) regurgitation. Although effective in reducing mitral regurgitation (MR) in the majority of cases, the clip implantation produces a double-orifice area that can result in altered MV biomechanics, particularly in term of hemodynamics and mechanical stress distribution on the leaflets. In this scenario, we combined the consistency of in vitro experimental platforms with the versatility of numerical simulations to investigate clip impact on MV functioning. The fluid dynamic determinants of the procedure were experimentally investigated under different working conditions (from 40bpm to 100bpm of simulated heart rate) on six swine hearts; subsequently, fluid dynamic data served as realistic boundary conditions in a computational framework able to quantitatively assess the post-procedural MV biomechanics. The finite element model of a human mitral valve featuring an isolated posterior leaflet prolapse was reconstructed from cardiac magnetic resonance. A complete as well as a marginal, sub-optimal grasping of the leaflets were finally simulated. The clipping procedure resulted in a properly coapting valve from the geometrical perspective in all the simulated configurations. Symmetrical complete grasping resulted in symmetrical distribution of the mechanical stress, while uncomplete asymmetrical grasping resulted in higher stress distribution, particularly on the prolapsing leaflet. This work pinpointed that the mechanical stress distribution following the clipping procedure is dependent on the cardiac hemodynamics and has a correlation with the proper execution of the grasping procedure, requiring accurate evaluation prior to clip delivery.

On the effects of leaflet microstructure and constitutive model on the closing behavior of the mitral valve

Recent long-term studies showed an unsatisfactory recurrence rate of severe mitral regurgitation 3-5 years after surgical repair, suggesting that excessive tissue stresses and the resulting strain-induced tissue failure are potential etiological factors controlling the success of surgical repair for treating mitral valve (MV) diseases. We hypothesized that restoring normal MV tissue stresses in MV repair techniques would ultimately lead to improved repair durability through the restoration of MV normal homeostatic state. Therefore, we developed a micro- and macro- anatomically accurate MV finite element model by incorporating actual fiber microstructural architecture and a realistic structure-based constitutive model. We investigated MV closing behaviors, with extensive in vitro data used for validating the proposed model. Comparative and parametric studies were conducted to identify essential model fidelity and information for achieving desirable accuracy. More importantly, for the first time, the interrelationship between the local fiber ensemble behavior and the organ-level MV closing behavior was investigated using a computational simulation. These novel results indicated not only the appropriate parameter ranges, but also the importance of the microstructural tuning (i.e., straightening and re-orientation) of the collagen/elastin fiber networks at the macroscopic tissue level for facilitating the proper coaptation and natural functioning of the MV apparatus under physiological loading at the organ level. The proposed computational model would serve as a logical first step toward our long-term modeling goal-facilitating simulation-guided design of optimal surgical repair strategies for treating diseased MVs with significantly enhanced durability.

Biomechanical evaluation of the pathophysiologic developmental mechanisms of mitral valve prolapse: effect of valvular morphologic alteration

Mitral valve prolapse (MVP) refers to an excessive billowing of the mitral valve (MV) leaflets across the mitral annular plane into the left atrium during the systolic portion of the cardiac cycle. The underlying mechanisms for the development of MVP and mitral regurgitation in association with MV tissue remodeling are still unclear. We performed computational MV simulations to investigate the pathophysiologic developmental mechanisms of MVP. A parametric MV geometry model was utilized for this study. Posterior leaflet enlargement and posterior chordal elongation models were created by adjusting the geometry of the posterior leaflet and chordae, respectively. Dynamic finite element simulations of MV function were performed over the complete cardiac cycle. Computational simulations demonstrated that enlarging posterior leaflet area increased large stress concentration in the posterior leaflets and chordae, and posterior chordal elongation decreased leaflet coaptation. When MVP was accompanied by both posterior leaflet enlargement and chordal elongation simultaneously, the posterior leaflet was exposed to extremely large prolapse with a substantial lack of leaflet coaptation. These data indicate that MVP development is closely related to tissue alterations of the leaflets and chordae. This biomechanical evaluation strategy can help us better understand the pathophysiologic developmental mechanisms of MVP.

Movement of mitral fibrous components in an isolated porcine working heart model

BACKGROUND

There is little research regarding the movement of mitral fibrous components. We analyzed changes in mitral fibrous components in normal and deteriorated isolated working swine hearts.

METHODS

In 5 swine hearts, 6 sonomicrometry transducers were placed around the mitral annulus and 2 in the papillary muscle tip. During the working cycle, we evaluated the annular dimension and calculated the contraction range and contraction ratio during the cardiac cycle in normal and deteriorated modes.

RESULTS

The transverse (24.5 ± 2.3 vs. 27.4 ± 2.4 mm) and posterior longitudinal diameter (18.3 ± 7.0 vs. 22.5 ± 5.5 mm) increased significantly in deteriorated mode. The contraction range in transverse (1.8 ± 0.6 vs. 0.8 ± 0.7 mm) and posterior longitudinal (1.6 ± 0.6 vs. 0.8 ± 0.3 mm) diameters decreased significantly in deteriorated mode. The contraction range of the strut chordae was less than 1.0 mm in both modes, with no significant differences. The contraction ratio of the anterior strut chordae was significantly reduced in deteriorated mode (3.2 ± 1.1% vs. 2.2 ± 1.1%). The contraction ratio of the annulus was significantly lower in deteriorated mode with respect to transverse (6.9 ± 2.1% vs. 2.9 ± 2.9%) and longitudinal (13.3 ± 4.5% vs. 8.6 ± 5.1%) diameters.

CONCLUSIONS

In the deteriorated hearts, the mitral annulus was dilated and contractility decreased. The length of the strut chordae differed 1 mm between the deteriorated and normal modes; however, the contraction ratio of the anterior chordae during the cardiac cycle was reduced, indicating increased stretching.

Personalized Computational Modeling of Mitral Valve Prolapse: Virtual Leaflet Resection

Posterior leaflet prolapse following chordal elongation or rupture is one of the primary valvular diseases in patients with degenerative mitral valves (MVs). Quadrangular resection followed by ring annuloplasty is a reliable and reproducible surgical repair technique for treatment of posterior leaflet prolapse. Virtual MV repair simulation of leaflet resection in association with patient-specific 3D echocardiographic data can provide quantitative biomechanical and physiologic characteristics of pre- and post-resection MV function. We have developed a solid personalized computational simulation protocol to perform virtual MV repair using standard clinical guidelines of posterior leaflet resection with annuloplasty ring implantation. A virtual MV model was created using 3D echocardiographic data of a patient with posterior chordal rupture and severe mitral regurgitation. A quadrangle-shaped leaflet portion in the prolapsed posterior leaflet was removed, and virtual plication and suturing were performed. An annuloplasty ring of proper size was reconstructed and virtual ring annuloplasty was performed by superimposing the ring and the mitral annulus. Following the quadrangular resection and ring annuloplasty simulations, patient-specific annular motion and physiologic transvalvular pressure gradient were implemented and dynamic finite element simulation of MV function was performed. The pre-resection MV demonstrated a substantial lack of leaflet coaptation which directly correlated with the severe mitral regurgitation. Excessive stress concentration was found along the free marginal edge of the posterior leaflet involving the chordal rupture. Following the virtual resection and ring annuloplasty, the severity of the posterior leaflet prolapse markedly decreased. Excessive stress concentration disappeared over both anterior and posterior leaflets, and complete leaflet coaptation was effectively restored. This novel personalized virtual MV repair strategy has great potential to help with preoperative selection of the patient-specific optimal MV repair techniques, allow innovative surgical planning to expect improved efficacy of MV repair with more predictable outcomes, and ultimately provide more effective medical care for the patient.

Effect of Congenital Anomalies of the Papillary Muscles on Mitral Valve Function

Parachute mitral valves (PMVs) and parachute-like asymmetric mitral valves (PLAMVs) are associated with congenital anomalies of the papillary muscles. Current imaging modalities cannot provide detailed biomechanical information. This study describes computational evaluation techniques based on three-dimensional (3D) echocardiographic data to determine the biomechanical and physiologic characteristics of PMVs and PLAMVs. The closing and opening mechanics of a normal mitral valve (MV), two types of PLAMV with different degrees of asymmetry, and a true PMV were investigated. MV geometric data in a patient with a normal MV was acquired from 3D echocardiography. The pathologic MVs were modeled by altering the configuration of the papillary muscles in the normal MV model. Dynamic finite element simulations of the normal MV, PLAMVs, and true PMV were performed. There was a strong correlation between the reduction of mitral orifice size and the degree of asymmetry of the papillary muscle location. The PLAMVs demonstrated decreased leaflet coaptation and tenting height. The true PMV revealed severely wrinkled leaflet deformation and narrowed interchordal spaces, leading to uneven leaflet coaptation. There were considerable decreases in leaflet coaptation and abnormal leaflet deformation corresponding to the anomalous location of the papillary muscle tips. This computational MV evaluation strategy provides a powerful tool to better understand biomechanical and pathophysiologic MV abnormalities.

Automatic mitral annulus tracking in volumetric ultrasound using non-rigid image registration

Analysis of mitral annular dynamics plays an important role in the diagnosis and selection of optimal valve repair strategies, but remains cumbersome and time-consuming if performed manually. In this paper we propose non-rigid image registration to automatically track the annulus in 3D ultrasound images for both normal and pathological valves, and compare the performance against manual tracing. Relevant clinical properties such as annular area, circumference and excursion could be extracted reliably by the tracking algorithm. The root-mean-square error, calculated as the difference between the manually traced landmarks (18 in total) and the automatic tracking, was 1.96 ± 0.46 mm over 10 valves (5 healthy and 5 diseased) which is within the clinically acceptable error range.

Functional and Biomechanical Effects of the Edge-to-Edge Repair in the Setting of Mitral Regurgitation: Consolidated Knowledge and Novel Tools to Gain Insight into Its Percutaneous Implementation

Mitral regurgitation is the most prevalent heart valve disease in the western population. When severe, it requires surgical treatment, repair being the preferred option. The edge-to-edge repair technique treats mitral regurgitation by suturing the leaflets together and creating a double-orifice valve. Due to its relative simplicity and versatility, it has become progressively more widespread. Recently, its percutaneous version has become feasible, and has raised interest thanks to the positive results of the Mitraclip(®) device. Edge-to-edge features and evolution have stimulated debate and multidisciplinary research by both clinicians and engineers. After providing an overview of representative studies in the field, here we propose a novel computational approach to the most recent percutaneous evolution of the edge-to-edge technique. Image-based structural finite element models of three mitral valves affected by posterior prolapse were derived from cine-cardiac magnetic resonance imaging. The models accounted for the patient-specific 3D geometry of the valve, including leaflet compound curvature pattern, patient-specific motion of annulus and papillary muscles, and hyperelastic and anisotropic mechanical properties of tissues. The biomechanics of the three valves throughout the entire cardiac cycle was simulated before and after Mitraclip(®) implantation, assessing the biomechanical impact of the procedure. For all three simulated MVs, Mitraclip(®) implantation significantly improved systolic leaflets coaptation, without inducing major alterations in systolic peak stresses. Diastolic orifice area was decreased, by up to 58.9%, and leaflets diastolic stresses became comparable, although lower, to systolic ones. Despite established knowledge on the edge-to-edge surgical repair, latest technological advances make its percutanoues implementation a challenging field of research. The modeling approach herein proposed may be expanded to analyze clinical scenarios that are currently critical for Mitraclip(®) implantation, helping the search for possible solutions.

FINITE ELEMENT MODELING OF THE HUMAN MITRAL VALVE: IMPLICATIONS OF MORPHOLOGIES AND DYNAMICS OF THE ANNULUS AND THE CHORDAE TENDINEAE

Objectives: To investigate the influences caused by special morphologies and dynamics of the substructures of mitral valve by the explicit finite element program LS-DYNA. Methods: A new finite element model for the mitral apparatus characterized by layered structure of leaflets tissue, saddle shape and contraction of annulus, an approximately accurate morphology of chordae tendineae was developed. The coaptation length, leaflets stress and strain of the present model were compared with those of two auxiliary models, one with planar annulus and the other with fixed annulus. The tensile function and force distribution of chordae tendineae were analyzed in the models with and without chordae tendineae. Results: The stretch ratios computed by the present model were most closely to the experimental data. The leaflets instantly turned over to the atrial side and larger load was observed in the model without chordae tendineae. Besides, tensile force was highly correlated with average diameter of chordae tendineae (r = 0.965). Conclusion: The saddle shape of annulus benefits valve coaptation and the contraction of annulus could help decrease loads on leaflets and prevent stress concentrating excessively. Chordae tendineae could bear partial loads on the leaflets, and prevent the leaflets to turn over to the side of the atrium and help the valve close successfully.

A novel finite element-based patient-specific mitral valve repair: virtual ring annuloplasty

Alterations of normal mitral valve (MV) function lead to mitral insufficiency, i.e., mitral regurgitation (MR). Mitral repair is the most popular and most efficient surgical intervention for MR treatment. An annuloplasty ring is implanted following complex reconstructive MV repairs to prevent potential reoccurrence of MR. We have developed a novel finite element (FE)-based simulation protocol to perform patient-specific virtual ring annuloplasty following the standard clinical guideline procedure. A virtual MV was created using 3D echocardiographic data in a patient with mitral annular dilation. Proper type and size of the ring were determined in consideration of the MV apparatus geometry. The ring was positioned over the patient MV model and annuloplasty was simulated. Dynamic simulation of MV function across the complete cardiac cycle was performed. Virtual patient-specific annuloplasty simulation well demonstrated morphologic information of the MV apparatus before and after ring implantation. Dynamic simulation of MV function following ring annuloplasty demonstrated markedly reduced stress distribution across the MV leaflets and annulus as well as restored leaflet coaptation compared to pre-annuloplasty. This novel FE-based patient-specific MV repair simulation technique provides quantitative information of functional improvement following ring annuloplasty. Virtual MV repair strategy may effectively evaluate and predict interventional treatment for MV pathology.

Computational modeling of cardiac valve function and intervention

In the past two decades, major advances have been made in the clinical evaluation and treatment of valvular heart disease owing to the advent of noninvasive cardiac imaging modalities. In clinical practice, valvular disease evaluation is typically performed on two-dimensional (2D) images, even though most imaging modalities offer three-dimensional (3D) volumetric, time-resolved data. Such 3D data offer researchers the possibility to reconstruct the 3D geometry of heart valves at a patient-specific level. When these data are integrated with computational models, native heart valve biomechanical function can be investigated, and preoperative planning tools can be developed. In this review, we outline the advances in valve geometry reconstruction, tissue property modeling, and loading and boundary definitions for the purpose of realistic computational structural analysis of cardiac valve function and intervention.

Effect of leaflet-to-chordae contact interaction on computational mitral valve evaluation

BACKGROUND

Computational simulation using numerical analysis methods can help to assess the complex biomechanical and functional characteristics of the mitral valve (MV) apparatus. It is important to correctly determine physical contact interaction between the MV apparatus components during computational MV evaluation. We hypothesize that leaflet-to-chordae contact interaction plays an important role in computational MV evaluation, specifically in quantitating the degree of leaflet coaptation directly related to the severity of mitral regurgitation (MR). In this study, we have performed dynamic finite element simulations of MV function with and without leaflet-to-chordae contact interaction, and determined the effect of leaflet-to-chordae contact interaction on the computational MV evaluation.

METHODS

Computational virtual MV models were created using the MV geometric data in a patient with normal MV without MR and another with pathologic MV with MR obtained from 3D echocardiography. Computational MV simulation with full contact interaction was specified to incorporate entire physically available contact interactions between the leaflets and chordae tendineae. Computational MV simulation without leaflet-to-chordae contact interaction was specified by defining the anterior and posterior leaflets as the only contact inclusion.

RESULTS

Without leaflet-to-chordae contact interaction, the computational MV simulations demonstrated physically unrealistic contact interactions between the leaflets and chordae. With leaflet-to-chordae contact interaction, the anterior marginal chordae retained the proper contact with the posterior leaflet during the entire systole. The size of the non-contact region in the simulation with leaflet-to-chordae contact interaction was much larger than for the simulation with only leaflet-to-leaflet contact.

CONCLUSIONS

We have successfully demonstrated the effect of leaflet-to-chordae contact interaction on determining leaflet coaptation in computational dynamic MV evaluation. We found that physically realistic contact interactions between the leaflets and chordae should be considered to accurately quantitate leaflet coaptation for MV simulation. Computational evaluation of MV function that allows precise quantitation of leaflet coaptation has great potential to better quantitate the severity of MR.

New concepts for mitral valve imaging

The high complexity of the mitral valve (MV) anatomy and function is not yet fully understood. Studying especially the dynamic movement and interaction of MV components to describe MV physiology during the cardiac cycle remains a challenge. Imaging is the key to assessing details of MV disease and to studying the lesion and dysfunction of MV according to Carpentier. With the advances of computational geometrical and biomechanical MV models, improved quantification and characterization of the MV has been realized. Geometrical models can be divided into rigid and dynamic models. Both models are based on reconstruction techniques of echocardiographic or computed tomographic data sets. They allow detailed analysis of MV morphology and dynamics throughout the cardiac cycle. Biomechanical models aim to simulate the biomechanics of MV to allow for examination and analysis of the MV structure with blood flow. Two categories of biomechanical MV models can be distinguished: structural models and fluid-structure interaction (FSI) models. The complex structure and dynamics of MV apparatus throughout the cardiac cycle can be analyzed with different types of computational models. These represent substantial progress in the diagnosis of structural heart disease since MV morphology and dynamics can be studied in unprecedented detail. It is conceivable that MV modeling will contribute significantly to the understanding of the MV.

Mitral valve function following ischemic cardiomyopathy: a biomechanical perspective

Ischemic mitral valve (MV) is a common complication of pathologic remodeling of the left ventricle due to acute and chronic coronary artery diseases. It frequently represents the pathologic consequences of increased tethering forces and reduced coaptation of the MV leaflets. Ischemic MV function has been investigated from a biomechanical perspective using finite element-based computational MV evaluation techniques. A virtual 3D MV model was created utilizing 3D echocardiographic data in a patient with normal MV. Two types of ischemic MVs containing asymmetric medial-dominant or symmetric leaflet tenting were modeled by altering the configuration of the normal papillary muscle (PM) locations. Computational simulations of MV function were performed using dynamic finite element methods, and biomechanical information across the MV apparatus was evaluated. The ischemic MV with medial-dominant leaflet tenting demonstrated distinct large stress distributions in the posteromedial commissural region due to the medial PM displacement toward the apical-medial direction resulting in a lack of leaflet coaptation. In the ischemic MV with balanced leaflet tenting, mitral incompetency with incomplete leaflet coaptation was clearly identified all around the paracommissural regions. This computational MV evaluation strategy has the potential for improving diagnosis of ischemic mitral regurgitation and treatment of ischemic MVs.

Mitral valve repair using ePTFE sutures for ruptured mitral chordae tendineae: a computational simulation study

Mitral valve (MV) repair using expanded polytetrafluoroethylene sutures is an established and preferred interventional method to resolve the complex pathophysiologic problems associated with chordal rupture. We developed a novel computational evaluation protocol to determine the effect of the artificial sutures on restoring MV function following valve repair. A virtual MV was created using three-dimensional echocardiographic data in a patient with ruptured mitral chordae tendineae (RMCT). Virtual repairs were designed by adding artificial sutures between the papillary muscles and the posterior leaflet where the native chordae were ruptured. Dynamic finite element simulations were performed to evaluate pre- and post-repair MV function. Abnormal posterior leaflet prolapse and mitral regurgitation was clearly demonstrated in the MV with ruptured chordae. Following virtual repair to reconstruct ruptured chordae, the severity of the posterior leaflet prolapse decreased and stress concentration was markedly reduced both in the leaflet tissue and the intact native chordae. Complete leaflet coaptation was restored when four or six sutures were utilized. Computational simulations provided quantitative information of functional improvement following MV repair. This novel simulation strategy may provide a powerful tool for evaluation and prediction of interventional treatment for RMCT.

Material properties of aged human mitral valve leaflets

This study aimed to characterize the mechanical properties of aged human anterior mitral leaflets (AML) and posterior mitral leaflets (PML). The AML and PML samples from explanted human hearts (n = 21, mean age of 82.62 ± 8.77-years-old) were subjected to planar biaxial mechanical tests. The material stiffness, extensibility, and degree of anisotropy of the leaflet samples were quantified. The microstructure of the samples was assessed through histology. Both the AML and PML samples exhibited a nonlinear and anisotropic behavior with the circumferential direction being stiffer than the radial direction. The AML samples were significantly stiffer than the PML samples in both directions, suggesting that they should be modeled with separate sets of material properties in computational studies. Histological analysis indicated the changes in the tissue elastic constituents, including the fragmented and disorganized elastin network, the presence of fibrosis and proteoglycan/glycosaminoglycan infiltration and calcification, suggesting possible valvular degenerative characteristics in the aged human leaflet samples. Overall, stiffness increased and areal strain decreased with calcification severity. In addition, leaflet tissues from hypertensive individuals also exhibited a higher stiffness and low areal strain than normotensive individuals. There are significant differences in the mechanical properties of the two human mitral valve leaflets from this advanced age group. The morphologic changes in the tissue composition and structure also infer the structural and functional difference between aged human valves and those of animals.

Mechanics of healthy and functionally diseased mitral valves: a critical review

The mitral valve is a complex apparatus with multiple constituents that work cohesively to ensure unidirectional flow between the left atrium and ventricle. Disruption to any or all of the components-the annulus, leaflets, chordae, and papillary muscles-can lead to backflow of blood, or regurgitation, into the left atrium, which deleteriously effects patient health. Through the years, a myriad of surgical repairs have been proposed; however, a careful appreciation for the underlying structural mechanics can help optimize long-term repair durability and inform medical device design. In this review, we aim to present the experimental methods and significant results that have shaped the current understanding of mitral valve mechanics. Data will be presented for all components of the mitral valve apparatus in control, pathological, and repaired conditions from human, animal, and in vitro studies. Finally, current strategies of patient specific and noninvasive surgical planning will be critically outlined.

The effect of patient-specific annular motion on dynamic simulation of mitral valve function

Most surgical procedures for patients with mitral regurgitation (MR) focus on optimization of annular dimension and shape utilizing ring annuloplasty to restore normal annular geometry, increase leaflet coaptation, and reduce regurgitation. Computational studies may provide insight on the effect of annular motion on mitral valve (MV) function through the incorporation of patient-specific MV apparatus geometry from clinical imaging modalities such as echocardiography. In the present study, we have developed a novel algorithm for modeling patient-specific annular motion across the cardiac cycle to further improve our virtual MV modeling and simulation strategy. The MV apparatus including the leaflets, annulus, and location of papillary muscle tips was identified using patient 3D echocardiography data at end diastole and peak systole and converted to virtual MV model. Dynamic annular motion was modeled by incorporating the ECG-gated time-varying scaled annular displacement across the cardiac cycle. We performed dynamic finite element (FE) simulation of two sets of patient data with respect to the presence of MR. Annular morphology, stress distribution across the leaflets and annulus, and contact stress distribution were determined to assess the effect of annular motion on MV function and leaflet coaptation. The effect of dynamic annular motion clearly demonstrated reduced regions with large stress values and provided an improved accuracy in determining the location of improper leaflet coaptation. This strategy has the potential to better quantitate the extent of pathologic MV and better evaluate functional restoration following MV repair.

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.