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

FEBio FINESSE: An Open-Source Finite Element Simulation Approach to Estimate In Vivo Heart Valve Strains Using Shape Enforcement

PURPOSE

Finite element simulations are an enticing tool to evaluate heart valve function; however, patient-specific simulations derived from 3D echocardiography are hampered by several technical challenges. The objective of this work is to develop an open-source method to enforce matching between finite element simulations and in vivo image-derived heart valve geometry in the absence of patient-specific material properties, leaflet thickness, and chordae tendineae structures.

METHODS

We evaluate FEBio Finite Element Simulations with Shape Enforcement (FINESSE) using three synthetic test cases considering a range of model complexity. FINESSE is then used to estimate the in vivo valve behavior and leaflet strains for three pediatric patients.

RESULTS

Our results suggest that FINESSE can be used to enforce finite element simulations to match an image-derived surface and estimate the first principal leaflet strains within ± 0.03 strain. Key considerations include: (i) defining the user-defined penalty, (ii) omitting the leaflet commissures to improve simulation convergence, and (iii) emulating the chordae tendineae behavior via prescribed leaflet free edge motion or a chordae emulating force. In all patient-specific cases, FINESSE matched the target surface with median errors of approximately the smallest voxel dimension. Further analysis revealed valve-specific findings, such as the tricuspid valve leaflet strains of a 2-day old patient with HLHS being larger than those of two 13-year old patients.

CONCLUSIONS

FEBio FINESSE can be used to estimate patient-specific in vivo heart valve leaflet strains. The development of this open-source pipeline will enable future studies to begin linking in vivo leaflet mechanics with patient outcomes.

Atrial functional mitral regurgitation in cardiology and cardiac surgery

Functional or secondary mitral regurgitation (MR) is a clear and present danger to cardiovascular health, with heightened morbidity and mortality rates. Secondary MR is caused by an imbalance between two sets of forces. There are two forces at play here. One keeps the mitral leaflets tethered, while the other closes them. The evidence clearly shows inadequate coaptation. Functional MR (FMR) is the typical form of MR. It is almost always caused by dysfunction and alterations of the left ventricle (LV) geometry. It occurs in both ischemic and non-ischemic disease states. Atrial FMR (AFMR) is a disease that has only recently come to be acknowledged. This phenomenon arises when mitral annular enlargement is caused by left atrial enlargement. This preserves the geometry and function of the LV. AFMR is most frequently encountered in individuals with chronic atrial fibrillation or heart failure, in whom a normal ejection fraction is present. Published studies and ongoing research vary in their definition of AFMR, but there is no doubt that AFMR exists. This review definitively explains the pathophysiology of AFMR and demonstrates the necessity of a common working standard for the definition of AFMR. This is essential to warrant cohesiveness in the data reported and to drive forward the much-needed research into the outcomes and treatment strategies in this critical field. A number of high-quality studies have demonstrated that restrictive mitral annuloplasty and transcatheter procedure based on edge-to-edge repair are effective in reducing MR and alleviating symptoms. The pathophysiology, echocardiographic diagnosis, and treatment of AFMR are thoroughly reviewed in this comprehensive review.

Bayesian Optimization-Based Inverse Finite Element Analysis for Atrioventricular Heart Valves

Inverse finite element analysis (iFEA) of the atrioventricular heart valves (AHVs) can provide insights into the in-vivo valvular function, such as in-vivo tissue strains; however, there are several limitations in the current state-of-the-art that iFEA has not been widely employed to predict the in-vivo, patient-specific AHV leaflet mechanical responses. In this exploratory study, we propose the use of Bayesian optimization (BO) to study the AHV functional behaviors in-vivo. We analyzed the efficacy of Bayesian optimization to estimate the isotropic Lee-Sacks material coefficients in three benchmark problems: (i) an inflation test, (ii) a simplified leaflet contact model, and (iii) an idealized AHV model. Then, we applied the developed BO-iFEA framework to predict the leaflet properties for a patient-specific tricuspid valve under a congenital heart defect condition. We found that the BO could accurately construct the objective function surface compared to the one from a [Formula: see text] grid search analysis. Additionally, in all cases the proposed BO-iFEA framework yielded material parameter predictions with average element errors less than 0.02 mm/mm (normalized by the simulation-specific characteristic length). Nonetheless, the solutions were not unique due to the presence of a long-valley minima region in the objective function surfaces. Parameter sets along this valley can yield functionally equivalent outcomes (i.e., closing behavior) and are typically observed in the inverse analysis or parameter estimation for the nonlinear mechanical responses of the AHV. In this study, our key contributions include: (i) a first-of-its-kind demonstration of the BO method used for the AHV iFEA; and (ii) the evaluation of a candidate AHV in-silico modeling approach wherein the chordae could be substituted with equivalent displacement boundary conditions, rendering the better iFEA convergence and a smoother objective surface.

Utilization of Engineering Advances for Detailed Biomechanical Characterization of the Mitral-Ventricular Relationship to Optimize Repair Strategies: A Comprehensive Review

The geometrical details and biomechanical relationships of the mitral valve-left ventricular apparatus are very complex and have posed as an area of research interest for decades. These characteristics play a major role in identifying and perfecting the optimal approaches to treat diseases of this system when the restoration of biomechanical and mechano-biological conditions becomes the main target. Over the years, engineering approaches have helped to revolutionize the field in this regard. Furthermore, advanced modelling modalities have contributed greatly to the development of novel devices and less invasive strategies. This article provides an overview and narrative of the evolution of mitral valve therapy with special focus on two diseases frequently encountered by cardiac surgeons and interventional cardiologists: ischemic and degenerative mitral regurgitation.

Imaging Considerations and Clinical Implications of Mitral Annular Disjunction

Mitral annular disjunction is increasingly recognized as an important anatomic feature of mitral valve disease. The presence of mitral annular disjunction, defined as separation between the left atrial wall at the point of mitral valve insertion and the left ventricular free wall, has been associated with increased degeneration of the mitral valve and increased incidence of sudden cardiac death. The clinical importance of this entity necessitates standard reporting on cardiovascular imaging reports if patients are to receive adequate risk stratification and management. We provide a narrative review of the literature pertaining to mitral annular disjunction, its clinical implications, and areas needing further research.

Structural Heart Valve Disease in the Era of Change and Innovation: The Crosstalk between Medical Sciences and Engineering

In recent years, both cardiology and cardiovascular surgery have witnessed an era of consistently evolving changes which have dramatically transformed the course and management of cardiovascular disease [...].

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

The role of the extracellular matrix in the development of heart valve disease: Underestimation or undercomprehension?

The function of metalloproteinases of the extracellular matrix and their inhibitors has emerged with a crucial role in valve diseases. Both the expression of matrix metalloproteinases and their inhibitors are susceptible to modification in patients with severe mitral insufficiency. This process is due to substantial changes in the collagen structure during mechanical stress on the mitral valve leaflets. Several studies have measured the level of deformation of the mitral leaflets with the use of the finite element analysis method by establishing the stiffness of the cellular and extracellular elements of the mitral valve leaflets. Evidence suggested the possible underestimation of the stiffness of the leaflets. This implies greater stress on the components of the extracellular matrix in the circumferential and radial strains that involve the mitral leaflets during chronic regurgitation. The remodeling process during mechanical stress phenomena involves both the cellular compartment and the extracellular matrix and can be adaptive or maladaptive as showed in patients who receive a pulmonary autograft to replace the diseased aortic valve. However, adaptive remodeling can be driven using resorbable polymers that interfere with the extracellular matrix. Further investigation is required for the understanding of the mechanisms that determine the structural changes of the extracellular matrix and to prevent them.

Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves

Approximately 1.6 million patients in the United States are affected by tricuspid valve regurgitation, which occurs when the tricuspid valve does not close properly to prevent backward blood flow into the right atrium. Despite its critical role in proper cardiac function, the tricuspid valve has received limited research attention compared to the mitral and aortic valves on the left side of the heart. As a result, proper valvular function and the pathologies that may cause dysfunction remain poorly understood. To promote further investigations of the biomechanical behavior and response of the tricuspid valve, this work establishes a parameter-based approach that provides a template for tricuspid valve modeling and simulation. The proposed tricuspid valve parameterization presents a comprehensive description of the leaflets and the complex chordae tendineae for capturing the typical three-cusp structural deformation observed from medical data. This simulation framework develops a practical procedure for modeling tricuspid valves and offers a robust, flexible approach to analyze the performance and effectiveness of various valve configurations using isogeometric analysis. The proposed methods also establish a baseline to examine the tricuspid valve's structural deformation, perform future investigations of native valve configurations under healthy and disease conditions, and optimize prosthetic valve designs.

Heart Valve Biomechanics: The Frontiers of Modeling Modalities and the Expansive Capabilities of Ex Vivo Heart Simulation

The field of heart valve biomechanics is a rapidly expanding, highly clinically relevant area of research. While most valvular pathologies are rooted in biomechanical changes, the technologies for studying these pathologies and identifying treatments have largely been limited. Nonetheless, significant advancements are underway to better understand the biomechanics of heart valves, pathologies, and interventional therapeutics, and these advancements have largely been driven by crucial in silico, ex vivo, and in vivo modeling technologies. These modalities represent cutting-edge abilities for generating novel insights regarding native, disease, and repair physiologies, and each has unique advantages and limitations for advancing study in this field. In particular, novel ex vivo modeling technologies represent an especially promising class of translatable research that leverages the advantages from both in silico and in vivo modeling to provide deep quantitative and qualitative insights on valvular biomechanics. The frontiers of this work are being discovered by innovative research groups that have used creative, interdisciplinary approaches toward recapitulating in vivo physiology, changing the landscape of clinical understanding and practice for cardiovascular surgery and medicine.

Putative Circulating MicroRNAs Are Able to Identify Patients with Mitral Valve Prolapse and Severe Regurgitation

Mitral valve prolapse (MVP) associated with severe mitral regurgitation is a debilitating disease with no pharmacological therapies available. MicroRNAs (miRNA) represent an emerging class of circulating biomarkers that have never been evaluated in MVP human plasma. Our aim was to identify a possible miRNA signature that is able to discriminate MVP patients from healthy subjects (CTRL) and to shed light on the putative altered molecular pathways in MVP. We evaluated a plasma miRNA profile using Human MicroRNA Card A followed by real-time PCR validations. In addition, to assess the discriminative power of selected miRNAs, we implemented a machine learning analysis. MiRNA profiling and validations revealed that miR-140-3p, 150-5p, 210-3p, 451a, and 487a-3p were significantly upregulated in MVP, while miR-223-3p, 323a-3p, 340-5p, and 361-5p were significantly downregulated in MVP compared to CTRL (p ≤ 0.01). Functional analysis identified several biological processes possible linked to MVP. In addition, machine learning analysis correctly classified MVP patients from CTRL with high accuracy (0.93) and an area under the receiving operator characteristic curve (AUC) of 0.97. To the best of our knowledge, this is the first study performed on human plasma, showing a strong association between miRNAs and MVP. Thus, a circulating molecular signature could be used as a first-line, fast, and cheap screening tool for MVP identification.

The time has come to extend the expiration limit of cryopreserved allograft heart valves

Despite the wide choice of commercial heart valve prostheses, cryopreserved semilunar allograft heart valves (C-AHV) are required, and successfully transplanted in selected groups of patients. The expiration limit (EL) criteria have not been defined yet. Most Tissue Establishments (TE) use the EL of 5 years. From physiological, functional, and surgical point of view, the morphology and mechanical properties of aortic and pulmonary roots represent basic features limiting the EL of C-AHV. The aim of this work was to review methods of AHV tissue structural analysis and mechanical testing from the perspective of suitability for EL validation studies. Microscopic structure analysis of great arterial wall and semilunar leaflets tissue should clearly demonstrate cells as well as the extracellular matrix components by highly reproducible and specific histological staining procedures. Quantitative morphometry using stereological grids has proved to be effective, as the exact statistics was feasible. From mechanical testing methods, tensile test was the most suitable. Young's moduli of elasticity, ultimate stress and strain were shown to represent most important AHV tissue mechanical characteristics, suitable for exact statistical analysis. C-AHV are prepared by many different protocols, so as each TE has to work out own EL for C-AHV.

Mitral regurgitation after transcatheter aortic valve replacement

Patients undergoing transcatheter aortic valve replacement (TAVR) might have an associated significant MR that can potentially lead to left ventricular (LV) failure after procedure. Considering the specific alterations in the mitral valve in TAVR scenario and the widespread use of TAVR in recent years, it appears important to know and understand the anatomical, functional and clinical implications to develop adequate strategies for the future. Patients with severe mitral regurgitation (MR) have been generally excluded from randomized clinical trials, making poor the impact that associated MR can have on clinical outcomes after TAVR. Several factors must be considered whose presence influences the severity of MR. For example, the elevated prevalence of coronary disease with consequent ischemic MR may account for LV dilation observed at the end stage of aortic stenosis. Evidence randomized studies and registries suggests that the rate of concomitant moderate-to-severe MR in patients undergoing TAVR oscillates between 2% and 33%, and patients with moderate to severe MR may have hemodynamic frailty with clinical deterioration during mechanical intervention. Short- and long-term outcomes, including cardiac mortality, appear to be influenced by the existence of preoperative moderate-to-severe MR or by the postprocedural worsening of mild MR, generally due to adverse LV remodeling. The incidence and the prognostic effect of concomitant MR in patients undergoing TAVR requires specific attention as might trigger adjunctive strategy treatment which should be carefully evaluated in clinical trials.

KEYWORDS

Mitral regurgitation (MR); mitral valve; transcatheter aortic valve; transcatheter aortic valve replacement (TAVR).

Mitral regurgitation: lessons learned from COAPT and MITRA-Fr

Recent studies about percutaneous treatment of secondary mitral regurgitation (MR) underlined the importance of left ventricular geometry and features of mitral valve as determinants of procedural and long-term success. Guideline-directed medical therapy (GDMT), transcatheter mitral valve treatment (TMVT) and surgical procedures (mitral valve replacement, mitral valve repair at level of the annulus or subvalvular apparatus) have been extensively evaluated but not adequately compared in current clinical studies. A detailed analysis of the results of the study about transcatheter mitral valve repair would allow to evaluate the safety and effectiveness of such procedure and would provide potential indications for improving the quality of percutaneous and surgical repair in patients with moderate-to-severe secondary MR. Patients with proportionate MR (i.e., MR severity is proportional to the amount of left ventricular dilatation) are prone to respond to the optimization of medical therapy, while patients with disproportionate MR (i.e., MR severity is disproportionately higher than predicted by left ventricular dilatation, with high EROA and small left ventricle) are likely to benefit from additional repair. The identification of specific subpopulation of "high responders", based on the anatomic characteristics of the mitral valve and the relative dimensions of the annulus, the regurgitation and the left ventricle, can also apply to medical therapy. However, some pivotal component of MR (such as the symmetry of tethering and the differences in biomechanical features of leaflets) are not adequately investigated in current studies and warrant further evaluation.

A Finite Element Analysis Study from 3D CT to Predict Transcatheter Heart Valve Thrombosis

BACKGROUND

Transcatheter aortic valve replacement has proved its safety and effectiveness in intermediate- to high-risk and inoperable patients with severe aortic stenosis. However, despite current guideline recommendations, the use of transcatheter aortic valve replacement (TAVR) to treat severe aortic valve stenosis caused by degenerative leaflet thickening and calcification has not been widely adopted in low-risk patients. This reluctance among both cardiac surgeons and cardiologists could be due to concerns regarding clinical and subclinical valve thrombosis. Stent performance alongside increased aortic root and leaflet stresses in surgical bioprostheses has been correlated with complications such as thrombosis, migration and structural valve degeneration.

MATERIALS AND METHODS

Self-expandable catheter-based aortic valve replacement (Medtronic, Minneapolis, MN, USA), which was received by patients who developed transcatheter heart valve thrombosis, was investigated using high-resolution biomodelling from computed tomography scanning. Calcific blocks were extracted from a 250 CT multi-slice image for precise three-dimensional geometry image reconstruction of the root and leaflets.

RESULTS

Distortion of the stent was observed with incomplete cranial and caudal expansion of the device. The incomplete deployment of the stent was evident in the presence of uncrushed refractory bulky calcifications. This resulted in incomplete alignment of the device within the aortic root and potential dislodgment.

CONCLUSION

A Finite Element Analysis (FEA) investigation can anticipate the presence of calcified refractory blocks, the deformation of the prosthetic stent and the development of paravalvular orifice, and it may prevent subclinical and clinical TAVR thrombosis. Here we clearly demonstrate that using exact geometry from high-resolution CT scans in association with FEA allows detection of persistent bulky calcifications that may contribute to thrombus formation after TAVR procedure.

Modeling the mitral valve

This work is concerned with modeling and simulation of the mitral valve, one of the four valves in the human heart. The valve is composed of leaflets, the free edges of which are supported by a system of chordae, which themselves are anchored to the papillary muscles inside the left ventricle. First, we examine valve anatomy and present the results of original dissections. These display the gross anatomy and information on fiber structure of the mitral valve. Next, we build a model valve following a design-based methodology, meaning that we derive the model geometry and the forces that are needed to support a given load and construct the model accordingly. We incorporate information from the dissections to specify the fiber topology of this model. We assume the valve achieves mechanical equilibrium while supporting a static pressure load. The solution to the resulting differential equations determines the pressurized configuration of the valve model. To complete the model, we then specify a constitutive law based on a stress-strain relation consistent with experimental data that achieves the necessary forces computed in previous steps. Finally, using the immersed boundary method, we simulate the model valve in fluid in a computer test chamber. The model opens easily and closes without leak when driven by physiological pressures over multiple beats. Further, its closure is robust to driving pressures that lack atrial systole or are much lower or higher than normal.

GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations

Finite element (FE) simulations are increasingly valuable in assessing and improving the performance of biomedical devices and procedures. Due to high computational demands such simulations may become difficult or even infeasible, especially when considering nearly incompressible and anisotropic material models prevalent in analyses of soft tissues. Implementations of GPGPU-based explicit FEs predominantly cover isotropic materials, e.g. the neo-Hookean model. To elucidate the computational expense of anisotropic materials, we implement the Gasser-Ogden-Holzapfel dispersed, fiber-reinforced model and compare solution times against the neo-Hookean model. Implementations of GPGPU-based explicit FEs conventionally rely on single-point (under) integration. To elucidate the expense of full and selective-reduced integration (more reliable) we implement both and compare corresponding solution times against those generated using underintegration. To better understand the advancement of hardware, we compare results generated using representative Nvidia GPGPUs from three recent generations: Fermi (C2075), Kepler (K20c), and Maxwell (GTX980). We explore scaling by solving the same boundary value problem (an extension-inflation test on a segment of human aorta) with progressively larger FE meshes. Our results demonstrate substantial improvements in simulation speeds relative to two benchmark FE codes (up to 300[Formula: see text] while maintaining accuracy), and thus open many avenues to novel applications in biomechanics and medicine.

A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves

This work formulates frictionless contact between solid bodies in terms of a repulsive potential energy term and illustrates how numerical integration of the resulting forces is computationally similar to the "pinball algorithm" proposed and studied by Belytschko and collaborators in the 1990s. We thereby arrive at a numerical approach that has both the theoretical advantages of a potential-based formulation and the algorithmic simplicity, computational efficiency, and geometrical versatility of pinball contact. The singular nature of the contact potential requires a specialized nonlinear solver and an adaptive time stepping scheme to ensure reliable convergence of implicit dynamic calculations. We illustrate the effectiveness of this numerical method by simulating several benchmark problems and the structural mechanics of the right atrioventricular (tricuspid) heart valve. Atrioventricular valve closure involves contact between every combination of shell surfaces, edges of shells, and cables, but our formulation handles all contact scenarios in a unified manner. We take advantage of this versatility to demonstrate the effects of chordal rupture on tricuspid valve coaptation behavior.

Biomechanical Properties and Mechanobiology of Cardiac ECM

The heart is comprised of cardiac cells and extracellular matrix (ECM) which function together to pump blood throughout the body, provide organs with nutrients and oxygen, and remove metabolic wastes. Cardiac ECM provides a scaffold to cardiac cells and contributes to the mechanical properties and function of the cardiac tissue. Recently, more evidence suggests that cardiac ECM plays an active role in cardiac remodeling in response to mechanical loads. To that end, we provide an overview of the structure and function of the heart and the currently available in vivo and ex vivo mechanical measurements of cardiac tissues. We also review the biomechanical properties of cardiac tissues including the myocardium and heart valves, with a discussion on the differences between the right ventricle and left ventricle. Lastly, we go into the mechanical factors involved in cardiac remodeling and review the mechanobiology of cardiac tissues, i.e., the biomechanical responses at the cellular and tissue level, with an emphasis on the impact on the cardiac ECM. The regulation of cardiac ECM on cell function, which is a new and open area of research, is also briefly discussed. Future investigation into the ECM deposition and the interaction of cardiac cells and ECM components for mechanotransduction can assist to understand cardiac remodeling and inspire new therapies for cardiac diseases.

Method for the unique identification of hyperelastic material properties using full-field measures. Application to the passive myocardium material response

Quantitative measurement of the material properties (eg, stiffness) of biological tissues is poised to become a powerful diagnostic tool. There are currently several methods in the literature to estimating material stiffness, and we extend this work by formulating a framework that leads to uniquely identified material properties. We design an approach to work with full-field displacement data-ie, we assume the displacement field due to the applied forces is known both on the boundaries and also within the interior of the body of interest-and seek stiffness parameters that lead to balanced internal and external forces in a model. For in vivo applications, the displacement data can be acquired clinically using magnetic resonance imaging while the forces may be computed from pressure measurements, eg, through catheterization. We outline a set of conditions under which the least-square force error objective function is convex, yielding uniquely identified material properties. An important component of our framework is a new numerical strategy to formulate polyconvex material energy laws that are linear in the material properties and provide one optimal description of the available experimental data. An outcome of our approach is the analysis of the reliability of the identified material properties, even for material laws that do not admit unique property identification. Lastly, we evaluate our approach using passive myocardium experimental data at the material point and show its application to identifying myocardial stiffness with an in silico experiment modeling the passive filling of the left ventricle.

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.

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.

In-vivo heterogeneous functional and residual strains in human aortic valve leaflets

Residual and physiological functional strains in soft tissues are known to play an important role in modulating organ stress distributions. Yet, no known comprehensive information on residual strains exist, or non-invasive techniques to quantify in-vivo deformations for the aortic valve (AV) leaflets. Herein we present a completely non-invasive approach for determining heterogeneous strains - both functional and residual - in semilunar valves and apply it to normal human AV leaflets. Transesophageal 3D echocardiographic (3DE) images of the AV were acquired from open-heart transplant patients, with each AV leaflet excised after heart explant and then imaged in a flattened configuration ex-vivo. Using an established spline parameterization of both 3DE segmentations and digitized ex-vivo images (Aggarwal et al., 2014), surface strains were calculated for deformation between the ex-vivo and three in-vivo configurations: fully open, just-coapted, and fully-loaded. Results indicated that leaflet area increased by an average of 20% from the ex-vivo to in-vivo open states, with a highly heterogeneous strain field. The increase in area from open to just-coapted state was the highest at an average of 25%, while that from just-coapted to fully-loaded remained almost unaltered. Going from the ex-vivo to in-vivo mid-systole configurations, the leaflet area near the basal attachment shrank slightly, whereas the free edge expanded by ~10%. This was accompanied by a 10° -20° shear along the circumferential-radial direction. Moreover, the principal stretches aligned approximately with the circumferential and radial directions for all cases, with the highest stretch being along the radial direction. Collectively, these results indicated that even though the AV did not support any measurable pressure gradient in the just-coapted state, the leaflets were significantly pre-strained with respect to the excised state. Furthermore, the collagen fibers of the leaflet were almost fully recruited in the just-coapted state, making the leaflet very stiff with marginal deformation under full pressure. Lastly, the deformation was always higher in the radial direction and lower along the circumferential one, the latter direction made stiffer by the preferential alignment of collagen fibers. These results provide significant insight into the distribution of residual strains and the in-vivo strains encountered during valve opening and closing in AV leaflets, and will form an important component of the tool that can evaluate valve׳s functional properties in a non-invasive manner.

The Impact of Fluid Inertia on In Vivo Estimation of Mitral Valve Leaflet Constitutive Properties and Mechanics

We examine the influence of the added mass effect (fluid inertia) on mitral valve leaflet stress during isovolumetric phases. To study this effect, oscillating flow is applied to a flexible membrane at various frequencies to control inertia. Resulting membrane strain is calculated through a three-dimensional reconstruction of markers from stereo images. To investigate the effect in vivo, the analysis is repeated on a published dataset for an ovine mitral valve (Journal of Biomechanics 42(16): 2697-2701). The membrane experiment demonstrates that the relationship between pressure and strain must be corrected with a fluid inertia term if the ratio of inertia to pressure differential approaches 1. In the mitral valve, this ratio reaches 0.7 during isovolumetric contraction for an acceleration of 6 m/s(2). Acceleration is reduced by 72% during isovolumetric relaxation. Fluid acceleration also varies along the leaflet during isovolumetric phases, resulting in spatial variations in stress. These results demonstrate that fluid inertia may be the source of the temporally and spatially varying stiffness measurements previously seen through inverse finite element analysis of in vivo data during isovolumetric phases. This study demonstrates that there is a need to account for added mass effects when analyzing in vivo constitutive relationships of heart valves.

A meso-scale layer-specific structural constitutive model of the mitral heart valve leaflets

Fundamental to developing a deeper understanding of pathophysiological remodeling in mitral valve (MV) disease is the development of an accurate tissue-level constitutive model. In the present work, we developed a novel meso-scale (i.e. at the level of the fiber, 10-100 μm in length scale) structural constitutive model (MSSCM) for MV leaflet tissues. Due to its four-layer structure, we focused on the contributions from the distinct collagen and elastin fiber networks within each tissue layer. Requisite collagen and elastin fibrous structural information for each layer were quantified using second harmonic generation microscopy and conventional histology. A comprehensive mechanical dataset was also used to guide model formulation and parameter estimation. Furthermore, novel to tissue-level structural constitutive modeling approaches, we allowed the collagen fiber recruitment function to vary with orientation. Results indicated that the MSSCM predicted a surprisingly consistent mean effective collagen fiber modulus of 162.72 MPa, and demonstrated excellent predictive capability for extra-physiological loading regimes. There were also anterior-posterior leaflet-specific differences, such as tighter collagen and elastin fiber orientation distributions (ODF) in the anterior leaflet, and a thicker and stiffer atrialis in the posterior leaflet. While a degree of angular variance was observed, the tight valvular tissue ODF also left little room for any physically meaningful angular variance in fiber mechanical responses. Finally, a novel fibril-level (0.1-1 μm) validation approach was used to compare the predicted collagen fiber/fibril mechanical behavior with extant MV small angle X-ray scattering data. Results demonstrated excellent agreement, indicating that the MSSCM fully captures the tissue-level function. Future utilization of the MSSCM in computational models of the MV will aid in producing highly accurate simulations in non-physiological loading states that can occur in repair situations, as well as guide the form of simplified models for real-time simulation tools.

Finite Element Modeling of Mitral Valve Repair

The mitral valve is a complex structure regulating forward flow of blood between the left atrium and left ventricle (LV). Multiple disease processes can affect its proper function, and when these diseases cause severe mitral regurgitation (MR), optimal treatment is repair of the native valve. The mitral valve (MV) is a dynamic structure with multiple components that have complex interactions. Computational modeling through finite element (FE) analysis is a valuable tool to delineate the biomechanical properties of the mitral valve and understand its diseases and their repairs. In this review, we present an overview of relevant mitral valve diseases, and describe the evolution of FE models of surgical valve repair techniques.

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.

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.

Novel Mitral Repair Device for the Treatment of Severe Mitral Regurgitation: Preclinical Ovine Acute and Chronic Implantation Model

Objective

A project is now underway to implement a novel percutaneous mitral repair system for severe mitral regurgitation (MR). The initial phase of the project consists of proof-of-concept by testing device characteristics using open surgical implantation. When surgical proof-of-concept of the intended percutaneous design is completed, a second phase of the project will consist of in vivo testing of the percutaneous transseptal system. The device is currently being designed to fold into a 17F catheter system and to unfold within the left atrium where attachment is accomplished using a reversible anchoring system. The purpose of this study was to show functionality of the device in elimination of MR using the open surgical method.

Methods

We have performed surgical prototype device implantation in 5 acute and 7 chronic sheep preparations. We created a P2-flail model of severe (4+) MR in the 12 sheep. Via a minimally invasive left thoracotomy incision and open repair on cardiopulmonary bypass, the device was implanted to determine efficacy of elimination of severe MR. Implantation was considered successful if 4+ regurgitation was converted to 1+ MR or lower. Left ventriculography and epicardial 2-dimensional/3-dimensional echocardiography were used to assess repair; serial 2-dimensional/3-dimensional transthoracic echocardiography was used to assess long-term mitral repair status.

Results

Twelve sheep had surgical creation of severe (4+) MR by cutting all chordae to the P2 scallop of the mitral valve; this preparation was tested and was found to produce 100% acute fatality without repair of the mitral valve. Five sheep had acute implantation of the device with elimination of regurgitation in 5/5 sheep. Seven sheep had chronic (1–7 month) implantation of the device. The device was tested in the chronic model for clinical status, residual regurgitation, thrombosis, and histopathology. All sheep had mitigation of MR and survived to the intended date of death.

Conclusions

Proof-of-concept of a novel percutaneous mitral repair device has been completed using an ovine P2-flail severe MR model. The device has characteristics that will allow its use in posterior leaflet degenerative disease and functional/secondary MR. Open, minimally invasive, and robotic surgical implantation of the device can also be developed as an alternative to the percutaneous approach.

Strain balance of papillary muscles as a prerequisite for successful mitral valve repair in patients with mitral valve prolapse due to fibroelastic deficiency

AIMS

The aim of this study was to assess the papillary muscle strain as a contributor to recurrent mitral regurgitation (MR) after mitral valve repair for fibroelastic deficiency.

METHODS AND RESULTS

Sixty-four patients with isolated posterior mitral valve prolapse and severe MR referred for surgery were prospectively recruited between 2008 and 2012. Two- and three-dimensional echocardiography and speckle tracking were performed in all patients. The longitudinal strain of the anterolateral (AL) and posteromedial (PM) papillary muscles was individually calculated as well as the global longitudinal strain of both papillary muscles was measured before and after mitral repair and normalized to left ventricle end-diastolic volume. Eight patients (12.5%) had at least moderate MR 6 months after mitral repair. The longitudinal strain of the AL (preop -4.94 ± 2.2 vs. postop -3.28 ± 1.3, P < 0.001) and the PM papillary muscles (preop -12.64 ± 5.3 vs. postop -4.12 ± 6.77, P < 0.001) as well as the global strain of both papillary muscles (preop -7.59 ± 3.48 vs. postop -1.07 ± 6, P < 0.001) were all reduced after surgical repair. The longitudinal strain of the PM papillary muscle was the strongest predictor of recurrent MR (when less than or equal to -14.78). The global preoperative papillary muscle strain was also a determinant of recurrent MR when the global strain was greater than -9.05% (area under the curve: 0.895, sensitivity: 100%, and specificity: 76.8%).

CONCLUSIONS

Patients with isolated posterior mitral leaflet prolapse are less likely having any residual MR post repair when the global papillary muscle strain of both papillary muscles is close or equal to zero. Strain of the papillary muscles may be an important determinant in predicting residual MR in patients who undergo mitral valve repair.

Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery

Local skin flaps have revolutionized reconstructive surgery. Mechanical loading is critical for flap survival: Excessive tissue tension reduces blood supply and induces tissue necrosis. However, skin flaps have never been analyzed mechanically. Here we explore the stress profiles of two common flap designs, direct advancement flaps and double back-cut flaps. Our simulations predict a direct correlation between regions of maximum stress and tissue necrosis. This suggests that elevated stress could serve as predictor for flap failure. Our model is a promising step towards computer-guided reconstructive surgery with the goal to minimize stress, accelerate healing, minimize scarring, and optimize tissue use.

An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Estimation of regional tissue stresses in the functioning heart valve remains an important goal in our understanding of normal valve function and in developing novel engineered tissue strategies for valvular repair and replacement. Methods to accurately estimate regional tissue stresses are thus needed for this purpose, and in particular to develop accurate, statistically informed means to validate computational models of valve function. Moreover, there exists no currently accepted method to evaluate engineered heart valve tissues and replacement heart valve biomaterials undergoing valvular stresses in blood contact. While we have utilized mitral valve anterior leaflet valvuloplasty as an experimental approach to address this limitation, robust computational techniques to estimate implant stresses are required. In the present study, we developed a novel numerical analysis approach for estimation of the in-vivo stresses of the central region of the mitral valve anterior leaflet (MVAL) delimited by a sonocrystal transducer array. The in-vivo material properties of the MVAL were simulated using an inverse FE modeling approach based on three pseudo-hyperelastic constitutive models: the neo-Hookean, exponential-type isotropic, and full collagen-fiber mapped transversely isotropic models. A series of numerical replications with varying structural configurations were developed by incorporating measured statistical variations in MVAL local preferred fiber directions and fiber splay. These model replications were then used to investigate how known variations in the valve tissue microstructure influence the estimated ROI stresses and its variation at each time point during a cardiac cycle. Simulations were also able to include estimates of the variation in tissue stresses for an individual specimen dataset over the cardiac cycle. Of the three material models, the transversely anisotropic model produced the most accurate results, with ROI averaged stresses at the fully-loaded state of 432.6±46.5 kPa and 241.4±40.5 kPa in the radial and circumferential directions, respectively. We conclude that the present approach can provide robust instantaneous mean and variation estimates of tissue stresses of the central regions of the MVAL.

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.

Applications of computational modeling in cardiac surgery

Although computational modeling is common in many areas of science and engineering, only recently have advances in experimental techniques and medical imaging allowed this tool to be applied in cardiac surgery. Despite its infancy in cardiac surgery, computational modeling has been useful in calculating the effects of clinical devices and surgical procedures. In this review, we present several examples that demonstrate the capabilities of computational cardiac modeling in cardiac surgery. Specifically, we demonstrate its ability to simulate surgery, predict myofiber stress and pump function, and quantify changes to regional myocardial material properties. In addition, issues that would need to be resolved in order for computational modeling to play a greater role in cardiac surgery are discussed.

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.

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 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.

In vivo determination of elastic properties of the human aorta based on 4D ultrasound data

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.

A fully implicit finite element method for bidomain models of cardiac electromechanics

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.

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.

Finite element modeling of mitral valve dynamic deformation using patient-specific multi-slices computed tomography scans

The objective of this study was to develop a patient-specific finite element (FE) model of a human mitral valve. The geometry of the mitral valve was reconstructed from multi-slice computed tomography (MSCT) scans at middle diastole with distinguishable mitral leaflet thickness, chordal origins, chordal insertion points, and papillary muscle locations. Mitral annulus and papillary muscle dynamic motions were also quantified from MSCT scans and prescribed as boundary conditions for the FE simulation. Material properties of the human mitral leaflet tissues were obtained from biaxial tests and characterized by an anisotropic hyperelastic material model. In vivo dynamic closing of the mitral valve was simulated. The closed shape of the mitral valve output from the simulation was similar to the mitral valve geometry reconstructed from MSCT images at middle systole. Forces from the anterolateral and posteromedial papillary muscle groups at middle systole were 4.51 N and 5.17 N, respectively. The average maximum principal stress of the midsection of the anterior mitral leaflet was approximately 160 kPa at the systolic peak. Results demonstrated that the developed FE model could closely replicate in vivo mitral valve dynamic motion during middle diastole and systole. This model may serve as a basis for utilizing computational simulations to obtain a better understanding of mitral valve mechanics, disease and surgical repair.