First finite element model of the left ventricle with mitral valve: insights into ischemic mitral regurgitation

Simulated Effects of Acute Left Ventricular Myocardial Infarction on Mitral Regurgitation in an Ovine Model

Ischemic mitral regurgitation (IMR) occurs from incomplete coaptation of the mitral valve (MV) after myocardial infarction (MI), typically worsened by continued remodeling of the left ventricular (LV). The importance of LV remodeling is clear as IMR is induced by the post-MI dual mechanisms of mitral annular dilation and leaflet tethering from papillary muscle (PM) distension via the MV chordae tendineae (MVCT). However, the detailed etiology of IMR remains poorly understood, in large part due to the complex interactions of the MV and the post-MI LV remodeling processes. Given the patient-specific anatomical complexities of the IMR disease processes, simulation-based approaches represent an ideal approach to improve our understanding of this deadly disease. However, development of patient-specific models of left ventricle-mitral valve (LV-MV) interactions in IMR are complicated by the substantial variability and complexity of the MR etiology itself, making it difficult to extract underlying mechanisms from clinical data alone. To address these shortcomings, we developed a detailed ovine LV-MV finite element (FE) model based on extant comprehensive ovine experimental data. First, an extant ovine LV FE model (Sci. Rep. 2021 Jun 29;11(1):13466) was extended to incorporate the MV using a high fidelity ovine in vivo derived MV leaflet geometry. As it is not currently possible to image the MVCT in vivo, a functionally equivalent MVCT network was developed to create the final LV-MV model. Interestingly, in pilot studies, the MV leaflet strains did not agree well with known in vivo MV leaflet strain fields. We then incorporated previously reported MV leaflet prestrains (J. Biomech. Eng. 2023 Nov 1;145(11):111002) in the simulations. The resulting LV-MV model produced excellent agreement with the known in vivo ovine MV leaflet strains and deformed shapes in the normal state. We then simulated the effects of regional acute infarctions of varying sizes and anatomical locations by shutting down the local myocardial contractility. The remaining healthy (noninfarcted) myocardium mechanical behaviors were maintained, but allowed to adjust their active contractile patterns to maintain the prescribed pressure-volume loop behaviors in the acute post-MI state. For all cases studied, the LV-MV simulation demonstrated excellent agreement with known LV and MV in vivo strains and MV regurgitation orifice areas. Infarct location was shown to play a critical role in resultant MV leaflet strain fields. Specifically, extensional deformations of the posterior leaflets occurred in the posterobasal and laterobasal infarcts, while compressive deformations of the anterior leaflet were observed in the anterobasal infarct. Moreover, the simulated posterobasal infarct induced the largest MV regurgitation orifice area, consistent with experimental observations. The present study is the first detailed LV-MV simulation that reveals the important role of MV leaflet prestrain and functionally equivalent MVCT for accurate predictions of LV-MV interactions. Importantly, the current study further underscored simulation-based methods in understanding MV function as an integral part of the LV.

Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

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.

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.

Comparative modeling of the mitral valve in normal and prolapse conditions

Introduction

Computational modeling is one of the best non-invasive approaches to predicting the functional behavior of the mitral valve (MV) in health and disease. Mitral valve prolapse (MVP) due to partial or complete chordae tendineae rapture is the most common valvular disease and results in mitral regurgitation (MR).

Methods

In this study, Image-based fluid-structure interaction (FSI) models of the human MV are developed in the normal physiological and posterior leaflet prolapse conditions. Detailed geometry of the healthy human MV is derived from Computed Tomography imaging data. To provide prolapse condition, some chords attached to the posterior leaflet are removed from the healthy valve. Both normal and prolapsed valves are embedded separately in a straight tubular blood volume and simulated under physiological systolic pressure loads. The Arbitrary Lagrangian-Eulerian finite element method is used to accommodate the deforming intersection boundaries of the blood and MV.

Results

The stress values in the mitral components, and also flow patterns including the regurgitant flow rates are obtained and compared in both conditions through the simulation. These simulations have the potential to improve the treatment of patients with MVP, and also help surgeons to have more realistic insight into the dynamics of the MV in health and prolapse.

Conclusion

In the prolapse model, computational results show incomplete leaflet coaptation, higher MR severity, and also a significant increment of posterior leaflet stress compared to the normal valve. Moreover, it is found more deviation of the regurgitant jet towards the left atrium wall due to the posterior leaflet prolapse.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

Computational Fluid Dynamics (CFD) is used to assist in designing artificial valves and planning procedures, focusing on local flow features. However, assessing the impact on overall cardiovascular function or predicting longer-term outcomes may requires more comprehensive whole heart CFD models. Fitting such models to patient data requires numerous computationally expensive simulations, and depends on specific clinical measurements to constrain model parameters, hampering clinical adoption. Surrogate models can help to accelerate the fitting process while accounting for the added uncertainty. We create a validated patient-specific four-chamber heart CFD model based on the Navier-Stokes-Brinkman (NSB) equations and test Gaussian Process Emulators (GPEs) as a surrogate model for performing a variance-based global sensitivity analysis (GSA). GSA identified preload as the dominant driver of flow in both the right and left side of the heart, respectively. Left-right differences were seen in terms of vascular outflow resistances, with pulmonary artery resistance having a much larger impact on flow than aortic resistance. Our results suggest that GPEs can be used to identify parameters in personalized whole heart CFD models, and highlight the importance of accurate preload measurements.

Texas TriValve 1.0 : a reverse‑engineered, open model of the human tricuspid valve

Nearly 1.6 million Americans suffer from a leaking tricuspid heart valve. To make matters worse, current valve repair options are far from optimal leading to recurrence of leakage in up to 30% of patients. We submit that a critical step toward improving outcomes is to better understand the "forgotten" valve. High-fidelity computer models may help in this endeavour. However, the existing models are limited by averaged or idealized geometries, material properties, and boundary conditions. In our current work, we overcome the limitations of existing models by (reverse) engineering the tricuspid valve from a beating human heart in an organ preservation system. The resulting finite-element model faithfully captures the kinematics and kinetics of the native tricuspid valve as validated against echocardiographic data and others' previous work. To showcase the value of our model, we also use it to simulate disease-induced and repair-induced changes to valve geometry and mechanics. Specifically, we simulate and compare the effectiveness of tricuspid valve repair via surgical annuloplasty and via transcatheter edge-to-edge repair. Importantly, our model is openly available for others to use. Thus, our model will allow us and others to perform virtual experiments on the healthy, diseased, and repaired tricuspid valve to better understand the valve itself and to optimize tricuspid valve repair for better patient outcomes.

Alterations in Human Mitral Valve Mechanical Properties Secondary to Left Ventricular Remodeling: A Biaxial Mechanical Study

Secondary mitral regurgitation occurs when a left ventricular problem causes leaking of the mitral valve. The altered left ventricular geometry changes the orientation of the subvalvular apparatus, thereby affecting the mechanical stress on the mitral valve. This in turn leads to active remodeling of the mitral valve, in order to compensate for the ventricular remodeling. In this study, a biomechanical analysis was performed on eight human mitral valves with secondary mitral regurgitation and ten healthy human mitral valves to better understand this pathophysiology and its effect on the mechanical properties of these tissues. Samples were obtained from the anterior and posterior leaflet and used for planar biaxial mechanical experiments. Uniaxial experiments were performed on four groups of mitral valve chords: anterior basal, anterior marginal, posterior basal and posterior marginal chords. The mechanical response of the mitral valve leaflets was fitted to the May-Newman and Yin constitutive model, whereas the material parameters of the third order Ogden model were determined for the chord samples. Next, stiffnesses calculated at low and high stress levels were statistically analyzed. Leaflet samples with secondary mitral regurgitation showed a small thickness increase and a change in anisotropy index compared to healthy control valves. Diseased leaflets were more compliant circumferentially and stiffer radially, resulting in anisotropic samples with the radial direction being stiffest. In addition, chord samples were slightly thicker and less stiff at high stress in secondary mitral regurgitation, when grouped per leaflet type and insertion region. These results confirm mechanical alterations due to the pathophysiological valvular changes caused by left ventricular remodeling. It is important that these changes in mechanical behavior are incorporated into computational models of the mitral valve.

In Vitro Mitral Valve Model with Unrestricted Ventricular Access: Using Vacuum to Close the Valve and Enable Static Trans-Mitral Pressure

Current in vitro models of the left heart establish the pressure difference required to close the mitral valve by sealing and pressurizing the ventricular side of the valve, limiting important access to the subvalvular apparatus. This paper describes and evaluates a system that establishes physiological pressure differences across the valve using vacuum on the atrial side. The subvalvular apparatus is open to atmospheric pressure and accessible by tools and sensors, establishing a novel technique for experimentation on atrioventricular valves. Porcine mitral valves were excised and closed by vacuum within the atrial chamber. Images were used to document and analyze closure of the leaflets. Papillary muscle force and regurgitant flow rate were measured to be 4.07 N at 120 mmHg and approximately 12.1 ml/s respectively, both of which are within clinically relevant ranges. The relative ease of these measurements demonstrates the usefulness of improved ventricular access at peak pressure/force closure.

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.

In Vivo Image-Based 4D Modeling of Competent and Regurgitant Mitral Valve Dynamics

BACKGROUND

In vivo characterization of mitral valve dynamics relies on image analysis algorithms that accurately reconstruct valve morphology and motion from clinical images. The goal of such algorithms is to provide patient-specific descriptions of both competent and regurgitant mitral valves, which can be used as input to biomechanical analyses and provide insights into the pathophysiology of diseases like ischemic mitral regurgitation (IMR).

OBJECTIVE

The goal is to generate accurate image-based representations of valve dynamics that visually and quantitatively capture normal and pathological valve function.

METHODS

We present a novel framework for 4D segmentation and geometric modeling of the mitral valve in real-time 3D echocardiography (rt-3DE), an imaging modality used for pre-operative surgical planning of mitral interventions. The framework integrates groupwise multi-atlas label fusion and template-based medial modeling with Kalman filtering to generate quantitatively descriptive and temporally consistent models of valve dynamics.

RESULTS

The algorithm is evaluated on rt-3DE data series from 28 patients: 14 with normal mitral valve morphology and 14 with severe IMR. In these 28 data series that total 613 individual 3DE images, each 3D mitral valve segmentation is validated against manual tracing, and temporal consistency between segmentations is demonstrated.

CONCLUSIONS

Automated 4D image analysis allows for reliable non-invasive modeling of the mitral valve over the cardiac cycle for comparison of annular and leaflet dynamics in pathological and normal mitral valves. Future studies can apply this algorithm to cardiovascular mechanics applications, including patient-specific strain estimation, fluid dynamics simulation, inverse finite element analysis, and risk stratification for surgical treatment.

Effect of Edge-to-Edge Mitral Valve Repair on Chordal Strain: Fluid-Structure Interaction Simulations

Edge-to-edge repair for mitral valve regurgitation is being increasingly performed in high-surgical risk patients using minimally invasive mitral clipping devices. Known procedural complications include chordal rupture and mitral leaflet perforation. Hence, it is important to quantitatively evaluate the effect of edge-to-edge repair on chordal integrity. in this study, we employ a computational mitral valve model to simulate functional mitral regurgitation (FMR) by creating papillary muscle displacement. Edge-to-edge repair is then modeled by simulated coaptation of the mid portion of the mitral leaflets. in the setting of simulated FMR, edge-to-edge repair was shown to sustain low regurgitant orifice area, until a two fold increase in the inter-papillary muscle distance as compared to the normal mitral valve. Strain in the chordae was evaluated near the papillary muscles and the leaflets. Following edge-to-edge repair, strain near the papillary muscles did not significantly change relative to the unrepaired valve, while strain near the leaflets increased significantly relative to the unrepaired valve. These data demonstrate the potential for computational simulations to aid in the pre-procedural evaluation of possible complications such as chordal rupture and leaflet perforation following percutaneous edge-to-edge repair.

Fluid-Structure Interaction Analysis of Subject-Specific Mitral Valve Regurgitation Treatment with an Intra-Valvular Spacer

Mitral regurgitation imposes a significant symptomatic burden on patients who are not candidates for conventional surgery. For these patients, transcatheter repair and replacement devices are emerging as alternative options. One such device is an intravalvular balloon or spacer that is inserted between the mitral valve leaflets to fill the gap that gives rise to mitral regurgitation. In this study, we apply a large-deformation fluid-structure interaction analysis to a fully 3D subject-specific mitral valve model to assess the efficacy of the intra-valvular spacer for reducing mitral regurgitation severity. The model includes a topologically 3D subvalvular apparatus with unprecedented detail. Results show that device fixation and anchoring at the location of the subject’s regurgitant orifice is imperative for optimal reduction of mitral regurgitation.

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.

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.

Mechanical effects of MitraClip on leaflet stress and myocardial strain in functional mitral regurgitation - A finite element modeling study

Purpose

MitraClip is the sole percutaneous device approved for functional mitral regurgitation (MR; FMR) but MR recurs in over one third of patients. As device-induced mechanical effects are a potential cause for MR recurrence, we tested the hypothesis that MitraClip increases leaflet stress and procedure-related strain in sub-valvular left ventricular (LV) myocardium in FMR associated with coronary disease (FMR-CAD).

Methods

Simulations were performed using finite element models of the LV + mitral valve based on MRI of 5 sheep with FMR-CAD. Models were modified to have a 20% increase in LV volume (↑LV_VOLUME) and MitraClip was simulated with contracting beam elements (virtual sutures) placed between nodes in the center edge of the anterior (AL) and posterior (PL) mitral leaflets. Effects of MitraClip on leaflet stress in the peri-MitraClip region of AL and PL, septo-lateral annular diameter (SLAD), and procedure-related radial strain (E_rr) in the sub-valvular myocardium were calculated.

Results

MitraClip increased peri-MitraClip leaflet stress at end-diastole (ED) by 22.3±7.1 kPa (p<0.0001) in AL and 14.8±1.2 kPa (p<0.0001) in PL. MitraClip decreased SLAD by 6.1±2.2 mm (p<0.0001) and increased E_rr in the sub-valvular lateral LV myocardium at ED by 0.09±0.04 (p<0.0001)). Furthermore, MitraClip in ↑LV_VOLUME was associated with persistent effects at ED but also at end-systole where peri-MitraClip leaflet stress was increased in AL by 31.9±14.4 kPa (p = 0.0268) and in PL by 22.5±23.7 kPa (p = 0.0101).

Conclusions

MitraClip for FMR-CAD increases mitral leaflet stress and radial strain in LV sub-valvular myocardium. Mechanical effects of MitraClip are augmented by LV enlargement.

Some Effects of Different Constitutive Laws on FSI Simulation for the Mitral Valve

In this paper, three different constitutive laws for mitral leaflets and two laws for chordae tendineae are selected to study their effects on mitral valve dynamics with fluid-structure interaction. We first fit these three mitral leaflet constitutive laws and two chordae tendineae laws with experimental data. The fluid-structure interaction is implemented in an immersed boundary framework with finite element extension for solid, that is the hybrid immersed boundary/finite element(IB/FE) method. We specifically compare the fluid-structure results of different constitutive laws since fluid-structure interaction is the physiological loading environment. This allows us to look at the peak jet velocity, the closure regurgitation volume, and the orifice area. Our numerical results show that different constitutive laws can affect mitral valve dynamics, such as the transvalvular flow rate, closure regurgitation and the orifice area, while the differences in fiber strain and stress are insignificant because all leaflet constitutive laws are fitted to the same set of experimental data. In addition, when an exponential constitutive law of chordae tendineae is used, a lower closure regurgitation flow is observed compared to that of a linear material model. In conclusion, combining numerical dynamic simulations and static experimental tests, we are able to identify suitable constitutive laws for dynamic behaviour of mitral leaflets and chordae under physiological conditions.

User-dependent variability in mitral valve segmentation and its impact on CFD-computed hemodynamic parameters

PURPOSE

While novel tools for segmentation of the mitral valve are often based on automatic image processing, they mostly require manual interaction by a proficient user. Those segmentations are essential for numerical support of mitral valve treatment using computational fluid dynamics, where the reconstructed geometry is incorporated into a simulation domain. To quantify the uncertainty and reliability of hemodynamic simulations, it is crucial to examine the influence of user-dependent variability in valve segmentation.

METHODS

Previously, the inter-user variability of landmarks in mitral valve segmentation was investigated. Here, the inter-user variability of geometric parameters of the mitral valve, projected orifice area (OA) and projected annulus area (AA), is investigated for 10 mitral valve geometries, each segmented by three users. Furthermore, the propagation of those variations into numerically calculated hemodynamics, i.e., the blood flow velocity, was investigated.

RESULTS

Among the three geometric valve parameters, AA was least user-dependent. Almost all deviations to the mean were below 10%. Larger variations were observed for OA. Variations observed for the numerically calculated hemodynamics were in the same order of magnitude as those of geometric parameters. No correlation between variation of geometric parameters and variation of calculated hemodynamic parameters was found.

CONCLUSION

Errors introduced due to the user-dependency were of the same size as the variations of calculated hemodynamics. The variation was thereby of the same scale as deviations in clinical measurements of blood flow velocity using Doppler echocardiography. Since no correlation between geometric and hemodynamic uncertainty was found, further investigation of the complex relationship between anatomy, leaflet shape and flow is necessary.

Euler's Elastica-Based Biomechanics of the Papillary Muscle Approximation in Ischemic Mitral Valve Regurgitation: A Simple 2D Analytical Model

Ischemic mitral regurgitation (IMR) occurs as an adverse consequence of left ventricle remodeling post-myocardial infarction. A change in mitral valve configuration with an imbalance between closing and tethering forces underlie this pathological condition. These abnormalities lead to impaired leaflet coaptation and a variable degree of mitral regurgitation, which can in turn influence the ventricular filling status, the heart rhythm and the afterload regardless of the residual ischemic insult. The IMR correction can be pursued through under-sizing mitral annuloplasty and papillary muscle approximation to restore the mitral valve and left ventricle physiological geometry to, consequently, achieve normalization of the engaged physical forces. Because the structures involved undergo extremely large deformations, a biomechanics model based on the Euler's Elastica -the mitral leaflet- interlaced with nonlinear chordae tendineae anchored on papillary muscles has been constructed to elucidate the interactions between closing and tethering forces. The model takes into account the actual updated geometrical and mechanical features of the valvular and subvalvular apparatuses in physiological and IMR conditions, as well as in case of papillary muscle approximation, finally furnishing ad hoc geometry-based mathematical relations that could be utilised to support-and optimize-the relevant choices in cardiac surgery.

Fluid-structure interaction assessment of blood flow hemodynamics and leaflet stress during mitral regurgitation

The aim of this study is to simulate the Mitral Regurgitation (MR) disease progression from mild to severe intensity. A Fluid Structure Interaction (FSI) model was developed to extract the hemodynamic parameters of blood flow in mitral regurgitation (MR) during systole. A two-dimensional (2D) geometry of the mitral valve was built based on the data resulting from Magnetic Resonance Imaging (MRI) dimensional measurements. The leaflets were assumed to be elastic. Using COMSOL software, the hemodynamic parameters of blood flow including velocity, pressure, and Von Mises stress contours were obtained by moving arbitrary Lagrange-Euler mesh. The results were obtained for normal and MR cases. They showed the effects of the abnormal distance between the leaflets on the amount of returned flow. Furthermore, the deformation of the leaflets was measured during systole. The results were found to be consistent with the relevant literature.

Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization

Ischemic mitral regurgitation (IMR) is a currently prevalent disease in the US that is projected to become increasingly common as the aging population grows. In recent years, image-based simulations of mitral valve (MV) function have improved significantly, providing new tools to refine IMR treatment. However, clinical implementation of MV simulations has long been hindered as the in vivo MV chordae tendineae (MVCT) geometry cannot be captured with sufficient fidelity for computational modeling. In the current study, we addressed this challenge by developing a method to produce functionally equivalent MVCT models that can be built from the image-based MV leaflet geometry alone. We began our analysis using extant micron-resolution 3D imaging datasets to first build anatomically accurate MV models. We then systematically simplified the native MVCT structure to generate a series of synthetic models by consecutively removing key anatomic features, such as the thickness variations, branching patterns, and chordal origin distributions. In addition, through topology optimization, we identified the minimal structural complexity required to capture the native MVCT behavior. To assess the performance and predictive power of each synthetic model, we analyzed their performance by comparing the mismatch in simulated MV closed shape, as well as the strain and stress tensors, to ground-truth MV models. Interestingly, our results revealed a substantial redundancy in the anatomic structure of native chordal anatomy. We showed that the closing behavior of complete MV apparatus under normal, diseased, and surgically repaired scenarios can be faithfully replicated by a functionally equivalent MVCT model comprised of two representative papillary muscle heads, single strand chords, and a uniform insertion distribution with a density of 15 insertions/cm2. Hence, even though the complete sub-valvular structure is mostly missing in in vivo MV images, we believe our approach will allow for the development of patient-specific complete MV models for surgical repair planning.

Development of a fluid-structure interaction model to simulate mitral valve malcoaptation

OBJECT

Mitral regurgitation (MR) is a condition in which the mitral valve does not prevent the reversal of blood flow from the left ventricle into the left atrium. This study aimed at numerically developing a model to mimic MR and poor leaflet coaptation and also comparing the performance of a normal mitral valve to that of the MR conditions at different gap junctions of 1, 3 and 5 mm between the anterior and posterior leaflets.

RESULTS

The results revealed no blood flow to the left ventricle when a gap between the leaflets was 0 mm. However, MR increased this blood flow, with increases in the velocity and pressure within the atrium. However, the pressure within the aorta did not vary meaningfully (ranging from 22 kPa for a 'healthy' model to 25 kPa for severe MR).

CONCLUSIONS

The findings from this study have implications not only for understanding the changes in pressure and velocity as a result of MR in the ventricle, atrium or aorta, but also for the development of a computational model suitable for clinical translation when diagnosing and determining treatment for MR.

Finite element analysis of annuloplasty and papillary muscle relocation on a patient-specific mitral regurgitation model

Objectives

Functional mitral regurgitation (FMR) is a significant complication of left ventricle (LV) dysfunction associated with poor prognosis and commonly treated by undersized ring annuloplasty. This study aimed to quantitatively simulate the treatment outcomes and mitral valve (MV) biomechanics following ring annulopalsty and papillary muscle relocation (PMR) procedures for a FMR patient.

Methods

We utilized a validated finite element model of the left heart for a patient with severe FMR and LV dilation from our previous study and simulated virtual ring annuloplasty procedures with various sizes of Edwards Classic and GeoForm annuloplasty rings. The model included detailed geometries of the left ventricle, mitral valve, and chordae tendineae, and incorporated age- and gender- matched nonlinear, anisotropic hyperelastic tissue material properties, and simulated chordal tethering at diastole due to LV dilation.

Results

Ring annuloplasty with either the Classic or GeoForm ring improved leaflet coaptation and increased the total leaflet closing force while increased posterior mitral leaflet (PML) stresses and strains. Classic rings resulted in larger coaptation forces and areas compared to GeoForm rings. The PMR procedure further improved the leaflet coaptation, decreased the PML stress and strain for both ring shapes and all sizes in this patient model.

Conclusions

This study demonstrated that a rigorously developed patient-specific computational model can provide useful insights into annuloplasty repair techniques for the treatment of FMR patients and could potentially serve as a tool to assist in pre-operative planning for MV repair surgical or interventional procedures.

Computational Pre-surgical Planning of Arterial Patch Reconstruction: Parametric Limits and In Vitro Validation

Surgical treatment of congenital heart disease (CHD) involves complex vascular reconstructions utilizing artificial and native surgical materials. A successful surgical reconstruction achieves an optimal hemodynamic profile through the graft in spite of the complex post-operative vessel growth pattern and the altered pressure loading. This paper proposes a new in silico patient-specific pre-surgical planning framework for patch reconstruction and investigates its computational feasibility. The proposed protocol is applied to the patch repair of main pulmonary artery (MPA) stenosis in the Tetralogy of Fallot CHD template. The effects of stenosis grade, the three-dimensional (3D) shape of the surgical incision and material properties of the artificial patch are investigated. The release of residual stresses due to the surgical incision and the extra opening of the incision gap for patch implantation are simulated through a quasi-static finite-element vascular model with shell elements. Implantation of different unloaded patch shapes is simulated. The patched PA configuration is pressurized to the physiological post-operative blood pressure levels of 25 and 45 mmHg and the consequent post-operative stress distributions and patched artery shapes are computed. Stress–strain data obtained in-house, through the biaxial tensile tests for the mechanical properties of common surgical patch materials, Dacron, Polytetrafluoroethylene, human pericardium and porcine xenopericardium, are employed to represent the mechanical behavior of the patch material. Finite-element model is experimentally validated through the actual patch surgery reconstructions performed on the 3D printed anatomical stenosis replicas. The post-operative recovery of the initially narrowed lumen area and post-op tortuosity are quantified for all modeled cases. A computational fluid dynamics solver is used to evaluate post-operative pressure drop through the patch-reconstructed outflow tract. According to our findings, the shorter incisions made at the throat result in relatively low local peak stress values compared to other patch design alternatives. Longer cut and double patch cases are the most effective in repairing the initial stenosis level. After the patch insertion, the pressure drop in the artery due to blood flow decreases from 9.8 to 1.35 mmHg in the conventional surgical configuration. These results are in line with the clinical experience where a pressure gradient at or above 50 mmHg through the MPA can be an indication to intervene. The main strength of the proposed pre-surgical planning framework is its capability to predict the intra-operative and post-operative 3D vascular shape changes due to intramural pressure, cut length and configuration, for both artificial and native patch materials.

Personalised computational cardiology: Patient-specific modelling in cardiac mechanics and biomaterial injection therapies for myocardial infarction

Predictive computational modelling in biomedical research offers the potential to integrate diverse data, uncover biological mechanisms that are not easily accessible through experimental methods and expose gaps in knowledge requiring further research. Recent developments in computing and diagnostic technologies have initiated the advancement of computational models in terms of complexity and specificity. Consequently, computational modelling can increasingly be utilised as enabling and complementing modality in the clinic—with medical decisions and interventions being personalised. Myocardial infarction and heart failure are amongst the leading causes of death globally despite optimal modern treatment. The development of novel MI therapies is challenging and may be greatly facilitated through predictive modelling. Here, we review the advances in patient-specific modelling of cardiac mechanics, distinguishing specificity in cardiac geometry, myofibre architecture and mechanical tissue properties. Thereafter, the focus narrows to the mechanics of the infarcted heart and treatment of myocardial infarction with particular attention on intramyocardial biomaterial delivery.

Patient-Specific Computational Analysis of Ventricular Mechanics in Pulmonary Arterial Hypertension

Patient-specific biventricular computational models associated with a normal subject and a pulmonary arterial hypertension (PAH) patient were developed to investigate the disease effects on ventricular mechanics. These models were developed using geometry reconstructed from magnetic resonance (MR) images, and constitutive descriptors of passive and active mechanics in cardiac tissues. Model parameter values associated with ventricular mechanical properties and myofiber architecture were obtained by fitting the models with measured pressure-volume loops and circumferential strain calculated from MR images using a hyperelastic warping method. Results show that the peak right ventricle (RV) pressure was substantially higher in the PAH patient (65 mmHg versus 20 mmHg), who also has a significantly reduced ejection fraction (EF) in both ventricles (left ventricle (LV): 39% versus 66% and RV: 18% versus 64%). Peak systolic circumferential strain was comparatively lower in both the left ventricle (LV) and RV free wall (RVFW) of the PAH patient (LV: -6.8% versus -13.2% and RVFW: -2.1% versus -9.4%). Passive stiffness, contractility, and myofiber stress in the PAH patient were all found to be substantially increased in both ventricles, whereas septum wall in the PAH patient possessed a smaller curvature than that in the LV free wall. Simulations using the PAH model revealed an approximately linear relationship between the septum curvature and the transseptal pressure gradient at both early-diastole and end-systole. These findings suggest that PAH can induce LV remodeling, and septum curvature measurements may be useful in quantifying transseptal pressure gradient in PAH patients.

Comprehensive computational assessment of blood flow characteristics of left ventricle based on in-vivo MRI in presence of artificial myocardial infarction

BACKGROUND

Understanding the effects of cardiac diseases on the heart's functionality which is the purpose of many biomedical researches, directly affects the diagnostic and therapeutic methods. Myocardial infarction (MI) is a common complication of cardiac ischemia, however, the impact of MI on the left ventricle (LV) flow patterns has not been widely considered by computational fluid dynamics studies thus far.

METHODS

In this study, we present an insightful numerical method that creates an artificial MI on an image-based fluid-structure interactional model of normal LV to investigate its influence on the flow in comparison with the normal case. Seventeen different models were developed to evaluate the effects of location, percentage, myocardial material properties and dilation size of MI on the LV's performance, area strain, wall displacement, pressure-volume loop, wall shear stress and velocity field.

RESULTS

The results show that MI considerably changes blood flow features which are fully dependent on MI parameters. For the case of constant MI location, the effect of a decrease of infarcted myocardium stiffness, increase of dilation size and increase of MI percentage are mostly similar. Although the location differences of MI under other constant conditions have similar impact on the ejection fraction, they also lead to dissimilar variations in the LV flow pattern and other indicators.

CONCLUSIONS

The presented model showed a capable computational method for investigating various mechanical MI conditions with respect to cardiac flow pattern. The perspective of this model development seems to be an applicable tool for MI clinical diagnosis and prediction of complications related to MI.

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.

A coupled mitral valve-left ventricle model with fluid-structure interaction

Understanding the interaction between the valves and walls of the heart is important in assessing and subsequently treating heart dysfunction. This study presents an integrated model of the mitral valve (MV) coupled to the left ventricle (LV), with the geometry derived from in vivo clinical magnetic resonance images. Numerical simulations using this coupled MV-LV model are developed using an immersed boundary/finite element method. The model incorporates detailed valvular features, left ventricular contraction, nonlinear soft tissue mechanics, and fluid-mediated interactions between the MV and LV wall. We use the model to simulate cardiac function from diastole to systole. Numerically predicted LV pump function agrees well with in vivo data of the imaged healthy volunteer, including the peak aortic flow rate, the systolic ejection duration, and the LV ejection fraction. In vivo MV dynamics are qualitatively captured. We further demonstrate that the diastolic filling pressure increases significantly with impaired myocardial active relaxation to maintain a normal cardiac output. This is consistent with clinical observations. The coupled model has the potential to advance our fundamental knowledge of mechanisms underlying MV-LV interaction, and help in risk stratification and optimisation of therapies for heart diseases.

Utility of cardiac magnetic resonance for evaluation of mitral regurgitation prior to mitral valve surgery

Mitral regurgitation (MR) is a common cause of morbidity worldwide and an accepted indication for interventional therapies which aim to reduce or resolve adverse clinical outcomes associated with MR. Cardiac magnetic resonance (CMR) provides highly accurate means of assessing MR, including a variety of approaches that can measure MR based on quantitative flow. Additionally, CMR is widely accepted as a reference standard for cardiac chamber quantification, enabling reliable detection of subtle changes in cardiac chamber size and function so as to guide decision-making regarding timing of mitral valve directed therapies. Beyond geometric imaging, CMR enables tissue characterization of ischemia and infarction in the left ventricular (LV) myocardium as well as within the mitral valve apparatus, thus enabling identification of structural substrates for MR. This review provides an overview of established and emerging CMR approaches to measure valvular regurgitation, including relative utility of different approaches for patients with primary or secondary MR. Clinical outcomes studies are discussed with focus on data demonstrating advantages of CMR for guiding diagnosis, risk stratification, and management of patients with known or suspected MR. Comparative data is reviewed with focus on diagnostic performance of CMR in comparison to conventional assessment via echocardiography (echo). Emerging literature is reviewed concerning potential new approaches that utilize CMR tissue characterization to guide clinical decision-making in order to improve therapeutic outcomes and clinical prognosis for patients with MR.

Fluid-structure interaction and structural analyses using a comprehensive mitral valve model with 3D chordal structure

Over the years, three-dimensional models of the mitral valve have generally been organized around a simplified anatomy. Leaflets have been typically modeled as membranes, tethered to discrete chordae typically modeled as one-dimensional, non-linear cables. Yet, recent, high-resolution medical images have revealed that there is no clear boundary between the chordae and the leaflets. In fact, the mitral valve has been revealed to be more of a webbed structure whose architecture is continuous with the chordae and their extensions into the leaflets. Such detailed images can serve as the basis of anatomically accurate, subject-specific models, wherein the entire valve is modeled with solid elements that more faithfully represent the chordae, the leaflets, and the transition between the two. These models have the potential to enhance our understanding of mitral valve mechanics and to re-examine the role of the mitral valve chordae, which heretofore have been considered to be 'invisible' to the fluid and to be of secondary importance to the leaflets. However, these new models also require a rethinking of modeling assumptions. In this study, we examine the conventional practice of loading the leaflets only and not the chordae in order to study the structural response of the mitral valve apparatus. Specifically, we demonstrate that fully resolved 3D models of the mitral valve require a fluid-structure interaction analysis to correctly load the valve even in the case of quasi-static mechanics. While a fluid-structure interaction mode is still more computationally expensive than a structural-only model, we also show that advances in GPU computing have made such models tractable. Copyright © 2016 John Wiley & Sons, Ltd.

Fluid-Structure Interaction Analysis of Ruptured Mitral Chordae Tendineae

The chordal structure is a part of mitral valve geometry that has been commonly neglected or simplified in computational modeling due to its complexity. However, these simplifications cannot be used when investigating the roles of individual chordae tendineae in mitral valve closure. For the first time, advancements in imaging, computational techniques, and hardware technology make it possible to create models of the mitral valve without simplifications to its complex geometry, and to quickly run validated computer simulations that more realistically capture its function. Such simulations can then be used for a detailed analysis of chordae-related diseases. In this work, a comprehensive model of a subject-specific mitral valve with detailed chordal structure is used to analyze the distinct role played by individual chordae in closure of the mitral valve leaflets. Mitral closure was simulated for 51 possible chordal rupture points. Resultant regurgitant orifice area and strain change in the chordae at the papillary muscle tips were then calculated to examine the role of each ruptured chorda in the mitral valve closure. For certain subclassifications of chordae, regurgitant orifice area was found to trend positively with ruptured chordal diameter, and strain changes correlated negatively with regurgitant orifice area. Further advancements in clinical imaging modalities, coupled with the next generation of computational techniques will enable more physiologically realistic simulations.

Undersized Mitral Annuloplasty Increases Strain in the Proximal Lateral Left Ventricular Wall

BACKGROUND

Recurrence of mitral regurgitation (MR) after undersized mitral annuloplasty (MA) for ischemic MR is as high as 60%, with the recurrence rate likely due to continued dilation of the left ventricle (LV). To better understand the causes of recurrent MR, we studied the effect of undersized MA on strain in the LV wall. We hypothesize that the acute change in ventricular shape induced by MA will cause increased strain in regions nearest the mitral valve.

METHODS

Finite element models were previously reported, based on cardiac magnetic resonance images of 5 sheep with mild to moderate ischemic MR. A 24-mm saddle-shaped rigid annuloplasty ring was modeled and used to simulate virtual MA. Longitudinal and myofiber strains were calculated at end-diastole and end-systole, with preoperative early diastolic geometry as the reference state.

RESULTS

The undersized MA significantly increased longitudinal strain at end-diastole in the lateral LV wall. The effect was greatest in the proximal-lateral endocardial surface, where longitudinal strain after MA was approximately triple the preoperative strain (11.17% ± 2.15% vs 3.45% ± 0.92%, p = 0.0057). In contrast, postoperative end-diastolic fiber strain decreased in this same region (2.53% ± 2.14% vs 7.72% ± 1.79%, p = 0.0060). There were no significant changes in either strain type at end-systole.

CONCLUSIONS

Undersized MA increased longitudinal strain in the proximal lateral LV wall at end-diastole. This procedure-related strain at the proximal-lateral LV wall may foster continued LV enlargement and subsequent recurrence of mitral regurgitation.

Heart Valve Biomechanics and Underlying Mechanobiology

Heart valves control unidirectional blood flow within the heart during the cardiac cycle. They have a remarkable ability to withstand the demanding mechanical environment of the heart, achieving lifetime durability by processes involving the ongoing remodeling of the extracellular matrix. The focus of this review is on heart valve functional physiology, with insights into the link between disease-induced alterations in valve geometry, tissue stress, and the subsequent cell mechanobiological responses and tissue remodeling. We begin with an overview of the fundamentals of heart valve physiology and the characteristics and functions of valve interstitial cells (VICs). We then provide an overview of current experimental and computational approaches that connect VIC mechanobiological response to organ- and tissue-level deformations and improve our understanding of the underlying functional physiology of heart valves. We conclude with a summary of future trends and offer an outlook for the future of heart valve mechanobiology, specifically, multiscale modeling approaches, and the potential directions and possible challenges of research development. © 2016 American Physiological Society. Compr Physiol 6:1743-1780, 2016.

Neochord placement versus triangular resection in mitral valve repair: A finite element model

BACKGROUND

Recurrent mitral regurgitation after mitral valve repair is common, occurring in nearly 50% of patients within 10 years of surgery. Durability of repair is partly related to stress distribution over the mitral leaflets. We hypothesized that repair with neochords (NCs) results in lower stress than leaflet resection (LR).

MATERIALS AND METHODS

Magnetic resonance imaging and 3D echocardiography were performed before surgical repair of P2 prolapse in a single patient. A finite element model of the left ventricle and mitral valve was created previously, and the modeling program LS-DYNA was used to calculate leaflet stress for the following repairs: Triangular LR; LR with ring annuloplasty (LR + RA); One NC; Two NCs; and 2NC + RA.

RESULTS

(1) NC placement resulted in stable posterior leaflet stress: Baseline versus 2 NC at end diastole (ED), 12.1 versus 12.0 kPa, at end systole (ES) 20.3 versus 21.7 kPa. (2) In contrast, LR increased posterior leaflet stress: Baseline versus LR at ED 12.1 versus 40.8 kPa, at ES 20.3 versus 46.1 kPa. (3) All repair types reduced anterior leaflet stress: Baseline versus 2 NC versus LR 34.2 versus 25.8 versus 20.6 kPa at ED and 80.8 versus 76.8 versus 67.8 kPa at ES. (4) The addition of RA reduced leaflet stress relative to repair without RA.

CONCLUSIONS

Neochord repair restored normal leaflet coaptation without creating excessive leaflet stress, whereas leaflet resection more than doubled stress across the posterior leaflet. The excess stress created by leaflet resection was partially, but not completely, mitigated by ring annuloplasty.

Numerical modeling of heart valves using resistive Eulerian surfaces

The goal of this work is the development and numerical implementation of a mathematical model describing the functioning of heart valves. To couple the pulsatile blood flow with a highly deformable thin structure (the valve's leaflets), a resistive Eulerian surfaces framework is adopted. A lumped-parameter model helps to couple the movement of the leaflets with the blood dynamics. A reduced circulation model describes the systemic hemodynamics and provides a physiological pressure profile at the downstream boundary of the valve. The resulting model is relatively simple to describe for a healthy valve and pathological heart valve functioning while featuring an affordable computational burden. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method, and we report several numerical experiments for both two-dimensional and three-dimensional cases with the aim of illustrating its accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

High-resolution subject-specific mitral valve imaging and modeling: experimental and computational methods

The diversity of mitral valve (MV) geometries and multitude of surgical options for correction of MV diseases necessitates the use of computational modeling. Numerical simulations of the MV would allow surgeons and engineers to evaluate repairs, devices, procedures, and concepts before performing them and before moving on to more costly testing modalities. Constructing, tuning, and validating these models rely upon extensive in vitro characterization of valve structure, function, and response to change due to diseases. Micro-computed tomography ([Formula: see text]CT) allows for unmatched spatial resolution for soft tissue imaging. However, it is still technically challenging to obtain an accurate geometry of the diastolic MV. We discuss here the development of a novel technique for treating MV specimens with glutaraldehyde fixative in order to minimize geometric distortions in preparation for [Formula: see text]CT scanning. The technique provides a resulting MV geometry which is significantly more detailed in chordal structure, accurate in leaflet shape, and closer to its physiological diastolic geometry. In this paper, computational fluid-structure interaction (FSI) simulations are used to show the importance of more detailed subject-specific MV geometry with 3D chordal structure to simulate a proper closure validated against [Formula: see text]CT images of the closed valve. Two computational models, before and after use of the aforementioned technique, are used to simulate closure of the MV.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

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.

Mitral valve disease--morphology and mechanisms

Mitral valve disease is a frequent cause of heart failure and death. Emerging evidence indicates that the mitral valve is not a passive structure, but--even in adult life--remains dynamic and accessible for treatment. This concept motivates efforts to reduce the clinical progression of mitral valve disease through early detection and modification of underlying mechanisms. Discoveries of genetic mutations causing mitral valve elongation and prolapse have revealed that growth factor signalling and cell migration pathways are regulated by structural molecules in ways that can be modified to limit progression from developmental defects to valve degeneration with clinical complications. Mitral valve enlargement can determine left ventricular outflow tract obstruction in hypertrophic cardiomyopathy, and might be stimulated by potentially modifiable biological valvular-ventricular interactions. Mitral valve plasticity also allows adaptive growth in response to ventricular remodelling. However, adverse cellular and mechanobiological processes create relative leaflet deficiency in the ischaemic setting, leading to mitral regurgitation with increased heart failure and mortality. Our approach, which bridges clinicians and basic scientists, enables the correlation of observed disease with cellular and molecular mechanisms, leading to the discovery of new opportunities for improving the natural history of mitral valve disease.

Fluid-Structure Interaction Analysis of Papillary Muscle Forces Using a Comprehensive Mitral Valve Model with 3D Chordal Structure

Numerical models of native heart valves are being used to study valve biomechanics to aid design and development of repair procedures and replacement devices. These models have evolved from simple two-dimensional approximations to complex three-dimensional, fully coupled fluid-structure interaction (FSI) systems. Such simulations are useful for predicting the mechanical and hemodynamic loading on implanted valve devices. A current challenge for improving the accuracy of these predictions is choosing and implementing modeling boundary conditions. In order to address this challenge, we are utilizing an advanced in vitro system to validate FSI conditions for the mitral valve system. Explanted ovine mitral valves were mounted in an in vitro setup, and structural data for the mitral valve was acquired with [Formula: see text]CT. Experimental data from the in vitro ovine mitral valve system were used to validate the computational model. As the valve closes, the hemodynamic data, high speed leaflet dynamics, and force vectors from the in vitro system were compared to the results of the FSI simulation computational model. The total force of 2.6 N per papillary muscle is matched by the computational model. In vitro and in vivo force measurements enable validating and adjusting material parameters to improve the accuracy of computational models. The simulations can then be used to answer questions that are otherwise not possible to investigate experimentally. This work is important to maximize the validity of computational models of not just the mitral valve, but any biomechanical aspect using computational simulation in designing medical devices.

Intravesical tunnel length to ureteral diameter ratio insufficiently explains ureterovesical junction competence: A parametric simulation study

OBJECTIVE

In 1959, Paquin recommended a tunnel length five times the diameter of the ureter to prevent vesicoureteral reflux (VUR) during ureteral reimplants. In 1969, Lyon et al. challenged Paquin's conclusions and proposed that the ureteral orifice was more important than the intravesical tunnel for UVJ competence. It is not known if the two mechanisms of UVJ competence (tunnel length and UO spatial orientation) are interdependent or if one is more critical. Although in clinical practice Paquin's rule has stood the test of time, classical mechanics of materials would predict more coaptation (less reflux) with larger diameter ureters and this contradicts Paquin's rule. The aim of this study was to test Paquin's tunnel length theory by parametrically modeling the ureterovesical junction (UVJ) to determine variables critical for ureteral closure.

STUDY DESIGN

LS-DYNA finite-element simulation software was use to model ureteral collapse (Figure). Intravesical tunnel length, ureteral diameter, ureteral thickness and ureteral stiffness were all modeled. Changes in the pressure required to collapse the ureter were studied as each variable was changed on the model. The modeled ureteral orifice was not affected by changes in bladder volume (in a real bladder, bladder distention would pull the ureteral office open) and had no constraints (which could occur by suturing the ureteral orifice to a stiff bladder).

RESULTS

As predicted by classical mechanics of materials, the pressure required to collapse the ureter was inversely related to its diameter. Above 1 cm tunnel length, pressures required to collapse a ureter did not decrease by any significant amount. Increasing ureteral thickness or ureteral stiffness did increase the pressure required to collapse the ureter, but only significantly for ureteral thicknesses not commonly seen in practice (i.e. wall thickness of 2.5 mm in a 6.4 mm ureter).

DISCUSSION

Our model showed that for most ureters seen in clinical practice (3-30 mm in diameter), and when the ureteral orifice is not constrained by the bladder mucosa, a 1 cm tunnel would allow the ureter to collapse under low pressures. Contrary to Paquin's belief, larger diameter ureters collapsed more easily. It is important to understand that our model's main limitation was that it did not study the effects of the ureteral orifice, which in light of our findings must play an important role in preventing reflux as suggested by Lyon et al., in 1969. For example, a 3 cm ureteral orifice sutured to the bladder mucosa would be difficult to collapse as the bladder distends and pulls open the orifice. One way of compensating for a difficult to collapse ureteral orifice would be creating a larger diameter tunnel, but another would be to create a better ureteral orifice, perhaps by narrowing the diameter of the UO (distal ureteral tapering) and making it protrude into the bladder like a volcano (i.e. advancement sutures, or creating an intravesical nipple).

CONCLUSION

We hope that this new understanding of the variables involved in ureterovesical junction competence can lead to further refinement in our surgical techniques to correct vesicoureteral reflux.

Quantification and simulation of layer-specific mitral valve interstitial cells deformation under physiological loading

Within each of the four layers of mitral valve (MV) leaflet tissues there resides a heterogeneous population of interstitial cells that maintain the structural integrity of the MV tissue via protein biosynthesis and enzymatic degradation. There is increasing evidence that tissue stress-induced MV interstitial cell (MVIC) deformations can have deleterious effects on their biosynthetic states that are potentially related to the reduction of tissue-level maintenance and to subsequent organ-level failure. To better understand the interrelationships between tissue-level loading and cellular responses, we developed the following integrated experimental-computational approach. Since in vivo cellular deformations are not directly measurable, we quantified the in-situ layer-specific MVIC deformations for each of the four layers under a controlled biaxial tension loading device coupled to multi-photon microscopy. Next, we explored the interrelationship between the MVIC stiffness and deformation to layer-specific tissue mechanical and structural properties using a macro-micro finite element computational model. Experimental results indicated that the MVICs in the fibrosa and ventricularis layers deformed significantly more than those in the atrialis and spongiosa layers, reaching a nucleus aspect ratio of 3.3 under an estimated maximum physiological tension of 150N/m. The simulated MVIC moduli for the four layers were found to be all within a narrow range of 4.71-5.35kPa, suggesting that MVIC deformation is primarily controlled by each tissue layer's respective structure and mechanical behavior rather than the intrinsic MVIC stiffness. This novel result further suggests that while the MVICs may be phenotypically and biomechanically similar throughout the leaflet, they experience layer-specific mechanical stimulatory inputs due to distinct extracellular matrix architecture and mechanical behaviors of the four MV leaflet tissue layers. This also suggests that MVICs may behave in a layer-specific manner in response to mechanical stimuli in both normal and surgically modified MVs.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Human Cardiac Function Simulator for the Optimal Design of a Novel Annuloplasty Ring with a Sub-valvular Element for Correction of Ischemic Mitral Regurgitation

Ischemic mitral regurgitation is associated with substantial risk of death. We sought to: (1) detail significant recent improvements to the Dassault Systèmes human cardiac function simulator (HCFS); (2) use the HCFS to simulate normal cardiac function as well as pathologic function in the setting of posterior left ventricular (LV) papillary muscle infarction; and (3) debut our novel device for correction of ischemic mitral regurgitation. We synthesized two recent studies of human myocardial mechanics. The first study presented the robust and integrative finite element HCFS. Its primary limitation was its poor diastolic performance with an LV ejection fraction below 20% caused by overly stiff ex vivo porcine tissue parameters. The second study derived improved diastolic myocardial material parameters using in vivo MRI data from five normal human subjects. We combined these models to simulate ischemic mitral regurgitation by computationally infarcting an LV region including the posterior papillary muscle. Contact between our novel device and the mitral valve apparatus was simulated using Dassault Systèmes SIMULIA software. Incorporating improved cardiac geometry and diastolic myocardial material properties in the HCFS resulted in a realistic LV ejection fraction of 55%. Simulating infarction of posterior papillary muscle caused regurgitant mitral valve mechanics. Implementation of our novel device corrected valve dysfunction. Improvements in the current study to the HCFS permit increasingly accurate study of myocardial mechanics. The first application of this simulator to abnormal human cardiac function suggests that our novel annuloplasty ring with a sub-valvular element will correct ischemic mitral regurgitation.