On modelling and analysis of healthy and pathological human mitral valves: Two case studies

Generic framework for quantifying the influence of the mitral valve on ventricular blood flow

Blood flow within the left ventricle provides important information regarding cardiac function in health and disease. The mitral valve strongly influences the formation of flow structures and there exist various approaches for the representation of the valve in numerical models of left ventricular blood flow. However, a systematic comparison of the various mitral valve models is missing, making a priori decisions considering the overall model's context of use impossible. Within this study, a benchmark setup to compare the influence of mitral valve modeling strategies on intraventricular flow features was developed. Then, five mitral valve models of increasing complexity: no modeling, static wall, 2D and 3D porous medium with time-dependent porosity, and one-way fluid-structure interaction (FSI) were compared with each other. The flow features velocity, kinetic energy, transmitral pressure drop, vortex formation, flow asymmetry as well as computational cost and ease-of-implementation were evaluated. The one-way FSI approach provides the highest level of flow detail, which is accompanied by the highest numerical costs and challenges with the implementation. As an alternative, the porous medium approach with the expansion including time-dependent porosity provides good results with up to 10% deviations in the flow features (except the transmitral pressure drop) in comparison to the FSI model and only a fraction (11%) of numerical costs. However, jet propagation speed is highly underestimated by all alternative approaches to the FSI model. Taken together, our benchmark setup allows a quantitative comparison of various mitral valve modeling approaches and is provided to the scientific community for further testing and expansion.

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

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

A Computational Pipeline for Patient-Specific Prediction of the Postoperative Mitral Valve Functional State

While mitral valve (MV) repair remains the preferred clinical option for mitral regurgitation (MR) treatment, long-term outcomes remain suboptimal and difficult to predict. Furthermore, pre-operative optimization is complicated by the heterogeneity of MR presentations and the multiplicity of potential repair configurations. In the present work, we established a patient-specific MV computational pipeline based strictly on standard-of-care pre-operative imaging data to quantitatively predict the post-repair MV functional state. First, we established human mitral valve chordae tendinae (MVCT) geometric characteristics obtained from five CT-imaged excised human hearts. From these data, we developed a finite-element model of the full patient-specific MV apparatus that included MVCT papillary muscle origins obtained from both the in vitro study and the pre-operative three-dimensional echocardiography images. To functionally tune the patient-specific MV mechanical behavior, we simulated pre-operative MV closure and iteratively updated the leaflet and MVCT prestrains to minimize the mismatch between the simulated and target end-systolic geometries. Using the resultant fully calibrated MV model, we simulated undersized ring annuloplasty (URA) by defining the annular geometry directly from the ring geometry. In three human cases, the postoperative geometries were predicted to 1 mm of the target, and the MV leaflet strain fields demonstrated close agreement with noninvasive strain estimation technique targets. Interestingly, our model predicted increased posterior leaflet tethering after URA in two recurrent patients, which is the likely driver of long-term MV repair failure. In summary, the present pipeline was able to predict postoperative outcomes from pre-operative clinical data alone. This approach can thus lay the foundation for optimal tailored surgical planning for more durable repair, as well as development of mitral valve digital twins.

Mechanical Behavior and Collagen Structure of Degenerative Mitral Valve Leaflets and a Finite Element Model of Primary Mitral Regurgitation

Degenerative mitral valve disease is the main cause of primary mitral regurgitation with two phenotypes: fibroelastic deficiency (FED) often with localized myxomatous degeneration and diffuse myxomatous degeneration or Barlow's disease. Myxomatous degeneration disrupts the microstructure of the mitral valve leaflets, particularly the collagen fibers, which affects the mechanical behavior of the leaflets. The present study uses biaxial mechanical tests and second harmonic generation microscopy to examine the mechanical behavior of Barlow and FED tissue. Three tissue samples were harvested from a FED patient and one sample is from a Barlow patient. Then we use an appropriate constitutive model by excluding the collagen fibers under compression. Finally, we built an FE model based on the echocardiography of patients diagnosed with FED and Barlow and the characterized material model and collagen fiber orientation. The Barlow sample and the FED sample from the most affected segment showed different mechanical behavior and collagen structure compared to the other two FED samples. The FE model showed very good agreement with echocardiography with 2.02±1.8 mm and 1.05±0.79 mm point-to-mesh distance errors for Barlow and FED patients, respectively. It has also been shown that the exclusion of collagen fibers under compression provides versatility for the material model; it behaves stiff in the belly region, preventing excessive bulging, while it behaves very softly in the commissures to facilitate folding. STATEMENT OF SIGNIFICANCE: None.

Shannon entropy as a reliable score to diagnose human fibroelastic degenerative mitral chords: A micro-ct ex-vivo study

This paper is aimed at identifying by means of micro-CT the microstructural differences between normal and degenerative mitral marginal chordae tendineae. The control group is composed of 21 normal chords excised from 14 normal mitral valves from heart transplant recipients. The experimental group comprises 22 degenerative fibroelastic chords obtained at surgery from 11 pathological valves after mitral repair or replacement. In the control group the superficial endothelial cells and spongiosa layer remained intact, covering the wavy core collagen. In contrast, in the experimental group the collagen fibers were arranged as straightened thick bundles in a parallel configuration. 100 cross-sections were examined by micro-CT from each chord. Each image was randomized through the K-means machine learning algorithm and then, the global and local Shannon entropies were obtained. The optimum number of clusters, K, was estimated to maximize the differences between normal and degenerative chords in global and local Shannon entropy; the p-value after a nested ANOVA test was chosen as the parameter to be minimized. Optimum results were obtained with global Shannon entropy and 2≤K≤7, providing p < 0.01; for K=3, p = 2.86·10^-3. These findings open the door to novel perioperative diagnostic methods in order to avoid or reduce postoperative mitral valve regurgitation recurrences.

Structural and biomechanical characterizations of acellular porcine mitral valve scaffolds: anterior leaflets, posterior leaflets, and chordae tendineae

Mitral valve (MV) tissue engineering is still in its early stage, and one major challenge in MV tissue engineering is to identify appropriate scaffold materials. With the potential of acellular MV scaffolds being demonstrated recently, it is important to have a full understanding of the biomechanics of the native MV components and their acellular scaffolds. In this study, we have successfully characterized the structural and mechanical properties of porcine MV components, including anterior leaflet (AL), posterior leaflet (PL), strut chordae, and basal chordae, before and after decellularization. Quantitative DNA assay showed more than 90% reduction in DNA content, and Griffonia simplicifolia (GS) lectin immunohistochemistry confirmed the complete lack of porcine α-Gal antigen in the acellular MV components. In the acellular AL and PL, the atrialis, spongiosa, and fibrosa trilayered structure, along with its ECM constitutes, i.e., collagen fibers, elastin fibers, and portion of GAGs, were preserved. Nevertheless, the ECM of both AL and PL experienced a certain degree of disruption, exhibiting a less dense, porous ECM morphology. The overall anatomical morphology of the strut and basal chordae were also maintained after decellularization, with longitudinal morphology experiencing minimum disruption, but the cross-sectional morphology exhibiting evenly-distributed porous structure. In the acellular AL and PL, the nonlinear anisotropic biaxial mechanical behavior was overall preserved; however, uniaxial tensile tests showed that the removal of cellular content and the disruption of structural ECM did result in small decreases in maximum tensile modulus, tissue extensibility, failure stress, and failure strain for both MV leaflets and chordae.

Primeval outcomes of thoracoscopic transmitral myectomy with anterior mitral leaflet extension for hypertrophic obstructive cardiomyopathy

BACKGROUND

The transaortic Morrow procedure is the current gold standard for hypertrophic obstructive cardiomyopathy (HOCM) patients who are resistant to maximum drug therapy. It is controversial whether concomitant mitral valve intervention is necessary. Only a few centers apply for concomitant anterior mitral leaflet extension with a bovine or autologous pericardial patch to further decrease systolic anterior motion. Our aim is to assess the primeval outcomes of thoracoscopic transmitral myectomy with anterior mitral leaflet extension (TTM-AMLE) in symptomatic HOCM patients.

METHODS

Between April 2019 and November 2020, 18 consecutive HOCM patients who underwent TTM-AMLE were enrolled in this study. Preoperative, postoperative, and follow-up outcomes were compared and statistically analyzed.

RESULTS

The mean age was (50.17 ± 6.18) years and 10 (55.56%) were males. 18 (100%) patients had mitral regurgitation preoperatively, and they all successfully underwent TTM-AMLE with a median cardiopulmonary bypass and aortic cross-clamp time of 200.0 (150.8, 232.0), and 127.5 (116.0, 149.0) min, respectively. The median length of ICU stay was 2.7 (1.4, 5.2) days. The interventricular septum thickness was significantly reduced (from 18.03 ± 3.02 mm to 11.91 ± 1.66 mm, p < .001). There was no perioperative mortality, perforation of ventricular septum, or conversion to sternotomy observed. During a median follow-up of 18 months (IQR, 5-24 months), 1 (5.56%) patient had severe mitral regurgitation due to patch detachment and received reoperation. Moderate degree of mitral regurgitation and more than 50 mmHg in left ventricular outflow tract gradient were found in 2 (11.11%), and 1 (5.56%) patients, respectively. 1 (5.56%) patient who had second-degree atrioventricular block received permanent pacemaker implantation postoperatively. Overall, the maximum left ventricular outflow tract gradient (88.50 [59.50, 112.75] mmHg vs. 10.50 [7.00, 15.50] mmHg, p = .002), left ventricular outflow tract velocity (4.70 [3.86, 5.33] m/s vs. 1.60 [1.33, 1.95] m/s, p < .001) and the degree of mitral regurgitation (6.99 ± 4.47 cm² vs. 2.22 ± 1.51 cm² , p = .001) were significantly decreased, with a significant reduction in the proportion of systolic anterior motion (94.44% vs. 16.67%, p < .001).

CONCLUSIONS

The TTM-AMLE is a safe and effective surgical approach for selected patients with HOCM. In our series, it provides excellent relief of left ventricular outflow tract obstruction, while significantly eliminating mitral regurgitation. The early outcomes of TTM-AMLE are satisfactory, but further studies and longer follow-ups are awaited.

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.

Fluid structure computational model of simulating mitral valve motion in a contracting left ventricle

BACKGROUND

Fluid structure interaction simulations h hold promise in studying normal and abnormal cardiac function, including the effect of fluid dynamics on mitral valve (MV) leaflet motion. The goal of this study was to develop a 3D fluid structure interaction computational model to simulate bileaflet MV when interacting with blood motion in left ventricle (LV).

METHODS

The model consists of ideal geometric-shaped MV leaflets and the LV, with MV dimensions based on human anatomical measurements. An experimentally-based hyperelastic isotropic material was used to model the mechanical behaviour of the MV leaflets, with chordae tendineae and papillary muscle tips also incorporated. LV myocardial tissue was prescribed using a transverse isotropic hyperelastic formulation. Incompressible Navier-Stokes fluid formulations were used to govern the blood motion, and the Arbitrary Lagrangian Eulerian (ALE) method was employed to determine the mesh deformation of the fluid and solid domains due to trans-valvular pressure on MV boundaries and the resulting leaflet movement.

RESULTS

The LV-MV generic model was able to reproduce physiological MV leaflet opening and closing profiles resulting from the time-varying atrial and ventricular pressures, as well as simulating normal and prolapsed MV states. Additionally, the model was able to simulate blood flow patterns after insertion of a prosthetic MV with and without left ventricular outflow tract flow obstruction. In the MV-LV normal model, the regurgitant blood flow fraction was 10.1 %, with no abnormality in cardiac function according to the mitral regurgitation severity grades reported by the American Society of Echocardiography.

CONCLUSION

Our simulation approach provides insights into intraventricular fluid dynamics in a contracting LV with normal and prolapsed MV function, as well as aiding in the understanding of possible complications after transcatheter MV implantation prior to clinical trials.

Patient-Specific Three-Dimensional Ultrasound Derived Computational Modeling of the Mitral Valve

Several new techniques to repair the mitral valve affected by functional mitral regurgitation are in development. However, due to the heterogeneity of valve lesions between patients, predicting the outcomes of novel treatment approaches is challenging. We present a patient-specific, 3D ultrasound-derived computational model of the mitral valve for procedure planning, that faithfully mimics the pathological valve dynamics. 3D ultrasound images were obtained in three pigs induced with heart failure and which developed functional mitral regurgitation. For each case, images were segmented, and finite element model of mitral valve was constructed. Annular and papillary muscle dynamics were extracted and imposed as kinematic boundary conditions, and the chordae were pre-strained to induce valve tethering. Valve closure was simulated by applying physiologic transvalvular pressure on the leaflets. Agreement between simulation results and truth datasets was confirmed, with accurate location of regurgitation jets and coaptation defects. Inclusion of kinematic patient-specific boundary conditions was necessary to achieve these results, whereas use of idealized boundary conditions deviated from the truth dataset. Due to the impact of boundary conditions on the model, the effect of repair strategies on valve closure varied as well, indicating that our approach of using patient-specific boundary conditions for mitral valve modeling is valid.

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.

The Comparison of Different Constitutive Laws and Fiber Architectures for the Aortic Valve on Fluid-Structure Interaction Simulation

Built on the hybrid immersed boundary/finite element (IB/FE) method, fluid-structure interaction (FSI) simulations of aortic valve (AV) dynamics are performed with three different constitutive laws and two different fiber architectures for the AV leaflets. An idealized AV model is used and mounted in a straight tube, and a three-element Windkessel model is further attached to the aorta. After obtaining ex vivo biaxial tensile testing of porcine AV leaflets, we first determine the constitutive parameters of the selected three constitutive laws by matching the analytical stretch-stress relations derived from constitutive laws to the experimentally measured data. Both the average error and relevant R-squared value reveal that the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions could be more suitable for characterizing the mechanical behaviors of the AV leaflets. We then thoroughly compare the simulation results from both structural mechanics and hemodynamics. Compared to the other two constitutive laws, the anisotropic non-linear constitutive law with exponential terms for both the fiber and cross-fiber directions shows the larger leaflet displacements at the opened state, the largest forward jet flow, the smaller regurgitant flow. We further analyze hemodynamic parameters of the six different cases, including the regurgitant fraction, the mean transvalvular pressure gradient, the effective orifice area, and the energy loss of the left ventricle. We find that the fiber architecture with body-fitted orientation shows better dynamic behaviors in the leaflets, especially with the constitutive law using exponential terms for both the fiber and cross-fiber directions. In conclusion, both constitutive laws and fiber architectures can affect AV dynamics. Our results further suggest that the strain energy function with exponential terms for both the fiber and cross-fiber directions could be more suitable for describing the AV leaflet mechanical behaviors. Future experimental studies are needed to identify competent constitutive laws for the AV leaflets and their associated fiber orientations with controlled experiments. Although limitations exist in the present AV model, our results provide important information for selecting appropriate constitutive laws and fiber architectures when modeling AV dynamics.

Interactive editing of virtual chordae tendineae for the simulation of the mitral valve in a decision support system

PURPOSE

Decision support systems for mitral valve disease are an important step toward personalized surgery planning. A simulation of the mitral valve apparatus is required for decision support. Building a model of the chordae tendineae is an essential component of a mitral valve simulation. Due to image quality and artifacts, the chordae tendineae cannot be reliably detected in medical imaging.

METHODS

Using the position-based dynamics framework, we are able to realistically simulate the opening and closing of the mitral valve. Here, we present a heuristic method for building an initial chordae model needed for a successful simulation. In addition to the heuristic, we present an interactive editor to refine the chordae model and to further improve pathology reproduction as well as geometric approximation of the closed valve.

RESULTS

For evaluation, five mitral valves were reconstructed based on image sequences of patients scheduled for mitral valve surgery. We evaluated the approximation of the closed valves using either just the heuristic chordae model or a manually refined model. Using the manually refined models, prolapse was correctly reproduced in four of the five cases compared to two of the five cases when using the heuristic. In addition, using the editor improved the approximation in four cases.

CONCLUSIONS

Our approach is suitable to create realistically parameterized mitral valve apparatus reconstructions for the simulation of normally and abnormally closing valves in a decision support system.

Functional Grading of a Transversely Isotropic Hyperelastic Model with Applications in Modeling Tricuspid and Mitral Valve Transition Regions

Surgical simulators and injury-prediction human models require a combination of representative tissue geometry and accurate tissue material properties to predict realistic tool-tissue interaction forces and injury mechanisms, respectively. While biological tissues have been individually characterized, the transition regions between tissues have received limited research attention, potentially resulting in inaccuracies within simulations. In this work, an approach to characterize the transition regions in transversely isotropic (TI) soft tissues using functionally graded material (FGM) modeling is presented. The effect of nonlinearities and multi-regime nature of the TI model on the functional grading process is discussed. The proposed approach has been implemented to characterize the transition regions in the leaflet (LL), chordae tendinae (CT) and the papillary muscle (PM) of porcine tricuspid valve (TV) and mitral valve (MV). The FGM model is informed using high resolution morphological measurements of the collagen fiber orientation and tissue composition in the transition regions, and deformation characteristics predicted by the FGM model are numerically validated to experimental data using X-ray diffraction imaging. The results indicate feasibility of using the FGM approach in modeling soft-tissue transitions and has implications in improving physical representation of tissue deformation throughout the body using a scalable version of the proposed approach.

Mechanical and morphometric study of mitral valve chordae tendineae and related papillary muscle

The mitral valve (MV) apparatus is a complex mechanical structure including annulus, valve leaflets, papillary muscles (PMs) and connected chordae tendineae. Chordae anchor to the papillary muscles to help the valve open and close properly during one cardiac cycle. It is of paramount importance to understand the functional, mechanical, and microstructural properties of mitral valve chordae and connecting PMs. In particular, little is known about the biomechanical properties of the anterior and posterior papillary muscle and corresponding chords. In this work, we performed uniaxial and biaxial tensile tests on the anterolateral (APM) and posteromedial papillary muscle (PPM), and their respective corresponding chordae tendineae, chordae^APM and chordae^PPM, in porcine hearts. Histology was carried out to link the microstructure and macro-mechanical behavior of the chordae and PMs. Our results demonstrate that chordae^PPM are less in number, but significantly longer and stiffer than chordae^APM. These different biomechanical properties may be partially explained by the higher collagen core ratio and larger collagen fibril density of chordae^PPM_. No significant mechanical or microstructural differences were observed along the circumferential and longitudinal directions of APM and PPM samples. Data measured on chordae and PMs were further fitted with the Ogden and reduced Holzapfel - Ogden strain energy functions, respectively. This study presents the first comparative anatomical, mechanical, and structural dataset of porcine mitral valve chordae and related PMs. Results indicate that a PM based classification of chordae will need to be considered in the analysis of the MV function or planning a surgical treatment, which will also help developing more precise computational models of MV.

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.

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.

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.

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.

Transapical mitral valve repair with neochordae implantation: FSI analysis of neochordae number and complexity of leaflet prolapse

Transapical mitral valve repair with neochordae implantation is a relatively new minimally invasive technique to treat primary mitral regurgitation. Quantifying the complex biomechanical interaction and interdependence between the left heart structures and the neochordae during this procedure is technically challenging. The aim of this parametric computational study is to investigate the immediate effects of neochordae number and complexity of leaflet prolapse on restoring physiologic left heart dynamics after optimal transapical neochordae repair procedures. Neochordae implantation using three and four sutures was modeled under three clinically relevant prolapse conditions: isolated P2, multi-scallop P2/P3, and multi-scallop P2/P1. A fluid-structure interaction (FSI) modeling framework was used to evaluate the left heart dynamics under baseline, prerepair, and postrepair states. Despite immediate restoration of leaflet coaptation and no residual mitral regurgitation in all postrepair models, the average and peak stresses in the repaired scallop(s) increased >40% and >100%, respectively, compared with the baseline state. Additionally, anterior mitral leaflet marginal chordae tension increased >30%, while posterior mitral leaflet chordae tension decreased at least 30%. No marked differences in hemodynamic performance, in native and neochordae forces, and in leaflet stress were found when implanting three or four sutures. We report, to our knowledge, the first set of time-dependent in silico FSI human neochordae tension measurements during transapical neochordae repair. This work represents a further step towards an improved understanding of the biomechanical outcomes of minimally invasive mitral valve repair procedures.

Mechanics of Porcine Heart Valves' Strut Chordae Tendineae Investigated as a Leaflet-Chordae-Papillary Muscle Entity

Proper blood flow through the atrioventricular heart valves (AHVs) relies on the holistic function of the valve and subvalvular structures, and a failure of any component can lead to life-threatening heart disease. A comprehension of the mechanical characteristics of healthy valvular components is necessary for the refinement of heart valve computational models. In previous studies, the chordae tendineae have been mechanically characterized as individual structures, usually in a clamping-based approach, which may not accurately reflect the in vivo chordal interactions with the leaflet insertion and papillary muscles. In this study, we performed uniaxial mechanical testing of strut chordae tendineae of the AHVs under a unique tine-based leaflet-chordae-papillary muscle testing to observe the chordae mechanics while preserving the subvalvular component interactions. Results of this study provided insight to the disparity of chordae tissue stress-stretch responses between the mitral valve (MV) and the tricuspid valve (TV) under their respective emulated physiological loading. Specifically, strut chordae tendineae of the MV anterior leaflet had peak stretches of 1.09-1.16, while peak stretches of 1.08-1.11 were found for the TV anterior leaflet strut chordae. Constitutive parameters were also derived for the chordae tissue specimens using an Ogden model, which is useful for AHV computational model refinement. Results of this study are beneficial to the eventual improvement of treatment methods for valvular disease.

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.

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

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

An investigation of the glycosaminoglycan contribution to biaxial mechanical behaviours of porcine atrioventricular heart valve leaflets

The atrioventricular heart valve (AHV) leaflets have a complex microstructure composed of four distinct layers: atrialis, ventricularis, fibrosa and spongiosa. Specifically, the spongiosa layer is primarily proteoglycans and glycosaminoglycans (GAGs). Quantification of the GAGs' mechanical contribution to the overall leaflet function has been of recent focus for aortic valve leaflets, but this characterization has not been reported for the AHV leaflets. This study seeks to expand current GAG literature through novel mechanical characterizations of GAGs in AHV leaflets. For this characterization, mitral and tricuspid valve anterior leaflets (MVAL and TVAL, respectively) were: (i) tested by biaxial mechanical loading at varying loading ratios and by stress-relaxation procedures, (ii) enzymatically treated for removal of the GAGs and (iii) biaxially mechanically tested again under the same protocols as in step (i). Removal of the GAG contents from the leaflet was conducted using a 100 min enzyme treatment to achieve approximate 74.87% and 61.24% reductions of all GAGs from the MVAL and TVAL, respectively. Our main findings demonstrated that biaxial mechanical testing yielded a statistically significant difference in tissue extensibility after GAG removal and that stress-relaxation testing revealed a statistically significant smaller stress decay of the enzyme-treated tissue than untreated tissues. These novel findings illustrate the importance of GAGs in AHV leaflet behaviour, which can be employed to better inform heart valve therapeutics and computational models.

Mechanics of the Tricuspid Valve-From Clinical Diagnosis/Treatment, In-Vivo and In-Vitro Investigations, to Patient-Specific Biomechanical Modeling

Proper tricuspid valve (TV) function is essential to unidirectional blood flow through the right side of the heart. Alterations to the tricuspid valvular components, such as the TV annulus, may lead to functional tricuspid regurgitation (FTR), where the valve is unable to prevent undesired backflow of blood from the right ventricle into the right atrium during systole. Various treatment options are currently available for FTR; however, research for the tricuspid heart valve, functional tricuspid regurgitation, and the relevant treatment methodologies are limited due to the pervasive expectation among cardiac surgeons and cardiologists that FTR will naturally regress after repair of left-sided heart valve lesions. Recent studies have focused on (i) understanding the function of the TV and the initiation or progression of FTR using both in-vivo and in-vitro methods, (ii) quantifying the biomechanical properties of the tricuspid valve apparatus as well as its surrounding heart tissue, and (iii) performing computational modeling of the TV to provide new insight into its biomechanical and physiological function. This review paper focuses on these advances and summarizes recent research relevant to the TV within the scope of FTR. Moreover, this review also provides future perspectives and extensions critical to enhancing the current understanding of the functioning and remodeling tricuspid valve in both the healthy and pathophysiological states.

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.

EFFECT OF PAPILLARY MUSCLE DISPLACEMENT AND ANNULAR DILATION ON DEVELOPMENT OF FUNCTIONAL MITRAL REGURGITATION

Functional mitral regurgitation (FMR) occurs following left ventricle (LV) dysfunction with normal mitral valve (MV) leaflet. The progress and severity of FMR are closely related to LV dilatation, which often results in displacement of the papillary muscles (PMs) and enlargement of the mitral annulus. We investigated the effect of PM displacement and annular dilation on FMR development to better understand the complex intercorrelation between these pathologic alterations leading to FMR. Virtual MV modeling was performed to create a normal human MV, and several different types of PM displacement, annular dilation, and the combination of PM displacement and annular dilation mimicking the pathology of FMR were modeled. Dynamic finite element evaluation of MV function was performed across the complete cardiac cycle for the normal and FMR MV models. PM displacement to both lateral and apical directions revealed markedly reduced leaflet coaptation and large stress distribution in the P2 scallop. Annular dilation greater than 2% demonstrated the occurrence of leaflet malcoaptation and increased stresses near the anterior saddle-horn region. The pathologic MV model with annular dilation combined with PM displacement provides physiologically realistic biomechanical characteristics as the MVs having FMR. Simulation-based biomechanical evaluation of MV pathology related to LV chamber dilatation provides an excellent tool to better understand the pathophysiologic mechanism of FMR.

A comprehensive pipeline for multi-resolution modeling of the mitral valve: Validation, computational efficiency, and predictive capability

Multiple studies have demonstrated that the pathological geometries unique to each patient can affect the durability of mitral valve (MV) repairs. While computational modeling of the MV is a promising approach to improve the surgical outcomes, the complex MV geometry precludes use of simplified models. Moreover, the lack of complete in vivo geometric information presents significant challenges in the development of patient-specific computational models. There is thus a need to determine the level of detail necessary for predictive MV models. To address this issue, we have developed a novel pipeline for building attribute-rich computational models of MV with varying fidelity directly from the in vitro imaging data. The approach combines high-resolution geometric information from loaded and unloaded states to achieve a high level of anatomic detail, followed by mapping and parametric embedding of tissue attributes to build a high-resolution, attribute-rich computational models. Subsequent lower resolution models were then developed and evaluated by comparing the displacements and surface strains to those extracted from the imaging data. We then identified the critical levels of fidelity for building predictive MV models in the dilated and repaired states. We demonstrated that a model with a feature size of about 5 mm and mesh size of about 1 mm was sufficient to predict the overall MV shape, stress, and strain distributions with high accuracy. However, we also noted that more detailed models were found to be needed to simulate microstructural events. We conclude that the developed pipeline enables sufficiently complex models for biomechanical simulations of MV in normal, dilated, repaired states.

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.

Computational virtual evaluation of the effect of annuloplasty ring shape

Mitral regurgitation (MR) is a result of mitral valve (MV) pathology. Its etiology can be categorized as degenerative or functional MR. Ring annuloplasty aims to reconfigure a dilated mitral annulus to its normal size and shape. We investigated the effect of annuloplasty ring shape on MR outcome using our established 3-dimensional (3-D) echocardiography-based computational MV evaluation protocols. Virtual patient MV models were created from 3-D transesophageal echocardiographic data in patients with MR because of mitral annular dilation. Two distinct annuloplasty rings (Physio II and GeoForm) were designed and virtually implanted to the patient MVs. Dynamic finite element simulations of MV function were performed for each MV after virtual ring annuloplasty of either ring, and physiologic and biomechanical characteristics of MV function were compared. Excessive stress values appeared primarily in the midanterior and midposterior regions, and lack of leaflet coaptation was found in pre-annuloplasty patient MVs. Both rings demonstrated marked reduction of stresses and efficient leaflet coaptation. The Physio II ring demonstrated more evenly distributed stress reduction across the leaflets and annulus compared with the GeoForm ring. Conversely, the highly nonplanar curvature of the GeoForm ring more effectively increased leaflet coaptation compared with the Physio II ring. This indicates that the shape of annuloplasty ring affects post-annuloplasty physiologic and biomechanical conditions, which can lead to tissue alteration over a longer period after ring annuloplasty. This virtual ring annuloplasty simulation strategy provides detailed physiologic and biomechanical information and may help better plan the optimal ring selection and improved patient-specific MV repairs.

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.

DYNAMIC ANALYSIS OF HEALTHY AND EDGE-TO-EDGE REPAIRED MITRAL VALVE BEHAVIOR SUBJECTED TO HIGH G ACCELERATIONS

As the mitral leaflets have the greatest area among heart valves and bear the highest pressure load during systole, high G accelerations may result in mitral valve dysfunctions and it might affect the cardiovascular system drastically. In this study, dynamic behavior of healthy and repaired human mitral valves have been numerically simulated during the Early Systolic Phase and the Rapid Filling Phase in a cardiac cycle in high G accelerated environments. The aim of this study is to investigate the effects of accelerations on the stress and strain patterns and the configuration of human mitral valve. The geometrical model of the mitral valve has been developed based on in vivo and ex vivo anatomical measurements and the anisotropic nonlinear behavior of mitral leaflets has been modeled by a discrete constitutive approach. Mitral valve behavior has been simulated using an explicit dynamic finite element method to take into account inertial effects and dynamic responses. Analysis results reveal beside different stress–strain patterns generated on mitral leaflets, abnormal deformed configurations result from accelerations which can affect the circulation and the cardiovascular system. It is observed that situations similar to mitral diseases could rise from high G accelerated environments even though the valve maintains its normal physiological structure.

A transverse isotropic viscoelastic constitutive model for aortic valve tissue

A new anisotropic viscoelastic model is developed for application to the aortic valve (AV). The directional dependency in the mechanical properties of the valve, arising from the predominantly circumferential alignment of collagen fibres, is accounted for in the form of transverse isotropy. The rate dependency of the valve's mechanical behaviour is considered to stem from the viscous (η) dissipative effects of the AV matrix, and is incorporated as an explicit function of the deformation rate ([Formula: see text]). Model (material) parameters were determined from uniaxial tensile deformation tests of porcine AV specimens at various deformation rates, by fitting the model to each experimental dataset. It is shown that the model provides an excellent fit to the experimental data across all different rates and satisfies the condition of strict local convexity. Based on the fitting results, a nonlinear relationship between η and [Formula: see text] is established, highlighting a 'shear-thinning' behaviour for the AV with increase in the deformation rate. Using the model and these outcomes, the stress-deformation curves of the AV tissue under physiological deformation rates in both the circumferential and radial directions are predicted and presented. To verify the predictive capabilities of the model, the stress-deformation curves of AV specimens at an intermediate deformation rate were estimated and validated against the experimental data at that rate, showing an excellent agreement. While the model is primarily developed for application to the AV, it may be applied without the loss of generality to other collagenous soft tissues possessing a similar structure, with a single preferred direction of embedded collagen fibres.

Biological and mechanical evaluation of a Bio-Hybrid scaffold for autologous valve tissue engineering

Major challenge in heart valve tissue engineering for paediatric patients is the development of an autologous valve with regenerative capacity. Hybrid tissue engineering approach is recently gaining popularity to design scaffolds with desired biological and mechanical properties that can remodel post implantation. In this study, we fabricated aligned nanofibrous Bio-Hybrid scaffold made of decellularized bovine pericardium: polycaprolactone-chitosan with optimized polymer thickness to yield the desired biological and mechanical properties. CD44⁺, αSMA⁺, Vimentin⁺ and CD105^- human valve interstitial cells were isolated and seeded on these Bio-Hybrid scaffolds. Subsequent biological evaluation revealed interstitial cell proliferation with dense extra cellular matrix deposition that indicated the viability for growth and proliferation of seeded cells on the scaffolds. Uniaxial mechanical tests along axial direction showed that the Bio-Hybrid scaffolds has at least 20 times the strength of the native valves and its stiffness is nearly 3 times more than that of native valves. Biaxial and uniaxial mechanical studies on valve interstitial cells cultured Bio-Hybrid scaffolds revealed that the response along the axial and circumferential direction was different, similar to native valves. Overall, our findings suggest that Bio-Hybrid scaffold is a promising material for future development of regenerative heart valve constructs in children.

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.

Material modeling of cardiac valve tissue: Experiments, constitutive analysis and numerical investigation

A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.

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.

Personalized Computational Modeling of Mitral Valve Prolapse: Virtual Leaflet Resection

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

In vitro measurement of the coaptation force distribution in normal and functional regurgitant porcine mitral valves

Closure of the left atrioventricular orifice is achieved when the anterior and posterior leaflets of the mitral valve press together to form a coaptation zone along the free edge of the leaflets. This coaptation zone is critical to valve competency and is maintained by the support of the mitral annulus, chordae tendinae, and papillary muscles. Myocardial ischemia can lead to an altered performance of this mitral complex generating suboptimal mitral leaflet coaptation and a resultant regurgitant orifice. This paper reports on a two-part experiment undertaken to measure the dependence of coaptation force distribution on papillary muscle position in normal and functional regurgitant porcine mitral heart valves. Using a novel load sensor, the local coaptation force was measured in vitro at three locations (A1-P1, A2-P2, and A3-P3) along the coaptation zone. In part 1, the coaptation force was measured under static conditions in ten whole hearts. In part 2, the coaptation force was measured in four explanted mitral valves operating in a flow loop under physiological flow conditions. Here, two series of tests were undertaken corresponding to the normal and functional regurgitant state as determined by the position of the papillary muscles relative to the mitral valve annulus. The functional regurgitant state corresponded to grade 1. The static tests in part 1 revealed that the local force was directly proportional to the transmitral pressure and was nonuniformly distributed across the coaptation zone, been strongest at A1-P1. In part 2, tests of the valve in a normal state showed that the local force was again directly proportional to the transmitral pressure and was again nonuniform across the coaptation zone, been strongest at A1-P1 and weakest at A2-P2. Further tests performed on the same valves in a functional regurgitant state showed that the local force measured in the coaptation zone was directly proportional to the transmitral pressure. However, the force was now observed to be weakest at A1-P1 and strongest at A2-P2. Movement of the anterolateral papillary muscle (APM) away from both the annular and anterior-posterior (AP) planes was seen to contribute significantly to the altered force distribution in the coaptation zone. It was concluded that papillary muscle displacement typical of myocardial ischemia changes the coaptation force locally within the coaptation zone.

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

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

A finite strain nonlinear human mitral valve model with fluid-structure interaction

A computational human mitral valve (MV) model under physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally-based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used to characterize the mechanical behaviour of the MV tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with measurements from in vivo magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet and are concentrated around the annulus trigons and the belly of the leaflet. The results also show that the chordae play an important role in providing a secondary orifice for the flow when the valve opens. Although there are some discrepancies to be overcome in future work, our simulations show that the developed computational model is promising in mimicking the in vivo MV dynamics and providing important information that are not obtainable by in vivo measurements.

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

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

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.

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

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