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

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

A toolbox for generating scalable mitral valve morphometric models

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

Mechanical testing of glutaraldehyde cross-linked mitral valves. Part two: Elastic and viscoelastic properties of chordae tendineae

The aim of this study was to assess whether the mechanical properties of mitral valve chordae tendineae are sensitive to being cross-linked under load. A total 64 chordae were extracted from eight porcine hearts. Two chordae (posterior basal) from each heart were subjected to uniaxial ramp testing and six chordae (two strut, two anterior basal and two posterior basal) were subjected to dynamic mechanical analysis over frequencies between 0.5 and 10 Hz. Chordae were either cross-linked in tension or cross-linked in the absence of loading. Chordae cross-linked under load transitioned from high to low extension at a lower strain than cross-linked unloaded chordae (0.07 cf. 0.22), with greater pre-transitional (30.8 MPa cf. 5.78 MPa) and post-transitional (139 MPa cf. 74.1 MPa) moduli. The mean storage modulus of anterior strut chordae ranged from 48 to 54 MPa for cross-linked unloaded chordae, as compared to 53-61 MPa cross-linked loaded chordae. The mean loss modulus of anterior strut chordae ranged from 2.3 to 2.9 MPa for cross-linked unloaded chordae, as compared to 3.8-4.8 MPa cross-linked loaded chordae. The elastic and viscoelastic properties of chordae following glutaraldehyde cross-linking are dependent on the inclusion/exclusion of loading during the cross-linking process; with loading increasing the magnitude of the material properties measured.

Mechanical testing of glutaraldehyde cross-linked mitral valves. Part one: In vitro mechanical behaviour

The aim of this study was to perform an initial assessment, in vitro, of the feasibility of using a glutaraldehyde cross-linked porcine mitral valve to retain acute functionality, focusing on assessing mitral regurgitation. Six porcine hearts were tested using an in vitro simulator. Testing was repeated following cross-linking of mitral valves; where cross-linking was achieved by placing them in a glutaraldehyde solution. The simulator enabled systolic pressure on the ventricular side of the valve to be mimicked. Following testing, mitral valve leaflets underwent Scanning Electron Microscopy of the ventricular surface of both the anterior and posterior leaflets (1 cm² samples). The peak pressure withstood by cross-linked valves was significantly lower than for untreated valves (108 mmHg cf. 128 mmHg for untreated valves; p  < 0.05). The peak pressure was typically reached 0.5 s later than for the untreated valve. While both cross-linked and untreated valves exhibited endothelium denudation, the unfixed valve had less endothelial loss. Glutaraldehyde cross-linking of porcine mitral valves may be of potential value in assessing improved bioprosthetic mitral valve replacements. However, a more immobile valve exhibiting endothelial denudation (i.e. sclerosis) was a possible concerns identified following in vitro acute assessment.

The role of strut chordae in mitral valve competence during annular dilation

Strut chordae, on their own, are not typically thought to aid mitral valve competence. The aim of this study is to assess whether strut chordae aid mitral valve competence during acute annular dilation. Twelve porcine hearts were dissected and tested using an in vitro simulator, with the mitral annulus tested in either a 'normal' or a dilated configuration. The normal configuration included a diameter of 30 mm, a posterior leaflet 'radius' of 15 mm and a commissural corner 'radius' of 7.5 mm; the dilated annular template instead used dimensions of 50 mm, 25 mm and 12.5 mm, respectively. Each mitral valve underwent ten repeat tests with a target systolic pressure of 100 mmHg. No significant difference in the pressure was detected between the dilated and regular annuli for the mitral valves tested (95 ± 3 mmHg cf. 95 ± 2 mmHg). However, the volume of regurgitation for a dilated annulus was 28 ml greater than for a valve with a normal annulus. Following severing of strut chordae, there was a significant reduction in the systolic pressure withstood before regurgitation by mitral valves with dilated annuli (60 ± 29 mmHg cf. 95 ± 2 mmHg for normal annular dimensions; p < 0.05). In conclusion, strut chordae tendineae may play a role in aiding mitral valve competence during pathophysiology.

The role of strut chordae in mitral valve competence during annular dilation

Strut chordae, on their own, are not typically thought to aid mitral valve competence. The aim of this study is to assess whether strut chordae aid mitral valve competence during acute annular dilation. Twelve porcine hearts were dissected and tested using an in vitro simulator, with the mitral annulus tested in either a 'normal' or a dilated configuration. The normal configuration included a diameter of 30 mm, a posterior leaflet 'radius' of 15 mm and a commissural corner 'radius' of 7.5 mm; the dilated annular template instead used dimensions of 50 mm, 25 mm and 12.5 mm, respectively. Each mitral valve underwent ten repeat tests with a target systolic pressure of 100 mmHg. No significant difference in the pressure was detected between the dilated and regular annuli for the mitral valves tested (95 ± 3 mmHg cf. 95 ± 2 mmHg). However, the volume of regurgitation for a dilated annulus was 28 ml greater than for a valve with a normal annulus. Following severing of strut chordae, there was a significant reduction in the systolic pressure withstood before regurgitation by mitral valves with dilated annuli (60 ± 29 mmHg cf. 95 ± 2 mmHg for normal annular dimensions; p < 0.05). In conclusion, strut chordae tendineae may play a role in aiding mitral valve competence during pathophysiology.

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.

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.

Effect of glutaraldehyde based cross-linking on the viscoelasticity of mitral valve basal chordae tendineae

BACKGROUND

Mitral valve failure can require repair or replacement. Replacement bioprosthetic valves are treated with glutaraldehyde prior to implantation. The aim of this study was to determine the changes in mechanical properties following glutaraldehyde fixation of mitral valve chordae.

METHODS

To investigate the impact of glutaraldehyde on mitral valve chordae, 24 basal chordae were dissected from four porcine hearts. Anterior and posterior basal (including strut) chordae were used. All 24 chordae were subjected to a sinusoidally varying load (mean level 2N, dynamic amplitude 2N) over a frequency range of 0.5-10 Hz before and after glutaraldehyde treatment.

RESULTS

The storage and loss modulus of all chordal types decreased following glutaraldehyde fixation. The storage modulus ranged from: 108 to 119 MPa before fixation and 67.3-87.4 MPa following fixation for basal chordae; 52.3-58.4 MPa before fixation and 47.9-53.5 MPa following fixation for strut chordae. Similarly, the loss modulus ranged from: 5.47 to 6.25 MPa before fixation and 3.63-4.94 MPa following fixation for basal chordae; 2.60-2.97 MPa before fixation and 2.31-2.93 MPa following fixation for strut chordae.

CONCLUSION

The viscoelastic properties of mitral valve chordae are affected by glutaraldehyde fixation; in particular, the reduction in storage moduli decreased with an increase in chordal diameter.

Viscoelastic properties of mitral valve leaflets: An analysis of regional variation and frequency-dependency

The aim of this study was to determine the regional variation in viscoelastic properties of mitral valve leaflets over a range of physiological and patho-physiological frequencies. This included comparisons to be made between anterior and posterior leaflets, anterior leaflet clear and rough zones, and radial and circumferential leaflet orientation. Dynamic mechanical analysis was used to determine frequency-dependent viscoelastic properties. The valve leaflets were dissected from eight porcine hearts. The leaflets were loaded under a sinusoidal tensile displacement, with a mean dynamic peak to trough strain of 11%, applied to all leaflet samples at nine different frequencies, ranging from 0.5 to 10 Hz. The anterior leaflet has higher storage and loss stiffness than the posterior leaflet. The storage stiffness of circumferential tissue is greater than that of radially oriented valve tissue (2.0 ± 1.6 N/mm cf. 1.7 ± 0.9 N/mm; p < 0.05); however, the loss stiffness is greater for radial tissue (0.15 ± 0.07 cf. 0.14 ± 0.09 N/mm; p < 0.05). Likewise, the storage stiffness of the anterior leaflet clear zone is greater than that of the rough zone (2.4 ± 1.6 cf. 2.1 ± 1.2; p < 0.05), but the loss stiffness is greater for the rough zone (0.17 ± 0.09 N/mm cf. 0.14 ± 0.08 N/mm; p < 0.05). In conclusion, the viscoelastic properties of porcine mitral valve leaflets have regional variations, with dynamic stiffness being dependent on circumferential or radial orientation and on location at a clear or rough zones.

Evaluation of a transient, simultaneous, arbitrary Lagrange-Euler based multi-physics method for simulating the mitral heart valve

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.