Effect of mitral valve geometry on valve competence

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.

Mitral annular dynamics are influenced by left ventricular load and contractility in an acute animal model

The purpose of this study was to investigate the effects of loading conditions and left ventricular (LV) contractility on mitral annular dynamics. In 10 anesthetized pigs, eight piezoelectric transducers were implanted equidistantly around the mitral annulus. High-fidelity catheters measured left ventricular pressures and the slope of the end-systolic pressure-volume relationship (Ees ) determined LV contractility. Adjustments of pre- and afterload were done by constriction of the inferior caval vein and occlusion of the descending aorta. Mitral annulus area indexed to body surface area (MAAi ), annular circularity index (ACI), and non-planarity angle (NPA) were calculated by computational analysis. MAAi was more dynamic in response to loading interventions than ACI and NPA. However, MAAi maximal cyclical reduction (-Δr) and average deformational velocity (-v ¯ $$ \overline{v} $$ ) did not change accordingly (p = 0.31 and p = 0.22). Reduced Ees was associated to attenuation in MAAi -Δr and MAAi -v ¯ $$ \overline{v} $$ (r2  = 0.744; p = 0.001 and r2  = 0.467; p = 0.029). In conclusion, increased cardiac load and reduced LV contractility may cause deterioration of mitral annular dynamics, likely impairing coaptation and increasing susceptibility to valvular incompetence.

A toolbox for generating scalable mitral valve morphometric models

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

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

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

The Effect of Mechanical Overloading on Surface Roughness of the Coronary Arteries

Background

Surface roughness can be used to identify disease within biological tissues. Quantifying surface roughness in the coronary arteries aids in developing treatments for coronary heart disease. This study investigates the effect of extreme physiological loading on surface roughness, for example, due to a rupture of an artery.

Methods

The porcine left anterior descending (LAD) coronary arteries were dissected ex vivo. Mechanical overloading was applied to the arteries in the longitudinal direction to simulate extreme physiological loading. Surface roughness was calculated from three-dimensional reconstructed images. Surface roughness was measured before and after damage and after chemical processing to dehydrate tissue specimens.

Results

Control specimens confirmed that dehydration alone results in an increase of surface roughness in the circumferential direction only. No variation was noted between the hydrated healthy and damaged specimens, in both the longitudinal (0.91 ± 0.26 and 1.05 ± 0.25 μm) and circumferential (1.46 ± 0.38 and 1.47 ± 0.39 μm) directions. After dehydration, an increase in surface roughness was noted for damaged specimens in both the longitudinal (1.28 ± 0.33 μm) and circumferential (1.95 ± 0.56 μm) directions.

Conclusions

Mechanical overloading applied in the longitudinal direction did not significantly affect surface roughness. However, when combined with chemical processing, a significant increase in surface roughness was noted in both the circumferential and longitudinal directions. Mechanical overloading causes damage to the internal constituents of the arteries, which is significantly noticeable after dehydration of tissue.

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 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.

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.

Effects of freezing, fixation and dehydration on surface roughness properties of porcine left anterior descending coronary arteries

BACKGROUND

To allow measurements of surface roughness to be made of coronary arteries using various imaging techniques, chemical processing, such as fixation and dehydration, is commonly used. Standard protocols suggest storing fresh biological tissue at -40°C. The aim of this study was to quantify the changes caused by freezing and chemical processing to the surface roughness measurements of coronary arteries, and to determine whether correction factors are needed for surface roughness measurements of coronary arteries following chemical processes typically used before imaging these arteries.

METHODS

Porcine left anterior descending coronary arteries were dissected ex vivo. Surface roughness was then calculated following three-dimensional reconstruction of surface images obtained using an optical microscope. Surface roughness was measured before and after a freeze cycle to assess changes during freezing, after chemical fixation, and again after dehydration, to determine changes during these steps of chemical processing.

RESULTS

No significant difference was caused due to the freeze cycle (p>0.05). There was no significant difference in the longitudinally measured surface roughness (Ra_L=0.99±0.39μm; p>0.05) of coronary arteries following fixation and dehydration either. However, the circumferentially measured surface roughness increased significantly following a combined method of processing (Ra_C=1.36±0.40, compared 1.98±0.27μm, respectively; p<0.05). A correction factor can compensate for the change Ra_Cβ=Ra_C1+0.46in Ra_C due to processing of tissue, Where Ra_Cβ, the corrected Ra_C, had a mean of 1.31±0.21μm.

CONCLUSIONS

Independently, freezing, fixation and dehydration do not alter the surface roughness of coronary arteries. Combined, however, fixation and dehydration significantly increase the circumferential, but not longitudinal, surface roughness of coronary arteries.

Dynamic Viscoelasticity and Surface Properties of Porcine Left Anterior Descending Coronary Arteries

The aim of this study was, for the first time, to measure and compare quantitatively the viscoelastic properties and surface roughness of coronary arteries. Porcine left anterior descending coronary arteries were dissected ex vivo. Viscoelastic properties were measured longitudinally using dynamic mechanical analysis, for a range of frequencies from 0.5 to 10 Hz. Surface roughness was calculated following three-dimensional reconstructed of surface images obtained using an optical microscope. Storage modulus ranged from 14.47 to 25.82 MPa, and was found to be frequency-dependent, decreasing as the frequency increased. Storage was greater than the loss modulus, with the latter found to be frequency-independent with a mean value of 2.10 ± 0.33 MPa. The circumferential surface roughness was significantly greater (p < 0.05) than the longitudinal surface roughness, ranging from 0.73 to 2.83 and 0.35 to 0.92 µm, respectively. However, if surface roughness values were corrected for shrinkage during processing, circumferential and longitudinal surface roughness were not significantly different (1.04 ± 0.47, 0.89 ± 0.27 µm, respectively; p > 0.05). No correlation was found between the viscoelastic properties and surface roughness. It is feasible to quantitatively measure the viscoelastic properties of coronary arteries and the roughness of their endothelial surface.

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.

Biomechanical assessment of surgical repair of the mitral valve

Repair of the mitral valve is defined (loosely) as a procedure that alters the valve structure, without replacement, enabling the natural valve itself to continue to perform under the physical conditions to which it is exposed. As the mitral valve is driven by flow and pressure, it should be feasible to analyse and assess its function, failure and repair as a mechanical system. This article reviews the current state of mechanical evaluation of surgical repairs of the failed mitral valve of the heart. This review describes the anatomy and physiology of the mitral valve, followed by the failure of the mitral valve from a mechanical point of view. The surgical methods used to repair failed valves are introduced, while the use of engineering analysis to aid understanding of mitral valve repair is also reviewed. Finally, a section on recommendations for development and future uses of engineering techniques to surgical repair are presented.

MECHANICAL PROPERTIES OF CHORDAE TENDINEAE OF THE MITRAL HEART VALVE: YOUNG'S MODULUS, STRUCTURAL STIFFNESS, AND EFFECTS OF AGING

Young's modulus and structural stiffness were determined for chordae tendineae of the mitral valve from young (18–26 weeks) and old (over 2 years) porcine hearts. For chordae from the posterior leaflet of the valve, the Young's modulus values were significantly higher (p < 0.05) for the thinner marginal chordae (59 ± 31 MPa young; 88 ± 21 MPa old) than for the thicker basal chordae (31 ± 4 MPa young; 28 ± 9 MPa old). Marginal chordae (both anterior and posterior) had significantly higher (p < 0.05) value for their Young's modulus in old (88 ± 21 MPa anterior and posterior) than in young (62 ± 17 MPa anterior, 59 ± 18 MPa posterior) pig hearts. There was no significant difference in structural stiffness between marginal and basal (anterior and posterior leaflets) or between strut chordae (that are associated with anterior the leaflet only) and marginal and basal chordae. However, the value of structural stiffness of chordae was significantly higher (p < 0.05) for old (2.2 ± 0.2 kN/m) than for young (2.0 ± 0.4 kN/m) chordae. These results show that aging affects the properties of chordae and that all chordae need to be included in finite element models of valve function.

Subaortic stenosis associated with systolic anterior motion

Left ventricular outflow tract obstruction in children is classified according to the site of the obstruction into a supra-aortic type, valvular type, and subaortic type (subaortic stenosis). Subaortic stenosis, in turn, is classified into two major subtypes, i.e., a discrete type, which accounts for most cases and a tunnel type, and one minor subtype, the accessory mitral tissue type, which is rare. Systolic anterior motion (SAM) is a phenomenon that is commonly observed in hypertrophic cardiomyopathy. We report a rare case of subaortic stenosis associated with SAM, which was caused by cleft anterior mitral leaflet and an accessory papillary muscle. Surgical treatment was successful, and there were no complications.