The human mitral valve (MV) consists of a large anterior-medial leaflet and a smaller posterior lateral leaflet, which are both connected to the left ventricular papillary muscles via multiple fibrous chordae tendineae. An understanding of mitral valve bio-mechanics is pivotal for optimization of surgical procedures aimed at restoring normal mitral valve function in pathological subjects. Computational models can realistically capture the anatomical and functional features of the MV and hence can provide detailed spatial and temporal data that may not be easily obtained clinically or experimentally. This thesis therefore aims at developing a framework for the fluid-structure interaction modeling of the mitral valve using immersed boundary method.First, we model the dynamics of a prosthetic mitral valve under a realistic pressure load using a staggered grid version of a formally second-order accurate immersed boundary method. In this study, we demonstrate that when bending rigidity are included in both the mitral leaflets and chordae, the computational results has better agreements with experimental measurements. In addition, non-physical oscillations that occur upon valve closure are greatly reduced when bending forces are included in the model. These findings highlight the importance of accounting for the bending stiffness in the dynamic simulation of the mitral valve prosthesis. Furthermore, an in-vivo human mitral valve geometry model is derived from magnetic resonance imaging (MRI) data, and then is analysed using the immersed boundary method under a physiological left-atrium-ventricle pressure loading. An initial validation of the model is provided by comparing the computed opening shape and flow rates to clinical measurements from the volunteer who provided the anatomical data for constructing the mitral valve. The convex (with respect to the left ventricle) shape near annulus and concave shape near free edge of valve are observed in our simulation during diastole and systole when assigning physiological thickness to the anterior leaflet and posterior leaflet, which match perfectly with clinical observations. These results suggest that differences in the thickness of the leaflets play an important role in maintaining the physiological curvature of the mitral valve. These features bring out a question that is the relatively simple isotropic material fibre model sufficient to describe the mitral valve leaflets. The real valve is anisotropic, with collagen fibres distributed along the circumferential direction. To this end, the further improved in-vivo human mitral valve geometry model, which incorporating spatial annulus ring, is then simulated under a physiological pressure loading with a finite element version of the immersed boundary method that is able to incorporate experimentally oriented constitutive laws for elasticity models. A hypo-elastic transversely isotropic material constitutive law is used to characterize the mechanical behaviour of the mitral valve tissue based on recent biaxial tests on healthy human leaflets. Simulation results exhibit better agreement and reduced oscillations in flow rate compared with experiment measurements and previous simulation and show that the maximum principal stress and strain is carried by the collagen fibres in the mitral leaflets in deep systole. These results show that the methodology in this study could generate a patient-specific finite element mitral valve model that closely replicated the in vivo mitral valve dynamic motion during diastole and systole. This model may be further developed to study mitral valve mechanics and disease to bring more insight of diagnosis, treatment, and prevention of patient valvular heart diseases.
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