The thesis presents a fluid-structure interaction studies on the hemodynamics of blood flow in the left ventricle and through the mitral valve. The virtual model consists of a mathematical model of the left ventricle coupled with a complex and structurally flexible bi-leaflet valve representing the mitral opening. The mitral valve is a bicuspid valve with anterior and posterior leaflets and it regulates unidirectional blood flow from the left atrium to the left ventricle in the diastole phase. The leaflets are made of chordae, annulus and papillary muscles. The goal of this study is to provide biomedical engineers and clinical physicians with a virtual laboratory tool to understand the dynamics of blood flow in a diseased heart and aid in the design of novel artificial heart valves. To this end, the simulation studies present an increasingly complex model of the heart to evaluate the vortex ring formation and evolution of the diastole phase in the left ventricle;​ and to characterize the septal-anterior motion in a diseased heart with obstructive hypertrophic cardiomyopathy. Finally, in collaboration with an industrial partner, the fluid-structure modeling framework was used to evaluate the performance of a new accelerated artificial valve tester.