  This thesis is concerned with modeling and simulation of the mitral valve,
one of the four valves in the human heart. The valve is composed of leaflets
attached to a ring, the free edges of which are supported by a system of
chordae, which themselves are anchored to muscles inside the heart. First, we
examine valve anatomy and show the results of original dissections. These
display the gross anatomy and information on fiber structure of the mitral
valve. Next, we build a model valve following a design-based approach to
elasticity. We incorporate information from the dissections to specify the
fiber topology of this model. We assume the valve achieves mechanical
equilibrium while supporting a static pressure load. The solution to the
resulting differential equations determines the pressurized configuration of
the valve model. To complete the model we then specify a constitutive law based
on experimental stress-strain relations from the literature. Finally, using the
immersed boundary method, we simulate the model valve in fluid in a computer
test chamber. The aim of this work is to determine the basic principles and
mechanisms underlying the anatomy and function of the mitral valve.
