  This work 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, the
free edges of which are supported by a system of chordae, which themselves are
anchored to the papillary muscles inside the left ventricle. First, we examine
valve anatomy and present 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 methodology, meaning that we
derive the model geometry and the forces that are needed to support a given
load, and construct the model accordingly. 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 a stress-strain relation consistent with experimental
data that achieves the necessary forces computed in previous steps. Finally,
using the immersed boundary method, we simulate the model valve in fluid in a
computer test chamber. The model opens easily and closes without leak when
driven by physiological pressures over multiple beats. Further, its closure is
robust to driving pressures that lack atrial systole or are much lower or
higher than normal.
