Modeling the Mitral Valve

TL;DR

This thesis develops a detailed computational model of the mitral valve, integrating anatomy, elasticity, and fluid dynamics to understand its function and underlying principles.

Contribution

It introduces a novel model combining anatomical data, fiber topology, and fluid-structure interaction simulations for the mitral valve.

Findings

Model accurately predicts valve deformation under pressure

Simulation reveals key mechanical principles of valve function

Integrates anatomy with fluid dynamics for comprehensive analysis

Abstract

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.