# Modeling the Mitral Valve

## TL;DR

This paper presents a comprehensive model of the mitral valve, combining anatomical data, mechanical modeling, and fluid simulation to accurately replicate its physiological function and robustness under various pressures.

## Contribution

It introduces a novel design-based modeling approach incorporating anatomical details and simulates valve dynamics using the immersed boundary method.

## Key findings

- Model opens and closes effectively under physiological pressures
- Closure remains robust under abnormal pressure conditions
- Incorporates detailed fiber topology based on dissections

## Abstract

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.