Abstract

The numerical assessment of reconstructed aortic valves competence and leaflet design optimization rely on both coaptation characteristics and the diastolic valve configuration. These characteristics can be evaluated by the shell or membrane formulations. The membrane formulation is preferable for surgical aortic valve neocuspidization planning since it is easy to solve. The results on coaptation zone sensitivity to the anisotropy of aortic leaflet material are contradictive, and there are no comparisons of coaptation characteristics based on shell and membrane models for anisotropic materials. In our study, we explore for the first time how the reduced model and anisotropy of the leaflet material affect the coaptation zone and the diastolic configuration of the aortic valve. To this end, we propose the method to mimic the real, sutured neo-leaflet, and apply our numerical shell and membrane formulations to model the aortic valve under the quasi-static diastolic pressure varying material stiffness and anisotropy directions. The shell formulation usually provides a lesser coaptation zone than the membrane formulation, especially in the central zone. The material stiffness does influence the coaptation zone: it is smaller for stiffer material. Anisotropy of the leaflet material does not affect significantly the coaptation characteristics, but can impact the deformed leaflet configuration and produce a smaller displacement.

Highlights

  • Aortic valve disease is among the most common cardiovascular conditions that affect elderly people

  • We focus on coaptation of the aortic valve under quasi-static diastolic pressure since, usually, stress fields are addressed in the literature

  • We want to scrutinize how the reduced model and the leaflet material affects the coaptation zone and the diastolic configuration of the aortic valve. The results of such sensitivity analyses are important to develop the technology of aortic valve neocuspidization based on mathematical modeling

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Summary

Introduction

Aortic valve disease is among the most common cardiovascular conditions that affect elderly people. We study how model formulations and material stiffness/anisotropy influence the coaptation area and the deformed leaflet configuration To this end, we apply numerical shell and membrane formulations to solve quasi-static problems of the aortic valve under diastolic pressure, varying the material stiffness and anisotropy directions. We want to scrutinize how the reduced (shell/membrane) model and the leaflet material affects the coaptation zone and the diastolic configuration of the aortic valve. The results of such sensitivity analyses are important to develop the technology of aortic valve neocuspidization based on mathematical modeling.

Geometry of Leaflet Design
Kinematics of Shell
Hyperelasticity
Weak Formulation
Discretization
Discretization of Bending Part
External Forces
Discretized Equilibrium Equations
Computational Algorithms
Setting the Problems
Discussion
Full Text
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