A design-based model of the aortic valve for fluid-structure interaction

Alexander D Kaiser; Rohan Shad; William Hiesinger; Alison L Marsden

doi:10.1007/s10237-021-01516-7

A design-based model of the aortic valve for fluid-structure interaction

Biomech Model Mechanobiol. 2021 Dec;20(6):2413-2435. doi: 10.1007/s10237-021-01516-7. Epub 2021 Sep 21.

Authors

Alexander D Kaiser^{1

2

3}, Rohan Shad^{4

5}, William Hiesinger^{4

5}, Alison L Marsden^{6

7

4

8}

Affiliations

¹ Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA. alexdkaiser@stanford.edu.
² Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA. alexdkaiser@stanford.edu.
³ Stanford Cardiovascular Institute, Stanford, CA, USA. alexdkaiser@stanford.edu.
⁴ Stanford Cardiovascular Institute, Stanford, CA, USA.
⁵ Department of Cardiothoracic Surgery, Stanford University, Stanford, CA, USA.
⁶ Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA.
⁷ Department of Pediatrics (Cardiology), Stanford University, Stanford, CA, USA.
⁸ Department of Bioengineering, Stanford University, Stanford, CA, USA.

Abstract

This paper presents a new method for modeling the mechanics of the aortic valve and simulates its interaction with blood. As much as possible, the model construction is based on first principles, but such that the model is consistent with experimental observations. We require that tension in the leaflets must support a pressure, then derive a system of partial differential equations governing its mechanical equilibrium. The solution to these differential equations is referred to as the predicted loaded configuration; it includes the loaded leaflet geometry, fiber orientations and tensions needed to support the prescribed load. From this configuration, we derive a reference configuration and constitutive law. In fluid-structure interaction simulations with the immersed boundary method, the model seals reliably under physiological pressures and opens freely over multiple cardiac cycles. Further, model closure is robust to extreme hypo- and hypertensive pressures. Then, exploiting the unique features of this model construction, we conduct experiments on reference configurations, constitutive laws and gross morphology. These experiments suggest the following conclusions: (1) The loaded geometry, tensions and tangent moduli primarily determine model function. (2) Alterations to the reference configuration have little effect if the predicted loaded configuration is identical. (3) The leaflets must have sufficiently nonlinear material response to function over a variety of pressures. (4) Valve performance is highly sensitive to free edge length and leaflet height. These conclusions suggest appropriate gross morphology and material properties for the design of prosthetic aortic valves. In future studies, our aortic valve modeling framework can be used with patient-specific models of vascular or cardiac flow.

Keywords: Aortic valve; Aortic valve fluid-structure interaction; Aortic valve mechanics; Aortic valve modeling; Heart valve modeling; Immersed boundary method.

MeSH terms

Aortic Valve / anatomy & histology*
Aortic Valve / physiology*
Computer Simulation
Humans
Models, Cardiovascular*
Pressure
Prosthesis Design*
Rheology*

Abstract

MeSH terms

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