Modeling the mitral valve

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 designbased 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.

Controlled Comparison of Simulated Hemodynamics across Tricuspid and Bicuspid Aortic Valves

“…By tuning free parameters in these differential equations, this construction allowed us to design a model that is consistent with known anatomy and material properties. This method was previously applied to create realistic and effective mitral valve models for FSI simulations [21,20].…”

Exploring cardiac form and function: A length‐scale computational biology approach

“…To adequately cover the progress that has been made at this level, we feel an entire review is warranted. As such, we refer the reader to the work being done by Cranford et al (2018;Villongco, Krummen, Omens, & McCulloch, 2016), Trayanova and Winslow (2011;Yu et al, 2019), as well as Kaiser, McQueen, and Peskin (2019), among many others, for advancements at this scale.…”

Image-Based Computational Hemodynamics Analysis of Systolic Obstruction in Hypertrophic Cardiomyopathy

“…In this regard, two main standpoints are currently adopted: Fluid-Structure Interaction (FSI) simulations and prescribed-motion Computational Fluid Dynamics (CFD). The first approach consists in looking for the coupled solution of the fluid dynamics of blood flow and of the structure mechanics of the myocardium and cardiac valves, thus requiring a proper calibration of the mechanical parameters of the tissue, and possibly entailing a very high computational cost (Kunzelman et al, 2007;Su et al, 2014;Gao et al, 2017;Lassila et al, 2017;Karabelas et al, 2018;Collia et al, 2019;Feng et al, 2019;Kaiser et al, 2020;Meschini et al, 2021). On the other hand, in imagebased CFD, the patient-specific displacement of the myocardium and valves leaflets is reconstructed from kinetic medical images (such as cardiac cine-MRI) and then prescribed as endocardial displacement to obtain the fluid domain configuration.…”