An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations

Abstract

In order to achieve a more realistic and accurate computational simulation of native and bioprosthetic heart valve dynamics, a finite shell element model was developed. Experimentally derived and uncoupled in-plane and bending behaviors were implemented into a fully nonlinear stress resultant shell element. Validation studies compared the planar biaxial extension and three-point bending simulations to the experimental data and demonstrated excellent fidelity. Dynamic simulations of a pericardial bioprosthetic heart valve with the developed shell element model showed significant differences in the deformation characteristics compared to the simulation with an assumed isotropic bending model. The new finite shell element model developed in the present study can also incorporate various types of constitutive models and is expected to help us to understand the complex dynamics of native and bioprosthetic heart valve function in physiological and pathological conditions.

Effect of bending rigidity in a dynamic model of a polyurethane prosthetic mitral valve

“…Recently, their model has been applied to predict the mechanical difference between the healthy mitral valve and the valve in a hypertrophic obstructive cardiomyopathic heart (Prot et al 2010) and active muscle contraction (Skallerud et al 2011). Kim et al (Kim et al 2007, 2008Kim 2009) carried out dynamic simulations of a pericardial bioprosthetic heart valve based on a FE shell model, although their primary focus is on the aortic valve. Maisano et al (2005) and Votta et al (2007Votta et al ( , 2008 used patient-specific FE models to analyse the effects of annuloplasty procedures.…”

Emerging Trends in Heart Valve Engineering: Part IV. Computational Modeling and Experimental Studies

“…in which pðx; tÞ is a Lagrange multiplier for the incompressibility constraint and v À1 x; t ð Þ is the material coordinate corresponding to physical coordinate x at time t. Various strain-energy functionals have been developed to describe heart valves, 156 including native 106 and bioprosthetic 84,85 valve leaflets. To determine the stress distribution within the leaflets in a static or quasi-static configuration, the fluid dynamics and the momentum of the solid may be neglected to solve the equilibrium problem:…”

Inverse formulation for geometrically exact stress resultant shells

“…Only recently the bending properties of some tissues have been investigated [34] and incorporated into shell models [35]. Also, considerable difficulty exists in deriving a bending property consistently from a 3D energy function, especially under the incompressibility constraint [36,37].…”

“…Existing studies suggest that the influence of shear moduli on the membrane deformation can be ignored in a wide range of values of the shear moduli [35,37].…”