Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions (1703.09265v1)

Abstract: The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid-structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibility of the coupled fluid-structure system in Eulerian form. Interaction between Lagrangian and Eulerian variables is mediated by integral equations with Dirac delta function kernels. The IB method provides a unified formulation for fluid-structure interaction models involving both thin elastic boundaries and also thick viscoelastic bodies. In this work, we describe the application of an adaptive, staggered-grid version of the IB method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve. Our model describes the thin leaflets of the aortic valve as immersed elastic boundaries, and describes the wall of the aortic root as a thick, semi-rigid elastic structure. A physiological left-ventricular pressure waveform is used to drive flow through the model valve, and dynamic pressure loading conditions are provided by a reduced (zero-dimensional) circulation model that has been fit to clinical data. We use this model and method to simulate aortic valve dynamics over multiple cardiac cycles. The model is shown to approach rapidly a periodic steady state in which physiological cardiac output is obtained at physiological pressures. These realistic flow rates are not specified in the model, however. Instead, they emerge from the fluid-structure interaction simulation.

• The paper introduces an application of the immersed boundary (IB) method to model aortic heart valve fluid dynamics under realistic physiological driving and loading conditions.
• An adaptive, staggered-grid version of the IB method with adaptive mesh refinement (AMR) is used to enhance computational efficiency, spatial resolution, and volume conservation properties.
• The model successfully achieves a periodic steady-state simulating realistic fluid dynamics, cardiac output, and pressures, offering insights for cardiovascular medicine and prosthetic valve design.

Immersed Boundary Model of Aortic Heart Valve Dynamics with Physiological Driving and Loading Conditions

The paper by Boyce E. Griffith introduces an application of the immersed boundary (IB) method for modeling the fluid dynamics associated with the aortic heart valve, incorporating physiological driving and loading conditions. The IB method is particularly effective at handling fluid-structure interactions involving structures submerged within incompressible fluids. In this case, the aortic valve leaflets and the walls of the aortic root are modeled as immersed elastic structures with anatomical and biomechanical characteristics derived from clinical and physiological data.

Model Overview

The model describes the aortic valve leaflets using a thin elastic boundary framework, while the aortic root is modeled as a thick viscoelastic body. A realistic left-ventricular pressure waveform is applied to drive the fluid flow through the valve, and the dynamic loading conditions are provided by a reduced circulation model, emulating physiological pressure conditions. The immersion of the valve is executed through the interaction of Lagrangian descriptors detailing the elasticity and Eulerian descriptors managing the fluid properties like incompressibility and viscosity, linked through integral equations with Dirac delta functions.

Methodology

The paper details the use of an adaptive, staggered-grid version of the IB method. This involves discretizing Lagrangian equations on a curvilinear mesh aligned with the fibers in the valve leaflets and Eulerian equations on a Cartesian grid. This grid, equipped with adaptive mesh refinement (AMR), ensures computational efficiency and accuracy, particularly in areas of high complexity, such as fluid-structure interfaces close to the valve leaflets. This adaptive technique enhances spatial resolution dynamically to capture the complexities of valve dynamics faithfully.

The staggered-grid discretization is highlighted as yielding superior volume conservation properties and better resolution of pressure discontinuities than previous cell-centered methods. This advancement supports improved simulations of the physiologically realistic interaction between pressure and flow dynamics across the aortic valve.

Numerical Results

The simulations conducted demonstrate the model's ability to achieve a periodic steady-state of fluid dynamics through multiple cardiac cycles, corresponding to realistic cardiac output and pressures. These outcomes are noteworthy for emerging naturally from the model based on the fluid-structure interaction simulation rather than predefined flow rates.

Implications and Future Directions

The implications of the research extend to clinical domains where enhanced understanding of valve dynamics could support the design and optimization of prosthetic heart valves. The ability to simulate physiological conditions accurately opens pathways to more precise diagnostic tools and therapeutic strategies for aortic valve dysfunction.

Looking ahead, the paper suggests further refinement in the description of the elastic properties of the valve leaflets and aortic root. Incorporating experimental constitutive models could render simulations even more insightful. Moreover, the development of an implicit version of the model would mitigate timestep restrictions, thereby facilitating higher-resolution simulations critical for understanding subtle fluid-dynamic phenomena.

Overall, this work sets a methodological benchmark for using the IB method in simulating complex physiological fluid-structure interactions, with potential translational impacts on cardiovascular medicine and bioengineering. As the computational power and numerical methods evolve, such models will likely be instrumental in bridging the gap between computational simulations and clinical applications.