Image-based immersed boundary model of the aortic root

Abstract

Each year, approximately 300,000 heart valve repair or replacement procedures are performed worldwide, including approximately 70,000 aortic valve replacement surgeries in the United States alone. Computational platforms for simulating cardiovascular devices such as prosthetic heart valves promise to improve device design and assist in treatment planning, including patient-specific device selection. This paper describes progress in constructing anatomically and physiologically realistic immersed boundary (IB) models of the dynamics of the aortic root and ascending aorta. This work builds on earlier IB models of fluid-structure interaction (FSI) in the aortic root, which previously achieved realistic hemodynamics over multiple cardiac cycles, but which also were limited to simplified aortic geometries and idealized descriptions of the biomechanics of the aortic valve cusps. By contrast, the model described herein uses an anatomical geometry reconstructed from patient-specific computed tomography angiography (CTA) data, and employs a description of the elasticity of the aortic valve leaflets based on a fiber-reinforced constitutive model fit to experimental tensile test data. The resulting model generates physiological pressures in both systole and diastole, and yields realistic cardiac output and stroke volume at physiological Reynolds numbers. Contact between the valve leaflets during diastole is handled automatically by the IB method, yielding a fully competent valve model that supports a physiological diastolic pressure load without regurgitation. Numerical tests show that the model is able to resolve the leaflet biomechanics in diastole and early systole at practical grid spacings. The model is also used to examine differences in the mechanics and fluid dynamics yielded by fresh valve leaflets and glutaraldehyde-fixed leaflets similar to those used in bioprosthetic heart valves. Although there are large differences in the leaflet deformations during diastole, the differences in the open configurations of the valve models are relatively small, and nearly identical hemodynamics are obtained in all cases considered.

Modeling the mitral valve

“…Similar studies on modeling valves showed similar results. One study using IBAMR to study aortic valve mechanics compared simulations with fine-grid resolutions of ∆x = 7.8 · 10 −2 cm and 3.9 · 10 −2 cm [16], and another compared simulations with fine-grid resolutions of ∆x = 8.6 · 10 −2 cm and 4.3 · 10 −2 cm [25]. Both found only minor differences between flow fields and cumulative flow through the valve at these resolutions when controlling for delta function widths.…”

Fluid–Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator

“…Briefly, leaflet deformations are described by the mapping = (X, t) between reference coordinates X and current coordinates x at time t. The valve leaflets are treated as anisotropic, incompressible, hyperelastic materials. For a hyperelastic material, the first Piola-Kirchho↵ stress P is related to a strain-energy functional (F) via [21]…”

“…The wall of the aortic test section is glass. To avoid the expensive linear solvers required by exactly imposing the rigidity constraint within the present computational framework [48], we instead use a penalty method that models the test section as a sti↵ neo-Hookean material with [21]…”

“…Flamini et al [20] used an IB approach to simulate aortic valve FSI across multiple cardiac cycles, but they used a simplified description of the aortic valve mechanics. Hasan et al [21] also used an IB approach to simulate FSI in a subject-specific aortic root model, and they used realistic hyperelastic constitutive models to describe the valve leaflets, but their model has not been validated. In addition, neither study used subject-specific driving or loading conditions.…”

An immersed interface method for discrete surfaces

“…This approach was further extended by Griffith et al [6] to use adaptive mesh refinement. This methodology has enabled modeling in a number of application areas, including cardiac dynamics [7,8,9,10,11,12,13,14,15], platelet adhesion [16], esophageal transport [17,18,19], heart development [20,21], insect flight [22,23], and undulatory swimming [24,25,26,27,28,29,30].…”