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EVALUATION OF THE EFFECT OF SKIN FRICTION ON THE PERFORMANCE OF A PROSTHETIC AORTIC VALVE USING FLUIDSTRUCTURE INTERACTION SIMULATIONS K.H. Dellimore1, I. H. Kemp2, C. Scheffer3, H.S. Weich4 and A.F. Doubell5

1. ABSTRACT The performance of a 19 mm diameter prosthetic aortic valve at a heart rate of 72bpm was investigated during systole, through fluid-structure interaction simulations using four different leaflet skin friction coefficients (0.0, 9.24x10-4, 4.80x10-2 and 4.80x10-1). The numerical predictions were validated against experimental data for the systolic transvalvular pressure gradient (STVPG) and yielded reasonable qualitative and quantitative agreement (rms error < 13% in all cases). Increasing the leaflet skin friction was found to increase the magnitude of the STVPG, increase the peak velocity and decrease the valve orifice area when the leaflets were fully open, which are consistent with the effects of calcific stenosis. However, the results for the leaflet dynamics during opening and closing were inconsistent with expectation since increasing the leaflet skin friction decreased rapid valve closing time and had a negligible effect on the ejection time and rapid valve opening time. The deficiencies in the numerical predictions may be attributed to the use of a constant leaflet elastic modulus in the simulations. 2. INTRODUCTION Aortic valve stenosis caused by progressive calcification of aortic valve leaflets is among the leading causes of aortic valve disease in the elderly and is the most common reason for prosthetic valve replacement in adults [1]. Over the past fifty years there have been several advances in the development of prosthetic aortic replacement valves; however, many challenges still remain due to their poor long-term durability caused by calcification and mechanical failure [2]. Further research is needed to improve their longevity and to advance our understanding of their operation. Many previous studies have investigated the mechanics and functioning of native and prosthetic aortic valves using numerical simulations. Advances in computational power have allowed the fluidstructure interaction (FSI) between the valve and blood flow to be modeled numerically. In particular work by Carmody et al. [3], De Hart et al. [4], Van Loon et al. [5] and Nobili et al. [6] has underscored the strong coupling between the blood flow and the valve structure. However, these previous studies have not considered leaflet skin friction, which may influence valve function, especially under calcific conditions. Previous work by Clark [7] suggests that the flow surfaces of a calcified valve may be hydraulically rough due to calcium deposition which can lead to increased turbulence levels within the valve. It is therefore useful to account for leaflet skin friction, in addition to FSI, when modeling prosthetic valves since it may provide insight into valve 1

Department of M&M Engineering, Stellenbosch University, Private Bag X1, Matieland, South Africa Department of M&M Engineering, Stellenbosch University, Private Bag X1, Matieland, South Africa 3 Department of M&M Engineering, Stellenbosch University, Private Bag X1, Matieland, South Africa 4 Division of Cardiology, Tygerberg Hospital, Private Bag X1, Tygerberg, South Africa 5 Division of Cardiology, Tygerberg Hospital, Private Bag X1, Tygerberg, South Africa 2

performance under calcific conditions which can lead to valve failure. This paper investigates the performance of a 19 mm diameter prosthetic aortic valve at a heart rate of 72 bpm during systole, through FSI simulations using four different leaflet skin friction coefficients. The results are compared to experimental measurements from Kemp [8] and insights into valve behavior under calcific conditions are presented. 3. NUMERICAL SIMULATION DETAILS 3.1 Prosthetic aortic valve geometry

FIG. 1. (a) Prototype prosthetic aortic valve and (b) Valve mesh The prosthetic valve that was modeled is based on an un-calcified 19mm (inner diameter) stented prototype tricuspid valve which was fabricated by hand and tested at a heart rate of 72bpm in a cardiac pulse duplicator by Kemp [8]. The valve leaflets were made from kangaroo pericardium, treated with the ADAPT® anticalcification process and were attached to the stent with a curved geometry (Fig. 1 a), using CV-7 suturing. 3.2 Mesh generation A single valve leaflet, including the stent support structure, was modeled (Fig. 1 b). A finite element mesh was generated using MD.Patran based on a 3-D CAD model of the 19mm inner diameter valve. The valve mesh is composed of separate leaflet and stent domains. Four-noded quadrilateral 2-D shell Key-Hoff Langrangian elements with three integration points were used for the leaflet and stent structure, while Eulerian 3-D solid elements were used for the fluid. The coupling surface between the fluid and structural domain was formed by creating a closed volume using Lagrangian shell elements. The first couple was formed using the leaflet, a portion of the stent and a dummy surface connecting the leaflet free edge and the stent. This couple facilitates flow behind the leaflet. The second closed volume was formed using the inflow boundary, the stent (excluding the portion used for the first couple), the leaflet, the same dummy surface as in the first couple and the outflow boundary. Each of these closed volumes is then assigned to an Euler domain. The coupling surface between the two closed volumes acts as a boundary for the flow of material in the Eulerian mesh, while the stresses in the Eulerian material exert forces on the surface causing the Lagrangian mesh to distort. A grid independence test showed that a mesh with 7929 structural elements and 25,056 fluid elements was sufficient to resolve laminar and turbulent flow through the valve. 3.3 Leaflet, stent and fluid properties The material properties of the valve leaflet were specified based on the values reported

by Kemp [8] (Table 1) and were assumed to be linearly isotropic, since the valve experiences very little strain during systole. The stent structure supporting the leaflets was cobalt-chrome and the fluid in the valve was assumed to be incompressible and Newtonian based on previous work [3-6]. The fluid density and dynamic viscosity were prescribed to match human blood with a hematocrit of 45% at a temperature of 37 0C [8]. Due to the limitations of the FSI solver it was only possible to specify a constant value for the leaflet skin friction coefficient (Cf). In the absence of leaflet wall shear stress (w) measurements from Kemp, data from the literature was used to provide estimates for Cf [9-10]. However, due to the lack of a consensus in the literature, three different Cf values were used, which span the range of wall shear stress values reported in the literature (0.3 Pa