Experimental measurement of dynamic fluid shear stress on the ventricular surface of the aortic valve leaflet

Abstract

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact causes and mechanisms of AV calcification are unclear, although previous studies suggest that mechanical forces play a role. It has been clinically demonstrated that calcification preferentially occurs on the aortic surface of the AV. This is hypothesized to be due to differences in the mechanical environments on the two sides of the valve. It is thus necessary to characterize fluid shear forces acting on both sides of the leaflet to test this hypothesis. The current study is one of two studies characterizing dynamic shear stress on both sides of the AV leaflets. In the current study, shear stresses on the ventricular surface of the AV leaflets were measured experimentally on two prosthetic AV models with transparent leaflets in an in vitro pulsatile flow loop using two-component Laser Doppler Velocimetry (LDV). Experimental measurements were utilized to validate a theoretical model of AV ventricular surface shear stress based on the Womersley profile in a straight tube, with corrections for the opening angle of the valve leaflets. This theoretical model was applied to in vivo data based on MRI-derived volumetric flow rates and valve dimension obtained from the literature. Experimental results showed that ventricular surface shear stress was dominated by the streamwise component. The systolic shear stress waveform resembled a half-sinusoid during systole and peaks at 64-71 dyn/cm(2), and reversed in direction at the end of systole for 15-25 ms, and reached a significant negative magnitude of 40-51 dyn/cm(2). Shear stresses from the theoretical model applied to in vivo data showed that shear stresses peaked at 77-92 dyn/cm(2) and reversed in direction for substantial period of time (108-110 ms) during late systole with peak negative shear stress of 35-38 dyn/cm(2).

Fig. 1

Polymeric valve models used for the study: (a) Valve 1, and (b) Valve 2; and (c) the acrylic chamber with idealized sinus geometry used to house the valves

Fig. 2

a Definition of directions of velocity and shear stress measurements. The streamwise direction is defined as the direction pointing downstream, while the non-streamwise direction is defined as the direction from one commissure to the next. b Schematic of LDV velocity measurement scheme. Velocities in both streamwise and non-streamwise directions are measured at intervals of 88microns along a straight line at the center of the valve leaflet

Fig. 3

Simulated pressure and flow conditions for (a) valve 1 and (b) valve 2

Fig. 4

a Reflected light intensity map: ensemble-averaged reflected light intensity at various measurement points along the line of measurement at the center of the valve over time. b Valves leaflet position over the cardiac cycle, segmented from the reflected light intensity maps, represented by the distance of the leaflets from its position when valve is closed

Fig. 5

Images of (a) valve 1 and (b) valve 2 with one leaflet colored with marker, subjected to steady flow rates of 20L/min. Valve opening angles were found to be 72.1° in valve 1 and 77.4° in valve 2

Fig. 6

Representative LDV measured velocity map: phase-locked ensemble-averaged velocity at all measurement points along the line of measurement at the center of the valve over time. Velocity map is shown for (a) the streamwise velocity, and (b) the non-streamwise velocity

Fig. 7

Representative sample plot of the ensemble-averaged velocities and standard deviation of these velocities versus distance from the leaflet surface, and the best-fit least square parabolic curve (at 260 and 320 ms for valve 1), demonstrating that the parabolic profile fits well with the measured velocity

Fig. 8

Flow profiles for various time points for (a) valve 1 and (b) valve 2. Flow reversal was observed during late systole, where velocities reversed in the boundary layer first. Flow profiles normalized by peak velocity, distinguished between early systole and late systole, excluding all flow profiles during flow reversals for (c) valve 1 and (d) valve 2. Flow development was observable in the normalized profiles

Fig. 9

Plots of fluid shear stresses on the ventricular surface of the valves computed from measured velocities for (a) Valve 1 and (b) Valve 2. Point 2 is at the middle of the leaflet, Point 1 is 0.32 mm upstream of point 2, while Point 3 is 0.32 mm downstream of Point 2

Fig. 10

Flow profiles at various time points for the volumetric flow waveform of (a) Valve 1 and (b) Valve 2; and flow profiles at various time points normalized by the tube centerline velocity for the flow waveform of (c) Valve 1 and (d) Valve 2, calculated from the Womersley solution for the straight tube using the same flow rate as those used in the experiments

Fig. 11

Shear stresses measured in the polymeric valves in vitro less the shear stresses calculated with the simulation assuming the same volumetric flow rates and the same channel dimension. This deviation between the two datasets can be explained by the taper angle in the actual valves leaflets during systole, which contrasts with the lack of taper angle in the simulations

Fig. 12

In vivo flow curve acquired with PC-MRI, obtained from a Powell et al. (2000), and b Langerak et al. Langerak et al. (2001), and the ventricular surface shear stress on the aortic valve, calculated with theoretical simulations

Fig. 13

Flow profiles near the ventricular surface of the aortic valve for in vivo flow curves from a Powell et al. b Langerak et al. Flow profiles normalized by centerline velocities for c Powell et al. d Powell et al. (2000), Langerak et al. (2001)