The role of valve stiffness in the insurgence of deep vein thrombosis

Figures

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  Fig. 1. Vortex formation in the presence of flexible valves. a A Schematic diagram of mask alignment through the fluorescent light of an inverted microscope. The mask was designed in order to produce the desired valve size through a 20× objective. b Optical image of the flexible valve obtained. The length of the valve is about 330 µm, the width of each leaflet starts at about 45 µm and it tapers towards the tip. The initial gap in between the leaflets when there is no flow is about 30 µm. The scale bar represents 100 µm. c The top image is a velocity profile map with the site of vortex formation at the tip of the valve designated by the dashed line. Images below (from left to right) represent the vortex getting larger with increased flow rate (valve properties: 2% w/v [PI] and 40% w/v [PEGDA]).

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  Fig. 2. Vortex characteristics. a Vortex area increases as ≈Re2.7 (dashed line, R2 = 0.9057). b Circulation correlates with Re; the size of the marker point represents the minimum and maximum circulation calculated for the vortex developing at the tip of the valve and the dotted line represents a logarithmic fit (R2 = 0.9788).

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  Fig. 3. Vortex size dependence on flow rate for three different stiffnesses of the valve. a The size of the vortex increases linearly as the flow rate and/or the stiffness increases. The lines are linear fits. b Dependence of the degree of valve opening on flow rate for three different valve stiffnesses. Here, the smaller the distance from the channel wall the more the valve is open. As a consequence, for more flexible valves (lower Young’s modulus) the distance from the channel wall is smaller for a fixed flow rate compared to more rigid valve and the vortex associated is smaller (see panel a). In the plot, the grey area represents the region where no vortices were observed, independently of the stiffness of the valve tested. The error bars represent standard error.

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  Fig. 4. Accumulation behaviour for valves of different stiffness. a Positive correlation between valve stiffness and size of the aggregate formed by the accumulation of polystyrene particles of 3 µm (left, 0.1% w/v) and 10 µm (right, 1% w/v) in diameter in the case of symmetrical valve rigidity and pulsed flow condition (0–100 mbar, 1 Hz). The valves were made of 50% [PEGDA] and, 4, 6, or 8% [PI], respectively from softer to stiffer. The data were analysed statistically using one-way ANOVA followed by Tukey post hoc test. b Typical accumulation behaviour over time for 10 µm polystyrene particles (1% w/v) in diameter in the case of symmetrical valve rigidity and pulsed flow condition (0–100 mbar, 1 Hz). The scale bars represent 100 µm.

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  Fig. 5. Accumulation behaviour for symmetrical and asymmetrical valves. Time-lapse images of particles building up over time on symmetrical (top) and asymmetrical (bottom) valves; both are 4% (w/v) PI and 50% (w/v) PEGDA but the right-hand side leaflet on the asymmetrical valve was exposed to UV light for a longer time compared to the left-hand side leaflet (500 and 300 ms, respectively) resulting in an asymmetrical stiffness. The scale bars represent 100 µm.

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  Fig. 6. Platelets accumulation for symmetrical and asymmetrical valves. a Time-lapse images of blood aggregate building up over time on stiff symmetrical valves (see also Supplementary Movie 5). The aggregate forms rapidly within 30–40 s of pulsed flow conditions as shown by the fluorescently labelled platelets accumulating at the tip of the leaflets. It then increases slowly until eventually it detaches (in this case after 93 s). The arrow indicates the aggregate and the scale bar represents 100 µm. b Growth of the aggregate over time showing initial fast growth followed by a plateau and eventually detachment (as identified by the sudden fluorescence signal decay). At its maximum size the surface coverage was about 1200 µm2 on the valve tip. c Time-lapse images of blood aggregate building up over time on asymmetrical valves (see also Supplementary Movie 6). The aggregate forms slowly behind one of the leaflets. The arrow indicates the aggregate and the scale bar represents 100 µm. d The size of the aggregate becomes substantial after about 20 min and keeps growing exponentially. The continuous line is an exponential growth fit. The error bars represent standard error.

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  Fig. 7. In situ Young’s modulus evaluation. a A schematic diagram of how the deflection, hx is measured. b The deflections measured for different flow rates. c Zoomed in of the circled region in panel b designating the small linear deflection (first six points) which is used to calculate the Young’s modulus in plot D. Panel b and c refer to the case of 50% PEGDA concentration. The data shown in panel d refers to a fixed concentration of PI equal to 4% (w/v). The error bars represent standard error.

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  Fig. 8. Vortex formation at Re = 163. A vortex forms at the valve tip (here only half vortex is shown as observed from multiple positions acquisition).