Variation of strain on the membrane surface against downward displacement.

<p>(A) A snapshot of the regular grid of displacement vectors computed using the particle image velocimetry (PIV) algorithm. This set of displacement vectors tracks the motion of the marker positions as the holding plate is displaced downwards by 3.5 mm. The white circle and the red polygonal line denote the boundary of the culture surface and the boundary for strain computation presented in (E), respectively. (B – D) Mean and standard deviation of the radial (E_rr), circumferential (E_cc), and shear (E_rc) components of the strain field over the entire culture surface, respectively, plotted against corresponding downward holding plate displacement during one loading-unloading cycle. At each holding plate displacement, data points from the four membranes are horizontally staggered to allow results from individual membranes to be seen. The data points in red indicate the loading phase, during which the holding plate is being displaced downward from its initial position (0 mm) to a maximum of 11.5 mm; the data points in blue indicate the unloading phase, during which the holding plate is displaced back to its initial position. The shear strain is consistently zero regardless of the displacement of the holding plate. The curves for the radial and circumferential strains show strong overlap. Some hysteresis is seen when the membrane is unloaded; however, upon returning to the zero position, E_rr and E_cc are both consistently zero. (E) Color intensity maps of the radial and circumferential components of strain over the culture surface of membrane 4 in (B), (C), and (D) during loading phase and displaced downward by 3.5 mm (top panel), 5.5 mm (middle panel), and 9.5 mm (bottom panel). The coefficient of variation (CV), defined as the ratio of the standard deviation to the mean, is given for each intensity map.