Quantifying fluid shear stress in a rocking culture dish

Fluid shear stress (FSS) is an important stimulus for cell functions. Compared with the well established parallel-plate and cone-and-plate systems, a rocking "see-saw" system offers some advantages such as easy operation, low cost, and high throughput. However, the FSS spatiotemporal pattern in the system has not been quantified. In the present study, we developed a lubrication-based model to analyze the FSS distributions in a rocking rectangular culture dish. We identified an important parameter (the critical flip angle) that dictates the overall FSS behaviors and suggested the right conditions to achieving temporally oscillating and spatially relatively uniform FSS. If the maximal rocking angle is kept smaller than the critical flip angle, which is defined as the angle when the fluid free surface intersects the outer edge of the dish bottom, the dish bottom remains covered with a thin layer of culture medium. The spatial variations of the peak FSS within the central 84% and 50% dish bottom are limited to 41% and 17%, respectively. The magnitude of FSS was found to be proportional to the fluid viscosity and the maximal rocking angle, and inversely proportional to the square of the fluid depth-to-length ratio and the rocking period. For a commercial rectangular dish (length of 37.6mm) filled with approximately 2 mL culture medium, the FSS at the center of the dish bottom is expected to be on the order of 0.9 dyn/cm(2) when the dish is rocked +5 degrees at 1 cycle/s. Our analysis suggests that a rocking "see-saw" system, if controlled well, can be used as an alternative method to provide low-magnitude, dynamic FSS to cultured cells.