Spatial and temporal resolution of shear in an orbiting petri dish

Abstract

It is well documented that physiological and morphological properties of anchored cells are influenced by fluid shear stress. Common orbital shakers provide a means of simultaneously applying shear stress to cells for tens to hundreds of cases by loading the shaker with multiple dishes. However, the complex flow in orbiting dishes is amenable to analytical solution for resolving shear created by the fluid motion only for simplified conditions. The only existing quantification of shear in this flow is an equation that estimates a constant scalar value of shear for the entire surface of the dish. In practice, wall shear stress (WSS) will be oscillatory rather than steady due to the travelling waveform and will vary across the surface of the dish at any instant in time. This article presents a computational model that provides complete spatial and temporal resolution of WSS over the bottom surface of a dish throughout the orbital cycle. The model is reasonably well validated by the analytical solution, with resultant WSS magnitudes that are within 0.99 ± 0.42 dyne/cm(2) . The model results were compared to tangential WSS magnitudes obtained using one-dimensional optical velocimetry at discreet locations on the bottom of an orbiting dish. The experimental minimum and maximum WSS at 1 mm from the center of the dish were 6 and 7 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 8.5 dyne/cm(2) . The experimental minimum and maximum WSS at 12 mm from the center of the dish were 6 and 16 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 14 dyne/cm(2) . Discrepancies between the experimental and computational data may be attributed to a sparse sampling rate for the experimental probe, a sharp gradient at the sample area which could cause the unidirectional probe to be inaccurate if its location were not precise, and too few particles to track and a scattering of the signal by the free surface when the liquid is shallow.

Impedance analysis of endothelial cells undergoing orbital shear stress.

“…This analytical solution provides a single wall shear stress value, but the levels of shear that are generated in a dish on an orbital shaker are non-uniform. Thomas et al (2011) described the results of a computational fluid dynamics (CFD) simulation of flow in an orbiting dish at orbital speeds of 60, 90, 120, 150, 180, and 210 rpm assuming the same constant values that were used by Dardik et al (2005).…”

“…The density of the liquid in the dish was taken to be 997.3 kg/m 3 , with a viscosity of 0.00101 kg/m-s (Thomas et al, 2011). Equation (8) has been commonly used to estimate shear stress values in orbiting dishes.…”

“…Approximate peak wall shear stress values from the CFD simulation were listed as follows for radial locations of 4.25 mm, 12.8 mm, and 16.4 mm from the center of the dish (Thomas et al, 2011). At 60 rpm, wall shear stress was nearly constant at 0.4 dynes/cm 2 at all three radial positions.…”

“…Colleagues at our institution performed a CFD simulation using our physical parameters (Thomas et al, 2011) and assuming the same above-mentioned constant values of Dardik et al (2005). The dimensions of the system were taken into account for A visualization of the shear stress contour created on the bottom of the orbiting cylinder in the simulation was supplied by our colleagues in the form of Figure 13, which is seen below (units in dynes/cm 2 ).…”

Computational modeling of shear forces and experimental validation of endothelial cell responses in an orbital well shaker system

“…Computational models based on computational fluid dynamics were used to describe fluid behavior in rotating cell culture dishes (Berson et al 2008;Thomas et al 2011;Salek et al 2012). These models predicted that orbital shaker generates a flow more closely mimicking the pulsatile flow generated by the beating heart in vivo.…”