Separating Fluid Shear Stress from Acceleration during Vibrations in Vitro: Identification of Mechanical Signals Modulating the Cellular Response

Abstract

The identification of the physical mechanism(s) by which cells can sense vibrations requires the determination of the cellular mechanical environment. Here, we quantified vibration-induced fluid shear stresses in vitro and tested whether this system allows for the separation of two mechanical parameters previously proposed to drive the cellular response to vibration - fluid shear and peak accelerations. When peak accelerations of the oscillatory horizontal motions were set at 1g and 60Hz, peak fluid shear stresses acting on the cell layer reached 0.5Pa. A 3.5-fold increase in fluid viscosity increased peak fluid shear stresses 2.6-fold while doubling fluid volume in the well caused a 2-fold decrease in fluid shear. Fluid shear was positively related to peak acceleration magnitude and inversely related to vibration frequency. These data demonstrated that peak shear stress can be effectively separated from peak acceleration by controlling specific levels of vibration frequency, acceleration, and/or fluid viscosity. As an example for exploiting these relations, we tested the relevance of shear stress in promoting COX-2 expression in osteoblast like cells. Across different vibration frequencies and fluid viscosities, neither the level of generated fluid shear nor the frequency of the signal were able to consistently account for differences in the relative increase in COX-2 expression between groups, emphasizing that the eventual identification of the physical mechanism(s) requires a detailed quantification of the cellular mechanical environment.

Figure 1. Experimental and computational methods used to describe fluid motions at the well bottom

(a) Schematic of the Particle Image Velocimetry (PIV) setup. A high-speed camera recorded the motions of 1μm red fluorescent polystyrene particles vibrating within a fluid filled chamber attached to a microscope slide. Fluid shear was quantified by comparing the motion of the slide surface to the particle motions measured at 37.5μm distance intervals. (b) A fluid filled cell culture well was modeled as viscous fluid within a rigid well with the Finite Element Method (FEM). Vibration induced fluid shear at the bottom of the well was calculated by computing the relative velocity between wall and fluid assuming linear velocity gradients.

Figure 2. Shear rates between fluid and the well bottom as determined by PIV

PIV showed a steep non-linear increase in shear rate towards the surface of the glass slide (bottom of the well).

Figure 3. Motions of the well and the fluid as determined by speckle photography

(a) Displacement of the well, during 1g, 60Hz oscillatory motions. (b) Elevation of the fluid surface near the side-wall of the well (vertical red line in inset) as a function of vibration frequency. Non-linear surface motions at frequencies around 10Hz are indicative of resonance behavior. (c) Upon completion of one full oscillatory cycle, out-of-phase fluid displacements relative to the well demonstrated sloshing behavior are visualized in the mid-sagittal plane of the well.

Figure 4. Fluid velocities and shear stress determined by FEM

(a) Velocity profile of the rigid well (solid-red), fluid velocity (dashed-red), and fluid shear at Point B (see Figure 4b) during a 60Hz, 1g oscillatory motion. The phase difference between the well and the fluid was $\frac{\pi }{10}$ radians. (b) The velocity profile of the viscous fluid at t=0.005s during the 1g, 60Hz oscillatory motion of the rigid well (in black). Shown is a mid-sagittal plane of the well. Points A, B, and C were used to compare relative fluid velocities against the linear solution depicted in Table 1. (c) Histogram with the distribution of fluid nodes subjected to a given level of fluid shear at t=0.005s. In spite of spatial non-uniformity, approximately 75% of the well surface received shear stresses within 20% of the peak shear stress magnitude.

Figure 5. Validation of FEM simulations by PIV

Comparison of shear rates between FEM and PIV at heights of 150, 300, 450 and 600μm from the well bottom. Measurements were taken in a well with a total fluid height of 5mm.

Figure 6. Modulation of fluid shear by vibration parameters

Peak fluid shear stress was modulated by vibration acceleration magnitude and vibration frequency, demonstrating that different combinations of frequency and acceleration can produce identical shear stress values.

Figure 7. Change in COX-2 expression of MC3T3-E1 cells exposed to five different frequencies under low-shear (0% dextran) and high-shear (6% dextran) conditions

Fluid shear for each frequency is represented by horizontal black bars. Shear at 10Hz could not be quantified because of resonance behavior of the fluid at this frequency. P<0.05: * against 0Hz, † against10Hz, ‡ against 30Hz, § against 60Hz, ¥ against 100Hz.