Computational analysis of fluid flow within a device for applying biaxial strain to cultured cells

Abstract

In vitro systems for applying mechanical strain to cultured cells are commonly used to investigate cellular mechanotransduction pathways in a variety of cell types. These systems often apply mechanical forces to a flexible membrane on which cells are cultured. A consequence of the motion of the membrane in these systems is the generation of flow and the unintended application of shear stress to the cells. We recently described a flexible system for applying mechanical strain to cultured cells, which uses a linear motor to drive a piston array to create biaxial strain within multiwell culture plates. To better understand the fluidic stresses generated by this system and other systems of this type, we created a computational fluid dynamics model to simulate the flow during the mechanical loading cycle. Alterations in the frequency or maximal strain magnitude led to a linear increase in the average fluid velocity within the well and a nonlinear increase in the shear stress at the culture surface over the ranges tested (0.5-2.0 Hz and 1-10% maximal strain). For all cases, the applied shear stresses were relatively low and on the order of millipascal with a dynamic waveform having a primary and secondary peak in the shear stress over a single mechanical strain cycle. These findings should be considered when interpreting experimental results using these devices, particularly in the case when the cell type used is sensitive to low magnitude, oscillatory shear stresses.

Fig. 1

(a) Photograph of device for applying mechanical stretch to culture cells. (b) Photograph of a single well with flexible cell culture substrate. (c) Diagram of the application of mechanical strain to the well through the displacement of the piston and the top view of the geometry of the culture well used for the studies.

Fig. 2

(a) Optimized mesh used in the simulations. (b) Displacement profile of piston. Dashed lines denote the location of the walls of the well. (c) Displacement of the bottom of the well during the simulation. Plotted are the shear stress of the bottom of the well during the motion. The displacement for 10% maximal strain at 1 Hz is shown.

Fig. 3

Maximal magnitude of velocity within the well at frequency plotted on a coronal plane cut through the center of the well (time point varied with frequency of loading). The plotted time was chosen as the time when there was the maximum velocity in the coronal slice from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Maximum strains of 1%, 5%, and 10% were investigated per frequency. Higher velocity is observed toward the middle of the well. To aid visualization, the displacement of the membrane is not shown in the simulation.

Fig. 4

Maximal magnitude of velocity within the system for each of the frequencies tested (0.5, 1, and 2 Hz) as the membrane displaces. The plotted time was chosen as the time when there was the maximum velocity in the horizontal slices from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Horizontal cut planes through the well with the bottom, middle, and top of the well are shown. Maximum strains of 1%, 5%, and 10% were investigated at each frequency. The bottom plane shows the velocity of the displacing surface, and the top plane shows the velocity at the top of the well. Higher velocity is observed toward the middle of the well. To aid visualization, the displacement of the membrane is not shown in the simulation.

Fig. 5

Fluid velocity and shear stress during mechanical loading, averaged over the entire well or culture surface. (a) Average fluid velocity for the entire well averaged over time in the final cycle of the simulation. (b) Average shear stress on the culture surface averaged over time in the final cycle of the simulation.

Fig. 6

Velocity isosurfaces for the time with maximal velocity for each frequency of loading (0.5, 1, and 2 Hz) as the membrane displaces. Maximum strains of 1%, 5%, and 10% were investigated at each frequency. The plotted time was chosen as the time when there was the maximum velocity in the well from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Each isosurface color shows a surface with a constant velocity within the well in millimeter per second. Higher velocity is observed toward the middle of the well.

Fig. 7

(a) Average shear stress over the first cycles of loading for the total, central, and outer regions of the bottom surface of the well. Conditions shown are for 10% maximal strain and 1 Hz frequency of loading. (b) Average shear stress on the bottom of the plate over the last cycle of the simulation.

Fig. 8

Maximal shear stress on the surfaces of the well during the loading cycle. Within each frequency group, the time point chosen is held constant and is set for the time of maximal shear stress. Maximum strains of 1%, 5%, and 10% were investigated per frequency. The plotted time was chosen as the time when there was the maximum shear stress on the well surfaces from all time points examined in the last cycle of loading. Plotted times are from the last cycle of loading for 0.5 Hz (time = 14.5 s), 1 Hz (time = 14.25 s), and 2 Hz (time = 14.625 s). Higher shear stress is observed toward the wall. The quarter front wall has been removed to aid visualization.

Fig. 9

Circumferential average of shear stresses on the culture surface during last cycle of the simulation. The zero point indicates the center of the well with an average taken circumferentially at each radius. Graphs shown are for 10% maximal strain and 1 Hz frequency of loading.

Fig. 10

Circumferential average shear stress during last cycle of the simulation. The zero point indicates the center of the well with an average taken circumferentially at each radius. All frequencies (0.5, 1, and 2 Hz) and maximal strain (1%, 5%, and 10%) are shown.