Computational Analysis of Fluid Flow Within a Device for Applying Biaxial Strain to Cultured Cells

Mechanical forces are important in embryonic development [1] and key factor in the pathogenesis of many diseases including cardiovascular disease [1–3], cancer [4,5], and neurological disorders [6,7]. A variety of devices have been developed to study the effects of mechanical forces on the cells through the application of mechanical strain [8–10]. These systems most commonly involve growing cultured cells on a flexible substrate and applying forces to the substrate with a piston [11–14] or through pneumatic pressure [15–17]. While a key advantage of in vitro systems is the ability to isolate a single cell type and create a well-defined mechanical environment, it is a fundamental limitation of these systems that the movement of the flexible culture substrate generates fluid flow that also applies shear forces to cells in culture. As many cell types are sensitive to fluid shear forces as well as mechanical stretch, the generation of flow may also cause a response from the cells. Thus, it is critical to understand the fluidic forces within these systems to account for this potential confounding factor in these experiments. In particular, endothelial cells have been shown to respond to shear stresses and mechanical strain, leading to modulation of the immune cell interactions [18–20], coagulation factors [21], and vasomotor tone [22,23]. As flow is inevitably generated within the systems that apply mechanical strain, it is unclear what part of the response is induced from the flow or the mechanical stretch. A similar situation is relevant to many cell types including osteoblasts [24,25], vascular smooth muscle cells [26,27], and mesenchymal stem cells [28,29], all of which have shown to have potent mechanobiological responses to mechanical strain in culture and respond strongly to shear forces. There have been only limited attempts to understand the shear forces during the application of mechanical stretch to cultured cells. One previous study used a 2D model of shear stresses in a pneumatically driven system [30] while another used a highly simplified model of flat wall displacement to estimate the order of magnitude of the shear stress generated during the motion of the piston [13]. We recently created a novel device that allows application of complex mechanical stretch waveforms to cultured cells in a six-well format [12]. While we have validated the strain applied by this system in terms of flexible membrane distention, it remains unclear what the nature of the flow is within this system during mechanical loading. Here, we have created a computational simulation of the flow within a culture well with a flexible bottom during the application of mechanical strain. In our model, displacement of the flexible membrane leads to the generation of fluid flow. In the actual system, the pistons are mounted on a rigid plate that is coupled to a linear motor allowing arbitrary displacements and the application of complex temporal strain profiles. In our model, we simulated several common loading profiles including the application of sinusoidal load of 0.5–2.0 Hz and displacements that generate 1–10% maximal strain on the culture membrane. Our results are useful for interpreting the potential effects of shear stress in the many experimental studies that have applied mechanical strain to cultured cells and provide a computational analysis of the flow within these in vitro mechanical loading devices. Moreover, we demonstrate that motion of the membrane within the well leads to the generation of low level oscillatory shear stress that has been shown to alter the function of endothelial cells [19,31,32]. Thus, the analysis presented here may be relevant to many systems in which mechanical forces are applied to cells through displacement of a flexible membrane.