A model for shear stress-induced deformation of a flow sensor on the surface of vascular endothelial cells

Fluid mechanical shear stress elicits humoral, metabolic, and structural responses in vascular endothelial cells (ECs); however, the mechanisms involved in shear stress sensing and transduction remain incompletely understood. Beyond being responsive to shear stress, ECs distinguish among and respond differently to different types of shear stress. Recent observations suggest that endothelial shear stress sensing may occur through direct interaction of the flow with cell-surface structures that act as primary flow sensors. This paper presents a mathematical model for the shear stress-induced deformation of a flow sensor on the EC surface. The sensor is modeled as a cytoskeleton-coupled viscoelastic structure exhibiting standard linear solid behavior. Since ECs respond differently to different types of flow, the deformation and resulting velocity of the sensor in response to steady, non-reversing pulsatile, and oscillatory flow have been studied. Furthermore, the sensitivity of the results to changes in various model parameters including the magnitude of applied shear stress, the constants that characterize the viscoelastic behavior, and the pulsatile flow frequency (f) has been investigated. The results have demonstrated that in response to a suddenly applied shear stress, the sensor exhibits a level of instantaneous deformation followed by gradual creeping to the long-term response. The peak deformation increases linearly with the magnitude of the applied shear stress and decreases for viscoelastic constants that correspond to stiffer sensors. While the sensor deformation depends on f for low f values, the deformation becomes f-independent above a critical threshold frequency. Finally, the peak sensor deformation is considerably larger for steady and non-reversing pulsatile flow than for oscillatory flow. If the extent of sensor deformation correlates with the intensity of flow-mediated endothelial signaling, then our results suggest possible mechanisms by which ECs distinguish among steady, non-reversing pulsatile, and oscillatory shear stress.