Abstract
Arterial endothelial cell (EC) responsiveness to flow is essential for normal vascular function and plays a role in the development of atherosclerosis. EC flow responses may involve sensing of the mechanical stimulus at the cell surface with subsequent transmission via cytoskeleton to intracellular transduction sites. We had previously modeled flow-induced deformation of EC-surface flow sensors represented as viscoelastic materials with standard linear solid behavior (Kelvin bodies). In the present article, we extend the analysis to arbitrary networks of viscoelastic structures connected in series and/or parallel. Application of the model to a system of two Kelvin bodies in parallel reveals that flow induces an instantaneous deformation followed by creeping to the asymptotic response. The force divides equally between the two bodies when they have identical viscoelastic properties. When one body is stiffer than the other, a larger fraction of the applied force is directed to the stiffer body. We have also probed the impact of steady and oscillatory flow on simple sensor-cytoskeleton-nucleus networks. The results demonstrated that, consistent with the experimentally observed temporal chronology of EC flow responses, the flow sensor attains its peak deformation faster than intracellular structures and the nucleus deforms more rapidly than cytoskeletal elements. The results have also revealed that a 1-Hz oscillatory flow induces significantly smaller deformations than steady flow. These results may provide insight into the mechanisms behind the experimental observations that a number of EC responses induced by steady flow are not induced by oscillatory flow.