An Exploration of Cell Stress and Deformation Under Shear Flow

The biological response of bone cells (osteoblasts and/or osteocytes) to mechanical loading is an important basic science topic in the mechanism of mechano-signal transduction in bone adaptation to mechanical loading. The characterization of this mechanism of signal transduction is crucial in the understanding of the etiology of age-related bone loss, bone loss during space flight and the optimal design of implants for total joint replacements. It has been hypothesized that deformation-generated fluid shear stress is one of the major mechanical stimuli that bone cells respond to. Many in vitro experiments utilize a parallel-plate flow chamber by imposing fluid shear stress on cultured osteoblasts. For example, changes in intracellular Ca++ levels and mitogen-activated protein kinase (MAPK) phosphorylation has been quantified in response to applied shear flow [1,2]. In these studies, the flow shear stress at the wall of the flow chamber τ wall = 6 μ Q w h 2 , where Q is the volumetric flow rate, w and h are the width and height of the flow chamber, respectively, and μ is the media viscosity. However, this wall shear stress may not indicate the actual stress state which bone cells experience, which depends on the details of the flow-cell interaction, including the mechanical properties of the cell, the attachment condition of the cell to the wall as well as the cell density. In order to obtain a quantitative relationship between the biological response of bone cells to applied shear flow, it is necessary to quantify in detail the flow-cell interaction in a typical shear flow experiment. The objective of this study was to quantify the shear stress within the cell under applied shear flow, incorporating fully coupled flow and solid deformation analyses using the finite element technique. Specifically, we examined the influence of the elastic modulus of the cell and the spacing distance between cells on the shear stress within the cell.