Numerical Study On The Stress Exerted On Osteoblasts And Focal Adhesions By Chamber Fluid Flow And Cell-substrate Interstitial Fluid Flow

Osteoblasts,as seed cells of bone tissue engineering,are largely affected by fluid shear stress(FSS)generated by fluid flow in bone tissue.Therefore,FSS is an important mechanical stimulation for osteoblasts,which affects cellular behavior such as proliferation,differentiation,and migration of osteoblasts.In vitro,FSS is applied to osteoblasts typically using parallel plate flow chambers(PPFC)or microfluidic channels.By using a numerical simulation method based on the PPFC,the stress,strain and cell deformation caused by the flow across the upper surface of the cell have been obtained in previous studies.Despite,little attention has been paid to the interstitial fluid flow between cells and the underlying substrate.The adherent cells are connected to the substrate through focal adhesions(FAs).When FSS is applied,the fluid not only flows across the upper surface of the cell to generate a chamber fluid flow(CFF),but also a small portion of the fluid flows through the interstitial space between the cell and the substrate,resulting in interstitial fluid flow(IFF).Exploring the effect of cell-substrate IFF helps to further the understanding of the phenomena observed in the experiment and the mechanisms by which cells respond to FSS.Since the cell-substrate IFF is difficult to observe and measure experimentally,this paper aims to employ a numerical simulation method to investigate the mechanical stress exerted on osteoblasts and focal adhesions.Meanwhile,the effect of the CFF across the upper surface of cells is investigated as well.The main works and conclusions are summarized as follows:(1)Establishing a geometric model containing osteoblasts and cell-substrate interstitial spaceAccording to the design principle of PPFC in which the width of the chamber is much larger than the height and the fact that osteoblasts in the flow chamber are subjected to a stable,uniform,and fully developed shear flow stimulation,in this study,the length,width and height of the rectangular flow chamber were set to 4 mm,2.4 mm and 0.1 mm,respectively.According to experimental observations and existing literatures,osteoblasts were further idealized as flat semi-ellipsoids with a long axis of 50?m,a short axis of 40?m,and a height 6?m.The long axis of osteoblasts was perpendicular/parallel to the direction of fluid flow.Since FAs have a certain of size and height,according to the reported data,the FAs were idealized as a small cylinder with a height of 100 nm and an initial radius of 1?m.The osteoblasts were connected to the substrate by 20 identical cylindrical FAs distributed evenly at the edge of osteoblasts.The effect of all other properties of the substrate was neglected.Thereafter,SolidWorks10.0,a three-dimensional modeling software,was used to establish a geometric model containing a luminal space on the upper surface of osteoblasts and a interstitial space between the cell and the substrate.(2)Numerical simulation of the distribution of shear stress/ pressure on osteoblasts induced by CFFThe established geometric model with a FA radius of 1?m was meshed using software Gambit 2.4.6,and then the divided mesh was input into the Fluent for parameter selection and condition setting.The main control conditions include:(1)According to the velocity function with a parabola distribution,which was obtained when the shear flow with an average inlet velocity of 16.62mm/s reached a fully developed state,a UDF(user-defined function)file was written to give the boundary condition of inlet velocity;(2)To judge the convergence of calculation,the residual standard was set,and the wall shear stress on the cell surface and the focal adhesion and the difference between the outlet and inlet mass flow rates were monitored as well.The mesh-independence was verified by densifying the meshes near the cell surface and the focal adhesions to form three meshing schemes.The results show that the shear stress generated by the CFF on the surface of osteoblasts distributed with a certain rule,regardless of the perpendicular or parallel orientation of the long axis to the fluid flow direction.Specifically,the shear stress at the top of the cell was the largest;the shear stress became reduced from the top to the bottom of the cell.The maximum pressure appears at the upstream face while the minimum pressure appears at the downstream face.These results are consistent with the reported ones in the literatures,indicating that the established geometric model is reasonable in this study.(3)Numerical simulation of the stress distribution on osteoblasts induced by cell-substrate IFFUsing the established geometric model with a FA radius of 1?m and the boundary condition for inlet velocity of 16.62mm/s,a series of calculations were conducted and the results showed that the cell-substrate IFF leads to local concentration of shear stress on the underside of the osteoblasts and the compression stress by the cell-substrate IFF gradually decreases along the direction of the fluid flow.(4)Numerical simulation of the effect of the average inlet flow velocity and FA radius on the IFF and its stress on FAsThe FA radius was set as 0.5?m,1?m,and 1.5?m,respectively,and the average inlet velocity was set as 16.62 mm/s,33.24 mm/s,and 49.86 mm/s.Three calculations were performed for each geometric model to obtain the shear and compression stress exerted on different sites of the focal adhesions by cell-substrate IFF.The results show that,when the focal adhesion radius was identical,the shear stress on the focal adhesion increased with the increase of the inlet velocity,which implies that the increased shear stress on the focal adhesion might promote the formation and growth of focal adhesions and thus contributing to cell stability.On the other hand,when the inlet velocity was identical,with the increase of the FA radius,the IFF-generated shear stress decreased at the ends of the long axis of the cell yet demonstrated no significant change at the ends of the short axis of the cell.(5)Numerical simulation of the effect of cell orientation on the stress of FAs generated by cell-substrate IFFThe orientation of the semi-ellipsoidal osteoblast in the geometric model was set to have the long axis of osteoblasts parallel to the direction of fluid flow.Three geometric models with the FA radius as 0.5?m,1?m and 1.5?m were established and the average inlet flow velocity was set as 16.62 mm/s.The calculation results indicate that the shear stress distribution on FAs by IFF was similar in all the three models.Specifically,the maximum shear stress on FAs occurred at the two ends of the cell long axis whereas the minimum shear stress appeared at the two ends of the short axis of the cell.This tendency is consistent with the experimental observations that the osteoblasts with their long axis parallel to the direction of fluid flow stay in the most stable state.In summary,based on the fact that osteoblasts in the flow chamber are connected to the substrate through focal adhesions of a certain size and height,the geometric model containing the cell-substrate interstitial space was constructed.A series of numerical simulations provided the stress distributions on osteoblasts generated by CFF and cell-substrate IFF.At the same time,the effects of inlet flow velocity,focal adhesion radius,and cell orientation on the cell-substrate IFF and the resulting stress distribution on FAs were investigated as well.In this paper,the cell-substrate IFF was considered in addition to CFF,which provides a new idea and theoretical guidance for exploring the cellular mechanisms by which osteoblasts respond to fluid flow stimulation.