Modification Of Theoretical Growth Rate Model Of Mscs On Three-dimensional Scaffold Under Fluid Shear Stress

Bone tissue is a load-bearing organ with complex structure.Once severely damaged,the bone is difficult to achieve self-repair.Nowadays,bone tissue engineering has been considered as one of the most effective ways to treat large segmental bone defects.When constructing a bone tissue engineering graft in vitro,a suitable perfusion bioreactor is usually used to incubate three-dimensional(3D)cell-scaffold complex for a period of time in order to obtain bone tissue engineering grafts with better repair effect.On the one hand,perfusion culture can enhance nutrient exchange and oxygen transport in the cell-scaffold complex;on the other hand,it can provide appropriate mode and intensity of fluid shear stress stimulation for the cell-scaffold complex,and ultimately achieve uniform distribution,massive proliferation and directional differentiation of seed cells in the 3D scaffold.However,the theoretical model of this process is not perfect,especially when the seed cells are stem cells.Based on the previous study of our laboratory,rat's bone marrow mesenchymal stem cells(MSCs)were compounded with3D scaffolds with suitable stiffness(local stiffness in 37.70±19.60 kPa)in this study,which was stimulated with fluid shear stress in different modes and intensities by a home-made bioreactor for different time.Firstly,the effects of different fluid shear stress on cell proliferation and osteogenic differentiation were investigated.Secondly,the effect of fluid shear stress on the single cell growth rate of MSCs was fitted,and the theoretical model of MSCs'growth rate in vitro was modified,which provided a basis for the establishment of the growth model of MSCs in vitro.The main results of this research are as follows:(1)Effect of fluid shear stress on the proliferation and osteogenic differentiation ofMSCsUnder static culture,the number of cells increased first and then decreased with time.The variation tendency of the number of cells under 0.015 Pa and 0.0075 Pa fluid shear stress stimulation was consistent with that of static culture.The differences among these three conditions were the time of peak appearing and the peak value.Under the condition of static culture,the number of cells reached the peak value 2.28?10~5 at the14th d,which was 5.25±0.77 times than that at 0 d.The number of cells under the0.0075 Pa unidirectional fluid shear stress reached a peak at 10th d,and the number of cells was 2.20?10~5.The number of cells under unidirectional fluid shear stress of 0.015Pa reached the peak at 7th d,and the number was 2.88?10~5.Under oscillatory perfusion culture,the number of cells reached the peak at 14th d,the value was 2.89?10~5(0.015Pa)and 2.33?10~5(0.0075 Pa).The number of cells which were stimulated by 0.0225 Pa shear stress increased over time both under unidirectional and oscillatory flows.In perfusion group,the distribution of cells and the deposition of extracellular matrix at each time point were better than those in the static group.The cells in the unidirectional perfusion stimulation group showed a more concentrated distribution.The extracellular matrix deposition was more in the oscillatory perfusion stimulation group than unidirectional perfusion stimulation group under the same intensity.Perfusion stimulation could promote the collagen secretion of MSCs,and the largest amount of collagen deposition occured after treatment with perfusion stimulation for 7 d.Compared with unidirectional perfusion group,oscillatory perfusion group could enhance the secretion of collagen,which was positively correlated with shear stress intensity.The results of immunohistochemical staining for osteopontin(OPN)and osteocalcin(OCN)showed that perfusion stimulation could promote osteogenic differentiation of rat MSCs,and the ability of promoting bone differentiation was stronger under the mode of oscillation than unidirectional mode.In addition,the ability of promoting osteogenic differentiation of these two modes of shear stress increased along with the increase of intensity of shear stress.(2)Modification of theoretical model of MSCs'single cell growth rate under fluidshear stressBased on the difference of single cell growth rate between the shear stress groups and the static culture group,the mathematical model of the effect of shear stress on MSCs single cell growth rate was established.Meanwhile,after the overall analysis of the observed samples,the formulas of the influence of unidirectional g(?,t)and oscillatory f(?,t)fluid shear stress on the single cell growth rate of MSCs were obtained by regression analysis with Excel table,and thus the theoretical model of MSCs'single cell growth rate under fluid shear stress could be corrected.In summary,this paper investigates the effects of fluid shear stress on the proliferation and osteogenic differentiation of MSCs combined with suitable matrix stiffness 3D scaffolds.The results indicated that high(0.0225 Pa)oscillatory shear stress could better promote proliferation and osteogenic differentiation of MSCs in vitro.Furthermore,a mathematical model of the growth rate of MSCs in vitro with time and shear stress changes was established,which achieved the revision of the single cell growth rate of MSCs in vitro culture.This model can provide a theoretical basis for optimizing the culture conditions in vitro.