Numerical Investigation of the Strain Stiffening Behavior of Mesenchymal Stem Cells on Elastic Substrates

Abstract

In order to accurately predict the cellular response, it is necessary, along with other factors, to consider the effect of the cell spreading on the substrate. Also, the core tensions, due to the cell spreading, play a crucial role in the fate of a stem cell. Therefore, the exact prediction of these tensions is of particular importance. The effect of the strain stiffening of a mesenchymal cell, in a two-dimensional model, was investigated numerically using finite element method, by exerting a time function displacement, to the cytoplasm boundary. Utilizing Schwartz-Christoffel transformation, a model for cell-spreading was proposed that can be used to achieve accurate cellular responses. Three different models are considered. In the first model, the cell is treated as a non-alive material. That is, the mechanical properties remain constant on the substrate. Two other models, the linear and exponential strain-stiffening, are active models. By comparing the results of these models with the experimental results, it was found that the assumption that the cell is inactive departs the response from the exact amount. Therefore, considering the cell’s living nature, in both linear and exponential models, leads to more similarity of the results, both the tension value and the slope of the variations, with the experimental observations. Furthermore, by increasing the amount of the cell spreading, the difference in the amount of the nucleus stress in active models with the inactive model increases, so that the predicted tension by the linear model reaches 2.3 times that predicted by the non-alive model