Mechanical modeling of biological cells in microinjection

Microinjection is an effective technique to introduce foreign materials into a biological cell. Although some semi-automatic and fully-automatic microinjection systems have been developed, a full understanding of the mechanical response of biological cells to injection operation remains deficient. In this paper, a new mechanical model based on membrane theory is proposed. This model establishes a relationship between the injection force and the deformation of biological cells with the quasi-static equilibrium equations, which are solved by the Runge-Kutta numerical method. Based on this model, other mechanical responses can also be inferred, such as the effect of the injector radius, the membrane stress and tension distribution, internal cell pressure, and the deformed cell shape. To verify the proposed model, experiments are performed on microinjection of zebrafish embryos at different developmental stages and medaka embryos at the blastula stage. It is demonstrated that the modeling results agree well with the experimental data, which shows that the proposed model can be used to estimate the mechanical properties of cell biomembranes. (In this paper, biomembrane refers to the membrane-like structures enveloping cells.)