Models of maximum stress and strain of zebrafish embryos under indentation

Micro-injection of zebrafish embryo is widely applied in biology for the analysis of early developmental processes. The success of a micro-injection to a large extent depends on the mechanical interaction between the micro-pipette and the membrane of the zebrafish embryo. In this paper, we present the development of (i) a maximum stress model of the deformed membrane with respect to the depth of indentation, (ii) a family-of-conics elongation model to determine the length of the deformed membrane for the estimation of the maximum strain at a given indentation depth, and (iii) an experimental system to generate the required data for these two models. The significance of these results is that the estimated maximum stress provides a performance target for the penetration process, while the estimated corresponding maximum strain serves as an indicator of the extent of deformation sustained by the embryo prior to penetration. Implications of these modeling and experimental results are discussed in the context of optimizing the process of micro-injection.