A Fractional Viscoelastic Mechanical Model for Speed Optimization of Robotic Cell Microinjection

Robotic microinjection has been widely applied in the biomedical field as an effective means of cell micromanipulation. To improve the survival rate and efficiency of injection, the puncture speed should be designed properly to minimize cell damage. However, due to the complex viscoelastic mechanical properties of cells and the physical constraints of micromanipulation systems, speed optimization has become a very challenging task. To this end, this article proposes a new fractional model to accurately describe the viscoelastic mechanical properties of cells, and develops a speed optimization method based on this model to achieve minimal cell damage. Different from the traditional integer models, the proposed model is implemented by introducing a fractional viscoelastic element “spring-pot” to replace the viscous damping in the classical standard linear solid model. By this way, the model can simultaneously characterize the power-law relaxation and creep behaviors of cells in microinjection with higher accuracy and fewer parameters. In addition, with the proposed model and a class of polynomials, the speed optimization problem is formulated and solved to minimize the cell deformation subjected to physical constraints. To verify the effectiveness of the proposed model and optimization algorithm, zebrafish embryo injections are carried out on the designed robotic micromanipulation system. The simulation and experimental results show that benefiting from the proposed model, the third-order speed trajectory provides the minimum cell deformation of 275.6 
$\mu$
m at the puncture time of 0.21 s in comparison with the traditional integer models, and the degree of cell damage is improved by nearly 14% compared with the commonly used constant speed.