Dynamic modelling, simulation and experiments of a micro-cutter with applications to cell perforation

The nonlinear three-dimensional dynamic equations of motion of a micro-cutter driven longitudinally at ultrasonic operating frequencies are derived using Kane's method. The micro-cutter is assumed to be immersed in a fluid, and in contact with an oocyte, which is to be perforated by the micro-cutter. The micro-cutter is modelled as an Euler-Bernoulli cantilever beam attached to a moving base. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. It is assumed that there is no slip between the micro-cutter tip and the embryo membrane. The model presented demonstrates that the longitudinal excitation input of a micropipette results in excitation of out-of-plane, lateral motion due to the nonlinear dynamic coupling of the dynamics. Experimental results of membrane perforation are presented in the work supporting oocyte micro-cutter observations regarding suitable frequencies of excitation for effective oocyte membrane perforation.