Dynamic modelling and embryo zona pellucida perforation experiments with piezoelectric actuated micro-needles

In this paper, the nonlinear three-dimensional dynamics of a micro-needle driven at ultrasonic operating frequencies is briefly derived. The micro-needle is simulated as an Euler-Bernoulli cantilever beam attached to a moving base. The equations of motion of cutting micro-needle are derived with Kane's method. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. Furthermore, the elastic and centroidal axes of the cross-section of the micro-needle coincide so that eccentricity effects are not considered. The micro-needle is modelled with contact with an embryo zone pellucida, submerged in a fluid medium. The surrounding fluid is modeled as incompressible using the Morison equation. From the simulation model, resonant frequencies are determined. Experimental work is presented for perforation of mouse zona pellucida with the micro-needle PZT actuator driven at different frequencies. Experimental tests are conducted to determine a threshold frequency below which PZT actuated zona perforation is unsuccessful.