  We introduce a dynamic event-triggering mechanism for regulating the axonal
growth of a neuron. We apply boundary actuation at the soma (the part of a
neuron that contains the nucleus) and regulate the dynamics of tubulin
concentration and axon length. The control law is formulated by applying a
Zero-Order Hold (ZOH) to a continuous-time controller which guides the axon to
reach the desired length. The proposed dynamic event-triggering mechanism
determines the specific time instants at which control inputs are sampled from
the continuous-time control law. We establish the existence of a minimum
dwell-time between two triggering times that ensures avoidance of Zeno
behavior. Through employing the Lyapunov analysis with PDE backstepping, we
prove the local stability of the closed-loop system in $L_2$-norm, initially
for the target system, and subsequently for the original system. The
effectiveness of the proposed method is showcased through numerical
simulations.
