Mechanical-Based Model for Extra-Fine Needle Tip Deflection Until Breaching of Tissue Surface

Accurate estimation of needle deflection is necessary to successfully steer the needle to targets located deep inside the body. In particular, the deflection that occurs until the tissue surface is breached differs according to the tissue shape and stiffness. This topic has not been a focus of previous work. In the present paper, we propose a model with which to estimate the needle deflection that occurs until breaching of the tissue surface with consideration of the tissue shape and stiffness. This model comprises a cantilever beam supported by virtual springs that represent the interaction forces between the needle tip and tissue surface. The effects of different insertion angles and tissue stiffness on needle deflection are represented by changing the spring constants. The model was used in experiments involving four different insertion angles (0º, 15º, 30º, and 45º) and three different polyvinyl chloride (PVC) phantoms with different stiffness (100, 75, and 50%). We verified the proposed model with the 80% PVC phantom and showed a maximum error of 0.04 mm.