  Percutaneous needle insertions are commonly performed for diagnostic and
therapeutic purposes as an effective alternative to more invasive surgical
procedures. However, the outcome of needle-based approaches relies heavily on
the accuracy of needle placement, which remains a challenge even with robot
assistance and medical imaging guidance due to needle deflection caused by
contact with soft tissues. In this paper, we present a novel mechanics-based 2D
bevel-tip needle model that can account for the effect of nonlinear
strain-dependent behavior of biological soft tissues under compression.
Real-time finite element simulation allows multiple control inputs along the
length of the needle with full three-degree-of-freedom (DOF) planar needle
motions. Cross-validation studies using custom-designed multi-layer tissue
phantoms as well as heterogeneous chicken breast tissues result in less than
1mm in-plane errors for insertions reaching depths of up to 61 mm,
demonstrating the validity and generalizability of the proposed method.
