  Steerable needles are capable of accurately targeting difficult-to-reach
clinical sites in the body. By bending around sensitive anatomical structures,
steerable needles have the potential to reduce the invasiveness of many medical
procedures. However, inserting these needles with curved trajectories increases
the risk of tissue shearing due to large forces being exerted on the
surrounding tissue by the needle's shaft. Such shearing can cause significant
damage to surrounding tissue, potentially worsening patient outcomes. In this
work, we derive a tissue and needle force model based on a Cosserat string
formulation, which describes the normal forces and frictional forces along the
shaft as a function of the planned needle path, friction parameters, and tip
piercing force. We then incorporate this force model as a cost function in an
asymptotically near-optimal motion planner and demonstrate the ability to plan
motions that consider the tissue normal forces from the needle shaft during
planning in a simulated steering environment and a simulated lung tumor biopsy
scenario. By planning motions for the needle that aim to minimize the tissue
normal force explicitly, our method plans needle paths that reduce the risk of
tissue shearing while still reaching desired targets in the body.
