PMC

The torque from neighboring elements and the damping from the tissue act on each small element of the needle.

After inserting, the protruding needle tip was attached to a hall effect angle sensor. The tip and base angles were measured as the needle was stationary and as the needle moved through the tissue. The needle angles and torque exerted at the base were measured in multiple tissues at multiple lengths.

While the needle was translating at 0.25 cm/sec through 10 cm of tissue, we applied a sinusoidal chirp function to the needle base at frequencies from 0.1 Hz to 4 Hz. The above plot shows the responses for the open-loop, modeled dynamics, and feedback controlled conditions.

For each material, the needle base was rotated 90° over 20 sec, and then held stationary for 10 sec. Each tissue had enough friction to cause significant torsional lag at the tip. At t = 30 sec, the needle was retracted 0.5 cm to break the stiction, which caused the needle tip to snap to the correct angle in most materials.

For a single material (porcine gel), the needle tip lag was tested at multiple depths. The base was successively rotated 90° clockwise over 20 sec, held stationary for 10 sec, and rotated 90° counterclockwise over 20 sec. At t = 60 sec, the needle was retracted 0.5 cm. The tip lag increases with increased insertion depth.

For a single material (plastisol), the needle base was quickly rotated 90° while the needle was retracted at 0.25 cm/sec through three depths. The tip takes longer to settle to the base angle when inserted through more tissue. There is a significant lag for about two seconds, which can cause errors in the trajectory. Each depth is the average of 10 trials.