Incorporating target registration error into robotic bone milling

Robots have been shown to be useful in assisting surgeons in a variety of bone drilling and milling procedures. Examples include commercial systems for joint repair or replacement surgeries, with in vitro feasibility recently shown for mastoidectomy. Typically, the robot is guided along a path planned on a CT image that has been registered to the physical anatomy in the operating room, which is in turn registered to the robot. The registrations often take advantage of the high accuracy of fiducial registration, but, because no real-world registration is perfect, the drill guided by the robot will inevitably deviate from its planned path. The extent of the deviation can vary from point to point along the path because of the spatial variation of target registration error. The allowable deviation can also vary spatially based on the necessary safety margin between the drill tip and various nearby anatomical structures along the path. Knowledge of the expected spatial distribution of registration error can be obtained from theoretical models or experimental measurements and used to modify the planned path. The objective of such modifications is to achieve desired probabilities for sparing specified structures. This approach has previously been studied for drilling straight holes but has not yet been generalized to milling procedures, such as mastoidectomy, in which cavities of more general shapes must be created. In this work, we present a general method for altering any path to achieve specified probabilities for any spatial arrangement of structures to be protected. We validate the method via numerical simulations in the context of mastoidectomy.