D.Glozman, A.Fischer, M.Shoham
This investigation proposes an efficient registration method for
robotic-assisted surgery. Registration is a critical stage in
robotic–assisted surgery, in which a geometric relationship such as
position and orientation of the patient’s bone relative to the robot’s
tools is established intra-operatively. Current registration techniques
often need implantation of artificial fiducial markers or digitizing
devices such as optic or magnetic sensors or laser scanners, which
complicate the registration procedure.
The registration process described in this paper uses a surface matching technique, and thus does not require any marker implant. The following three ideas simplify the registration process. First, the robot itself is used as a digitizer eliminating the need for an extra localizer. Second, bone modeling is based on the multi-resolution technique  for adaptive registration . Third, an algorithm to determine the minimal number and location of sampled points needed for registration was developed, thus easing the intra-operatively sampling process.
The proposed method was applied to Total Knee Arthroplasty (TKA) procedure, and special care was taken in adapting the method to the surgical application in hand.
In TKA, the distal, femoral, and proximal tibial compartments are
resected and replaced with two prosthetic components. About 200,000 cases
are performed annually in the US. Progress in implant design and surgical
technique led to success rates close to 85% . During the intervention,
the articular surfaces of the femur and the tibia are replaced by two
prosthetic components. Alignment errors of such components largely
exceeding 1 deg in orientation and 1 mm in position can severely affect
the kinematic and kinetic functionality of the operated limb and might
eventually lead to implant failure. Therefore, careful pre-and
intra-operative planning is required. Using robotic assistance during the
execution phase represents a way to improve the absolute accuracy in
positioning and guiding surgical tools. Robotic execution of the planned
bone resections can ensure further improvement of the procedure because of
the higher intrinsic geometric accuracy of a robot as compared to that of
a human operator. Based on prior experiments in orthopedic surgery, it is
expected that a robotic assistant will overcome implant misalignment which
is the major cause for aseptic loosening and failure in TKA.
Since we plan to use a robot in the surgical procedures, it can also be
used as a digitizer, thus considerably reducing the potential inaccuracies
in reference frame registration. The registration is then performed
directly between the bone and the robot, which in turn guides the surgical
tools. For speeding up the computation we introduce the hierarchical
multi-resolution approach and use a level of detail data model.
To ensure the required accuracy of 1deg rotation and 1mm translation, we explore the subject of optimal number of sampling points and their location. The search for the best sampling points is viewed from the grasping theory point of view . Mathematically, it is possible to view the problem of choosing optimal sampling points for registration as that of grasping the bone with a multi-fingered hand. The contacts between the fingertips and the grasped object are modeled as frictionless point contacts. Each contact is modeled as a virtual linear spring directed normal to the surface passing through the point of contact. In order to determine the optimal set of sampling points for each set of points, a worst case transformation is calculated. That is, we look for the bone motion which is minimally detected by the sensor. Among these motions, we choose the set of contact points that are maximally dislocated by the minimal motion. This configuration of the grasp gives the best stiffness properties; hence, the points of contact are the best candidates for sampling during registration.
Fig. 1. Sampling of the bone by the robot.