Probe guides are surgical fixtures that are rigidly attached to bone anchors in order to place a probe at a target with high
accuracy (RMS error < 1 mm). Applications include needle biopsy, the placement of electrodes for deep-brain
stimulation (DBS), spine surgery, and cochlear implant surgery. Targeting is based on pre-operative images, but
targeting errors can arise from three sources: (1) anchor localization error, (2) guide fabrication error, and (3) external
forces and torques. A well-established theory exists for the statistical prediction of target registration error (TRE) when
targeting is accomplished by means of tracked probes, but no such TRE theory is available for fixtured probe guides.
This paper provides that theory and shows that all three error sources can be accommodated in a remarkably simple
extension of existing theory. Both the guide and the bone with attached anchors are modeled as objects with rigid
sections and elastic sections, the latter of which are described by stiffness matrices. By relating minimization of elastic
energy for guide attachment to minimization of fiducial registration error for point registration, it is shown that the
expression for targeting error for the guide is identical to that for weighted rigid point registration if the weighting
matrices are properly derived from stiffness matrices and the covariance matrices for fiducial localization are augmented
with offsets in the anchor positions. An example of the application of the theory is provided for ear surgery.