Mathematical theory of stereotactic coordinate transformation: eliminationof rotational targeting error by addition of a third reference point - Technical note

All frame-based stereotactic procedures require localization of an anatomic al target within the coordinate system of the stereotactic frame. If the ta rget is defined by its coordinates given in a stereotactic atlas (indirect localization), the neurosurgeon faces the mathematical task of transforming atlas coordinates into frame coordinates. hi the method usually used, the frame coordinates of two reference points (the anterior and posterior commi ssures) are obtained from computerized tomography or magnetic resonance ima ges, and serve as the basis for the coordinate transformation. This two-poi nt algorithm relies on the additional assumption that the frame sits on the patient's head without exhibiting roll, that is, rotation about the antero posterior axis (y axis). Usually this assumption is nearly, but not exactly , correct. An amount of roll as small as 3 degrees can cause a targeting er ror on the order of 1 mm when a two-point algorithm is used. This potential source of error can be eliminated by using a new method of coordinate tran sformation, the derivation of which is mathematically reported in this arti cle. The new method requires a third reference point located in the midsagi ttal plane, in addition to the two commissural reference points.