Abstract: The eye muscles in humans are arranged such that they allow rotations of the globe about any axis in three-dimensional space. Only 3D analysis techniques will suffice to describe the sometimes complex dependencies between the elicited eye movements and the stimulation conditions. With the recent availability of modern 3D eye movement measurement techniques and the further development of appropriate mathematical descriptions, we are now able to study eye movements in all three degrees of freedom. This article describes the basic mathematical tools for 3D eye movement analysis like rotation vectors, reference frames, coordinate systems, and the concept of Listing's law. In a second part some clinical applications are presented. The close coupling between the vestibular and the oculomotor system suggests that by observing spontaneous and elicited eye movements in the case of an acute unilateral vestibular pathology we might be able to find out which parts of the vestibular system (that is, which of the semicircular canals or which of the otoliths) are affected. The rationale of such an analysis is based on the observation that electrical stimulation of single semicircular canal afferents in animals induces eye movements that lie roughly in the plane of the canal. It is, therefore, possible to deduce which canals cause the eye movements observed when only some parts of the vestibular system are defective. Thus, the analysis of 3D movements not only provides an improved understanding of how the brain organizes movement in 3D space, but also has the potential to significantly improve our diagnostic capabilities.
