On the Generation of Rapid Eye Movements in Three Dimensions

Lesion studies and single cell recording in the alert monkey have localized two generators for rapid eye movements. Horizontal saccades in the ipsilateral direction are generated in the paramedian pontine reticular formation (PPRF).’.’ Vertical saccades are bilaterally represented in the rostra1 interstitial nucleus of the medial longitudinal fasciculus (riMLF)3*4 and are abolished only by bilateral 1esiom5 However, Robinson and Zee6 have conjectured that vertical burst neurons fall into four functionally different populations with on-directions close to those of the vertical semicircular canals. Based on evidence from recording burst neuron activity in the riMLF and from studying the effects of focal chemical inactivation of neuron populations a t the recording sites, we have postulated that burst neurons in the riMLF should have their on-directions close to those of the vertical motoneurons on the ipsilateral side or, equivalently, close to those of the vertical semicircular canals on the ipsilateral side.’.* To discuss eye position in three dimensions and the on-directions of motoneurons and burst neurons, one needs a precisely defined coordinate system. In FIGURE 1 the Fick, Helmholtz, and Listing coordinates for eye position are shown. Every eye position can be characterized by its rotation matrix, R, which rotates the eye into its present position starting from the primary position. Every rotation in the oculomotor range is uniquely characterized by a three-dimensional rotation vector, r, where r/ I rl is the axis of R defined by the right hand rule, and ( r ( is the rotation angle. In this paper we shall examine only first-order effects and use the linear approximation of R(r) acting on any vector q; R ( r ) q = q + r A q (A: vector product). With respect to the craniotopic system in FIGURE 1 we decompose r = te, vez he3, so that in the linear approximation h = 3, v = cp. and t = 9 holds. The change in eye position from R ( r , ) with components (t,, v,, h,) to R(r2) with (t2, v2, h2) is described by the saccade vector (At, hv, Ah) = (t2 ti , v2 v , , h2 hi ) . In what follows we shall use this vector description for rapid eye movements and neglect important eye-position-dependent higher-order effects, in particular those that have implication for Listing’s law in eccentric eye positions? The unit vectors that describe the direction of activation of the semicircular canals