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Rotation Axes of Saccades a

If you plot eye velocity in three dimensions during a rapid gaze shift, or saccade, you get a closed loop in space beginning and ending a t zero velocity. Each point in the loop is the angular velocity vector of the eye a t some instant. This angular velocity vector, usually called w, is defined as shown in FIGURE 1. The vector lies along the axis about which the eye is currently rotating. It is oriented to accord with the right hand rule; that is, if you point your right thumb in the direction of w, your fingers curl round in the direction the eye is turning. The length of the vector represents how fast the eye is turning about the axis. In what follows, we shall be looking at the direction of the angular velocity vector, or, in other words, the instantaneous axis of eye rotation, during visually elicited, head-fixed saccades made by human subjects. The question we shall ask is: how are the rotation axes of different saccades oriented in space? This question has implications for the neural circuitry that generates saccades. For example, we shall see that saccade axes are widely and systematically distributed in all three dimensions. It follows that the eye velocity vector for visually elicited saccades with the head fixed has three degrees of freedom. This in turn has implications for the short-lead burst neurons that code the saccadic eye velocity command. In addition, rotation axes provide a test for the quaternion model of the saccadic system recently put forward by us.' This model uses a multiplicative computation of motor error where other models have used subtraction. We shall compare the saccade axes predicted by multiplicative and subtractive models to the actual axes of head-fixed saccades. We shall need a representation for three-dimensional eye position. We have argued elsewhere' that because of their computational efficiency, especially for questions involving rotation axes, the four-component rotational operators called quaternions are the best representation of eye position for oculomotor modeling. In this paper we show that quaternion vectors (made up of the last three components of these quaternions) are a useful way to present experimental data. The quaternion representation of eye position is described in METHODS. We conclude this introduction by reviewing Listing's law, which turns up repeatedly later in the paper. The law states that, given an eye position, e, the eye assumes only those orientations that can be reached from e by a single rotation about an axis in a particular plane: which we call the displacement plane associated with e. Primary position is the unique eye position in which the fixation line is orthogonal to the displacement plane; the displacement plane of primary position is called Listing's