Pursuit eye movements require a geometric transformation of velocity signals

Gunnar Blohm^1,2, Pierre Daye¹, Philippe Lefevre<sup>1

1</sup>CESAME and Lab. Neurophysiol., UCLouvain
²Dept. Physiology and Faculty of Arts & Science, Queen’s


It is well established that saccade planning requires a geometric transformation between the retinal stimulus and the desired motor plan to acquire the target (Crawford & Guitton 1997). However, this problem of reference frame transformations has never been considered for velocity signals. Therefore we asked whether a separate 3D visuomotor transformation of velocity signals was theoretically required by modeling the underlying geometry. We then tested our model predictions in a series of smooth pursuit experiments.

We used quaternions to model the 3D eye-in-head geometry. Our model predicted that a visuomotor velocity transformation would require the use of extra-retinal eye-in-head position and should include three different components; (1) because of the eye’s spherical projection geometry, the same retinal velocity should result in different interpretations of velocity direction depending on eye-in-head position, (2) false torsion due to off-axes eye positions must be compensated for and (3) ocular torsion (e.g. due to the VOR) must be accounted for.

We tested these 3 predictions separately on human subjects. Subjects were required either to pursue an eccentric moving target viewed under different vertical eye positions (prediction 1), to pursue a target previously foveated at different oblique positions (prediction 2) or to make a fast head roll to either shoulder while maintaining fixation in order to obtain large eye torsion because of dynamic VOR and then to pursue a moving target (prediction 3). 3D eye-in-head position was measured at 400Hz using a Chronos Video head-mounted eye tracker and head-in-space position and orientation was sampled at 200Hz using a Codamotion active infrared marker tracking device. We analyzed the open-loop gaze pursuit response, i.e. the first 100ms after pursuit onset (velocity threshold detection). We then compared the observed pursuit response to the prediction of the model to determine whether 3D geometry was or was not taken into account in the visuomotor velocity transformation.

We found that for all 3 components of the velocity conversion geometry, human behavior was accurate. This suggests that the brain indeed performs a complete 3D visuomotor velocity transformation for smooth pursuit eye movements that is different from the previously described visuomotor transformation of position signals for saccades. Since pursuit direction was accurate even for torsional values outside of Listing’s plane in our head-roll condition (prediction 3), we rule out the possibility that the velocity transformation geometry we describe here could be accounted for by the mechanical properties of the plant, e.g. through pulleys.