Transforming retinal velocity into 3D motor coordinates for pursuit eye movements

Saccade planning requires a geometric transformation between the retinal stimulus position and the desired motor plan to acquire the target. This reference frame transformation problem has, however, 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 used quaternions to model the 3D eye-in-head geometry. Our model predicted that a visuomotor velocity transformation would require extra-retinal 3D eye-in-head position to convert the retinal velocity input into spatially accurate behavior and includes three different components; (1) the same retinal velocity results in different eye rotation axes depending on eyein-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. To test these predictions, subjects were required either to pursue a moving target viewed under different vertical (prediction 1) or oblique (prediction 2) eye positions, or viewed under different head roll angles generating VOR-induced eye torsion (prediction 3). We measured 3D eye and head orientation and analyzed the openloop gaze pursuit response, i.e. the first 100ms after pursuit onset. We then compared the observed pursuit response to the predictions of the model: if no transformation was performed, pursuit direction should best correlate with the retinal target movement direction; a complete 3D velocity transformation would be reflected in spatially accurate pursuit. We found that for all 3 predictions, the direction of pursuit initiation was spatially accurate and did not follow the retinal (no transformation) hypothesis. This suggests that the brain 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. Keywords— visuomotor transformation, reference frames, geometry, smooth pursuit, retinal slip.