A three-layered neural network model was used to explore the organization of the vestibulo-ocular reflex (VOR). The dynamic model was trained using recurrent back-propagation to produce compensatory, long duration eye muscle motoneuron outputs in response to short duration vestibular afferent head velocity inputs. The network learned to produce this response prolongation, known as velocity storage, by developing complex, lateral inhibitory interac(cid:173) tions among the interneurons. These had the low baseline, long time constant, rectified and skewed responses that are characteristic of real VOR inter(cid:173) neurons. The model suggests that all of these features are interrelated and result from lateral inhibition.
1 SIGNAL PROCESSING IN THE VOR The VOR stabilizes the visual image by producing eye rotations that are nearly equal and opposite to head rotations (Wilson and Melvill Jones 1979). The VOR utilizes head rotational velocity signals, which originate in the semicircular canal receptors of the inner ear, to control contractions of the extraocular muscles. The reflex is coor(cid:173) dinated by brainstem interneurons in the vestibular nuclei (VN), that relay signals from canal afferent sensory neurons to eye muscle motoneurons.
A Recurrent Neural Network Model of Velocity Storage
The VN intemeurons, however, do more than just relay signals. Among other func(cid:173) tions, the VN neurons process the canal afferent signals, stretching out their time con(cid:173) stants by about four times before transmitting this signal to the motoneurons. This time constant prolongation, which is one of the clearest examples of signal processing in motor neurophysiology, has been termed velocity storage (Raphan et al. 1979). The neural mechanisms underlying velocity storage, however, remain unidentified.
The VOR is bilaterally symmetric (Wilson and Melvill Jones 1979). The semicircular canals operate in push-pull pairs, and the extraocular muscles are arranged in agonist/antagonist pairs. The VN are also arranged bilaterally and interact via in(cid:173) hibitory commissural connections. The commissures are necessary for velocity storage, which is eliminated by cutting the commissures in monkeys (Blair and Gavin 1981).
When the overall V OR fails to compensate for head rotations, the visual image is not stabilized but moves across the retina at a velocity that is equal to the amount of VOR error. This 'retinal slip' signal is transmitted back to the VN, and is known to modify VOR operation (Wilson and Melvill Jones 1979). Thus the VOR can be modeled beautifully as a three-layered neural network, complete with recurrent connections and error signal back-propagation at the VN level. By modeling the VOR as a neural net(cid:173) work, insight can be gained into the global organization of this reflex.
Figure 1: Architecture of the Horizontal VOR Neural Network Model. lhc and rhc, left and right horizontal canal afferents; Ivn and rvn, left and right VN neurons; lr and mr, lateral and medial rectus motoneurons of the left eye. This and all subsequent figures are redrawn from Anastasio (1991), with permission.