Humans and most other animals rely strongly on vision to interact with their environment. Images of the surroundings are not acquired using camera-like smooth continuous panning movement. Rather, they are obtained from a mosaics of still-shots acquired through saccadic eye movements which brings the fovea on elements of particular interest. Because it is the region of the retina with the highest resolution, interesting peripheral objects are brought to the fovea for detailed scrutiny. This scrutiny can only be successfully undertaken if the eyes are stabilized relative to the surroundings. Indeed, visual acuity deteriorates precipitously with image motion of more than a few degrees per second ([Westheimer and McKee1975]). Head movements can therefore seriously affect visual acuity if they are not counterbalanced properly. The part of the nervous system that generates the eye movements required to compensate these head movements is the vestibulo-ocular reflex (VOR).
The VOR is a relatively simple reflex that stabilizes gaze during head movements. It uses head motion information from the inner ear to produce rapid eye rotations in order to sustain a high level of visual acuity during brisk head movements. Its response is fast and occurs within 15 ms of head movement onset. The fastest response is only requires through three synapses from the encoding of head rotation in the vestibular canals afferents in the inner ear to the extraocular muscles of the eyeball (fig. 1). The response amplitude is, in general, a complex function of sensorimotor 'context', which includes the location of the axis of rotation, linear and angular head velocity, vergence angle (i.e. target distance), and eye position (i.e. target eccentricity) (fig. 2).
Figure 1: Diagram of the main VOR
pathways. The three neurons arc reflex consists of vestibular
semicircular canal afferents, the vestibular nucleus and the ocular
motorneurons. The vestibular semicircular canal afferents carry the
angular velocity and acceleration signals of head motion. The
vestibular nucleus integrates information from the canals and other
brain areas. The ocular motorneurons innervate the extraocular muscles
of the eyeball. The three neurons arc reflex generates the earliest
response of the VOR with a delay of less than 15 ms. The cerebellum is
part of a side loop which contributes later in the VOR response. It
receives many different types of neural inputs carried by mossy fibers
to the granule cells. Three inputs coming from the vestibular
semicircular canals, the vestibular nucleus and the prepositus
hypoglossi are indicated. The prepositus hypoglossi is a nucleus that
is part of the eye movement neural integrator. The neural integrator
integrates the eye velocity signal to obtain an eye position
signal. The eye position signal is needed by the ocular motorneurons
to correctly rotate the eye. The axons of granule cells in the
cerebellum form the parallel fibers which innervate the complex
denditric tree of Purkinje cells. The Purkinje cells are the sole
output of the cerebellum which inhibit neurons in the vestibular
nucleus and the deep cerebellar nuclei (not shown). The inferior olive
neurons receive excitatory inputs from brain stem nuclei (not shown);
olivary neurons are electrotonically coupled through gap junctions and
their axons form the climbing fibers which strongly activate the
Purkinje cells. The inferior olive also receive inhibitory inputs from
the deep cerebellar nuclei (not shown) and other brain stem nuclei
like the prepositus hypoglossi.
Figure 2: Illustration of experimental VOR eye
responses to abrupt horizontal head rotation. The diagram on the left
illustrates the different conditions used in studying the horizontal
VOR: two different eye vergence to a near and far target are shown, as
well as two different locations of the axis of rotation behind the
eyes and in front of the eyes. The direction of head and eye rotation
is also indicated with curved arrows. (Note that a man is shown in the
illustration, yet the experiments were performed with rhesus monkeys
(Snyder and King, 1992)). The graphics on the right shows the eye
responses to an abrupt horizontal head rotation (bottom trace) under
different conditions. The first two eye velocity traces from the top
are for the axis of rotation located 12.5 cm behind the eye (posterior
axis), and the third trace is for the axis of rotation located 3.5 cm
in front of the eye (anterior axis). The first and third traces are
for a near target at 9 cm, and the second trace is obtained for a far
target at 220 cm. Hence, from the top: the first trace is for a near
target with the posterior axis, the second is for a far target with
the posterior axis, and the third trace is for a near target with the
anterior axis. With the posterior axis, the peak eye velocity response
for the near target is more than twice the response for the far
target. Moreover, for a near target, the response with the anterior
axis was almost one fourth of the response for the posterior axis.
The response amplitude, within a determined sensorimotor context, is also slowly adaptive ([Lisberger1988]). This adaptation serves to calibrate the reflex which operates as an open-loop control system for the first 50 to 80 ms. Performance is regulated so that counter-rotation of the eyes accurately compensates for head movements to keep images fixed on the retina. This slow adaptation is abolished with lesion of the cerebellum ([Robinson1976]), and accumulated evidence points to the cerebellar cortex and the vestibular nucleus in the brain stem as two putative sites of learning ([du Lac et al.1995]).
Because of its anatomical and physiological homogeneity, the cerebellum may be performing the same type of computations on its different inputs (e.g. [Bloedel1992]; [Schmahmann1996]). Therefore, a cerebellar model developed for some other system (e.g. arm motor control), should also provide insights, in principle, into the role of the cerebellum in the VOR. Conversely, by studying a relatively simple reflex, the interaction of the cerebellum in the VOR may be more readily understood than with a more complex system, and the knowledge gained should generalize to more complex behaviors.
Although the VOR is a relatively simple neural system, it has many advantages: 1) The input head movements and output eye movements of the VOR can be well characterized and described psychophysicallyl; 2) The function of the VOR is understood -- to stabilize images on the retina; 3) The relative ease of access of the nuclei involved in the VOR for electrode recordings, and ease of identification. 4) Adaptation of the VOR is a good example of motor learning in the central nervous system.
5) The VOR exhibits complex sensorimotor integration. For these reasons, the VOR is an ideal candidate for a behavior that can be understood on a wide range of levels from the molecular to the systems levels.
Many interesting questions can be addressed in studying the VOR. How do neurons encode information ? How do neurons combine their information ? What computations are performed by neurons ? In what coordinate system is the information represented ? How is plasticity mediated in the nervous system ? How are time delays and delayed feedback dealt with in the nervous system ? Can neural signals be temporally integrated in the nervous system and how ? Can predictive signals be constructed in the nervous system ? This dissertation addresses many of these questions.
The general goal of the dissertation is to lay down foundations upon which it is possible to interpret the encoding and firing of neurons in the VOR pathways, specifically in the cerebellum and the vestibular nucleus. In four chapters, theoretical models are developed from which simulated neural responses are obtained and compared to physiological and psychophysical data. In particular, computational models of the VOR suggest how sensorimotor signals are integrated in the central nervous system. Other chapters focus on the special role of the cerebellum in the computation of the VOR and in its adaptation.
Chapter 2 introduces the Adaptive VOR Gain Model. This model describes the VOR plasticity in the cerebellum and vestibular nucleus within a simplified VOR model. Chapters 3, 5 and 6 present a series of models which describe the VOR with increasing precision and details; they are, respectively, the Global VOR Model, the Simplified Motor Coordinate VOR Model and the Full Motor Coordinate VOR Model. These three chapters are based on a common model, the Kinematic VOR Model which describes the geometrically relationship between the head velocity and head acceleration inputs and the eye velocity and eye acceleration outputs. The Global VOR Model in chapter 3 proposes a mapping from the velocity equation of the Kinematic VOR Model to known VOR anatomy to suggest computations and cell responses at different nuclei in the VOR pathway. Chapter 4 introduces the Predictive Cerebellar Model which uses the Global VOR Model of chapter 3 to describe the predictive modulation of the VOR gain with vergence as reported by Snyder and King (Snyder92a). The Simplified Motor Coordinate VOR Model of chapter 5 uses the velocity and acceleration equations of the Kinematic VOR Model to construct two models with only a few parameters to replicate, with increasing precision, the psychophysical data on the VOR as recorded by Snyder and King (1992). The Full Motor Coordinate Model of chapter 6 implements the model of chapter 5 in the full coordinate systems of the vestibular canals and extraocular muscles, demonstrates the complexity of VOR calculations, and gives examples of neural responses expected from the model.