Neural Control of Three-Dimensional Gaze Shifts

J. Douglas Crawford¹ and Eliana M. Klier²

1. York Centre for Vision Research, Canadian Action and Perception Network, Neuroscience Graduate Diploma Program, Depts. of Psychology, Biology and Kinesiology & Health Sciences, York University, Toronto, Ontario M3J 1P3

2. Dept. of Anatomy and Neurobiology, Washington University School of Medicine, St. Louis, Missouri 63108

Mailing Address:

Dr. Doug Crawford (jdc@yorku.ca)

York Centre for Vision Research,

Room 1012B, Computer Science and Engineering Bldg.,

York University,

4700 Keele Street, Toronto, Ontario, Canada, M3J 1P3

Phone: (416) 736-2100 x88621

Fax: (416) 736-5857

KEYWORDS: eye, head, torsion, brainstem, cortex

ACKNOWLEDGMENTS: Supported by the Canadian Institutes of Health Research and the Canada Research Chair Program

Abstract

In laboratory conditions, with the head restrained and held upright, eye-in-head orientation vectors are constrained to a tilted two-dimensional (2-D) range called Listing’s plane. However, in most real-world conditions gaze control utilizes a 3-D range. For example, when the head is allowed to move naturally, the accompanying saccades and VOR movements include coordinated torsional components; out of, and then back into Listing’s plane. The head itself rotates more like a set of Fick Gimbals, resulting in a non-planar range of orientation vectors. To control this complex behavior, the brainstem reticular formation appears to have struck upon an elegant solution: it encodes the 3-D components of posture and movement in coordinates that align with the Listing and Fick behavioral constraints, such that its control signals collapse to 2-D (zero torsion) when these constraints are upheld, but it retains the capacity for torsional control whenever required. In contrast, the superior colliculus and cortex appear to only encode 2-D gaze direction. Surprisingly, after many years of research on this topic, we still know very little - other than a few clues - about the neural mechanisms that transform high-level 2-D gaze direction commands into the 3-D control signals for eye and head orientation.

Listing’s and Donders’ laws

Most oculomotor studies are primarily concerned with the control of 2-D gaze direction, i.e., how the brain points the visual axis towards objects of interest. However there are two important areas where one needs to consider the 3-D orientation of the eye. The first involves any kind of visual stimulus that activates the retina beyond the fovea, because here the spatial pattern of retinal stimulation depends both on the configuration of the stimulus in space and the torsional orientation of the eyes around the visual axis. The second (which will be the focus of this review) relates to gaze control: the eye is equipped with the musculature to rotate in 3-D. As we shall see, the eyes can and do rotate about nearly any combination of components about the vertical (left / right), horizontal (up/down) and torsional (clockwise / counterclockwise) axes (Note that directions are defined here from the subject’s perspective). As we shall see, torsion is not allowed to vary randomly: the brain usually sets a certain amount of torsion for a given 2-D gaze direction, and sometimes it actively generates a muscular contraction to rapidly change the direction and amount of ocular torsion.

In the 19^th century Donders proposed that for any one gaze direction, the eye assumes a unique orientation (one torsional value), no matter how it got there (Donders 1848). The precise value of this torsion was then described in Listing’s law. The origins of Listing’s law are somewhat obscure. Listing was a German mathematician who somehow intuited that the eye assumes only those orientations that can be reached from some central reference position by rotations about axes within a single plane. For one special reference position, the line of gaze is orthogonal to the associate plane of axes; this is called primary position, and the associated plane is called Listing’s plane. The best coordinate system to describe Listing’s law (Listing’s coordinates) can be defined by expressing eye orientations in terms of vectors aligned with the axes of rotation from primary position, scaling these vectors to the angle of rotation, and defining torsion as rotation about the head-fixed axis aligned with the primary gaze direction. Once this coordinate system is defined, Listing’s law is simple: it just says that torsion equals zero (Westheimer 1957). Examples of such data, in Listing’s coordinates, are provided in the chapter by Angelaki and are also shown here in Figs. 3C and 6B.

The description of Listing’s law in terms of axes of rotation is more complicated. Intuitively, one would think that the eye would rotate about an axis in Listing’s plane, but this is not what happens. In fact, if this is done, it causes a violation of Listing’s law (Crawford and Vilis 1991). As illustrated in the companion chapter by Angelaki, in order to keep eye position in Listing’s plane, the axis of eye rotation must tilt out of Listing’s plane in a position-dependent manner. This is a requirement of the laws of rotational kinematics (Tweed and Vilis 1986). (Many people find that this makes intuitive sense only after a couple of years of intense study; otherwise it is best left for mathematicians.)

Listing’s law was first described, and confirmed, by Helmholtz, with the clever use of visual after-images (von Helmholtz 1867). Modern recording techniques are more direct, and usually involve the placement of two search coils in the eye within a set of orthogonal magnetic fields. So far these experiments have not revealed any behavioral differences between the human and monkey, so we will site literature from both species together. These experiments have shown that Listing’s law is obeyed when the head is held upright and stationary during saccades and fixations (Ferman et al. 1987a, 1987b; Tweed and Vilis 1990; Straumann et al. 1990; Crawford and Vilis 1991). In monkeys Listing’s plane generally tilts back in the head whereas in humans its orientation seems to vary highly from subject to subject. Listing’s law is also obeyed during smooth pursuit eye movements (Haslwanter et al. 1991; Tweed et al. 1992) and gaze fixation during purely translational head movements (Angelaki 2000; Angekaki et al. 2003). It is obeyed in modified form during vergence movements (where the Listing’s planes of the two eyes tilt outward; Mok et al. 1992; Van Rijn et al. 1993) and when the head is stationary but not upright (resulting in either shifts or tilts; Crawford and Vilis 1991; Haslwanter et al. 1992). However, when the head rotates, vestibular and / or visual inputs can stabilize the retinal image of distant targets by rotating the eye about the same axis, but opposite direction, as the head, thus violating Listing’s law (Crawford and Vilis 1991; Fetter et al. 1992; Misslisch and Hess 2000). The common theme of these rules is that whenever there is a degrees of freedom problem (gaze direction is specified but not torsion) Listing’s law or some variant is used, but when specific torsional movements are required Listing’s law is violated (Crawford et al. 2003).

There has been a surprisingly long-lived, and often obscure controversy about whether Listing’s law is implemented mechanically or neurally (Tweed and Vilis 1987; Tweed and Vilis 1990; Crawford and Vilis 1991; Schnabolk and Raphan 1994; Crawford and Guitton 1997; Quaia and Optican 1998; Raphan 1998; Misslisch H, Tweed D. 2001; Angelaki 2003; Angelaki and Hess 2004). Rather than review this entire controversy we will simply state our own view, which is that in restrospect this argument was largely based on the conflation of two different computational issues. In order to produce Listing’s law, the oculomotor system must do two things: it must specify the desired 3-D orientation of the eye, and it then chose the correct axis of eye rotation for a given initial position. In the first kinematically correct model of the 3-D saccade generator, these two computations were done ‘neurally’ within one ‘Listing’s law box’. However, as described by Angelaki elsewhere in this volume, there is good evidence to suggest that the position-dependent axis tilts required to maintain eye position in Listing’s plane are implemented mechanically by the tissues surrounding the eye (Demer et al. 1995; 2002; Ghasia and Angelaki 2005; Klier et al. 2006). This simplifies some of the control issues associated with generating eye movements that stay within Listing’s plane. However, these mechanical position-dependencies cannot constrain the eye to Listing’s plane (if they did, the system would not be able to violate Listing’s law, which is often does).

More recent models of the 3-D saccade generator have separated the neural process of selecting the desired orientation of the eye (and then choosing the movement vector that will get it there) from the mechanical process that determines the required axis tilts (Crawford and Guitton 1997; Tweed 1997; Glasauer et al. 2001a, 2001b). These models demonstrate that an eye ‘plant’ optimized for Listing’s law will still only produce Listing’s law if it is given the right neural signals, and will violate Listing’s law if given different signals (Smith and Crawford 1998). Thus, Listing’s law is both neural and mechanical: it is the sequential product of neuromechanical control system.

Perhaps a second factor that has skewed our view of Listing’s law is that 90% of the studies done on 3-D ocular kinematics are done with the head artificially restrained. When the head is allowed to move naturally, a different picture emerges.

What happens to these rules when the head is not restrained?

Listing’s law is only upheld continuously when the head is restrained. When the head is allowed to move naturally the gaze control system shows quite different properties (again, the story is quite similar for both the human and the monkey, so we will refer to both literatures equally). Despite the additional complexity of eye-head coordination, the system still appears to follow certain ‘lawful’ kinematic relationships (see the chapter by Corneil in this volume), and 3-D control is no exception. If one understands the oculomotor rules described in the previous section, then one can understand the rules for eye-head coordination 1) by understanding how these rules interact, and 2) by understanding the analogous rules that apply to head movement.

Rule 1: as long as the subject holds the eye and head stationary in space, the eye in-head range (Fig. 1 C) is statistically indistinguishable from Listing’s plane (Straumann et al. 1991; Glenn and Vilis 1992; Radeau et al. 1994; Crawford et al. 1999). However, during gaze shifts torsional control becomes more complicated. It is well known that during large rapid gaze shifts, typically a visually-guided saccade occurs while the head is just starting to build up momentum in the same general direction. Once the eye reaches its target, the vestibular-ocular reflex turns on, causing the eye to roll back in the head so that gaze stays on target while the head completes its trajectory (Guitton 1992; see the companion chapter by Corneil for a more detailed review). The conundrum here for 3-D control is that, as stated above, saccades obey Listing’s law and the VOR does not. Left unchecked, the VOR would generally drive the eye quite far out of Listing’s plane. Apparently to avoid this, during head-free gaze shifts saccades take on anticipatory torsional components that are opposite and approximately equal to the oncoming torsional component of the VOR (Crawford and Vilis 1991; Tweed et al. 1997; Crawford et al. 1999). This results in the eye ending up back in Listing’s plane when the whole sequence is done (Fig. 1 D). Tweed and colleagues exploited this property to induced the ‘world record’ for eye torsion in healthy subjects, inducing people to generate saccades with torsional compoents up to 17º.Thus, continuous adherence to Listing’s law is an artifact of immobilizing the head.

In terms of the head movement itself, during gaze shifts the head follows its own version of Donders’ law, albeit less precisely than the eye and in a different form (Glenn and Vilis 1992; Radeau et al. 1994; Crawford et al. 1999). Instead of following Listing’s law, the head acts as if it rotates horizontally about a body-fixed vertical axis but vertically about a head-fixed horizontal axis, like a set of Fick Gimbals (Fig. 2). Torsion in this new coordinate system is again kept at a minimum in Fick coordinates but when these data are plotted in Listing’s coordinates this results in a non-planar range of orientation vectors that is consistently twisted at the oblique corners (Fig. 1B).

Like eye movements, head torsion is not always held at zero, even in Fick coordinates: during oblique gaze shifts the head take the shortest path from one corner of the range to the other in position space rather than curving along its Donders’ range (Crawford et al. 1999). Moreover, the Fick range is modified by gravity (shifting and tilting for body roll and pitch, respectively) in a fashion similar to Listing’s law (Misslisch et al. 1994), can be modified to Listing’s plane when the head alone is used to point gaze or to a shortest path strategy (resulting in a break down of Donders’ law) when head pointing is dissociated from gaze (Ceylan et al. 2000). Thus, much like Donders’ law for the eye, Donders’ law for the head is associated with its own intrinsic coordinate system, where zero torsion can be selected, or not, depending on task requirements.

The final range to consider is that of eye orientation in space, which one can think of as a 3-D version of gaze. Since Listing’s plane is fixed in the head, and since eye position contributes relatively little to head-free gaze fixations over a wide range, the eye and head constraints interact to produce a range of eye-in-space (gaze) orientations that also resemble the range produced by Fick Gimbals (Fig. 1 A). Moreover, since the control of head torsion is much sloppier than control of eye torsion (in the order of ±5º compared to ±º1), the resulting torsional range of the eye-in-space is even sloppier (Glenn and Vilis 1992; Crawford et al. 1999).

Premotor control of 3-D eye velocity and orientation

Figure 3A shows the classic Robinsonian model for oculomotor control (Robinson 1981). In this highly influential model, eye movements are encoded by a velocity signal, that is then integrated to provide a position signal, and the two are then summed at the level of motoneurons to rotate the eye against resistive viscous forces and hold it against elastic forces in the surrounding tissues. It turns out that this model does not translate well into 3-D if the movement signal encodes angular velocity (i.e., degrees / second about the physical axis of rotation) because 3-D orientation is not the derivative of 3-D velocity (Tweed and Vilis 1987). For example, during saccades angular velocity has torsional components (for the position-dependent axis tilts described above) that would be integrated to produce inappropriate torsional position signals. However, if the movement signal encodes derivatives - small changes in eye orientation divided by time (Crawford 1994; Crawford and Guitton 1997; Quaia and Optican 1998) - and feeds this to motoneurons for a plant that mechanically implements the torsional axis tilts (Demer et al. 1995; 2002), then this scheme works just fine for saccades. Angelaki and colleagues have verified this scheme by correlating motoneuron firing rate against the torsional components of eye velocity (Ghasia and Angelaki 2005), and analyzing the changes in eye position produced by motoneuron stimulation (Klier et al. 2006). This works nicely for saccades, but complicates the VOR, which does not receive eye orientation derivatives from the semicircular canals and does not like position-dependent axis tilts (these would destabilize vision). However, it is a fairly simple matter for the VOR to undo these tilts with the right interaction between eye position and velocity signals before integration (Smith and Crawford 1998).

So where then do the premotor signals arise for 3-D saccades and eye position? At this time, human brain imaging techniques have too many spatiotemporal limitations to address this question, so nearly everything we know about this system comes from physiological studies with awake, behaving animals. The horizontal velocity components of saccades are encoded by burst neurons in the paramedian pontine reticular formation (PPRF) (e.g., Luschei and Fuchs 1972) and the corresponding neural integrator for horizontal eye position is located in the nucleus prepositus hypoglossi (NPH) (e.g., Cannon and Robinson 1987). The corresponding circuits for vertical and torsional saccades are located in the midbrain (Fig. 6C). The rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF) possess burst neurons whose activity correlates to the vertical / torsional components of rapid eye movements (Buttner et al. 1977; King et al. 1979; Hepp et al. 1988; Crawford and Vilis 1992). The interstitial nucleus of Cajal (INC) appears to be the neural integration for vertical and torsional components (Fukushima 1987; Crawford et al. 1991; Helmchen et al. 1998). It has the right anatomy: the riMLF projects to the INC, and both project to the motoneurons for eye muscles that control vertical / torsional rotation. Moreover, we know of this arrangement because 1) the INC has activity related to vertical / torsional eye position, 2) pharmacological inactivation obliterates the ability to hold vertical / torsional eye positions (Fig. 3C), and 3) electrical stimulation of the INC produces vertical / torsional eye movements that hold their final position, as if one had ‘charged up’ a neural integrator (Fig. 3B).

The riMLF and INC appear to be similarly organized into pools of neurons with specific directional control very similar to those of the eye muscles and semicircular canals (see chapter?). Units on both sides of midline can be divided into randomly intermingled populations with upward or downward velocity or position tuning. However these same units are also tuned for clockwise components on the left side of midline and counterclockwise components on the right side (Crawford et al. 1991; Crawford and Vilis 1992). Taken together with the horizontal populations in the PPRF / NPH, this creates a set of neuron pools like those illustrated in Fig. 4. This configuration is fully 3-D but easily collapses to 2-D: whenever the oculomotor system requires a torsional component (as in the saccades that occur with head-free gaze shifts) it need only create an imbalance between activity in the left and right riMLF (and thus INC) so that clockwise and counterclockwise components do not balance to zero. But as long as these two sides are balanced (as in saccades with the head fixed) torsion will cancel and the residual horizontal and vertical components of activation will determine saccade direction (Crawford et al. 1991; Crawford and Vilis 1992).

This is all very well, but there is one hitch that is all too easy to take for granted. It depends on the non-trivial assumption that the neuron pools in Fig. 4 are organized in a coordinate system that aligns with Listing’s plane. It has been shown many times that the orientation of Listing’s plane in the head varies considerably from one subject to the next. If, for example, the PPRF encoded rotations about an earth-vertical axis with the head upright, in most subjects PPRF activation would drive eye position out of Listing’s plane. However, there is evidence that these coordinates do in fact align. First, inactivation of the riMLF leaves axes of rotation for horizontal saccades (presumably generated by the PPRF) that align with Listing’s plane, and unilateral co-activation of the up and down neuron populations of the riMLF produce rotations about an axis orthogonal to Listing’s plane (Crawford and Vilis 1992). Third, torsional drift during unilateral INC is perfectly orthogonal to Listing’s plane (Fig. 3C) and settles to a range of positions parallel to Listing’s plane (Crawford 1994). Each of these observations is only possible with the coordinate system we want: Listing’s coordinates.

To sum up, a series of observations simplify the control of 3-D saccades. 1) eye muscles encode derivatives, not angular velocity. 2) torsional control is arranged symmetrically across the brainstem. 3) the brainstem coordinates for saccades align with Listing’s plane. With this, and only this arrangement, saccades in Listing’s plane will result from the planar coding of 2-D movement vectors. But this still requires a very delicate balance of neural activation - no accident or trivial default - and torsional saccade components must be programmed very precisely when the head moves.

Premotor control of head orientation

As with the eye, there may be mechanical advantages for using a Fick-like coordinate system for head control. For gaze shifts to distant targets, one is mainly concerned with head orientation, but the head does not rotate in-place like the eye. Instead it rotates (and translates) much like an inverted pendulum, except that base is a flexible multi-jointed column (the cervical spine). The lower cervical vertebrae act somewhat like the vertical axis (for horizontal rotation), whereas vertical rotation (about the horizontal axis) occurs mainly about the higher cervical vertebrae (Vidal et al. 1986; Graf et al. 1995), as in a nested set of Fick axes. Nevertheless, it is once again clear that these mechanical factors do not constrain the head to a zero-torsion range. To convince oneself of this, one need only voluntarily roll the head torsionally from side to side. This means that, as in the oculomotor system, the neural control system for the head must be optimally matched to the mechanical stages of the control system.

Little is known about the neural control of 3-D head orientation (head movement studies are essentially impossible with current brain imaging techniques). However, there a few clues from animal models that, at least so far as gaze control is concerned, the oculomotor and head motor systems share both circuitry and control principles. First of all, electrical stimulation of higher-level gaze structures in the cortex, superior colliculus, and cerebellum evokes gaze shifts that involve movements of both the eyes and head (this topic will be taken up further in the next section). Moreover, this circuitry is shared down to the level of the brainstem. For example, in animals with unilateral stimulation of most PPRF sites produces ramp-like ipsilateral rotations of both the eyes and head (Gandhi et al. 2008). This implicates the PPRF in the control of both eye and head motion.

Similar observations have been made for the INC. The INC projects to spinal cord neurons involved in neck control via the intersitiospinal tract (Fukushima 1987; Fukushima et al. 1980, 1994). Unilateral stimulation of the INC (Fig. 5B) produces vertical / torsional head rotations following very similar directions and patterns similar to those seen in the eye (clockwise for left INC stimulation, counterclockwise for right INC stimulation, and final positions that are held until corrected) (Klier et al. 2002; 2007). As with the eye, unilateral inactivation of the INC produces a transient nystagmus-like pattern of torsional head drift (Fig. 5A) with corrective ‘quick phases’ that eventually dissipate, leaving the head tilted in a torticollis-like posture (Klier et al. 2002; Farshadmanesh et al. 2007). These observations have led us to suggest that the INC is the 3-D integrator not only for the eye, but also for head posture. However, head control is much more complex than eye control - with vastly greater inertia, an inverted pendulum structure, over-redundant musculature, multiple joints, and a nest of vestibular and proprioceptive reflex pathways (Perlmutter et al. 1999; Fukushima et al. 1994; Vidal et al. 1995) - one might better think of this ‘head integrator’ as determining a set-point for reflex control pathways.

We don’t know enough about these head premotor circuits to say if they are organized into the same neuron pools as the their corresponding oculomotor pools (or to what degree these eye and head pools share member units) but what we know so far is consistent with this notion. Moreover, there is also evidence that the head controller utilizes a coordinate system aligned with the head’s Donders constraint. Following INC inactivation, horizontal head positions continue to hold along the vertical axis of the Fick coordinate (Klier et al. 2002; Farshadmanesh et al. 2007), and during unilateral INC stimulation the head rotates about head-fixed horizontal axes – like the vertical axis for head rotation in Fick coordinates (Fig. 5B) (Klier et al. 2007). Thus, it appears likely that 1) both the eye and head are controlled by neural populations organized into coordinates like those shown in Fig. 4, and that 2) there is a continuous synergy between the neural, mechanical, and behavioral coordinates for head control, which would have the same advantages as described above for the eye.

Clinical significance

One of the many things that healthy people take for granted is that (other than some random scatter) Donders’ laws of the eye and head are normally obeyed during gaze fixations. However, this is not true in many clinical populations, for example those that experience ocular tilt (a tonic torsional offset of the eyes; Westheimer et al. 1975; Halmagyi et al. 1991; Brandt 1992; Ohashi et al. 1998), torsional nystagmus (torsional drift with intermittent corrective eye movements; Halmagyi and Hoyt 1991; Straumann et al. 2000; Glasauer et al. 2001), and spasmodic torticollis (Patterson and Little 1943; Medendorp et al. 1999; Agrawal et al. 2009). The latter (also known as cervical dystonia) is the most common type of dystonia, and involves abnormal offset in head posture that very often have a significant torsional component. Disorders of the motoneurons and eye muscles, including strabismus, are also generally associated with abnormal torsional positions (Sharpe et al. 2008). Each of these symptoms can be debilitating; physically, functionally, emotionally, and socially.

Damage or inappropriate activation of the reticular formation can explain some of these symptoms, at least some of the time. This basic science review does not have space for a comprehensive review of the clinical literature, but we can highlight one particular example that ties directly in the previous physiology. Acute unilateral damage to the INC produces an array of clinical symptoms include vertical gaze-paretic nystamus (an inability to hold eccentric eye positions), torsional nystagmus, and a combination of ocular tilt and torticollis away from the damaged side). Each of these symptoms has been associated with midbrain damage in the human.

It must be noted, when comparing physiology to pathology, that most laboratory studies measure early, acute, rapidly evolving affects that the clinician would rarely see. By the time the patient reaches a specialist they have likely settled to a more chronic state, perhaps even involving compensatory mechanisms. Moreover, nature is unlikely to be as pin-point accurate in her neurological insults as experimentalists are, so one needs to interpret patients in light of the overall function of the damaged area. Finally, behaviors that resemble ocular tilt and torticollis can also occur from unilateral INC stimulation (here on the ipsilateral side to the tilt). This means that in pathological states, structures such as these may be involved, but not the ultimate cause.

What is coded at higher levels of the gaze control system?

In the 1990s it was not known at what point in the gaze control system signals became 3-D (i.e., included a specified torsional command). Clearly this is the case in structures such as the INC and riMLF, but how far upstream does this go? As mentioned above, the first kinematically correct model of the 3-D saccade generator proposed that points on the superior colliculus (SC) encode specific 3-D saccade axes (Tweed and Vilis 1990), including the torsional axis components required to keep eye position in Listing’s plane. However, Van Opstal and colleagues showed, with a combination of unit recording and microstimulation, that the SC does not encode 3-D axes (Van Opstal et al. 1991; Hepp et al. 1993). Figure 6B replicates their result that stimulation of the SC (in the head-fixed monkey) evokes saccades with zero torsional components (and thus variable axes) independent of initial eye position. The latter results seems less surprising two decades later, now that we know that the position-dependent torsional axis tilts are still not implemented at the level of motoneurons (Klier et al. 2006). However, we also know now that in natural head-free conditions saccades are often accompanied by variable torsional components. At what point in the system are these added on? Does the SC produce a vector command with zero torsion, parallel to some other variable torsional controller, or does the SC simply code a 2-D gaze target, which is then converted somehow into a 3-D command downstream?

We tested this in a series of experiments in the head-free monkey, in combination with electrical stimulation of the SC, and several cortical gaze control structures, including the supplementary eye fields (SEF) frontal eye fields (FEF) and lateral intraparietal cortex (LIP). Stimulation of the SC, SEF, and FEF is known to evoke gaze shifts that involve both eye and head movements. The simple logic behind these experiments was that if the site encodes a specific amount of torsion (whether zero or non-zero) stimulation should consistently evoke gaze shifts with that same fixed torsional eye-in-head component. In general, this would produce violations of Donders’ and Listing’s law (even if the saccades had zero torsion). In contrast, if the site encodes 2-D gaze and 3-D control is elaborated downstream, then stimulation should evoke gaze shifts with normally coordinated torsional components in their saccades.

Figure 6 shows the typical result of SC stimulation. The same site that produced zero-torsion saccades with the head fixed produced saccades with torsional components with the head free, opposed to the oncoming VOR components just as in normal head-free gaze shifts (Klier et al. 2003). The final positions of the eye-in-head, eye-in-space, and head-in-space obeyed Listing’s and Donders’ laws just as well as in normal behavior (Fig. 6 A). Moreover, the eye-in-head showed the same pattern of torsional coordination, with saccades showing anticipatory torsion (interestingly, these stop when the head is fixed). We found the same results in the SEF (Martinez-Trujillo et al. 2003) and FEF (Ascencio-Monteon et al. 2005). The exception so far has been LIP (Constantin et al. 2009): this structure produces saccades with the correct torsion for an expected head-free gaze shift, but then no head movement (and thus no VOR) occurs. This might simply be because LIP is so far upstream from the premotor centres for eye and head control that stimulation does not properly access the full motor circuitry for a natural gaze shift. But in general, stimulation of high-level gaze control structures suggests that they are only concerned with pointing gaze in the right direction: 3-D control is elaborated at some point further downstream (Fig. 6D).

The 2-D to 3-D transformation

The most interesting question in 3-D gaze control remains to be solved: how are the higher-level 2-D signals for gaze decomposed and elaborated into 3-D commands for eye and head rotation? This gives rise to several sub-questions: how is zero torsion in Donders’ coordinates selected? How is this position range modified in behaviors that follow a different variation of Donders’ law? How does the brain correct torsional errors and select the right torsional saccade components to during head-free gaze shifts?

To repeat, we are not looking for the mechanism that causes saccade axes to tilt as a function of position: as explained above, there is now good agreement that this is done by orbital mechanics (Demer et al. 1995, 2002; Crawford and Guitton 1997; Tweed 1997; Quaia and Optican 1998; Raphan 1998; Smith and Crawford 1998; Ghasia and Angelaki 1995; Klier et al. 2006). Similarly, the neck may be mechanically suited for the axes used in the Fick Strategy (Vidal et al. 1985; Graf et al. 1995).

What we are looking for is the mechanism that actively chooses which Donders’ surface to use, when to modify it, when to correct deviations from this range. One cannot dismiss the theoretical possibility that eye muscle position-dependencies might be neurally modified in ways that could modify Listing’s plane (Demer et al. 2000), but this would require more, not less, neural complexity, and does not explain active torsional control. We first need to understand the main mechanism that sets torsional signals in the brainstem. It’s unlikely that this exists in a single, separate ‘Listing’s law box’. For example, in neural networks trained to perform these transformations the solution is distributed as torsional modulations in units that are also involved in other functions (Smith and Crawford 2005; Keith et al. 2007). Therefore, this may not be any easy process to pin down. However, there are several clues.

One way to examine this is to start at both ends of the system and see where 2-D meets 3-D. Searching from the highest level downward: if the cortex and superior colliculus normally just encode 2-D gaze direction (Van Opstal et al. 1991; Klier et al. 2003), then the 2-D to 3-D transformation for both the eyes and head must occur downstream (closer to the muscles). Searching from the lowest level up: since eye and head muscles, motoneurons, the neural integrator (INC and NHP), and premotor burst neurons (riMLF and PPRF) can rotate the eye about any axis and then hold it there (Hepp et al. 1988; Crawford and Vilis 1992), then the 2-D to 3-D transformation must occur at a functional level between the superior colliculus and premotor burst neurons (Fig. 6C). Finally, since premotor burst neuron (and neural integrator) coordinates align with Donders’ coordinates, with clockwise and counterclockwise control symmetric across midline (Crawford and Vilis 1992; Crawford 1994), the 2-D to 3-D transformation simplifies to balancing torsion to zero during head-fixed saccades and smooth pursuit.

These factors suggest that there may be a default mapping from 2-D superior colliculus outputs onto the correct balance of burst neuron activity to encode zero torsion displacements in Listing’s plane (and the Fick strategy for the head). However, this does not explain how these strategies are modified, and how the system maintains these ranges in the face of fairly common but brief violations. To do this, the system requires a modifyable set-point (technically, a set-surface) with a comparator (Crawford and Guitton 1997; Ceylan et al. 2000; Glasauer et al. 2001a, 2001b). In support of this, when the torsional neural integrator is inactivated and the head is tilted, saccades keep aiming the eye toward the torsionally shifted Listing’s plane even though the integrator deficit will not allow it to hold there (Crawford et al. 2003). This demonstrates that 1) the saccade generator actively maintains the desired set point for torsion, and 2) this set point is modulated by vestibular inputs. Furthermore, small errors in torsion (whether naturally or experimentally induced) are usually corrected by forthcoming saccades (Van Opstal et al. 1995; Lee et al. 2000) and these corrective components correlated to neural activity in the nucleus reticularis tegmenti pontis (NRTP) (Van Opstal et al. 1995). Since this is a cerebellar input nucleus, this implicates the cerebellum in the active control of torsion through saccades. Consistent with this, patients with cerebellar damage show offsets and widening of Listing’s planes (Straumann et al. 2000; Baier B, Dieterich M. 2009). Finally, another potential contributer is the central mesencephalic reticular formation (cMRF) nucleus located just lateral to the INC, which has functions related to saccades and eye-head coordination (Pathmanathan et al. 2006; Ugolini 2006), and has also been implicated in torticollis (Waitzman et al. 2000), but its role in 3-D eye control is not known. We will not understand the complete role of these structures until they are studied in 3-D / head free preparations - where torsional control of the eye is most obvious and most complex.

Finally, although this review has focused on the control of 3-D gaze, as stated above, the 3-D orientations of the eyes and head have extensive implications for higher level vision and early aspects of gaze control. Because of the high variability of eye torsion in space, and its effects on visual receptive fields (Keith et al. 2009), the visual system must account both for systematic and variable torsion. For example, the brain must monitor 3-D eye and head orientation to solve the binocular correspondence problem (Blohm et al. 2008), and to convert eye-centered visual information into useful commands for motor effectors (such as the eyes, head, and limb) organized in head or body coordinates (Klier et al. 2001). Such reference frame transformations can be done trivially - without comparisons with position - in purely translational systems, but the eyes and head primarily rotate. Thus, even when cortical mechanisms are primarily concerned with aiming 2-D gaze direction (or depth), they cannot operate independently from internal knowledge of 3-D eye & head orientation.

Conclusions

3-D gaze control is complex because it is not just the control of torsion: it is the control of horizontal, vertical and torsional components of rotation and all their interactions. Both theory and physiology show that torsion cannot be neatly separated from the other components. This 3-D view forces us to give up comfortable intuitions grounded in translational mathematics and leap into the odd, counter-intuitive world of rotational kinematics. In this review, we have tried to illustrate that some aspects of 3-D control are mechanical and some are neural, but overall it must be understood as a neuromechanical system. Moreover, 3-D gaze control is inseparable from the topics of eye-head coordination, and visual-vestibular integration. These factors combine to dictate that one cannot understand 3-D gaze control without understanding the complete neurophysiology of gaze control, and conversely, one cannot understand any component of this system without understanding how it fits within the 3-D entirety.

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Fig. 1. Donders’ laws for eye, head, and eye-in-space during head-free gaze fixations in the monkey (human data look the same). In each case torsional orientation is restricted compared to vertical and horizontal orientation. Panels A-C (left sides) plot tips of 3-D eye position vectors (horizontal component as a function of torsional component) in an orthogonal right-hand coordinate system. The right sides show 2-D surfaces fit to these ranges. In the 3-D gaze literature this is known as a ‘side view’, because it views axes of rotation (relative to the zero vector reference position) are viewed from the side. DL, UL, UR, and DR represent Down-Left, Up-Left, Up-Right, and Down-Right orientations. A: The range of eye orientation in space consistently follows a twisted ‘Fick’ range. B: The range of head orientation in space also follows a Fick range. C: The range of eye orientation relative to the head shows variable twists that is not significantly different from the (Listing’s) planar range seen in head-fixed saccades. D: Torsional eye-in-head position plotted during one multi-step gaze shift including a large horizontal head movement (not shown). Without the anticipatory torsional components in saccades (quick phases) the eye would be driven far from Listing’s plane. Adapted from Crawford et al. 1999.

Fig. 2. Schematic axes of rotation, and their dependence on orientation, in a Fick system, plotted in orthogonal Cartesian coordinates. Angular velocity (broken lines) is a vector parallel to the axis of rotation, scaled by the speed of rotation. The angular velocity of the eye and head generally follows the loops, starting at zero velocity, growing to maximum velocity, and then returning to zero. In each panel, five head pointing directions are shown (solid lines), each color coded to two velocity loops in opposite directions (dashed vs. dotted lines). A: Velocity loops for vertical rotations at five horizontal positions, viewed from above. B: Velocity loops for horizontal rotations at five vertical positions, viewed from the side. Real head data follow the same pattern, but are never as symmetric. Adapted from Klier et al. 2007.

Fig. 3. Evidence of a 3-D neural integrator for eye orientation, organized in Listing’s coordinates, in the interstitial nucleus of Cajal (INC). A: David A. Robinson’s seminal 1-D model of the saccade generator. Reticular formation burst neurons (BN) have a saturating estimate of desired eye velocity (V*) which is sent to the neural integrator (∫), which converts this into a desired eye position signal (E*). V* and E* are then scaled and summed at the motoneurons (MN) to provide the required signal to control the PLANT (eye and muscles). B: Torsional (T), vertical (V) and horizontal (H) components of eye position plotted against time during INC stimulation (S). The eye rotates primarily counterclockwise (CCW) or clockwise (CW) out of Listing’s plane during left and right INC stimulation respectively. Final eye position is held until the next saccade, which returns it to Listing’s plane. Similar data published in Crawford et al. 1991. C: Left side: eye orientation vectors during head-fixed fixations, plotted in Listing’s coordinates and viewed from the side. Right panel: following injection of muscimol into the the left INC, the eye drifts (gray traces) clockwise, orthogonal to Listing’s plane (LP) until the start of the next saccade (○). Right INC injection produces the opposite pattern. Similar data plotted in Crawford 1994.

Fig. 4. Schema of populations of neurons for eye and head orientation control in the nucleus preopositus hypoglossi (NPH) and interstitial nucleus of Cajal (INC). Six neural populations are shown, divided across the brainstem midline (vertical bar) with arrows indicating their directional control in a fashion very similar to the semicircular canals and eye muscles (where vertical and torsional components are combined). The filled color blocks show how these populations would be activated during clockwise (upper right panel), upward (lower left panel), and leftward (lower right panel) orientations. This schema only works if these population coordinate align with the intrinsic coordinates of behavior, i.e., Listing’s plane for the eye and Fick coordinates for the head. A similar organization is seen in the burst neurons that provide the velocity signal for the eye. Adapted from Crawford and Vilis 1992.

Fig. 5. Evidence of a neural integrator for head orientation in the INC, organized in Fick coordinates. A: Head (dark line) and gaze / eye-in-space (gray line) torsion plotted against time following muscimol injection. Shortly after injection (15 minutes here) both drift away from the regular upright position, while rapid movements attempt to correct this. Later (40 minutes here) the head settles in a torsionally shifted position,i.e., corrective movements cease. Adapted from Klier et al. 2002. B: During unilateral INC stimulation with the head free, the head rotates around vertical-torsional axes (clockwise for left INC; counterclockwise for right INC) that stay fixed relative to horizontal head orientation, as in a Fick gimbal. Conventions similar to Fig. 2A, but here real data are shown. Adapted from Klier et al. 2007.

Fig. 6. Stimulation of the superior colliculus (SC) produces gaze shifts with normal 3-D kinematics. A: At the end of stimulation-evoked movements, Gaze (eye-in space), Head, and Eye orientation vectors fall within the normal Donders’ ranges (compare to Fig. 1 A-C). B: When the head is immobilized, stimulation-evoked saccades (center plot) stay within the normal Listing’s plane range (left plot), viewed here from the side. When the head is freed, stimulation of the same site produces saccades (right plot) that flare out of Listing’s plane. Why? C: Plotting torsion against time, one can see that both head-free stimulation evoked saccades (left plots) and normal saccades (right plots) show the same pattern of anticipatory torsion (gray traces): negating the torsion in the following VOR (black traces). A-C adapted from Klier et al. 2003. D: Schematic saggital slice of monkey brainstem. The previous data suggest that the SC (black circle) encodes desired 2-D gaze, and this is somehow elaborated into 3-D commands at the level of the rostral intersititial nucleus of medial longitudinal fasciculus (riMLF), interstitial nucleus of Cajal (INC), paramedian pontine reticular formation (PPRF) and nucleus prepositus hypoglossi (NPH). III, IV, VI: 3^rd, 4^th, 6^th cranial nuclei contain motoneurons for eye muscles. Adapted from Henn et al. 1982.