Neural Activity in Oculomotor Neurons

In the early 1970s, several pioneering laboratories recorded the activity of single neurons in oculomotor nuclei while monitoring the eye movements of alert monkeys. They found that every OMN had the same characteristic firing pattern, organized about the eye's position and motion in the plane of its target extraocular muscle (Fig. 4). The clarity and constancy of the OMN responses galvanized sensorimotor neu-rophysiology, setting the stage for the analysis of circuits responsible for OMN responses and for tracing the antecedents of these activities further into the brain stem and then to the cerebral and cerebellar cortices.

Figure 3 Axes of rotation and muscles of the eye. The eye rotates about three axes to effect horizontal, vertical, and torsional movements. These rotations are implemented via six extraocular muscles for each eye, as shown. Adduction and abduction about the z axis are accomplished by the lateral and medial rectus muscles. Raising and lowering the eyes (x axis rotations) are accomplished by the inferior and superior rectus muscles in association with the inferior and superior obliques. Likewise, torsional movements (y axis rotations) require the inferior and superior obliques together with the superior and inferior rectus muscles.

1. Coding of Eye Position by Oculomotor Neurons

The relationship between the discharge rate of any OMN and the static position of the eye is a linear function of the eye's coordinate, 0, as measured along the pulling direction of the OMN's target muscle: RomN=A • (0—0O), where ROMN is spikes/sec, 0O is the

Topography Code Superior Rectus Muscle

Figure 4 Discharge characteristics of a neuron in the oculomotor nucleus (OMN). The firing rate of this neuron increased in association with downward eye movement. The upper set of traces shows spontaneous saccadic eye movements with intervening periods of fixation. The lower set shows smooth pursuit brought about by moving an object in front of the monkey. In each part the top trace has the neuron's spikes during the eye movement; the lower trace (solid line) is the vertical eye position. The dashed lines represent degrees of deviation from straight-ahead gaze; upward deflection corresponds to elevation and downward deflection to depression of the eye (adapted with permission from P. H. Schiller, Exp. Brain Res. 10, 347-362, 1970. copyright © 1970 by Springer-Verlag).

Figure 4 Discharge characteristics of a neuron in the oculomotor nucleus (OMN). The firing rate of this neuron increased in association with downward eye movement. The upper set of traces shows spontaneous saccadic eye movements with intervening periods of fixation. The lower set shows smooth pursuit brought about by moving an object in front of the monkey. In each part the top trace has the neuron's spikes during the eye movement; the lower trace (solid line) is the vertical eye position. The dashed lines represent degrees of deviation from straight-ahead gaze; upward deflection corresponds to elevation and downward deflection to depression of the eye (adapted with permission from P. H. Schiller, Exp. Brain Res. 10, 347-362, 1970. copyright © 1970 by Springer-Verlag).

OMN's recruitment position, or threshold, and a typical value for factor A is 4 Hz/deg. Most d0 are more than 15° in the "off" direction (i.e., 0O< 15°), meaning that most motor units are active during central fixation. Two nonlinear constraints on Romn are necessary, however: Romn=0 for all 0<0O, because neurons cannot have a negative rate, and ROMN < 500 because OMNs typically saturate at 500 Hz.

This linear relation reflects the passive physical properties of the eyeball in the orbit, namely the elastic forces that are constantly pulling the eye toward its central position with a force proportional to its eccentricity. Thus, larger deviations from the central position require proportionally larger muscular forces, which in turn require larger rates in the agonist muscle's OMNs. Larger eccentricities also require more relaxation in the antagonist muscle; however, the same equation, with the direction of 0 reversed, provides for relaxation of the antagonist OMNs as well.

2. Coding of Eye Velocity by Oculomotor Neurons

For the eye to be rotated at any appreciable velocity, its extraocular innervation must also overcome the viscous drag of the orbit, which is approximately proportional to rotational velocity. Indeed, OMNs have significantly higher or lower spike rates when crossing a given eye position as a function of tracking direction and velocity. Thus, a velocity factor must be added to the OMN equation, yielding ROMN=A • (0—0O) + B • (d0/dt). A typical value for velocity factor B is 1 Hz/deg/sec. The magnitude of this factor, like the threshold position (0O) and position factor (A), varies across the motor pool of each muscle; however, all OMNs require such a velocity term, as well as a position term, in their rate equation.

This basic equation holds for all OMNs during all types of eye movements. The velocity term has its most dramatic effect when the eyes move via saccades or quick phases (Fig. 4, top) because such rapid eye movements can approach 1OOO°/sec. Likewise, the nonlinear stipulation that 0<Romn<500 is very important in relation to rapid eye movements; in fact, most OMNs are saturated at their maximal rate during large saccades in their on direction, and most are briefly silenced during saccades in their off direction.

3. Causality

The rate equation for OMNs is instructive, but it is causally backwards because the data are from recordings in alert monkeys making natural eye movements, not from direct experimental manipulation of eyeballs. Presumably, the brain arrives at a goal for 0 and d0/dt and then provides appropriate rates for all OMNs, including the few from which neurophysiologists record. Consequently, the extraocular muscles contract and the eye moves to position 0 at velocity d0/dt. In other words, the causal equation is 0(t)=F(ROMN(t—t)), where t is the ~5-msec delay from OMN spikes to actual eye movement. The substantive questions are (i) how an appropriate eye position and velocity are reckoned by a hierarchy of oculomotor structures distributed across the brain and then (ii) how the appropriate ROMN for effecting that position and velocity are computed.

E. How the Eyes Are Coordinated and Constrained

The complexity of controlling 12 extraocular muscles is dramatically mitigated by several "laws" that reduce the degrees of freedom for controlling the eyes. These laws are implemented in the oculomotor anatomy near the output stage, and thus nearly all eye movements obey them.

1. Descartes-Sherrington's Law of Reciprocal Innervation

This law asserts that the six eye muscles of each eye act as three agonist/antagonist pairs (as discussed earlier), thus reducing the oculomotor system's degrees of freedom from 12 (the total number of extraocular muscles) to 6. Reciprocal innervation was implicit in the ROMN equation because the agonist and antagonist muscles of each pair lie in the same plane with reversed sign.

2. Hering's Law of Motor Correspondence

Hering's law halves the oculomotor systems degrees of freedom from 6 to 3 because it asserts that the two eyes act in unison (conjugately) for all eye movements excepting vergence. Thus, the brain operates as if there is only one eye, a cyclopean retina. This motor correspondence is accomplished by yoking pairs of muscles in the two eyes. For example, the lateral rectus of the right eye and the medial rectus of the left eye comprise a yoked pair. They receive the same commands and both effect a rightward movement.

The brain stem circuits for both reciprocal innervation and motor correspondence in horizontal eye movements (medial and lateral rectus) are shown in Fig. 5 for rapid eye movements, such as saccades, and in Fig. 6 for smooth/slow eye movements, such as VOR. The yoking for horizontal movements is straightforward: Signals entering the right abducens nucleus not only innervate motor neurons of the right eye's lateral rectus but also innervate interneurons within the abducens nucleus. These interneurons relay this signal, via the medial longitudinal fasciculus, to the contralateral oculomotor nucleus, synapsing on OMNs of the left eye's medial rectus. For reciprocal

Motor Strip Movement Muscles Neurons

O - Low Discharge Rates

Q ——— High Discharge Rates wwwm Inhibitory Projections

O - Low Discharge Rates

Q ——— High Discharge Rates wwwm Inhibitory Projections

Figure 5 Neural circuit for a conjugate rightward eye movement. Making a conjugate eye movement, as in this figure, invokes activity in the diagrammed neural circuit that implements both Hering's law (motor correspondence) and Descartes-Sherrington's law (reciprocal innervation). For a rightward eye movement, the yoked agonist muscles contracted are the right lateral rectus and left medial rectus, and the antagonist muscles relaxed/inhibited are the left lateral rectus and right medial rectus. In the example shown, a signal to make a rightward saccade originates in the left hemisphere (cortex and colliculus) and is transmitted via the excitatory burst neurons (EBN) to the motoneurons of the right lateral rectus in n. VI (abducens). In order to also contract the yoked muscle in the left eye (the medial rectus), and thereby make the movement conjugate, a set of non-motor neurons in n. VI relay the movement signal to contralateral n. III (oculomotor). Reciprocal innervation (inhibition of the two antagonist muscles) is accomplished by inhibitory burst neurons (IBN) that project to the left n. VI and thereby both directly inhibit motoneurons of the left lateral rectus and indirectly diminish contraction in the right medial rectus via the n. VI to n. III projection. Similar circuits accomplish motor correspondence and reciprocal innervation for the other extraocular muscles in order to carry out conjugate vertical and torsional movements.

innervation, an inhibitory copy of the command signal is routed to the contralateral abducens, which relaxes the contralateral lateral rectus and, by the yoking circuit, relaxes the ipsilateral medial rectus as well.

For the remaining eight muscles, yoking is less obvious. Each superior oblique and the opposite inferior rectus constitute one yoked pair, and each inferior oblique and opposite superior rectus another.

Diagram Conjugate Gaze The Eye

Figure 6 Neural circuit for the horizontal vestibuloocular reflex (VOR). The diagram depicts the rightward horizontal eye movements that compensate for leftward head rotation. The basic connectivity shown here serves all conjugate rightward eye movement (e.g., Fig. 5), regardless of the origin of the eye movement command signal. For the VOR, this signal originates in the semicircular canals and is communicated, via bipolar neurons in the vestibular ganglion (VG), to the vestibular nuclei (VN). The VN sends an excitatory projection to the contralateral oculomotor neurons in n. VI (abducens) and also sends an inhibitory projection to ipsilateral n. VI. The consequences of the increased activity from the left horizontal canal are reinforced by the decreased activity from the right horizontal canal, illustrating the push-pull operation of the canal pairs. An additional excitatory pathway (not illustrated) from the VN directly to the medial rectus motoneurons in ipsilateral n. III (oculomotor) gives the medial rectus its three-neuron VOR drive in addition to its four-neuron VOR drive via the contralateral n. VI.

These pairings reflect the true rotational axes of these muscles and their relation to the vestibular canals (Fig. 7).

3. Listing's and Donders' Laws and the Loss of Torsion

In primates torsional movements are severely constrained. For example, the human eye torts only a few degrees in response to a large sideways tilt (technically a "roll") of the head, whereas the rabbit eye torts up to

70°. The absence of significant torsional movement has an evolutionary advantage for stereoscopic vision.

Ocular torsion is classically summarized by the laws of Donders and Listing. Donders' law asserts that each eye direction (the combination of a particular azimuth and a particular elevation) has a unique torsion always associated with it, regardless of the sequence of eye movements used to achieve that particular azimuth/ elevation. This has important implications. First, although it takes three coordinates to specify a general rotation, Donders' law means that the eye has only 2 degrees of freedom, and thus only two angles (azimuth and elevation) need be specified. This is analogous to navigation; longitude and latitude suffice, even though locations on the ocean surface have three coordinates in space. Second, whereas 3D rotations are not commutative, Donders' law stipulates that human eye movements effectively are commutative.

Listing's law asserts Donders' law and more because it specifies the particular torsion associated with any final eye direction, whereas Donders' law only ensured that this torsion is unique. To find the torsional position that the eye will always assume at a particular azimuth and elevation, Listing's law instructs to find the axis in the frontal plane through the center of the eye (Listing's plane) such that a single rotation about that axis takes the eye from the primary position to the particular azimuth and elevation in question. This single rotation will obtain the orientation that the eye will always have at that azimuth and elevation, no matter the sequence of eye movements actually used to get there. This means that the human eye has zero torsion following purely horizontal or purely vertical movements from the primary position (these are called ''secondary'' positions). However, for a typical oblique direction (a ''tertiary'' eye position) the eye appears to have undergone a torsional rotation because real-world vertical lines no longer fall along the vertical meridian of the retina when fixated. This is often called a ''false torsion'' because the eye did not have to make a true torsional movement about the line of sight but, rather, only a single rotation about an axis in Listing's plane, which is orthogonal to the torsional axis.

The role of the extraocular muscles in controlling ocular torsion is complex. The medial and lateral rectus have minimal torsional movements; however, as noted earlier, the four remaining muscles (inferior oblique, superior oblique, superior rectus, and inferior rectus) all have both vertical and torsional actions (''mixed'' actions). Consequently, as Ewald Hering stated, elevation of gaze is effected ''only by the cooperation of the superior rectus and the inferior

Torsional Axis

Figure 7 Rotational axes of the eye muscles and canals. (Top, left and right) The axis of rotation for all extraocular muscles, except for the medial and lateral rectus (bottom, left and right). For each muscle, the direction, or sign, of the eye rotation is given by the left-hand rule: Point the thumb along the arrow and the curve of the (slightly closed) fingers indicates the eye rotation. The rotation axes of the six semicircular canals (bottom middle) are perpendicular to the canal planes depicted above (upper middle) and show (by the left-hand rule) the eye rotation evoked by stimulation of individual canals. It is easy to see which muscle axis in each eye best aligns with each canal's axis; those muscles receive the three-neuron excitatory projection from that canal. Although in the primate, the eyes have migrated from the side of the head to the front, the canals are little changed, and the primate's extraocular muscles have maintained their rotation axes in correspondence with the canals axes. The figure also graphically depicts the rationale of yoking of the inferior oblique with the contralateral superior rectus and the superior oblique with the contralateral inferior rectus. The angular difference in both cases is far less than the difference between the left and right obliques axes or the left and right superior-inferior rectus axes. This figure was inspired by Fig. 51 in Hering (1942). His axis values, which were used here, have the axis of the superior-inferior rectus as being 29° off the axis for purely vertical movements and the axis of the superior-inferior obliques as being 38° off the torsional movement axis. The [a, a', a"] parallelogram (top, left) is his geometrical construction of a pure elevation movement (with no torsion) from simultaneous contractions of the inferior oblique and superior rectus: Add the rotation axis vectors of these two muscles to obtain the axis for combined rotation.

Figure 7 Rotational axes of the eye muscles and canals. (Top, left and right) The axis of rotation for all extraocular muscles, except for the medial and lateral rectus (bottom, left and right). For each muscle, the direction, or sign, of the eye rotation is given by the left-hand rule: Point the thumb along the arrow and the curve of the (slightly closed) fingers indicates the eye rotation. The rotation axes of the six semicircular canals (bottom middle) are perpendicular to the canal planes depicted above (upper middle) and show (by the left-hand rule) the eye rotation evoked by stimulation of individual canals. It is easy to see which muscle axis in each eye best aligns with each canal's axis; those muscles receive the three-neuron excitatory projection from that canal. Although in the primate, the eyes have migrated from the side of the head to the front, the canals are little changed, and the primate's extraocular muscles have maintained their rotation axes in correspondence with the canals axes. The figure also graphically depicts the rationale of yoking of the inferior oblique with the contralateral superior rectus and the superior oblique with the contralateral inferior rectus. The angular difference in both cases is far less than the difference between the left and right obliques axes or the left and right superior-inferior rectus axes. This figure was inspired by Fig. 51 in Hering (1942). His axis values, which were used here, have the axis of the superior-inferior rectus as being 29° off the axis for purely vertical movements and the axis of the superior-inferior obliques as being 38° off the torsional movement axis. The [a, a', a"] parallelogram (top, left) is his geometrical construction of a pure elevation movement (with no torsion) from simultaneous contractions of the inferior oblique and superior rectus: Add the rotation axis vectors of these two muscles to obtain the axis for combined rotation.

oblique.'' Likewise, depression is effected by "cooperation of the inferior rectus with the superior oblique.'' This is analogous to lifting a barbell: If both arms lift with the same force, then the barbell will remain level, whereas if one arm exerts too much force then the barbell will tilt (tort) as it rises. Likewise, when the superior oblique and the inferior rectus are cocontracted, their downward forces are additive, but an extorsional force from increased tension in the superior oblique is canceled by an intorsional force from increased tension in the inferior oblique. Furthermore, the increased tension of the superior oblique and inferior rectus is always reciprocated by decreased tension of the inferior oblique and superior rectus, respectively. This results in a decrease in upward force, but with decreases in extorsion and intorsion canceling.

Thus, the eyes can move downward (or upward) with very little torsion, even though all four muscles involved have significant torsional actions.

Donders' and Listing's laws are not absolute or inherent in the passive properties of the eye. Large departures accompany convergence, head tilt, sleep, and certain neural pathologies. Torsional nystagmus, a clear violation of Donders' and Listing's laws, can be obtained with electrical stimulation of particular midbrain nuclei or individual canals and can also be a consequence of central disease.

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  • TED
    Which extra ocular muscle obeys Sherrington's law of reciprocal innervation?
    3 years ago

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