Head and Eye Coordination

Reading: R.J. Leigh & D.S. Zee, The Neurology of Eye Movements 4th Ed, Oxford Press (2006) chapter 7
review below:

Animals that don't make eye movements, like birds, do make head movements.
(Pigeons making back-and-forth [surge] head movements while walking...)
Sidebar on bird head rotation: As noted in the first lecture notes on "Why Make Eye Movements?", Birds have a minimum of 11 and a maximum of 25 cervical vertebrae (humans have 7). LINK to image

By "head movement" we mean neck muscles move the head with respect to the torso. The torso, in the case of the pigeon above, may also be moving (if locomoting forward, we are in the topic of optic flow--see notes at bottom of Direc Selec page)

VOR saturates if head rotates more than 60 deg/sec...

During running angular head velocity does not exceed 100°/sec
most energy of head rotation in the 0.5 - 5.0 Hz.

"What mechanisms operate to hold the head as a relatively stable platform during locomotion? Four main factors have been studied in humans:
(1) mechanical forces due to the inertial mass of the head and the muscles and tissues that support it.
(2) the vestibulocollic reflex by which vestibular inputs activate neck muscles to stabilize the head w.r.t. space.
(3) the cervicocollic reflex (CCR): the stretch refex of the neck muscles, which acts to stabilize the position w.r.t. the trunk.
(4) voluntary control of the neck muscles."

Stretch reflex: stretching of a muscle causes negative feedback to its motoneuron, to reduce contraction. Does CCR act to prevent oscillations of the head? "To stop the head from oscillating, the VCR and the CCR may adjust the ratio of the viscosity to elasticity of the neck muscles and connective tissues."

PPRF: paramedian pontine reticular formation
"Two classes of burst neurons in the PPRF of alert monkeys have been defined: those with discharge activity related to the size of he eye-in-orbit movement (ocular burst neurons) and others that discharge in relation to the size of the eye-in-space movment (gaze burst neurons)."

Eye-head saccades:
Appreciate that it is possible to see a target at the limit of your periphery, but not be able to foveate with a saccade alone. Thus a horizontal head rotation is made too. {sidebar on intraocular pressure, glaucoma and peripheral vision) See figure below.

One paradigm: At t=0 there is motion (say 30 deg/sec) of a small foveated target toward the periphery; the target will keep moving until it stops somewhere beyond the eye movement say (say 90 degrees). After a delay SP starts and will be aided by a small corrective saccade. The eyes can keep tracking the target until it approaches the limit of foveated eye position. About then the head starts moving in the same direction as the eyes. Until the gaze reaches the target, the eyes stays fixed to a peripheral angle--during which time VOR must be suppressed. When gaze (= head + eye) places the target on the fovea (of the one eye that can see the target...) VOR is "uninhibited" and continues until the head faces the target.

Movement to a target that appears away from foveal fixation. See L & Z Fig 7-2. unexpected vs predictable responses.

The saccade, with a latency of 200 msec, precedes the head rotation by about 50 msec.

SP and head movements:
See L&Z3 Fig 7-4, patient with loss of vestibular function, compared to normal. The head brake experiment: have the head rotate at same velocity as target, so no eye movement is required. Suddenly the head stops. In a normal subject the tracking continues smoothly, thx to SP operating "in the background". In the impaired subject catch-up saccades and too-slow SP ensue.

Model of head
rotational inertia of the head:

In fact the website
http://alexandria.tue.nl/extra2/200611939.pdf
cites a gm-cm^2 rotational inertial of a human head about the z-axis of 150,000.
Let's compromise and say 100,000.

Estimating K, the stiffness: How much deflection, in radians, would result from 1lb = 454 gm held in the mouth?
My guess: 0.1 rad. So torsional stiffness K is estimated to be
454gm * 980 cm/s^2 * 7 cm radius / 0.1 rad = 31,144,400 dyne-cm/radian = 31 x 10^6
Let's say the time constant Tau of head rotation is 450 msec, 3x greater than the eyeball in its orbit.
How is K related to Tau? Tau = B/K, so B = K*Tau = 14x 10^6 ; What are the units?

Let's use the following transfer function to model the mechanical load of the head:

where we have scaled the terms above by 10^6.
Is the head overdamped or underdamped?

More realistic: What to do about the torsional spring? Why does the head stop rotation where it does?