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Lecture 1
1) Introduction to Control Systems
2) Circuitry of Pathway
3) Models
Why Study Eye Movements?
- No joints in system
- Constant inertia (negligible)
Saccadic Eye Movements
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The Premotor Control of Saccades
1.) Cortex
2.) Superior Colliculus
3.) Brainstem
Another view
Extraocular Muscles
6 muscles per eye
4 recti muscles
- lateral/medial
- superior/inferior
2 oblique muscles
- superior/inferior
6 Muscles → provide 3D of freedom
1. Horizontal (focus of most research)
2. Vertical
3. Torsional
Extraocular Muscles
1.) Extraocular muscles consist of 2 distinct layers:
a)
A global layer with three types of singularly innervated (SI)
fibers, and one type of multiply innervated (MI) fiber, and 2)
an orbital layer with only 1 type of each (SI and MI).
b)
Fibers in each layer have different response properties (e.g.
fatigability or fusion frequency (contraction time)).
c)
MRI studies at UCLA (2000) have found sleeves of collagen
surrounded by smooth muscle tissue termed “muscle
pulleys”. The Global layer runs through the sleeve of the
pulley, while the orbital layer appears to insert on the pulley.
The function of these pulleys is not yet known: Hypotheses:
Linearization of system response and implementation of
Listings Law (3D eye motion).
Extraocular Muscles
2.)
It is not clear that Henneman’s Size Principle holds for
extraocular motoneurons:
Namely that motoneurons are recruited in an orderly manner
according to their cell body size; small neurons have the
lowest threshold for synaptic activation and are recruited by
the weakest afferent input.
3.)
All motoneurons participate in all types of eye movements,
fixation, smooth pursuit, saccades, the vestibulo-ocular
reflex and optokinetic reflex.
The Use of Control Systems for Understanding Eye Movements
A system is represented as:
Where x(t) is the input, and y(t) is the output. These are signals
that very as a function of time.
1) The goal of an engineer, is to design S, so that x results
in y.
2) The Neurobiologist already has S, and controls x,
observes y Then tries to guess what S is.
The VOR as an example:
Where:
H(t) is head velocity: here a step of velocity
and Ė (t) is slow-phase eye velocity
(note H(t) and Ė (t) are short hand for dH/dt, dE/dt)
So in this case the problem, is to find S, for the VOR
Mechanical System analysis:
How do you move your eye?
Consider some examples of mechanics to relate force to
eye movement:
1) Apply a force F to a spring of stiffness K, stretch it
to length L.
Hooks Law says: F = kL
Mechanical System analysis:
2) Apply a force F to a system characterized by a pure
viscosity (of coefficient r). A good example is a
hypodermic syringe.
If you push at a constant force, the plunger moves at a
constant velocity dL/dt, such that:
F = r dL/dt
Mechanical System analysis:
3) Put these 2 elements in series (this is a simplified muscle model):
This is called a visco-elasticity. The force is shared by the elasticity
(kL) and the viscosity (r dL/dt) so:
F = kL + r dL/dt
This is a first order differential equation and if our “system” was a
visco-elasticity, solving this equation for a given input should
produce the observed output.
Mechanical System analysis:
4) Now add a mass to the system:
From Newton’s law of motion
F = m d2L/dt2, where d2L/dt2 is acceleration
The system is now described by:
F = kL + r dL/dt + m d2L/dt2
Mechanics of Saccadic Eye Movements
The oculomotor plant:
Plant: devise which produces the final output
Oculomotor System: The 1) eye muscles, 2) orbital tissues, 3) globe
What is the output?
What is the input? Muscle tension, but hard to measure.
We can measure motoneuron drive to muscles
Eye Movements: Motoneurons
3 Motor Nuclei drive the
extraocular muscles
For Horizontal Eye Movements:
VI = Abducens
III = Oculomotor nucleus
Description of MN discharge rate
Consider 3 experiments:
Experiment 1: Monkey looks straight ahead
so that: dE/dt = 0, and E = 0
Finding: Neuron fires at a constant rate
Fr = Ro
Where:
(eq 1)
Fr → firing rate
Ro → is a constant (resting rate)
= ~100 spikes/sec
Description of MN discharge rate
Experiment 2: Monkey fixates (dE/dt = 0) at many
angles E.
Finding: Fr = Ro + kE
(eq 2)
Where:
k → 5 spike/s
Description of MN discharge rate
Experiment 3: Monkey makes smooth pursuit movements
through zero (E = 0) at many velocities dE/dt.
Finding: Fr = Ro + rdE/dt
Where:
r → 1 (spike/s)/(deg/s)
(eq 3)
Description of MN discharge rate
Description of MN
Fr = Ro
Fr = Ro + kE
Fr = Ro + rĖ
Fr = Ro + kE + rĖ
All together:
Fr-Ro = kE + rĖ
∆Fr = kE + rĖ
(eq 1)
(eq 2)
(eq 3)
(eq 4.)
Eq 4 provides a good description of MN activity during
eye movements, and so the system can be approximated
by a first order differential equation and the “system” is
described as visco-elasticic.
Test of the model
Another Experiment:
Different approach (Robinson 1964)
Put a suction contact lens on the eye
1) attach to a rod, which restrains the eye,
2) Cover the eye, and
3) Have subject fixate at different positions with
other
Finding:
F = a + bE
Test of the model
Yet another Experiment:
Put a suction contact lens on the eye
1) Tie a thread to it,
2) Cover the eye, and
3) Have subject fixate straight ahead (∆Fr = 0)
with the other
THEN: Pull the covered eye to one side and let go
Finding:
F = a + bE + cĖ
c/b = ~ 200 ms
Test of the model
Yet one last Experiment:
Put a suction contact lens on the eye
1) Attach a ball and socket joint to it,
2) and attach to a little cart on a friction-less sled
3) eye now has 100X normal inertia
THEN: Then ask subject to make saccades
Finding: Eye still lands in right place, so:
- system is not affected by the mass of eye
– inertia is not important
Description of MN discharge rate
Recall:
1) Fr = Ro + KE + rĖ
↓
2) Fr – Ro = KE + rĖ
if τe = r/k
E(t)
= R(1- e –t/τe)
E(t)
= R(1- e –1) if t = τe
= R(1 – 1/e)
= R(1 –1/2.7)
= R x .37
If : r =1, K =5, then τe = 250 ms..
Eye Dynamics with a step command of FR would be too slow.
Saccades can be on target in less than 100ms.
Recall: : Mechanical System analysis:
We put 2 elements in series (this is a simplified muscle model):
This is called a visco-elasticity. The force is shared by the elasticity
(kL) and the viscosity (r dL/dt) so:
F = kL + r dL/dt
This is a first order differential equation and if our “system” was a
visco-elasticity, solving this equation for a given input should
produce the observed output.
How Do Motoneurons Drive Eye Movement?
Fr = Ro + KE + rĖ
SO: to make a saccade a step
change in discharge would not
work.
What signal do the ocular
motoneurons send to the
extraocular muscles to generate
saccades?
Analysis of Motoneuron Signals
3) So what is the MN command to drive saccades?
Pulse:
Need an extra “burst” (pulse) in MN command signal in order to
complete saccade in a shorter time.
Note,
The pulse resembles velocity + The step resembles position
Linearity and Superposition:
The MN equation took the results from 3 experiments, and added them
together. Assumption: The system is linear. If we put in 2 signals,
the output is the same as as the sum of the response of each alone.
Analysis of Motoneuron Signals
3) So what is the MN command to drive saccades?
Where do pulse and step come from?
Hypothesis: A neural network integrates the pulse to create the step.
Sensory endings in extraocular fibers
Two types of mechanoreceptors are found in extraocular muscles
Muscle Spindles (stretch) and Golgi tendon organs (tension).
Early studies at the turn of the century led Sherrington to suggest that the
muscle spindles in these muscles mediated a stretch reflex similar to that
which he observed in skeletal muscles.
Briefly, the stretch reflex is evoked by stimulation of the muscle
spindles; passively stretching a muscle causes that muscle and its
synergists to contract, and its antagonists to relax, in effect opposing the
stretching force.
However, experiments in alert animals demonstrated that there is no
stretch reflex in the extraocular muscles.
So what do the proprioceptors do? Experiments in which a lesion was
made in this pathway by cutting the opthalmic nerve have demonstrated
that during vergence eye movements, the non-dominant eye tends to drift
medially.
Recording from a neuron in the left abducens nucleus:
A: The left eye is held relatively fixed by the experimenter.
B: A normal conjugate saccade of the same amplitude intended in A.
Step Command and the Neural Integrator
• The “integrator” is not perfect: it is “leaky”. In the dark, the
human eye drifts from attempted eccentric positions with a time
constant of 25s.
→ This is generally not a problem
• Model of the oculomotor neural integrator: Most utilize a system
of reverberating collaterals.
Motoneuron Discharges
Step
The “pulse” command drives the saccade but still needs a “step”
to hold the eye in its new position.
Proposal: Neural Integration (mathematical) of pulse command
produces step.
Evidence: Lesions of the nucleus prepositus and medial vestibular
nuclei cause problems with “gaze holding”.
Lecture II
Physiological and Theoretical
Models of Saccade Generation
Lateral
rectus
Basic Anatomical Circuit:
Horizontal Eye Movements
Abducens
nerve
Excitatory burst neuron
Motor
neuron
Nucleus
Prepositus
hypoglossi
Inhibitory
burst neuron
Basic Circuit:
Horizontal Eye Movements
The Premotor Control of Eye Movements
1.) Cortex
2.) Superior Colliculus
3.) Brainstem
Robinson model
SSaccades
are very accurate: Feedback Model to explain
MModel structure
- Local feedback (E*) used to bring eyes accurately on target
− NOTE: feed-back is not visual. Latencies of visual pathways are too long
(a minimum of 100ms).
MMain Features of Model
•
•
•
•
- Burst of activity from BN’s drives the saccade.
- Burst from BN’s is integrates by NI to hold eyes at new position.
- Internal estimate of eye position (E*) is fed back for comparison with desired eye
position (Ed).
Ed – E* = em → when em=0, no drive to BN’s → end.
Main limitation of this model
Ed is in head centered coordinates,
Superior colliculus (SC) is in not, it is in eye centered (retinocentric) coordinates.
→ Neurophysiological studies had demonstrated that the
SC saccade cells discharge the same for a saccade at a
given amplitude and direction, regardless of initial eye position.
Superior Colliculus
1) Superficial Layers:
Visual Responses, Discharge after appearance of a target to
limited part of the visual field.
2) Intermediate Layers:
Saccade related burst neurons, Discharge prior to saccadic eye
movements
Superior Colliculus: Motor Map
A) Stimulation studies:
Features of Motor Map:
Iso-amplitude line: medial/lateral
Iso-direction lines: rostral/caudal
Saccade vector is independent of initial
eye position.
Coordinated Eye-Head Gaze Shifts
Stimulation of Superior Colliculus at 2 Different Caudal Sites
1) A caudal site
2) A more caudal site
Freedman, Stanford, and Sparks, 1996
Superior Colliculus: Intermediate Layers
A) Cartoon
Neurons active before a
large (40 deg) saccade
B) Size of active zone
Top: Analysis of movement fields
of 4 cells for which the optimal
amplitude was 2, 5, 9 and 16 deg.
Amplitude converted: deg to mm.
Bottom: Same curves but normalized
and aligned. Size of active population
is the same for all amplitude saccades.
Jurgen’s Model for Saccade Generation
Main features of model
- To account for SC neurophysiology; the model input is the desired change
in eye position (∆Ed), not absolute eye positioning space.
- A second integrator is added which feedbacks an internal estimate ∆E* rather than E*
- ∆Ed - ∆E* = eµ → when eµ = 0, no drive to BN ∴ end of saccade.
Superior Colliculus: Saccade-Related Burst Neurons
- Projects to PPRF
(brainstem BN’s)
There is ambiguity in encoding
direction (deg) vs amplitude
(deg)
Example: For a single neuron:
saccades F & 6 produce the
same discharge.
Motor Map of Intermediate Layers of SC
Observation
Neurons in the SC burst for saccades of a certain direction and
amplitude.
QQuestion
What is discharge of neurons in the SC related to:
• The appearance of a target at a particular location on
the retinal map?
OR
T The generation of a saccadic eye movement of a
•
particular
amplitude?
Superior Colliculus: Sensory or Motor Response
Animal initially fixates a target (O) in all paradigms.
B, C : Single saccades trials:
Target O to target A – neurons fires (but not for O to B).
D:
Double-step saccade trial:
Target O to target B back to target O – before the B-O saccade
(which is of same amplitude as the O-A).
Jurgen’s Model for Saccade Generation
Main features of model
- To account for SC neurophysiology; the model input is the desired change
in eye position (∆Ed), not absolute eye positioning space.
- A second integrator is added which feedbacks an internal estimate ∆E* rather than E*
- ∆Ed - ∆E* = eµ → when eµ = 0, no drive to BN ∴ end of saccade.
The Moving Mountain Hypothesis
The models of Robinson and Jurgens employ an error signal (em)
to drive the burst neurons.
1)
Most recent models of saccade generation create the error signal
in the brainstem within the PPRF.
2)
However, it has also been recently argued that the output of the
superior colliculus in an error signal.
So the question arises: Is the superior colliculus in the feedback loop?
Activity of:
10 burst cells (left) and
10 buildup cells (right)
during a
50 deg horizontal saccade.
Spatial Distribution of :
burst cell (left) and
buildup cell (right) activity
prior to a
50 deg horizontal saccade.
Spatial Distribution of :
burst cell (left) and
buildup cell (right) activity
during a
50 deg horizontal saccade.
A Neurophysiological Model for Saccades
Test of Model?
Test: Moving Mountain Hypothesis
A.) Experimental Logic:
Injection of muscimol at a rostral
location should influence trajectory,
but not amplitude of large saccade.
B.) Experimental Results:
Trajectories and amplitude of 10 deg
saccades are affected.
Only trajectories of 20 deg saccades
are affected.
Test: Fixation Zone Hypothesis
A.) Experimental Logic:
Bilateral stimulation in rostral zone
should increase neuron activity,
which in turn will inhibit Burst and
Buildup cells, so saccades can not
be made.
B.) Experimental Results:
During rostral zone stimulation,
monkeys are unable to make
saccades to visual targets, until the
stimulation is turned off.
Fixation Zone:
Neurons Encode Gaze
Error
A.) Experimental Logic:
Record from neurons in
cats during multiple step
gaze shifts
B.) Experimental
Results:
Linear relationship
between GPE and FR at
end of plateau
Bergeron and Guitton, 2000
The Premotor Control of Eye Movements
1.) Cortex
2.) Superior Colliculus
3.) Brainstem