Models of Smooth Pursuit Eye Movements Freiburg 2014 · PDF fileKlinik für Neurologie Models of Smooth Pursuit Eye Movements Robinson‘s pursuit model (Biol Cybern 55: 43) Knapps

Klinik für Neurologie

Models of Smooth Pursuit Eye Movements


Peter Trillenberg & Rebekkan Lencer

Dept. of Neurology, University Hospital of Schleswig-Holstein, Campus Lübeck & University of Lübeck



Robinson‘s pursuit model(Biol Cybern 55: 43)

Knapps Ophthalmotrop (nach 1861)Berliner Medizinhistorisches Museum der Charité

What is a model?


Models of Smooth Pursuit Eye MovementsWhat is a Workshop?

ignorance

At least we knowwho theothers

are

blaQuestions

that aresupposed

to leadsomething

Answersthat lead to

newquestions

bla

Answersthat lead to

newquestions

bla

Answerwith nextnot slideprepared

Answerwith next

slideprepared

bla

shit

partial absence

ofignorance

Who cares …



Assignment #1:

Design a system that drives the eye to follow an object. Chose a simple plausible algorithm that does not necessarily employ mechanismsidentical to physiology!

time

posi

tion



Assignment #1:


time

posi

tion

∆ ∙ ∆



Assignment #1:


Show EXCEL #1

A B C D1 lambda …23 time Stim eye4 … …5 …. … =abxjsjhjh6 … … =abxjsjhjh



Assignment #1:


Show EXCEL #1

A B C D1 lambda …23 time Stim eye4 … …5 …. … =-C$1*(C5-B5)6 … … =C5+D5



Questions for assignment #1

1. Does the model hit a resting target?

2. Does the model follow a moving target?

3. What is the frequency characteristic of the model?

4. What is the fundamental difference between this model and eyemovements?



Questions for assignment #1

1. Does the model hit a resting target?Yes (asymptotically)

2. Does the model follow a moving target?Yes (but with a constant position error)

3. What is the frequency characteristic of the model?Low-Pass (G ->1 for low f, ->0 for high f)

4. What is the fundamental difference between this model and eyemovements?

Dichotomy between saccadic and pursuit system ignored



⇒

. . .

r.h.s.

11



Low pass element

pass

block

The Robinson pursuit model

„corner frequency“ 1/T


Models of Smooth Pursuit Eye MovementsGoals of eye movements

Correction of errors in eye position:saccades

Correction of errors in eye velocity:

OKNSmooth pursuit eye movementsVOR

medial: 45°

lateral: 90°

foveal*: 2°

*thumbnail at an armlength‘s distance



11

Naive for physiology With knowledge ofeye movementsystems



But:

How can the brain know the target velocity?



Naive for physiology With knowledge ofeye movementsystems

-+

How could this system be realized?(3 eyes, Antishake, vestibular organ)

„feedback loop“



-+

„gain element“

Assignment #2:

Explore the effects of a feedbackloop on a gain element!

More specifically: what is theoverall gain of the system as a function of g (ramp stimulus)?



Assignment #2:

Explore the effects of a feedback loop on a gain element! More specifically: what is the overall gain of the system as a function of g (ramp stimulus)?

Show EXCEL #2

A B C D1 gain g …23 time target vel Eye vel4 … …5 …. …6 … … =xfasgwjgjwhg



Show EXCEL #2

A B C D1 gain g …23 time target vel Eye vel4 … …5 …. …6 … … =C$1*(B5-C5)

Assignment #2:

Explore the effects of a feedback loop on a gain element! More specifically: what is the overall gain of the system as a function of g (ramp stimulus)?



-+

∙ ⟹ 1 ∙

1

⋅



Situation so far:

There is a negative feedback loop in the system.

This forces the system to work with high gains that render the systemunstable.

We have to get rid of this loop! Suggest something that makes targetvelocity enter the brain!

-+


Models of Smooth Pursuit Eye MovementsThe Robinson pursuit model

Assignment # 3

Make two suggestions for „Brain“!

Physicallydefined

neuronallydefined„efferencecopy“

++

-+



++

-+

11



++

-+

11

11

Assignment # 4

What does imply in reality?



++

-+


11

11



delay element:

⇒

. . .

r.h.s.



Robinson, Gordon & Gordon: Biol Cybern 55: 43 (1986)

Desired eyeacceleration

integration




Krauzlis & Lisberger, Neural Comput 1: 116

The Lisberger pursuit model



Assignment # 5

Explore the effect of a fixed delay of 100 ms on sine pursuit!

++

-+

11

11



Stimulus frequency

Stimulusperiod

Phase

0,3 Hz1 Hz5 Hz10 Hz



Stimulus frequency

Stimulusperiod

Phase

0,3 Hz 121 Hz 1000 ms 365 Hz 200 ms 180 Delay by a half wave10 Hz 100 ms 360 Delay by a full period

Speculate why these large phase shifts do not occur in reality?


Models of Smooth Pursuit Eye MovementsBeyond the Robinson pursuit model

Assigment # 6

Imagine ways to represent (horizontal) target motion forprediction!


Models of Smooth Pursuit Eye MovementsBeyond the Robinson pursuit model

If you know the stimulus is a sine: amplitude and frequency

The stimulus is a physical object => borrow ideas from physics


Models of Smooth Pursuit Eye MovementsProblems with control systems models

What is the problemassociated with thisapproach?

K1=3∙0.87∙fK2=tan(/8+2∙∙0.87·f∙( delays))-1

Van den Berg, Exp Brain Res (1988) 72: 95


Models of Smooth Pursuit Eye MovementsBeyond control systems models

Assigment # 5

If you know the stimulus is a sine: amplitude and frequency

The stimulus is a physical object => borrow ideas from physics

, /0 1… …

Assignment #7

Imagine examples (physically defined situations) for this approach to bepossible!

Always true

Never really true, alwaysapproximately true



Positionvelocity

Real stateof the target

Assumed stateof the target

Command tothe eye

Retinal errorand retinal slipvelocity

How do we learn the target dynamics?

⋯ ⋯

Shibata et al, Neural Networks 18 (2005) 213–224



Assumption on targetdynamics: general form


⋯ ⋯


Assignment #8: Apply this equation to a ramp target (constant velocity, linear change in position)





⋯ ⋯


Assignment #8: Apply this equation to a ramp target

10 1

works

Does it work here?





⋯ ⋯


Assignment #9: Apply this equation to a ramp target

10 1

works

doesn‘t work




Special case ramp: position increasing, velocityconstant

Special case sinussoidalstimulus with frequency/2


⋯ ⋯

10 1

cos sinsin cos






We have a representation for parameters that can facilitate prediction for a small number of stimuli

Suggest something to adjust these parameters to a given stimulus!

Positionvelocity

Real stateof the target

Assumed stateof the target

Command tothe eye

Retinal errorand retinal slipvelocity





⋯ ⋯

→








cos sinsin cos






What happens during target blanking?





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Documents

Models of Smooth Pursuit Eye Movements Freiburg 2014 · PDF fileKlinik für Neurologie Models of Smooth Pursuit Eye Movements Robinson‘s pursuit model (Biol Cybern 55: 43) Knapps