The Pupil Control System Omer Dushek and Heena Lakhani.
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Transcript of The Pupil Control System Omer Dushek and Heena Lakhani.
![Page 1: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/1.jpg)
The Pupil Control System
Omer Dushek and Heena Lakhani
![Page 2: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/2.jpg)
The Eye
![Page 3: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/3.jpg)
The Retina
![Page 4: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/4.jpg)
The Iris Muscles
![Page 5: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/5.jpg)
Assumptions• The light has constant intensity and is
shone constantly into the pupil• The light is shone on the edge of the pupil
and the location of the light does not change
• Direct relation between retinal neuron firing and iris muscles
• Parameters (Rmin, Rmax, R1, R2) for models 2 and 3
![Page 6: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/6.jpg)
MODEL 1
• Equations:– Firing rate is dependent on:
• pupil radius» amount of light that has contact with pupil
• df/dt= a*G(r)*Intensity
Change in radius of pupil• Firing rate• dr/dt= -b*f
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WRONG AND A DAY LOST!!!
• a*G(r)*Intensity is not a rate; it is actually the number of neurons firing
• Assuming instantaneous results; no delay rate
-The model does not yield oscillating
results; get decaying results
-Delay: 200 ms
• Different constants for pupil
constriction and dilation
![Page 8: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/8.jpg)
Introducing A Delay – Model 2 & 3
)))((( 01 FTtrgFkdt
dr
F0 – Optimal number of neurons firing
F1 – Number of neurons that will fire as a result of incident light.
k – scaling parameter
g(r) – Fraction of F1 actually making it through iris at radius r.
![Page 9: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/9.jpg)
Model 2
• Assume a form for g(r)
• Some analysis-Analytical solution? yup-only oscillatory solutions-prediction for delay
1)(:
/)(:
0)(:
2
221
1
rgrr
rrrgrrr
rgrr
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Model 3
• Assume a form for g(r)
• Analysis-Analytical solution? no-Can find linear stability
1)(:
)(:
0)(:
2
21
22
21
2
21
1
rgrr
rr
rrrgrrr
rgrr
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![Page 12: The Pupil Control System Omer Dushek and Heena Lakhani.](https://reader035.fdocuments.us/reader035/viewer/2022062712/56649caf5503460f94972a30/html5/thumbnails/12.jpg)
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Conclusions
• Evolutionary reason for rate of constriction/dilation of eye!
• Why should damping exist?• Application: eye disease detection