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The Pupil Control System
Omer Dushek and Heena Lakhani
The Eye
The Retina
The Iris Muscles
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
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
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
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.
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
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
Conclusions
• Evolutionary reason for rate of constriction/dilation of eye!
• Why should damping exist?• Application: eye disease detection