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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
dr
 k ( F1 g (r (t  T ))  F0 )
dt
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)
r  r1 : g (r )  0
r1  r  r2 : g (r )  r / r2
r  r2 : g (r )  1
• Some analysis
-Analytical solution? yup
-only oscillatory solutions
-prediction for delay
Model 3
• Assume a form for g(r)
r  r1 : g (r )  0
r r
r1  r  r2 : g (r )  2
r2  r
2
r  r2 : g (r )  1
• Analysis
-Analytical solution? no
-Can find linear stability
2
1
2
1
Conclusions
• Evolutionary reason for rate of constriction/dilation
of eye!
• Why should damping exist?
• Application: eye disease detection