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