The eye pupil changes its area to adjust the amount of light on the retina (Figu

Question

The eye pupil changes its area to adjust the amount of light on the retina (Figure 2). The rules that govern this reflex are as follows (all values of alpha are the same): The amount of light that strikes the retina, I(t), is a constant, beta, multiplied by the product of the incident light intensity, I_0(t), and the pupil area, A_p(t). (The constant beta represents the losses in the lens and the inner eyeball.) The retina causes the optic nerve to fire at a rate s_op(t), where the rate of change of s_op (t) is a constant, alpha, times the difference between a constant, C, times I(t) and s_op(t). i.e., if CI(t) > s_op(t) then s_op(t) increases, but if CI(t)

Explanation / Answer

following the rules

1. amount of light that strikes the retina, I(t) = beta*Io(t)*Ap(t)

Io(t) = incident light striking the eye, a function of time

Ap(t) = ara of pupil of the eye as a function of time

beta = constant

2. optic nerve firing rate, Sop(t)

d(Sop(t))/dt = alpha(C*I(t) - Sop(t))

C is a constant

alpha is a constnt

3. lateral geniculate body firing rate = Slg(t)

d(Slg(t))/dt = alpha(Sop(t) - Slg(t))

4. perectal nucleus firing rate = Spn(t)

d(Spn(t))/dt = alpha(Slg(t) - Spn(t))

5. Ap(t) = D*Spn(t-T) [ T is the delay in seconds, D is a proportionality constant]

so Ap(t) = D*Spn(t - T)

d(Ap(t))/dt = D*d(Spn(t - T))/dt = D*alpha(Slg(t) - Spn)t))

d(Spn(t))/dt = alpha(Slg(t) - Spn(t))

d(Slg(t))/dt = alpha(Sop(t) - Slg(t))

d(Sop(t))/dt = alpha(C*I(t) - Sop(t))

I(t) = beta*Io(t)*Ap(t)

this system of equations is the ordinary

differential equation which forms a rerlation between Io(t) and Ap(t)

this is an interdependent system of equations involving higher order differntials and products, and hence this is a non linear differential equatrion

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