# Photoreceptor Pigment Depletion

Formulas for modeling photopigment depletion have been formulated by Hecht (1935) and by Rushton and Henry (1968). Hecht's formulas were based on behavioral measurements and the assumption that photopigment depletion was the only adaptation mechanism. Though Hecht's work introduced great insight, this later assumption proved to be incorrect. As a result, the following equations are based on Rushton and Henry's measurements which were made with retinal densitometers which measured directly the amount of rhodopsin present in the living human retina. This measurement can, and was, made for both cones and rods. (see my Master's Thesis and/or Geisler 1978 for a more detailed explanation and example of its uses.)
# The general formula

dp Ip 1 - p
- ---- = ---- - -------
dt Q1 to

I : intensity of bleaching light in trolands
p : proportion of unbleached pigment (0..1)
t : time (sec)
Q1 : the energy required to reduce the proportion of unbleached pigment (p) from 1 to exp(-1) (in troland seconds)
to : the time constant for regeneration
Rushton and Henry (1968) found the following values for *cones*:

- Q1 : 2.4 x 10^6 troland seconds
- to : 120 seconds

# Useful derivative formulas

**Asymptotic proportion of unbleached pigment after exposure to a luminance for infinite time:**
Io
p = ------
Io + I

Io = Q1/to

p : proportion of unbleached pigment (0..1)
I : intensity of bleaching light in trolands
Io : the intensity of a steady light that bleaches half the photopigment
Rushton and Henry (1968) found the following for *cones*:

Io = 4.3 log trolands

Threshold measurements for *cones* can be multiplied by this equation in order to remove the effects of photopigment depletion.

**Proportion of unbleached pigment in the cones following a bleaching field**

-t
p = 1 - qo exp( ---- )
to

qo : initial proportion of bleached photopigment

t : time (sec)

to : the time constant for regeneration
Dark adaptation thresholds for *cones*can be multiplied by this equation to remove the effects of photopigment depletion.

Click here for conversions between trolands and other photometric units.

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Lance Hahn(lance@retina.anatomy.upenn.edu)