[fractionBleached] = ComputePhtopigmentBleaching(irradiance,[receptorType],[units],[source],[initialFraction],[timeUnits])

Compute fraction of photopigment bleached, given irradiance of light
reaching the eye.

There are two distinct uses, controlled by the value of initialFraction.

Usage 1 - If initialFraction is not passed or is empty, the steady state
fraction of pigment bleached is returned for each irradiance in the
passed input irradiance.

Usage 2 - If initialFraction is passed as a scalar, this is taken as the
time zero fraction bleached, and inputirradiance is taken to be the time
variying irradiance, with fractionBleached the time varying fraction

When time varying signals are handled, the unit of time is as specified
by the timeunits argument (default, msec).

As far as I can tell, the fundemantal measurements of the half-bleach
constant for human cones were made by Rushton and Henry (1968, Vision Research,
8, 617-631). This fact I learned from CVRL

I am pretty sure that the Rushton and Henry measurements were made for
560 nm light, and they give (see their Figure 2) a half-bleach constant
of 4.3 log10 trolands (20,000 td). This number is also given in Boynton
and Kaiser, Human Color Vision, 2nd edition, pp 211 and following. This
is the number you get here if you specify ‘Boynton’ as the source for the
cone bleaching data.

Elsewhere in the same paper, Rushton and Henry use another method and
come up with 29167 td) as the half-bleach constant. You can get this
number by specifying ‘RushtonHenryAlt’ as the source for the cone
constants. If you use isomemerizations here, the constant is scaled up
from the one derived above by the ratio (29167/(10^4.3)).

It’s probably fine to compute bleaching for L and M cones given retinal
illuminance in trolands, given that these are effects that matter over
log10 units. But trolands are not going to help much for the S-cones.
According to CVRL there aren’t good measurements for the half-bleaching
constant for S cones because putting enough short-wavelength light onto
the retina to bleach the S cones is not good for the eyes.

None-the-less, it seems nice to have this routine written so that it will
return a number if you give it irradiance either in trolands or in
isomerizations/cone-sec. For 560 nm light and the CIE 10 deg
fundamentals, I compute that 1 td is 137 isomerizations/cone-sec for L
cones and 110 isomerizations/cone-sec for M cones. Take the weighted
average value of (2*L + 1*M)/3 = 128 and multiply by (10.^4.3) to get a
half-bleach constant in isomerizations/cone-sec of 2.55e+06 (6.4 log10
isomerizations/cone-sec). [Computations done 6/2/14 using
IsomerizationsInEyeDemo and setting the fundamentals to ‘CIE10deg’ and
wavelength to 560 nm by hand in the code. These are for the ‘Boynton’

[ASIDE: I used 10 deg fundamentals to compute the bleaching constant
expressed in terms of isomerizations, because I figure that Rushton’s
measurements are based on a fairly large field. Because the macular
pigment absorbs a fair amount of light, this matters. If I compute
instead with 2-deg fundamentals, I get that 1 td is 23.7 L cone
isomerizations/cone-sec and 19.5 M cone isomerizations/cone-sec. These
two numbers are ballpark consistent with Rodiek page 475 who gives 18.3
and 15.9 for a monochromatic 540 THz light (555 nm)].

This paper
Burkhardt, D. A. “Light adaptation and photopigment
bleaching in cone photoreceptors in situ in the retina
of the turtle.” Journal of Neuroscience 14.3 (1994):
provides a half bleach constant for turtle cones of 5.57 expressed
in log10 R*/um2/sec, which could with some work be converted to
isomerizations/cone/sec for turtle cones. But it’s not
clear you want to use that number unless you are studying turtle.

This routine will do the computation either on the basis of input in
trolands or input in isomerization/cone-sec, using the appropirate
constant as above. Note that the computation of isomerizations takes
into account lens and macular pigment, while the troland value is the
straight troland value. A second advantage of using units of
isomerizations/cone-sec is that you can compute this for other regions of
the visual field and presumably the numbers will be about right. You can
also compute for S-cones on the assumption that the half-bleach constant
is the same for S-cones as for L- and M- cones.

As far as I can tell, the computations and analysis of bleaching do not
take into account changes in isomerization rate that occur because of
change in spectral sensitivity of cones with bleaching. That is, the
measurements are simply of steady state pigment density and are modeled
with a formula that assumes monochromatic light (see treatment in

irradiance – retinal irradiance specified as determined by units. If
initialFraction is empty, this is a single number and
steady state bleaching fraction is returned. If
initialFraction is a number, then this is a time series
of irradiance versus time, and fraction bleached for the
same times is returned.

‘cones’ – computations for cones. [Default]
‘rods’ – computations for rods.

units – units of irradiance
‘trolands’ input irradiance trolands. Note that the computation
only makes sense for L and M cones if this is the input.
This is photopic trolands if receptor type is ‘cones’.
[Default]. It is scotopic trolands if receptor type is
‘isomerizations’ nominal isomerization rate in
isomerizations/cone-sec, comptued taking into account
pre-retinal absorption as well as nominal cone axial
density. But not taking into account any pigment

source – source of underlying data
‘Boynton’ Boynton and Kaiser, Human Color Vision, 2nd edition,
pp. 211 and following. See intro text above. [Default]
‘RushtonHenryAlt’ - Rushton and Henry’s other half-bleach constant.
Only available for ‘cones’.
‘WyszeckiStiles’ - Wyszecki and Stiles (1982) give parameters on page

initialFraction – fraction of input bleached at time zero. If
empty, steady state fraction bleached is
returned. Default is empty.

timeUnits – units for time step on input and output
‘sec’ seconds
‘tenth’ tenths of seconds
‘hundredth’ hundredths of seconds
‘msec’ millseconds [Default]
‘tenthmsec’ tenths of milliseconds

05/23/14 dhb Wrote it.
05/26/14 dhb Clean up.
06/02/14 dhb Take isomerizations number based on 2:1 L:M assumed ratio.
12/18/18 dhb Modify header comments for possibility of passing time
varying signal. This breaks old usage that allowed
computing steady state bleaching for a set of vector
inputs, but I think that is OK.
08/19/19 dhb Added some information about Burkhardt (1994) to header
comment, and inserted a stub to use that information if
someone does the work to put the number from it into the
right units.
dhb Reorganized some code relative to source switch statement. Because
there was only one case this didn’t matter, but now I think it
is right if more cases.
01/09/21 dhb Finish off adding kinetics.
01/12/21 dhb Add in the alternate Rushton & Henry half-bleach constant
for cones.

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