LNT - a different semantic comment

[daleboyce@charter.net]

Hi all,



Since we have had quite a bit of traffic on LNT  I want to throw in a

question that I have never had answered to my satisfaction.



Microdosimetry tells us that at low dose. low LET exposure most cells

receive a small amount of ionization, but at low dose, high LET a few cells

get a lot of ionization.  However at high doses the average ionization per

cell is the same for low and high LET radiation.



Quality Factors and RBE's are determined from (relatively) low dose

exposures in vitro. Correct? The LNT model is developed from extrapolating

high dose effects to low dose.  At high dose the ionization density in cells

is similar in both high and low LET exposures.  SO.. why don't we

divide low dose, low LET dose by the Q.F.'s at instead of multiplying the

high LET dose?



Second observation wrt. the fact that a first order Taylor's expansion by

necessity approaches linearity near zero.  Several years ago I heard a

presentation that pointed out that the cancer rate was a power law with age.

If I remember correctly it was a fairly large power like in the N = 5 to 7

range. This was an indication of cancer induction (I should be careful here

to state that I don't mean the induction step used in medicine) being a many

step process. If one takes from that cancer caused by radiation exposure

also follows a power law, but not necessarily the same power, then the first

order Taylor's series is still is linear near zero.



Now get out and a spreadsheet at fill in column A with the counting numbers

1,2,3,4.... , and column B with A^N.  Pick you own favorite N > 1.

Highlight both columns and add a chart. Choose an x-y scatter chart.  Now

pick some value A greater than zero and draw a line back through zero. Once

you get any distance away from zero the linear model breaks down rapidly.



Moreover, if you pick a narrow range at large A and A^N it will be fairly

linear.  Its slope will be N*A^(N-1) and it will have a non- zero intercept.

In fact it will have a negative intercept. <tongue in cheel /on> I wouldn't

go so far as to call this a mathematical predictor of hormesis. <tomgue in

cheek /off>



If you now imagine large error bars in this narrow range you can force the

intercept to be a line through zero. However this line is meaningless

outside the range of values from which it was derived. Likewise, the LNT is

a meaningless predictor of health effect at low dose unless you can prove

that cancer rate is an N = 1 process.



That said. the LNT is still useful for setting exposure limits (as long as

you can keep the limits from racheting down). It is also useful at high

dose, within its applicable range, for arguing probable cause in litigation.

You have to be sure that it is within the applicable range i.e. the range

that has been statistically demostrated to cause a significant probability

of health effect, or you are violating the mathematical use of a series

expansion.



It is never reasonable to use LNT for estimating the rate of health effects

at low dose.



Dale

daleboyce@charter.net





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