[ RadSafe ] RE: ERR query: the exact form of LNT

Strom, Daniel J strom at pnl.gov
Tue Jan 15 11:21:57 CST 2008

I agree with you completely. As soon as one postulates that there is a
tumor probability per unit dose, that determines the rest of the
mathematics. Thanks for completing the discussion.
- Dan Strom 

The opinions expressed above, if any, are mine alone and have not been
reviewed or approved by Battelle, the Pacific Northwest National
Laboratory, or the U.S. Department of Energy.

Daniel J. Strom, Ph.D., CHP 
Energy and Environment Directorate, Pacific Northwest National
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From: Rainer.Facius at dlr.de [mailto:Rainer.Facius at dlr.de] 
Sent: Tuesday, January 15, 2008 05:23 AM
To: Strom, Daniel J; radsafe at radlab.nl
Cc: blc at pitt.edu
Subject: AW: ERR query: the exact form of LNT



Your equation 

P(n=0 | k, D) = EXP(-kD) 

for the probability to observe n = zero tumors after an exposure D
(implicitly) already presupposes that the expectation value, <n>, for
the additional tumors after this exposure is 

<n> = kD. 

It is already here where the LNT postulate discards from the universe of
possible dose response functions for 

<n> = F(D) 

all but the linear-no threshold function. Of course, any other (well
behaved) function F(D) allows for a Taylor expansion around some point,

F(D) = F(0) + D*F'(0) + D^2/2*F''(0) + D^3/6*F'''(0) + D^4/24*F''''(e*D)
for some e, 0<= e <= 1

In this version, the LNT postulate asserts that F''=F'''=F''''=...=0

In my interpretation, the Poisson distribution which you invoke has
nothing to do with F(D) - unless you maintain that the original, naive
target theory is sufficient to describe tumor induction. 

The equation for the Poisson probabilities has its proper application
when the confidence intervals for a given number, n, of observed tumors
have to be derived.


Kind regards, Rainer

Dr. Rainer Facius
German Aerospace Center
Institute of Aerospace Medicine
Linder Hoehe
51147 Koeln
Voice: +49 2203 601 3147 or 3150
FAX:   +49 2203 61970

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