Re: Pu Toxicity

[FRAMEP@ORAU.GOV]

Message authorized by:
/S=avest@magnus.acs.ohio-state.edu/O=ORAUSMTP/PRMD=ESNET/ADMD= /C=US/ at X400PO
On July 5, Albert West responded to the following part of a previous
          message of mine:

         " Cancer makes Pu an even greater risk (somebody please check the
           following numbers)"

His response is as follows (down to the line of asterisks):

          "Sure thing, my friend.  Sorry it's taken so long.

          Deaths from 0.1 mg Pu-239 (0.0001 g) inhaled: 0.1 mg =
          0.0001 g x 0.062 Ci/g = 6.2 E-6 Ci x 3.7 E10 Bq/Ci = 229,400
          Bq.  The EDE for Pu-239 inhaled is ca 1 E-4 Sv/Bq
          so 0.1 mg inhaled gives 229,400 Bq x 1 E-4 Sv/ Bq
          = 23 Sv or 2300 rem.

So far, so good.

          Given that the risk of death is @ 5 E-4/rem,
          the risk of death from 0.1 mg Pu-239 inhaled would be 2300
          rem x 5 E-4/rem  = 1. Thats high!

That's bogus.

          First of all 2300 x 5 E-4 is 1.15, greater than one.  That's
          a meaningless probability value.

          The linear relation (risk_per_unit)x(units) = (total risk)
          is only an approximation, the second term of a binomial
          expansion.  It works fine when the total risk is itself
          small (0.05 or less), but I wouldn't use it for general
          cases, any more than I'd use 1/2*m*v^2 for kinetic energy of
          all particles. (sometimes m=0; sometimes v is close to c.)


I'll cut to the chase.  The general expression is

[1 - risk_per_unit]^(units) = [1 - total_risk].

Intuitively, [1-risk_per_unit] is one's chance of *surviving* one unit.  One
need only *not survive* one of the (units) units (for which the total risk
for a single unit is assumed to be known) for the bad result predicted by
(total_risk) to ensue.

Using Paul's numbers with my formula, I got a total_risk of 0.68 or so.          
*  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *  *

          Albert, words cannot describe my sorrow at hearing a friend
          describe my calculations as bogus. However, I am grateful
          that you seem to agree with (or don't dispute) the key point
          of my message: the risk from inhaled plutonium is higher
          than that indicated in Wade's table.

          Clearly, what I was doing can lead to
          confusion, mea culpa.  Working backwards, I was calculating
          a quantity of inhaled plutonium that could be compared with
          the lethal levels of various other materials described in
          the table.  This was difficult because my calculated value
          (100 mg) had to cause death via lung cancer - a stochastic
          effect. No single quantity (i.e. dose) of Pu can be certain
          to cause lung cancer. What to do?  The logical approach was
          to calculate the quantity of Pu that would prove lethal for
          an average individual.  For my contrived purpose,  death had
          to be certain (risk of 1) and by definition it could be for
          our average human.  You are right, all the other numbers
          being a given, for a specific individual the risk from 0.1
          mg would be 0.68.  Chances are that specific individual dies
          via cancer, but death is not certain. Yes, a risk of 1 for a
          stochastic effect (or 1.15) is meaningless. Unless, it is
          for an individual who has died, and that is who I was
          working with.

          I did indeed drop significant digits in a few of my
          calculations; as you noted, 2300 x 5 E-4 is 1.15, not 1.  

     Your humble and obedient servant

          Paul Frame