In an attempt to corroborate findings of the National Cancer Institute (see discussion in Chapter 2), a simple calculation is presented to estimate the collective dose to the thyroids of the U.S. population that occurred from the release of ^{131}I from the nuclear weapons tests carried out in Nevada during the 1950s and 1960s. The collective dose can be estimated in an approximate way by use of the following equation:

which has the solution of

In eqns (1) and (2) the parameters are defined as follows:

*C* = Units-conversion constant, 390,625 mi^{-2} m^{-2} µCi MCi^{-1};

*S* = Amount of ^{131}I released by the tests, MCi;

*f*_{d} = Fraction of the ^{131}I released that is deposited within the continental U.S.;

*A* = Area of the continental U.S., mi^{2};

*a* = Mass-interception fraction for fallout retained on vegetation, m2 kg^{-1};

*MPD* = Mass (dry) per day of pasture or green chop consumed by a cow, kg day^{-1};

*f*_{m} = Fraction of cow's intake that is secreted in milk, day L^{-1};

*L* = Consumption rate of milk, L day^{-1};

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Exposure of the American People to Iodine-131 from Nevada Nuclear-Bomb Tests: Review of the National Cancer Institute Report and Public Health Implications
Appendix C
Calculation of Collective Thyroid Dose to the U.S. Population from the Release of 131I from the Nuclear Weapons Tests in Nevada
In an attempt to corroborate findings of the National Cancer Institute (see discussion in Chapter 2), a simple calculation is presented to estimate the collective dose to the thyroids of the U.S. population that occurred from the release of 131I from the nuclear weapons tests carried out in Nevada during the 1950s and 1960s. The collective dose can be estimated in an approximate way by use of the following equation:
which has the solution of
In eqns (1) and (2) the parameters are defined as follows:
C = Units-conversion constant, 390,625 mi-2 m-2 µCi MCi-1;
S = Amount of 131I released by the tests, MCi;
fd = Fraction of the 131I released that is deposited within the continental U.S.;
A = Area of the continental U.S., mi2;
a = Mass-interception fraction for fallout retained on vegetation, m2 kg-1;
MPD = Mass (dry) per day of pasture or green chop consumed by a cow, kg day-1;
fm = Fraction of cow's intake that is secreted in milk, day L-1;
L = Consumption rate of milk, L day-1;

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Exposure of the American People to Iodine-131 from Nevada Nuclear-Bomb Tests: Review of the National Cancer Institute Report and Public Health Implications
N = Number of persons in the U.S. in 1955;
NCF = Dose-conversion factor for the thyroid, rad mCi-1; and
λ = Effective rate of loss of 131I on pasture, day-1.
The amount, S, of 131I released by the tests at the Nevada Test Site was given in the NCI report from data derived by Hicks (1982, 1990). A reasonable estimate is 150 MCi, which may be considered as a geometric mean with a geometric standard deviation of 1.25. The latter value is based upon an estimate for a closely related parameter and is given by Ng et al. (1990).
The fraction, fd, of the 131I released by the tests that deposits within the continental United States is much more difficult to quantify. In a study to be published, Anspaugh and McArthur (1998) have determined that the amount of 137Cs remaining in the NTS and the Phase I and II areas of the ORERP study (see Church et al. 1990) is equivalent to 10 percent of that originally released. This may be considered as a lower bound on the amount deposited within the continental U.S. An upper bound could be considered as 1.00. Then, assuming that these bounds are the 5th and 95th percentile of a lognormal distribution, the geometric mean is 0.32 with a geometric standard deviation of 2.0. This value is also reasonably consistent with the independent estimate made by Beck et al. (1990) that 25-30 percent of 137Cs produced in the Nevada Tests was deposited within the continental U.S. The latter estimate was based upon drawing crude contours of deposition density as measured by gummed-film collectors and calculating that the fraction of 137Cs deposited within those contours was 21 percent (the estimates ranged from 5 percent for Operations Ranger and Hardtack II to 42 percent for Operation Tumbler-Snapper). An additional amount of about 10 percent was assumed to be deposited with local fallout; thus, the estimate of 25-30 percent of total fallout deposited within the continental U.S.
The area, A, of the continental U.S. according to data in Funk & Wagnalls (1994) is 3,119,963 square miles.
The mass-interception fraction, α, of 131I in fallout that is retained by pasture-type vegetation is taken to be 1.0 based on the article by Simon (1990). Further, the range is estimated to be from 0.5 to 2.0. This is approximately equivalent to a geometric mean of 1.0 with a geometric standard deviation of 1.52.
The dry mass consumption rate, MPD, for milk cows is based on the work by Koranda (1965), who reported an average value of 14 kg day-1. It is assumed here that this value can be characterized by a geometric standard deviation of 1.5; this would correspond to a geometric mean value of 13 kg day-1.
The classic value for the rate of secretion of 131I in milk, fm, is 0.005 day L-1 (Garner and Russell 1966). This value is assumed to be a geometric mean with a geometric standard deviation of 1.5.
The per capita consumption rate of milk, L, is taken from the NCI report. The value of 0.4 L day-1 is assumed to be a geometric mean with a geometric standard deviation of 1.5.

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Exposure of the American People to Iodine-131 from Nevada Nuclear-Bomb Tests: Review of the National Cancer Institute Report and Public Health Implications
The number of persons in the continental U.S. in 1955, N, is interpolated between the 1950 and 1960 census values reported in Funk & Wagnalls (1994). This value is 165,000,000.
The population-weighted dose-conversion factor for 131I-thyroid dose is about 2 rad mCi-1. This value is assumed to be a geometric mean with a geometric standard deviation of 1.8 (Ng et al. 1990) for an individual. For the average, we assume a geometric standard deviation of the mean of 1.5.
The controlling rate constant for the loss of 131I from the pasture-cow-milk system is the effective rate of loss of 131I from pasture λ. The nominal rate of loss independent of radioactive decay corresponds is 0.05 day-1 (Thompson 1965). A somewhat arbitrary value of a geometric standard deviation of 1.5 is assigned to this value. The rate of loss due to decay is 0.0862 day-1, and the effective rate of loss is 0.1362 day-1. The corresponding geometric mean is 0.137 day-1 with a geometric standard deviation of 1.5.
The product of all values indicated above, with the exception of the number of persons, is 2.3 rad, which is taken to be the geometric mean of the dose to the population of the U.S. The associated geometric standard deviation of this number is 3.4. The arithmetic average that corresponds to these values (see, for example, Ng et al. 1990) is 5 rad, which when multiplied by the number of persons produces a value of the collective dose of 8 × 108 person-rad. The comparable number provided in the NCI report is 4 × 108 person-rad.
Further, the 5th and 95th percentile ranges of the collective dose according to the simplified scheme derived here are 5 × 107 and 3 × 109 person-rad.
References
Anspaugh, L. R.; McArthur, R. D. Inventory and distribution of residual 137Cs on and near the Nevada Test Site (to be submitted).
Beck, H. A.; Helfer, I. K.; Bouville, A.; Dreicer, M. Estimates of fallout in the continental U.S. from Nevada weapons testing based on gummed-film monitoring data. Health Physics 59:565-576; 1990.
Church, B. W.; Wheeler, D. L.; Campbell, C. M.; Nutley, R. V.; Anspaugh, L. R. Overview of the Department of Energy's Off-Site Radiation Exposure Review Project (ORERP). Health Physics 59:503-510; 1990.
Funk & Wagnalls. The world almanac and book of facts 1995. In: Microsoft Bookshelf; 1994.
Garner, R. J.; Russell, R. S. Isotopes of iodine. In: Russell, R. S., ed.: Radioactivity and Human Diet. New York: Pergola Press; 1966.
Hicks, H. G. Calculation of the concentration of any radionuclide deposited on the ground by offsite fallout from a nuclear detonation. Health Physics 42:585-600; 1982.

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Exposure of the American People to Iodine-131 from Nevada Nuclear-Bomb Tests: Review of the National Cancer Institute Report and Public Health Implications
Hicks, H. G. Additional calculations of radionuclide production following nuclear explosions and Pu isotopic ratios for Nevada Test Site Events. Health Physics 59:515-523; 1990.
Koranda, J. J. Agricultural factors affecting the daily intake of fresh fallout by dairy cows. Livermore, CA: Lawrence Livermore National Laboratory; Report UCRL-12479; 1965.
Ng, Y. C.; Anspaugh, L. R.; Cederwall, R. T. ORERP internal dose estimates for individuals. Health Physics 59:693-713; 1990.
Simon, S. L. An analysis of vegetation interception data pertaining to close-in weapons test fallout. Health Physics 59:619-626; 1990.
Thompson, S. E. Effective half-life of fallout radionuclides on plants with special emphasis on iodine-131. Livermore, CA: Lawrence Livermore National Laboratory; Report UCRL-12388; 1965.