A Mathematical Analysis of the Transfer of Fission Products to Cowsʼ Milk

Abstract

A model is developed which allows mathematical treatment of the elimination of ingested fission products in milk. Equations are derived from the available experimental data which are used to predict the behaviour of a number of parent-daughter mixtures.IN MOST laboratory experiments on the transfer of fission products to milk, the change in concentration with time of a nuclide in milk has been studied following oral adminstration of a single dose. However, it is frequently desired to know what would be the course of events under more complex conditions of exposure of grazing animals. Prediction from single dose experiments to other situations has been shown to be but computation is tedious and would be eased if the curves relating change in concentration with time could be expressed mathematically. To date this has been attempted only for isotopes of iodine. (3) The purpose of the present paper is to postulate a simple model to provide a rational basis for mathemetical analysis of the existing experimental data and to use the model to predict the behaviour of parent-daughter mixtures which have not been studied experimentally. Udder I -Q m FIG. 1. Simplified compartmental model to describe metabolism of an ingested nuclide. &, , etc., represent the amounts of nuclide present in each compartment, rl, etc., are the rate constants describing transfer between compartments.

INVESTIGATIONS INTO THE CYCLING AND RECYCLING OF CERTAIN RADIONUCLIDES THROUGH THE MILK FOOD CHAIN. Final Report, December 15, 1963--December 14, 1966.

“…Of particular note is the work of Comar (39), Wasserman and Lengemann on the transfer of iodine-131 (40,41) and, strontium-9 0 (42,43,44) to milk, the work at the National Reactor Testing Station on iodine-131 (22,45), Garner's work (46,50) and the work of others (47) to milk (48,49,51) . All of these studies have let to empirical relations between the intake and output of radionucl ides in milk.…”

A Methodology for Calculation of Internal Dose Following Exposure to Radioactive Fallout from the Detonation of a Nuclear Fission Device

“…The second is to consider the cow's intake of feed that has been contaminated by the processes considered above, even though that contamination might have occurred at locations far removed from the cow's location. The following material on the concentration of short-lived radionuclides in milk follows Bunch (1966), Garner (1967), andKoranda et al (1971). The cow's rate of intake of radionuclide i, İ cow;i , is given by…”