FOOD-CHAIN KINETICS OF RADIONUCLIDES
775
DETERMINISTIC MODELS FOR HUMAN-FOOD-CHAIN KINETICS
The data summarized and discussed in the preceding pages have
served-—to illustrate the usefulness of deterministic exponential models
in providing at least a partial explanation of the early food-chain ki-
netics of radionuclides following a single fallout event. Although the
results of these studies are not conclusive, they are promising and
provide a basis for the supposition that similar models should be useful in the study of radionuclide transfers in food chains leading to man.
For example, suppose that an ordinary pasture is contaminated by
fallout from a single nuclear detonation or from a reactor accident and
that the milk produced by dairy cattle grazing in the contaminated
pasture is consumed by people living on the farm or in a nearbyvillage. If an estimate of the initial concentration of a given radionuclide,
N,, on pasture plants, Py, can be obtained from direct measurementor
predicted by a suitable fallout model, the subsequent concentration of
N, on pasture plants, P,, in cow milk, M,, and in the humantissue or
organ of reference, H,, can be estimated, with the assumptionsthat
P =P), M =0, and H =0 att = 0, by Eqs. 8 to 10:
P,= Pye
(8)
e7 Ant
ew rt
Mi = PoKmfm (<< —)
H.= PKaf»K
mee
c et
wh le = Ap)OAn= Ap)
)
+
e” \mt
p= Am)OAn— Am)
e7 ht
* (Ap — An) — An)
0)
where t = days after fallout
N,; =a given radionuclide (e.g., ®sr or ‘!z)
Py pe N,/g (dry) on pastureplants at t = 0
P, = pe N,/g (dry) on pastureplants at t > 0
M,=pc N;/ml (fresh) in milk produced at t > 0
H, = pe Ni/g (fresh) inthe human tissue or organ of reference att >0
Kn = dry weight (g) of plants consumed/volume (ml) of milk produced per day
K,, = volume (ml) of milk consumed per day/weight (g) of human
organ or tissue
f,, = fraction of ingested N; secreted in cow milk
f, =fraction of ingested N, deposited in human tissue or organ of
reference
A = 0.693/T
p = effective half-life of N, on pasture plants
T,, = effective half-life of N; in cow milk production
T, = effective half-life of N; in human tissue or organof reference