.
Re
407935
Mathematical Model of Transport Mechanisms
Influencing Strontium 90 Levels in Milk
ROBERT H. SHUMWAY
A A PART of its radiation surveillance
program, the Public Health Service maintains a network of milk sampling stations
throughout the United States. Measurements
of radionuclide concentrations in milk have
been reported since 1957. The original network consisted of five stations (St. Louis,
Sacramento, New York City, Cincinnati, and
Salt Lake City) reporting the concentration of
strontium 90 in raw milk. Since 1960 a processed milk network consisting of 60 stations
has been in operation, and values are reported
monthly in Radiological Health Data. Strontium 90 values in general have been slightly
lower for the processed than the raw milk, particularly in the St. Louis area. The raw milk
network has been in existence for a much longer
time, and fluctuations in deposition rates during the different testing situations have influenced the observed raw milk levels quite
markedly. Because of the longer timespan covered by the raw milk measurements, it is convenient to use these numbers as baseline data
to test any assumptions about the eifects of the
different factors influencing levels of strontium
90 in milk. Once the model incorporating the
effects of these factors is developed, predictions
for future levels in milk can be made.
In general, determination of the levels of
strontium 90 in milk is important because of
Mr, Shumway was formerly senior assistant health
services officer in the Research Branch, Division of
Radiological Health, Public Health Service. Mrs.
Sarah Pendleton, Kenneth H. Falter, and Mrs. Gay-
nell Jayson of the Research Branch assisted with the
computations.
Vol. 77, No. 12, December 1962
the extent to which milk contributes to total
dietary intake, which in turn determineslevels
of strontium 90 in bone. Accurate predictions
for strontium 90 content of milk should lead to
more accurate predictions for strontium 90 in
bone and the resultant dose to the bone marrow.
In this paper, the 5 years of data from the raw
milk sampling network are used to derive a
model representing the mechanisms involved in
the movement of strontium 90, from deposition
on the plant to incorporation into the milk.
Using variables derived from experimental observations, predictions are made for the levels
to be expected in milk for each station during
the spring and summer of 1962. An attempt is
made to document the validity of each assumption madein the chain of reasoning.
Other attempts based on empirically reasonable relationships have been used to fit past
milk data and to predict future levels. Dr.
Harold Knapp of the Atomic Energy Commission (7) has attempted to relate the strontium
90 level in milk to deposition rates and cumulative deposition. He assumed that the proper
function of the two factors should be a linear
one.
Average strontium 90 in milk expressed in micromicrocuries per liter—a.%14-@:%2
where
@,=average cumulative strontium 90 level in U.S. soil
expressed in millicuries per square mile
#:—average strontium 90 deposition for the preceding
month expressed in millicuries per square mile per
month
The relative contributions from soil and cur-
rent deposition can be deduced by estimating
the scale factors a, and a, from the experimental
1055