462 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



plutonium is represented by a system of linear, first-order, ordinjiry differential 

 equations, the general formula for which is 



n 11 



^=X^..Y,-Y,^Xj. = 1,2,3... n) (I) 



i=i i=i 



where j is the compartment of reference and all other compartments are designated i, Yi 

 is the amount (picocuries) of plutonium in compartment j at time t (days), and Xy and Xjj 

 are transfer coefficients (day" ' ) for flows into and out of compartment j. The positive 

 expression on the right side of Eq. 1 represents the flow rate into compartment j, and the 

 negative expression represents the flow rate out of compartment j. The amount present in 

 a given compartment at a given time, Yj(t), is therefore dependent on the rates of input 

 and output. 



In a general way, Fig. 1 and Eq. 1 identify the principal kinds of information needed 

 to estimate the transport of plutonium to man. The compartments of Fig. 1 indicate the 

 principal ecosystem components, and the arrows indicate the pathways of transport from 

 environment to man via inhalation and ingestion. Equation 1 suggests that intercompart- 

 mental How rates might be expressed as the product of a transfer coefficient and the 

 quantity of plutonium in the transmitting compartment. It was recognized, however, that 

 some parts of the transport system (Fig. 1) might not behave in accordance with the 

 first-order kinetics model suggested by Eq. 1. Consequently the objectives of the NAEG 

 plutonium studies were stated in broader terms. The general objectives related to the 

 estimation of potential human ingestion and inhalation rates were simply to (1) 

 determine plutonium concentrations in ecosystem components and (2) quantify the rates 

 of plutonium transfer among ecosystem components. 



In the remainder of this chapter, we discuss in turn each compartment of the 

 preliminary model (Fig. 1), soil, air, vegetation, herbivores (cattle), and man. In the 

 sections on soil, air, vegetation, and cattle, we describe what is known about the 

 compartment and discuss the processes that involve it in the transport of plutonium to 

 man. In the section on man, we provide methods for estimating plutonium inhalation and 

 ingestion rates, based on concentration in soil. These rates are used in the section on 

 Dose-Estimation Models to estimate organ burdens, cumulative doses, and dose 

 commitments by alternative methodologies. In the final section. Practical Applications, 

 we show how the results of the plutonium-transport and dose-estimation models can be 

 used to determine an "acceptable soil concentration." 



We wish to emphasize at the outset that this is not a definitive study of the behavior 

 of plutonium in desert ecosystems. It is merely an inquiry that asks how we can best use 

 the theory and data presently available to obtain a reasonable assessment of potential 

 hazards and a credible criterion on which to base preliminary consideration of 

 countermeasures that may or may not be planned and executed in the future. Our study 

 identifies some of the obstacles between present knowledge and a workable cleanup 

 criterion and recommends a pro tem path around these obstacles. In plotting this 

 sometimes tortuous path, we have encountered theory that cannot be applied for lack of 

 data, and we have encountered data that cannot be used because they are too scanty to 

 be fitted into the present theoretical framework. The result is a compromise between 

 knowledge and ignorance. We make use of the knowledge we have, but we are made 

 uneasy by the awareness that there are other paths, perhaps equally defensible, which 



