Figure 5. Expectation Value of Intake Divided by Intake at T/2 for a Single Exponential

DOE-STD-1121-98

(18)

0.1

Tim e Betw een Bioassay Measurem ents, T (units of T1/2)

Retention Function

The ratio in Eq. (17) is plotted in Figure 5. Clearly, the expectation value of the intake, <I>, given

bioassay result X and a uniform probability of intake throughout the interval between bioassay

measurements, is greater than the value of the intake calculated at the expectation value of the intake time,

<ti>.

There exists a time, tx, (0 # tx # T), such that an intake of <I> at tx would yield bioassay result X at

time T. This time is

(19)

A plot of tx (T/2) as given in Eq 19 is shown in Figure 7. Clearly, tx occurs earlier in time than T/2, and

an intake calculated at T/2 underestimates the expectation value of the intake over the range of 0 to T.

What value, then, <ti> or tx, should be used for computing DILs and DRLs? The time of the

expectation value of intake is what we're concerned with, not the expectation value of intake time.

Therefore, tx is the correct value. Use of T/2 rather than tx for calculating the DIL will result in a DIL that

is too high, depending on the nature of the intake retention function and the length of time between

bioassay measurements.