Page 316 - Industrial Ventilation Design Guidebook

272 CHAPTER 5 PHYSIOLOGICAL AND TOX1COLOGICAL CONSIDERATIONS

elimination rate constant & el has units of reciprocal time (e.g., min~' and
4
l
br ). For example, if the elimination rate constant is 0.5 h" the percentage
of the dose excreted after one, two, or three hours is the same, regardless
of the given dose. In this case, the percentage of the dose excreted is 43%,
even though the rate constant is 0,5/h (or 50%/h), because the dose re-
maining in the body (C) decreases continuously with time. The elimination
rate decreases (k e f C) when the dose remaining in the body (C) decreases.
The first-order elimination rate of the compound is mathematically ex-
pressed as an exponential equation C = C 0 • exp(~& f /0 where C is the
plasma concentration, k e\ the first-order elimination rate constant, and t
the time of blood sampling. With logarithmic transformation a straight
line is obtained:

where In C 0 represents the intercept and —k ei represents the slope of the line.
Therefore, the first-order elimination rate constants can be determined by uti-
lizing the slope of the In C versus time plot.
In addition to the elimination rate constant, the half-life (1-1/2) ' s an ~
other important parameter that characterizes the time-course of chemical
compounds in the body. The elimination half-life (£1/2) is the time to re-
duce the concentration of a chemical in plasma to half of its original
level. The relationship of half-life to the elimination rate constant is
ti/2 — Q.693/k e[ and, therefore, the half-life of a chemical compound can
be determined after the determination of k ei from the slope of the line.
The half-life can also be determined through visual inspection from the
log C versus time plot (Fig. 5.40). For compounds that are eliminated
through first-order kinetics, the time required for the plasma concentra-
tion to be decreased by one half is constant. It is important to understand
that the half-life of chemicals that are eliminated by first-order kinetics is
68 85 86
independent of dose. ' '
Two-Compartment Model
If the plotting of the logarithm of the plasma concentration against time
does not result in a straight line but rather in a curve, the use of multicompart-
ment models is required. Multicompartment models are required for com-
pounds that distribute to different organs at different rates. Such compounds
are usually lipid-soluble and reach equilibrium in lipid-containing organs rela-
tively slowly. This results in multiexponential elimination because chemical
compounds are eliminated in a reverse order as compared with their distibu-
tion. In the simplest case, this type of curve can be resolved into two exponen-
tial terms (a two-compartment model). Concentration can be expressed as
a
C = Ae + B@ where A and B are proportionality constants and a and J3 are
rate constants with dimensions of reciprocal time. During the distribution al-
pha phase, concentrations of the chemical in plasma decrease more rapidly
than they do in the postdistribution phase (beta). The length of the distribu-
tion phase may vary from minutes to hours to days. Whether the distribution
phase becomes apparent depends on the time of the sampling after the cessa-
tion of the exposure. Since most chemicals in the occupational environment