PRINCIPLES OF TOXICOLOGY

2.4 DISPOSITION: DISTRIBUTION AND ELIMINATION 47
Figure 2.7 Plot of the logarithm of the concentration versus time for the linear one-compartment open model. C0
is the concentration at time t = 0, assuming instantaneous distribution. (Reproduced with permission from
O’Flaherty, 1981, Figure 2.15a.)
Calculated from the terminal slope of a plot of the natural logarithm of the concentration in the
central compartment as a function of time, this half-life is designated the biological half-life. It
is the parameter most frequently used to characterize the in vivo kinetic behavior of an exogenous
compound.
Other features of chemical kinetic behavior or of mode of administration may be incorporated into
the model as appropriate. For example, there may be more than one peripheral tissue compartment, as
in Figure 2.1; or absorption, which is never truly instantaneous even for intravenous injection, may be
first-order instead. An oral exposure, in which the rate of absorption is usually considered to be directly
proportional to the amount remaining available in the GI tract, is an example of first-order uptake.
The important group of models that incorporate non-first-order kinetics should also be mentioned.
Absorption and distribution are conventionally considered to be passive, first-order processes unless
observation dictates otherwise. However, elimination often is not first-order. Frequently this is because
excretion or metabolism is saturable, or capacity-limited, due to a limitation on the maximum number
of active transport sites in organs of excretion or the maximum number of active sites on metabolizing
enzymes. When all active elimination sites are occupied, the elimination process is said to be saturated.
Kinetically it is a zero-order process, operating at a constant maximum rate independent of the amount
or concentration of the chemical in the body. At very low concentrations at which relatively few
elimination sites are occupied, capacity-limited kinetics reduces to pseudo-first-order kinetics. Capacity-limited
kinetics is often referred to as Michaelis–Menten kinetics, after the authors of an early paper
analyzing and interpreting this type of kinetic behavior. Classical kinetic models incorporating
Michaelis–Menten elimination have been developed.