Biology Reference
In-Depth Information
Metabolism occurs through the action of protein catalysts called
enzymes. Metabolism of drugs most often occurs in the liver, although
there are some enzymes in the bloodstream as well. Liver enzymes, such
as epoxide hydratase and the cytochrome P450 family, catalyze the
chemical modification of the drugs, often oxidizing them and making
them more amenable to excretion.
In excretion, the kidneys filter the blood and remove drugs as well as
metabolic wastes. Drugs may also be excreted by the liver in the bile, a
substance necessary for digesting fats. Bile is made by the liver, stored in
the gall bladder, and delivered into the small intestine. Drugs may
also be removed from the bloodstream by the lungs and then exhaled.
(If this sounds unlikely, just think of the ''breathalyzer'' commonly used
for testing persons suspected of driving under the influence of
alcohol!) By this point, it should be clear that we need to begin our
model construction by making some simplifying assumptions.
The simplest model would be to assume instantaneous entry of drug
into the bloodstream, followed by its gradual clearance from the
bloodstream. An intravenous injection might well approximate
instantaneous entry. It is known from experimental data that the
clearance rate of drugs from the bloodstream is generally proportional to
the amount present in the bloodstream. Therefore, we are looking at an
example of exponential decay—the reverse of our first population
model.
If C(t) is the drug concentration at time t, then the fact the drug is
eliminated from the bloodstream at a rate proportional to the amount
present can be expressed as:
dC
Þ
dt
¼
ð
t
rC
ð
t
Þ;
(1-29)
where r
>
0.
The negative sign on the right-hand side of (1-29) indicates the
derivative
dC
dt
of the concentration function C(t) is negative, and thus the
drug's concentration in the blood is decreasing.
E
XERCISE
1-15
Show that the solution of Eq. (1-29) is given by:
e
rt
C
ð
t
Þ¼
C
ð
0
Þ
:
(1-30)
Equation (1-29) has one parameter, represented by the elimination rate
constant r. Larger values of r correspond to faster elimination. By
