Biology Reference
In-Depth Information
concentration in the bloodstream to fall below 1% of the initial
concentration?
The following example shows how to mathematically model multiple
doses.
Example 1-3
.......................
A drug whose elimination constant is r hours
1
is first administered at
1:00
A
.
M
. at a dosage C
g/ml and in the same dosage every three hours
afterwards. What is the drug's concentration at 12:00 noon?
m
S
OLUTION
:
By 12:00 noon, we will have given four doses. The total concentration is
the sum of the concentrations of each dose. Because the doses were given
at different times, the effect at 12:00 noon is different for each dose, as
shown in Table 1-6.
The total concentration at 12:00 noon is then equal to:
Ce
11r
Ce
8r
Ce
5r
Ce
2r
Ce
2r
e
9r
e
6r
e
3r
þ
þ
þ
¼
ð
þ
þ
þ
1
Þ:
(1-31)
e
3r
, then
For a more compact form of Eq. (1-31), observe that if b
¼
b
2
e
6r
, and b
3
e
9r
. Thus, the concentration becomes:
¼
¼
Ce
2r
b
3
b
2
ð
þ
þ
b
þ
1
Þ:
(1-32)
From this example, we can extract a more general result. In the term
e
3r
, the number 3 arises from the time between dosages. Notice also that
the parenthetical expression contains four terms:
b
3
b
2
b
3
b
2
b
0
þ
þ
b
þ
1
¼
þ
þ
b
þ
;
(1-33)
Length of Time in Body
(hours) by 12:00 Noon
Residual Concentration from
the Dose at 12:00 Noon (
m
g/ml)
Time of Dose
Ce
11r
1:00
A
.
M
.
11
Ce
8r
4:00
A
.
M
.
8
Ce
5r
7:00
A
.
M
.
5
Ce
2r
10:00
A
.
M
.
2
TABLE 1-6.
Contribution of multiple doses to serum drug concentration.
