Biology Reference
In-Depth Information
and four doses have been given. The value C is the dosage, and the 2 in
Ce
2r
comes from the fact that it has been 2 hours from the last
administered dose.
E
XERCISE
1-18
We give a dosage of C
g/ml at 2-hour intervals. The elimination
constant is r hours
1
. There are six doses given. Give an expression for
the concentration 30 minutes after the last dose.
m
In general, the drug's concentration follows the pattern shown in
Figure 1-25.
If the drug is administered in dosages C at intervals of length T, then at
the end of the n-th period the concentration is:
n
n
1
n
2
e
Tr
e
Tr
e
Tr
e
Tr
¼
½ð
Þ
þð
Þ
þð
Þ
þ
...
þ
:
R
n
C
(1-34)
Thus, R
n
is the residual concentration from the first n doses immediately
before the next dose is administered. Immediately after the next dose,
the concentration rises to:
n
n
1
n
2
e
Tr
e
Tr
e
Tr
e
Tr
R
n
þ
C
¼
C
½ð
Þ
þð
Þ
þð
Þ
þ
...
þ
þ
1
(1-35)
To simplify expressions (1-34) and (1-35) and write them in closed form
(i.e., without using the ''and so on'' symbol ''
''), we need some
...
preliminary mathematics.
An expression of the form:
ab
3
ab
2
a
þ
ab
þ
þ
þ
...
(1-36)
20
18
16
14
12
10
8
6
4
2
0
0
10
20
30
40
50
60
70
80
Time
FIGURE 1-25.
Serum drug concentration with regular doses. A dose C
¼
10
g/ml is administered every
m
0.1 hours
1
.
T
¼
8 hours. The elimination constant for the drug is r
¼
