Biomedical Engineering Reference
In-Depth Information
0
@
1
A
0
@
1
A
0
@
1
A
g
K
10
K
10
K
10
0
@
1
A
0
@
1
A
0
@
1
A
g
g
K
10
g
K
10
g
0
1
0
1
g
K
10
K
10
K
10
ln
ln
g
g
Þ
K
10
ð
0
Þ
K
10
ð
0
¼
q
¼
q
K
K
2
2
@
10
g
A
@
10
g
A
e
e
g
g
0
1
0
1
0
1
0
1
0
1
0
1
g
K
10
K
10
K
10
K
10
K
10
g
K
10
K
10
g
g
g
g
@
A
¼
q
2
ð
@
A
¼
q
2
ð
0
Þ
g
K
g
K
0
Þ
g
K
g
K
@
A
@
A
@
A
@
A
1
K
g
K
g
10
10
10
10
10
10
0
1
0
0
1
1
A
¼
q
2
ð
0
1
0
@
1
A
K
10
K
10
g
K
10
K
10
g
¼
q
2
ð
0
Þ
g
K
K
10
g
0
Þ
g
K
K
10
g
@
A
@
@
A
@
A
1
K
g
K
g
g
10
10
10
10
0
@
1
A
K
10
K
10
g
¼
q
2
ð
0
Þ
g
K
ð
7
:
39
Þ
g
10
The maximum concentration of the drug is
K
10
K
10
c
1
ð
t
max
Þ¼
q
2
ð
0
Þ
g
K
g
ð
7
:
40
Þ
V
1
g
10
With an exponential
input,
the maximum drug concentration occurs at
time
t
¼
max
g
K
K
10
K
10
K
10
g
with value
q
2
ð
0
Þ
g
K
g
ln
according to Eqs. (7.38) and (7.40). When giving a
V
1
g
10
10
bolus injection, the maximum drug concentration occurs at time 0 with value
q
ð
0
Þ
2
accord-
ing to Example Problem 7.5. Thus, a bolus injection achieves a higher concentration of the
drug in the plasma and is faster than an exponential input.
When administering a drug in the body, the persistence of the drug is an important
parameter to judge the clinical effectiveness and to determine a dose administration
schedule. To produce a therapeutic effect, a minimum drug concentration in the plasma
is required so the drug can diffuse to its target site. Maximum drug concentration is an
important parameter, since a dosage at too high a level can be toxic. The next section
describes how to maintain a minimum and maximum dosage.
V
1
7.5.4 Repeat Dosages
To maintain the concentration of a drug in the body, the drug must be administered on a
regular basis to keep the concentration above a minimum value. For simplicity, assume the
model in Figure 7.8 and Eq. (7.29), and that the input is a series of boluses, with magnitude
