Biology Reference
In-Depth Information
E
XERCISE
1-20
Compute the exact value of the limit R for the example in Figure 1-25:
C
0.1 hours
1
, T
¼
10
g/ml, r
¼
¼
8 hours.
m
Knowing the MEC, the MTC, and the drug's half-life (or its elimination
rate constant r), we now want to design a therapeutic regimen with
maximal benefits. Equal doses C of the drug should be given at equal
time intervals T. Once the concentration reaches the MEC, it should
remain between the MEC and MTC.
The graph in Figure 1-25 shows that after a few dosages the drug's
concentration is almost between R and R
C. (In fact, this is not quite
correct, but the difference is so small that it is not enough to have an
effect on the treatment's safety or effectiveness.) Because one goal is to
maintain the concentration between the MEC and MTC, we can
determine R and C from the conditions:
þ
R
¼
MEC
;
R
þ
C
¼
MTC
:
(1-43)
Because the MEC and MTC are known for every drug, we can determine
the dose C as:
C
¼
MTC
MEC
:
(1-44)
Using these values for R and C in Eq. (1-42), we obtain:
C
MTC
MEC
MEC
¼
R
¼
1
¼
:
(1-45)
e
Tr
e
Tr
1
E
XERCISE
1-21
MTC
MEC
1
r
ln
MTC
Solve the equation MEC
¼
for T to show that T
¼
MEC
:
e
Tr
1
Requiring all doses to be the same has the obvious disadvantage that a
certain build-up period is required before the concentration reaches the
MEC. For some drugs, such as certain antidepressants, a slow build-up
is necessary to minimize side effects. For many other common drugs,
however, the dosage schedule tolerates a larger first dose to achieve the
maximal effective concentration as quickly as possible.
E
XERCISE
1-22
If a drug's MEC, MTC, and elimination constant r are known, determine
a drug intake schedule that maximizes the drug's therapeutic effect
under the following constraints:
