Example : A patient received a dose of 120 mg gentamicin given as a constant rate iv infusion over 1 hr. Three plasma samples were obtained and the conc were as follows:
| Time after end of administration |
Conc (mg/L) |
| 1 hr |
6.8 |
| 3 hr |
5.0 |
| 5 hr |
3.7 |
Calculate gentamicin t1/2, and Vd in this patient.
The pharmacokinetic parameters can be determined graphically:
There are two different ways to plot the plasma concentrations:
a- The x axis can be chosen to start from the beginning of drug administrations. So, the time for the three conc will be at 2 hr, 4 hr, and 6 hr on the time scale.
Cp at the end of
drug administration
Notice that in this case when you back
extrapolate the line that goes through
the three samples to determine the drug
conc at the end of drug administration,
it will be the drug conc at 1 hr.
b- The x axis can be chosen to start from the end of drug administrations. So, the time for the three conc will be at 1 hr, 3 hr, and 5 hr on the time scale.
Cp at the end of
drug administration
t 1/2
Cp = 7.94 mg/L
Notice that in this case the entire x axis
is shifted to the right by 1 hr.
Graphically the half life = 4.5 hr
k = 0.693/4.5 hr = 0.154 hr-1
7.94 mg/L =
120 mg/hr
0.154 hr -1 Vd
= 1-e-0.154 hr -1 1hr
Vd = 14 L
