| Section 1 - Pharmacokinetic Concepts |
Drugs are cleared primarily by the liver and kidneys. Excretion into the urine is a major route of elimination for metabolites and unchanged drug.
Most drugs are eliminated by a first-order process. With first-order elimination, the amount of drug eliminated is directly proportional to the serum drug concentration (SDC).
With first order elimination, at a certain point in therapy, the amount of drug administered during a dosing interval exactly replaces the amount of drug excreted. When this equilibrium occurs (rate in = rate out), steady-state is reached.
Clearance (CL)
Clearance can be thought of as the proportionality constant that makes the average
steady-state drug level equal to the rate of drug administration. Clearance
(rate out) can be calculated from the dose (rate in) and average steady-state
concentration:
Clearance is a descriptive term used to evaluate efficiency of drug removal
from the body. Clearance is not an indicator of how much drug is being removed;
it only represents the theoretical volume of blood which is totally cleared of drug
per unit time. Because clearance is a first-order process, the amount of
drug removed depends on the concentration.
Cl = (Dose / interval) / Cpss ave
Elimination rate constant (Kel)
Here is an example of a first order process:
The serum level curve observed from a drug eliminated by a first order process:
A plot of this same data using a log scale on the y-axis results in a straight line.
The slope of this straight line correlates to Kel.
Mathematically, this relationship may be represented by the following equation.
If we plug in post-distribution serum levels (i.e., peak and trough levels), and the
time difference between them, we can calculate a Kel which is specific for this patient:
Once we have the Kel, we can rearrange this equation to predict the time it takes
to reach a specific serum level. If we plug our target peak and trough
levels in, then we can use this equation to calculate an ideal dosing interval (tau):
With first-order elimination, the rate of elimination is directly proportional to
the serum drug concentration (SDC). There is a linear relationship between rate of
elimination and SDC. Although the amount of drug eliminated in a first-order
process changes with concentration, the fraction of a drug eliminated remains
constant. The elimination rate constant (Kel) represents the fraction
of drug eliminated per unit of time.
Time
(hrs)
Amount remaining
in body
Amount
eliminated
Fraction
eliminated
0
1000
-
-
1
850
150
0.15
2
723
127
0.15
3
614
109
0.15
4
522
92
0.15
5
444
78
0.15
Kel = ln(Peak / Trough) / time
tau = ln(Peak / Trough) / Kel
Half-life (t ½)
Another important parameter that relates to the rate of drug elimination is half-life (t ½).
The half-life is the time necessary for the concentration of drug in the plasma to decrease by half.
Both t ½ and Kel attempt to express the same idea, how quickly a drug is removed, and therefore,
how often a dose has to be administered. An important relationship between t ½ and Kel can be
shown by mathematical manipulation:
T ½ = 0.693 / Kel
Relationship between Kel, Vd, and CL
Summary
Kel (and t ½) are dependent upon clearance and the volume of distribution.
However, it is invalid to make any assumptions about the Vd or CL of
a drug based solely upon knowledge of its half-life.
Kel = CL / Vd
Section 1 - Pharmacokinetic Concepts
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