      Section 1 - Pharmacokinetic Concepts

### Elimination

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 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.

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:

Cl = (Dose / interval) / Cpss ave

Elimination rate constant (Kel)
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.

Here is an example of a first order process:

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

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:

Kel = ln(Peak / Trough) / time

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):

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
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

Summary

• Most drugs are eliminated by a first-order process.
• Steady-state is that equilibrium point where the amount of drug administered exactly replaces the amount of drug excreted.
• Clearance represents the theoretical volume of blood which is totally cleared of drug per unit time.
• Kel represents the fraction of drug eliminated per unit of time.
• The slope of a log-scale serum level decay curve correlates to Kel.
• t ½ is the time necessary for the concentration of drug in the plasma to decrease by half.      Section 1 - Pharmacokinetic Concepts