General Principles Of Pharmacology/First order model
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A simple, but useful, model for describing the absorption and elimination of a drug is the first-order, one compartment model. Mathematically it is expressed as:
When the rate of administration is instantaneous (or very fast, ka very large), as in an iv injection, the terms for ka drops out
and the equation can be written:
Since all of the drug is instantaneously absorbed, the fraction, f, of the dose absorbed becomes one, and the serum concentration
depends only upon the dose and the volume of distribution. The maximum serum concentration is D x Vd and is denoted Co:
Additionally, the rate of elimination is denoted, beta, in this case to reflect the fact that the time course is no longer contaminated by the rate of absorption:
If multiple (equal) doses of a drug are given at constant intervals, then a steady-state concentration will eventually be reached.
Approximately 94% of the ultimate steady-state value is achieved at approximately the fourth elimination half-life.
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