Components of Elimination
The elimination process (eliminatio) always begins after a drug reaches its initial concentration in the systemic circulation. To completely clear the chemical agent from the body, two basic mechanisms are involved:
- Biotransformation (metabolism): The process of chemical alteration of a drug's structure by the body's enzyme systems.
- Excretion: The final removal of the substance or its inactive metabolites into the external environment.
For precise clinical evaluation of these processes, pharmacologists use specialized mathematical tools based on the elimination rate constant ($k_{el}$) and the elimination half-life ($t_{1/2}$).
First-Order Kinetics
The vast majority of modern drugs follow first-order kinetics (linear kinetics). Its main pharmacological feature is that the rate of elimination is directly proportional to the drug concentration in the plasma. The higher the concentration of the substance, the faster it is eliminated by the body; the lower the concentration, the slower.
It is important to understand the key principle: over any given time unit, a constant fraction (percentage) of the administered dose is eliminated from the body, rather than a fixed amount. On a concentration-versus-time graph, this process appears as a curve showing an exponential (hyperbolic) decline.
Zero-Order Kinetics
This type of elimination occurs when hepatic enzyme systems or transporter proteins work at their maximum capacity. Saturation occurs when therapeutic or toxic concentrations are reached. Under such conditions, a further increase in the drug concentration in the blood does not lead to an acceleration of its excretion.
Features of zero-order kinetics:
- The rate of the process does not depend on the plasma concentration of the substance.
- Per unit of time, the body excretes a strictly defined amount of the substance (in grams or milligrams) rather than a percentage.
- On a graph, the process appears as a straight line, where the slope ($\tan \alpha$) corresponds to the elimination rate constant ($k_0$). Formula: $\tan \alpha = -k_0$.
Classic examples of substances subject to this kinetics include ethanol (aethanolum) and phenytoin (phenytoinum). For example, the elimination of pure ethanol occurs at a rate of about 10 grams per hour, regardless of the degree of intoxication.
Half-Life ($t_{1/2}$)
The elimination half-life is the exact time required for the plasma concentration of a drug to decrease by 50% from its initial value. For drugs following first-order kinetics, this parameter is a constant and does not depend on the administered dose (unlike zero-order kinetics).
Dynamics of plasma clearance after a single intravenous injection:
- In 1 half-life ($1 \times t_{1/2}$), 50% of the substance is removed.
- In 2 half-lives ($2 \times t_{1/2}$), 75% is eliminated.
- In 3.3 half-lives ($3.3 \times t_{1/2}$), 90% of the dose is eliminated (this is the clinically significant clearance threshold).
This parameter is critical in clinical practice: it is used to calculate dosing intervals and is necessary to maintain a constant therapeutic drug concentration in the blood (steady state).
Mathematically, the half-life is inversely proportional to the elimination rate constant ($k_{el}$). The basic calculation formula is: $t_{1/2} = \frac{\ln 2}{k_{el}} \approx \frac{0.693}{k_{el}}$