What elimination consists of
The elimination process (eliminatio) always begins after the drug reaches its initial concentration in the systemic circulation. To completely clear the body of a chemical agent, two basic mechanisms are involved:
- Biotransformation (metabolism). The process of chemical modification of a drug's structure by the body's enzyme systems.
- Excretion (elimination). The final removal of the substance or its inactive metabolites into the external environment.
For an accurate clinical evaluation of these processes, pharmacologists use a special mathematical apparatus based on the elimination rate constant ($k_{el}$) and the half-life ($t_{1/2}$).
First-order kinetics
The vast majority of modern drugs obey the rules of 1st-order kinetics (linear kinetics). Its main pharmacological feature is that the rate of elimination is directly proportional to the drug concentration in blood plasma. The higher the concentration of the substance, the faster it is eliminated by the body; the lower it is, the slower.
It is important to understand the key principle: over any given unit of time, a constant fraction (percentage) of the administered dose is eliminated from the body, rather than a fixed amount of the drug. On a concentration-versus-time graph, this process looks like a curve showing exponential (hyperbolic) decline.
Zero-order kinetics
This type of elimination occurs when hepatic enzyme systems or transporter proteins are working at their maximum capacity. Their saturation occurs upon reaching therapeutic or toxic concentrations. Under such conditions, a further increase in the drug concentration in the blood does not lead to an acceleration of its elimination.
Features of zero-order kinetics:
- The rate of the process does not depend on the concentration of the substance in blood plasma.
- Per unit of time, the body excretes a strictly defined amount of the substance (in grams or milligrams), rather than a percentage fraction.
- On the graph, the process looks like 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 such kinetics: ethanol (aethanolum) and phenytoin (phenytoinum). For example, the elimination of pure ethanol occurs at a rate of about 10 grams per 1 hour, regardless of the degree of intoxication.
Half-life ($t_{1/2}$)
Half-life is the exact time during which the concentration of a drug in plasma decreases by 50% of the initial value. For 1st-order kinetics drugs, this indicator is a constant and does not depend on the administered dose (unlike 0-order kinetics).
Dynamics of blood plasma clearance after a single intravenous administration:
- In 1 period ($1 \times t_{1/2}$), 50% of the substance is eliminated.
- In 2 periods ($2 \times t_{1/2}$), 75% is excreted.
- In 3.3 periods ($3.3 \times t_{1/2}$), 90% of the dose is eliminated (this is a clinically significant clearance threshold).
This parameter is critically important in clinical practice: it is used to calculate drug dosing intervals and is necessary to maintain a constant therapeutic concentration of the drug in the blood (steady state).
Mathematically, the half-life is inversely proportional to the elimination rate constant ($k_{el}$). The basic calculation formula is: $t_{1/2} = \frac{\ln 2}{k_{el}} \approx \frac{0.693}{k_{el}}$
Briefly: answers to topical questions
Which organs excrete drug substances?
- Kidneys (renes) — renal excretion, which is the main route of elimination of unchanged drugs and metabolites.
- Gastrointestinal tract (gastrointestinal tract) — excretion with bile into the intestinal lumen.
- Exocrine glands (glandulae exocrinae) — elimination through salivary, sweat, and mammary glands.
- Lungs (pulmones) — the pulmonary elimination pathway.
What phases are distinguished in the biotransformation of drugs?
- Phase I metabolism — includes oxidation, reduction, and hydrolysis reactions aimed at chemical modification of the molecule.
- Phase II metabolism — biosynthetic reactions (conjugation) consisting of the addition of polar endogenous groups to accelerate elimination.
Which drugs are eliminated according to zero-order kinetics?
- Ethanol (aethanolum) — pure ethanol, eliminated at a constant rate.
- Phenytoin (phenytoinum) — an antiepileptic agent characterized by nonlinear saturation kinetics at therapeutic concentrations.
What is total clearance (Cl) of a drug?
- Total clearance — the conditional volume of distribution of blood plasma or biological fluid that is completely cleared of a drug substance per unit of time.
- Dimension — measured in volume per time (e.g., ml/min, l/h) with a possible correction for body weight.
It is easy to remember the difference between kinetics orders through an analogy with warehouse workers. 1st-order kinetics: the more boxes are brought in, the more loaders come out for the shift (a constant percentage is eliminated, speed increases). 0-order kinetics: there is only one loader and he is already overloaded (saturation) — no matter how the mountain of boxes grows, he carries strictly one box per hour (a fixed amount is eliminated).
Class and exam questions
Does the half-life depend on the administered dose of the drug?
In first-order kinetics (typical for most drugs), the half-life is a constant value and does not depend on the dose. In zero-order kinetics, this relationship changes due to enzyme saturation.
How long does it take for a drug to be clinically completely eliminated from the body?
The removal of 90% of the active substance from the bloodstream is considered a clinically significant threshold. This occurs in approximately 3.3 half-lives after a single intravenous administration.
Why doesn't severe ethanol poisoning accelerate its elimination?
Ethanol is eliminated according to the laws of zero-order kinetics. Enzyme systems become fully saturated, and the body is able to metabolize only a strictly fixed amount of alcohol grams per hour, regardless of its huge concentration in the blood.
What else to study on this topic
- Phases of drug biotransformation in the liver
- Main excretion pathways and the concept of clearance
- Mathematical meaning of the elimination rate constant
- The concept of steady-state concentration and the time to reach it
- Calculation of dosing intervals based on pharmacokinetic parameters
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