Question 5(p.2)

College Answer

For a good answer it was expected that candidates would mention that if mechanisms for
elimination of a given drug become saturated, the kinetics approaches zero order, in which a constant amount of drug is eliminated per unit of time. First-order kinetics, is where a
constant fraction of drug in the body is eliminated per unit of time – that is, systems for
elimination of drugs such as metabolizing enzymes and transporters are not saturated, and
thus the absolute rate of elimination of the drug is essentially a linear function of its
concentration in plasma. Clearance varies with the concentration of drug. Drugs with a target concentration is more than the concentration at which half the maximal rate of elimination is reached have a narrow therapeutic index and zero order kinetics and therapeutic drug monitoring is most important – low therapeutic index and variable half life. In contrast to capacity-limited drug elimination, some drugs are cleared very readily by the organ of elimination, so that at any clinically realistic concentration of the drug, most of the drug in the blood perfusing the organ is eliminated on the first pass of the drug through it. The elimination of these drugs will thus depend primarily on the rate of drug delivery to the organ of elimination – have a high-extraction. Phenytoin provides an example of a drug for which metabolism becomes saturated in the therapeutic range of concentrations, and half-life can vary between 7 and 42 hours.

Syllabus – II 2a
Reference: Goodman and Gillman Chp 1

Discussion

Definitions and difference between first-order and zero-order kinetics:

• First order elimination kinetics: a constant proportion (eg. a percentage) of drug is eliminated per unit time.
• Zero order elimination kinetics: a constant amount (eg. so many milligrams) of drug is eliminated per unit time.
• First order kinetics is a concentration-dependent process (i.e. the higher the concentration, the faster the clearance), whereas zero order elimination rate is independent of concentration.
• Michaelis-Menten kinetics  describes enzymatic reactions where a maximum rate of reaction is reached when drug concentration achieves 100% enzyme saturation. Beyond this concentration, clearance will be zero-order.  The maximum rate of reaction in this instance is called V_max (i.e. maximum velocity). The concentration required to achieve 50% of this maximum reaction rate is called K_m
• Non-linear elimination kinetics is the term which describes drug clearance by Michaelis-Menten processes, where a drug at low concentration is cleared by first-order kinetics and at high concentrations by zero order kinetics (eg. phenytoin or ethanol). 

It might be helpful for the candidate to draw a crude diagram to illustrate what they mean:

Clinical relevance of these concepts:

• Drugs with zero-order elimination have a variable half-life, whereas drugs with first-order elimination will have a fixed predictable half life.
• Zero-order elimination may be very slow in a large overdose
• Drugs with non-linear elimination kinetics and a narrow therapeutic index require frequent plasma concentration monitoring 
• First-order elimination kinetics may be seen in normal therapeutic range (i.e the therapeutic range is well below K_m ) but in overdose the drug may be cleared with zero-order kinetics.

Examples relevant to intensive care practice:

• Gentamicin is a good example of first-order kinetics; its clearance is completely concentration-dependent because is is cleared by glomerular filtration, which is not a saturable process.
• Ethanol  is a good example of zero-order kinetics because the K_m of alcohol dehydrogenase is laughably low (~ 1mmol/L) and therefore the first drink typically saturates the enzymes up to V_max; thereafter the rate of its clearance is zero-order, at ~ 7-10g/hr.
• Phenytoin is a good example of a drug for which Michaelis-Menten elimination kinetics are important within the therapeutic range of plasma concentrations; it is cleared with first-order kinetics at low concentrations and with zero-order kinetics at high concentrations. 

Richens, Alan. "Clinical pharmacokinetics of phenytoin." Clinical pharmacokinetics 4.3 (1979): 153-169.

Richens, Alan, and Andrew Dunlop. "Serum-phenytoin levels in management of epilepsy." The Lancet 306.7928 (1975): 247-248.

Barza, Michael, et al. "Predictability of blood levels of gentamicin in man." Journal of Infectious Diseases 132.2 (1975): 165-174.

Goncalves‐Pereira, J., A. Martins, and P. Povoa. "Pharmacokinetics of gentamicin in critically ill patients: pilot study evaluating the first dose." Clinical Microbiology and Infection 16.8 (2010): 1258-1263.

Rangno, R. E., J. H. Kreeft, and D. S. Sitar. "Ethanol ‘dose‐dependent’elimination: Michaelis‐Menten v classical kinetic analysis." British Journal of Clinical Pharmacology 12.5 (1981): 667-673.

Cederbaum, Arthur I. "Alcohol metabolism." Clinics in liver disease 16.4 (2012): 667-685.