The discipline known as pharmacokinetics deals with the way drugs are absorbed, distributed, and eliminated by the body and how these processes can be described in quantitative terms. The pharmacokinetics of alcohol (ethyl alcohol or ethanol) is an important issue in forensic toxicology and clinical medicine, when the amount of alcohol in the body is estimated from the concentration measured in a blood sample.
The Swedish scientist Erik M.P. Widmark (1889-1945) made pioneer contributions to knowledge about the pharmacokinetics of ethanol during the early decades of the twentieth century. Widmark observed that after the peak concentration in blood had been reached, the disappearance phase seemed to follow a near straight-line course, suggesting that the system for metabolizing alcohol was saturated (fully occupied), so that the amount of alcohol metabolized each hour did not depend on the amount in the blood. This situation is termed a zero-order elimination process. (Zero-order kinetics is contrasted with first-order kinetics, in which the metabolic system [e.g., the liver] is not saturated and in which the amount of drug metabolized per hour increases as the amount presented to the metabolic system increases.) Figure 1 (left
Elimination Kinetics of Ethanol. Schematic diagram illustrating the elimination kinetics of ethanol. The left frame shows Widmark's zero-order model. The right frame shows Michaelis-Menten (MM) capacity-limited kinetics. An intravenous bolus dose of ethanol enters a volume V to produce a concentration C; ko is the zero-order elimination rate constant; Vmax is the maximum velocity of the reaction; and km is the Michaelis constant—the concentration of ethanol at half maximum velocity. Concentration-time profile are shown for zero-order and MM kinetics, and the mathematical expressions for the elimination rates are given.
frame) depicts zero-order elimination kinetics of ethanol after rapid intravenous infusion. Widmark used the Greek letter [ to represent the negative slope of the disappearance phase and not the notation ko used in Figure 1. The terminology and choice of symbols used in articles and books dealing with clinical pharmacokinetics are often confusing. Moreover, the concentrations of ethanol in blood and other body fluids are reported using many different units, such as g% w/v, mg/dl, g/l, mmol/l; 21.7 mmol/l = 100 mg/dl = 1 g/l = 0.1 g% w/v.
Zero-order kinetics implies that the elimination rate of ethanol is independent of the BLOOD ALCOHOL Concentration (BAC) and therefore ko should be the same regardless of the dose of ethanol administered; however, more recent studies have show that the slope of the BAC decay phase is steeper after larger doses of ethanol are ingested. Furthermore, when the BAC declines below about
10 mg/dl (0.01 g%, 2.17 mmol/l) the elimination curve of ethanol from blood flattens out and changes into a curvilinear decay profile.
Two different methods are described in the literature to portray the pharmacokinetics of ethanol. The method of choice seems to depend on the professional interests, the scientific background, and the training of those concerned. Specialists in forensic medicine and toxicology, as well as other disciplines, favor the mathematical approach developed by Widmark. In contrast, scientists with their basic training in pharmacy and pharmacology prefer Michaelis-Menten (MM) kinetics, that is, saturable or capacity-limited enzyme kinetics. The MM model is depicted in Figure 1 (right frame) after intravenous input of ethanol. A pseudolinear phase is evident for most of the elimination profile, provided that the BAC remains sufficiently high (> 10 mg/dl). At low substrate concentrations (C), a hockey-stick shape develops when data are plot ted on cartesian graph paper. Accordingly, when C is much greater than km, the elimination rate approaches its maximum velocity; — dC/dt = Vmax (Figure 1, right frame). When C is less than km the elimination rate is proportional to the substrate concentration; —dC/dt = (Vmax/km) C and the MM equation collapses into first-order kinetics. This collapsing of the model is a consequence of capacity-limited kinetics and does not reflect any sudden change in the order of the biochemical reaction.
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