The Widmark Equation

Figure 2 gives examples of the concentration-time profiles of ethanol obtained from oral and intravenous administration of a moderate dose. The ratio of the dose administered (D) to the initial extrapolated concentration of ethanol in blood (C0) is the apparent volume of distribution (Vd) having dimensions L/kg. This defines the relationship between the concentration of ethanol spread over the body weight (in kilograms, kg) and the concentration in the blood.

TABLE 1

Peak Blood Alcohol Concentration and Time to Reach the Peak after End of Drinking

TABLE 1

Peak Blood Alcohol Concentration and Time to Reach the Peak after End of Drinking

Dose

N

Peak BAC mg/dl

K

mg/dl h

Time to peak (min)3

g/kgl

mean

(range)

mean

(range)2

10

40

70

100

0.34

6

56

(43-67)

12

(9-14)

5

1

0.51

16

74

(54-91)

13

(10-14)

11

3

1

1

0.68

83

92

(52-136)

13

(9-17)

33

26

21

3

0.85

44

120

(83-178)

15

(12-18)

13

24

7

Maximum concentration of ethanol in capillary (fingertip) blood and the time of reaching the peak after end of drinking. The zero-order rate of elimination of ethanol from blood (k„) is also given. The subjects drank neat whiskey within 15—25 minutes after an overnight 10-hour fast.

Maximum concentration of ethanol in capillary (fingertip) blood and the time of reaching the peak after end of drinking. The zero-order rate of elimination of ethanol from blood (k„) is also given. The subjects drank neat whiskey within 15—25 minutes after an overnight 10-hour fast.

'g ethanol/kg = 0.036 oz ethanol/kg. 2Zero-order elimination rate.

'Number of subjects reaching their peak BAC at 10, 40, 70 and 100 min., measured from end of drinking.

Equation [1] is known as the Widmark equation; it is widely used to estimate alcohol in the body from measurements of alcohol in the blood. Widmark found that the average Vd for men was 0.68, with a range from 0.51-0.85, but in women the volume of distribution was less—with an average of 0.55 and a range of 0.44-0.66. These differences between the sexes stem from differences in body-tissue composition; proportionally, women carry more fat but less water than do men. Accordingly, women reach higher BACs than men if the same dose of ethanol is given according to body weight. A similar observation was made in studies of men with widely different ages, because body water decreases in the elderly. By dividing the dose of ethanol administered (g/kg) by the time needed to reach zero BAC (time0) one obtains an estimate of the rate of clearance of ethanol from the body. This calculation neglects the nonlinear phase of ethanol elimination beginning at BAC below 10 mg/dl but does include the contribution from any first-pass metabolism occurring in the liver and gut.

If equation [1] is combined with the expression for zero-order elimination kinetics (C = C0 — k0t) rearrangement gives equations [2] and [3]:

Equation [2] can be used to estimate the amount (dose D) of alcohol a person has consumed from knowledge of his or her BAC (C). Similarly, equation [3] allows estimating the BAC (C) that might exist after drinking a known amount of ethanol. For best results when using these equations, absorption and distribution of ethanol must be complete at the time of sampling blood. Owing to inter-and intra-individual variations in the pharmacoki-netic parameters Vd and k0 the results obtained are subject to considerable uncertainty. This uncertainty should be allowed for when these calculations are made for legal purposes, for example, in trials concerned with DRIVING UNDER THE INFLUENCE of alcohol. A variability of ± 20 percent seems appropriate for most situations.

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