PARAMETERS V m. AND K m FOR ELIMINATION OF ALCOHOL IN YOUNG MALE SUBJECTS FOLLOWING LOW DOSES OF ALCOHOL

Transcription

1 Akdiol A AkohoHtm, VoL 24, No. 6, pp ,1989 Printed in Great Britain / Pcrgwnoo Press pic 1990 Medical Council on Alcobobsm PARAMETERS V m. AND K m FOR ELIMINATION OF ALCOHOL IN YOUNG MALE SUBJECTS FOLLOWING LOW DOSES OF ALCOHOL JOHN G. WAGNER,*f PAUL K. WILKINSON* and DEREK A. GANES* 'College of Pharmacy and Department of Pharmacology and Upjohn Centre for Clinical Pharmacology, Medical School, The University of Michigan, Ann Arbor, MI 48109, and ^College of Pharmacy, The University of Michigan, Ann Arbor, MI 48109, U.S.A. (First received 9 January 1989; accepted for publication 13 June 1989) Abstract Seventy-four (44 under fasting conditions and 30 following oral liquid meals) sets of post-absorptive human capillary blood alcohol concentration-time data were computer-fitted to the integrated form of the Michaelis-Menten equation by numerical integration by nonlinear least squares to provide 74 pairs of the kinetic V m. and K m parameter values. The parameters were highly correlated (r = 0.915) by orthogonal least squares. Eight of the fasting subjects received four different oral doses of alcohol and fourteen subjects each received three different alcohol treatments. Intra-subject variances of V m., K m and the ratio V m. K m were calculated from the multiple treatments. Inter-subject variances were calculated from the 22 mean values of each parameter. Each parameter and the intra-subject variances of the parameters were found to be log normally distributed. The liquid meals (carbohydrate, fat and protein separately) appeared not to affect the parameter values. The computer fittings were all excellent as evidenced by the relatively small standard deviations of the estimated parameters and other statistical measures of fit. INTRODUCTION There are two principal models for alcohol elimination in man. These are: (a) the zero order or constant rate model of Widmark (1932, 1933); (b) the Michaelis-Menten model of Lunquist and Wolthers (1958). These two models have recently been reconciled, both qualitatively and quantitatively (unpublished work). One of the keys to this reconciliation is that post-absorptive single dose blood alcohol concentration-time data are not described by the Michaelis-Menten equation per se (Michaelis and Menten, 1913), but rather by the integrated form of the Michaelis-Menten equation which was published by Henri (1902) prior to the Michaelis-Menten equation. A third model was described by Rangno et al. (1981) who fitted intravenous and oral plasma ethanol concentration-time data to the two fauthor for correspondence. Present address: Research and Development Center, R. P. Scherer Corporation, Ann Arbor, MI 48108, U.S.A. compartment open model with central compartment input by first order kinetics and central compartment elimination by Michaelis- Menten kinetics. However, Sedman and Wagner (1974) studied this latter model and found that there was no valid method to obtain initial estimates of the distribution rate constants, k i2 and k 2 i, for computer fitting and that the computer-fitted final estimates of these two parameters depended upon the initial values used in the fitting. A fourth model included the effect of the dose of alcohol on stomach emptying, first order absorption in the intestine and Michaelis-Menten elimination from blood (Wilkinson et al., 1978). Two reviews (Hawkins and Kalant, 1972; Holford, 1987) have summarized most of the pharmacokinetics of ethanol. We have published several articles in which post-infusion intravenous and post-absorptive oral blood alcohol concentration-time data have been fitted to the integrated form of the Michaelis-Menten equation (Henri, 1902) by numerical integration of the Michaelis-Menten 555

2 556 J. G. WAGNER, P. K. WILKINSON and D. A. GANES equation using the digital computer program NONLIN (Metzler, 1969). Several sets of mean concentrations, obtained following diferent alcohol treatments, have been fitted simultaneously (Wagner et al., 1976; Lin et al., 1976; Sedman etal., 19766). However, in only a few cases have individual subject sets of alcohol concentration-time data been fitted to obtain V m > and K m values (Wagner and Patel, 1972; Wilkinson, 1976; Wilkinson et al., 1977; Wagner, 1983). The purposes of the present article were to report the results of fitting 74 individual subject sets of alcohol capillary blood alcohol concentration-time data, to compare the maximum velocity of ethanol elimination V m - (mg/dl per hr) and the Michaelis constant K m (mg/dl) values obtained in fasting vs fed subjects, to estimate intra- and inter-subject variation of the V m. and K m values and to study the distribution of the V m > and K m values. In addition, volume of distribution as a fraction of body weight (VIW in I/kg) and maximal velocity per unit body weight iy,jw in g/kg per hr) are also calculated and reported. EXPERIMENTAL Source and nature of data In study I, eight fasting (10-hr) nonalcoholic male volunteers with a mean body weight of 74.6 kg (range 66-89) were each administered 15, 30, 45 and 60 ml of 95% alcohol in orange juice (total volume 150 ml) in a cross-over fashion at 1-week intervals. The 60 ml dose corresponds to approximately 1 mol. of ethanol or an average dose of g/kg. Capillary blood ethanol concentrations were measured at 0, 0.167, 0.33, 0.5, 0.667, 0.833, 1, 1.167, 1.333, 1.5, 1.75, 2, 2.5, 3, 3.5, 4, 4.5, 4.75, 5, 5.25, 5.5, 5.75, 6, 6.25, 6.5, 6.75, and 7 hr after alcohol administration. In Study II, fourteen different nonalcoholic male volunteers with a mean body weight of 78.2 kg (range kg) were each administered 45 ml of 95% ethanol three times at 1-week intervals. Two treatments were under fasting conditions, namely A (Subjects 3, 4, 5, 12, 13 and 14), who received 8 fl. oz. of tap water followed 10 min later by the alcohol mixed with 105 ml of orange juice and E (Subjects 3, 4, 6, 7, 8 and 10), who received the alcohol diluted to 750 ml with tap water. Five treatments involved food consumption as follows; B (Subjects 6, 8, 9, 11, 13 and 14), who ingested 8 fl. oz. of light cream followed 10 min later by the alcohol mixed with 105 ml of orange juice; C (Subjects 1, 2, 5, 6, 8 and 12), who received 20 g of Somagen (protein) in 8 fl. oz. of tap water followed 10 min later by the alcohol mixed with 105 ml of orange juice; D (Subjects 1, 2, 7, 10, 13 and 14), who received 8 fl. oz. of flavoured glucose solution (80 g of glucose) followed 10 min later by the alcohol in 105 ml of orange juice; F (Subjects 1, 22, 3, 4, 9 and 11), who received alcohol and 50 g of glucose diluted to 750 ml with tap water; and G (Subjects 5, 7, 9, 10, 11 and 12), who received the alcohol and 100 g of glucose diluted to 750 ml with tap water. The study was a mixed model balanced incomplete block design. Capillary blood ethanol concentrations were measured from 26 to 28 times after dosing. In both studies, alcohol was measured in the whole capillary blood by a head-space gas-chromatographic method (Wilkinson et al., 1975). Detailed protocols and all alcohol concentrations are available (Wilkinson, 1976). Some interpretation of the data has been published previously (Wagner et al., 1976; Wilkinson, 1976; Sedman etal., 1976a, b; Lin et al., 1976; Wilkinson et al., 1977, 1978; Wagner, 1986). The 15 ml of 95% alcohol (11.25 g ethanol) data of study I were excluded in calculating VI W and VJW, because the Co concentrations were inordinately low presumably because of a large first-pass effect. Hence in the combined studies there were eight normal young male volunteers each of whom received four oral alcohol treatments and 14 normal male volunteers each of whom received three oral alcohol treatments making a total of 74 data sets. In both studies, alcohol was given at 8:00 hr and in fasting subjects food was excluded from 22:00 hr the previous night to 4 hr after dosing. Both study protocols were approved by an Institutional Review Board and all subjects signed a written consent form.

3 KINETICS OF ALCOHOL ELIMINATION 557 Estimation of Michaelis-Menten parameters andauc Capillary whole blood alcohol concentration-time data, excluding data in the absorptive phase, but including all data at and subsequent to the start of the linear decline (e.g. in Fig. 1 from to 5.75 hr) were fitted by numerical integration of the Michaelis-Menten equation (equation 1) to the integrated form, namely equation 2 (Henri, 1902), using the program NONLJN (Metzler, 1969) and a microcomputer with 1/C/ weighting. dc At v m. c Q> C o - C + K m In = V m.t (1) (2) In equations 1 and 2, C is the estimated concentration at time /, V m - is the maximal velocity of elimination (mg/dl per hr), K m is the Michaelis constant (mg/dl) and C o is the zero time concentration of alcohol (mg/dl). Estimated parameters in the fittings were C o, V m > and K m. An illustration of such fitting is shown in Fig. 1. In these fittings, the mean alcohol concentration-time data for the given treatment were fitted first, then the estimated Subject 4 Treatment R 2J3 3J) TIME (HOURS) Fig. 1. Example of fit of post-absorptive capillary whole blood cthanoj concentration-time data to equation 2. Data are for Subject 4 given treatment A in Study II. The estimated parameters were Q, > g/1, V m - = g/ (1-hr) and K m = g/1, which are shown, but with different units in row 2 of Table 1. parameters from that fitting were used as initial estimates for the fitting of the individual subject concentration-time data. This appeared to circumvent the problems discussed by Metzler and Tong (1981). The area under the alcohol concentrationtime curve (AUC), including data in the absorptive phase (not shown in the example in Fig. 1), was estimated using the trapezoidal rule. Regressions Peak blood alcohol concentrations (mg/dl) under fasting conditions were related to the dose of alcohol (g/kg) by linear least squares regression using equation (3), wherein Peak = (slope) (D/W) (3) D/W symbolizes the dose (D) divided by the body weight (W). Data used were peaks after all doses in Study I and after treatments A and E of Study II (N = 44). Other authors (Coldwell, 1957; and O'Niell et al., 1983) previously reported such linear relationships. AUC in fasting subjects was related to the dose of alcohol by fitting to a parabola forced through the origin (equation 4) using the program MINSQ (Lamson, 1987) and a microcomputer. AUC = a x (D/W) + a 2 (D/W) 2 (4) Equation 4 was derived by Wagner (1973) and used by Wagner (1986). A fit was also made where AUC was divided by body weight and related to the dose per unit body weight, as shown in equation 5. AUC = a,' (D/W) + a 2 ' (D/W) 2 (5) W Data obtained in fasting subjects were fitted with equations 4 and 5, including areas after all doses in Study I and after treatments A and E of Study II (N = 44). K m was correlated with V m - (N = 74) using orthogonal least squares, where the minimized deviations are those perpendicular to the regression line. V m - was correlated with Q> (N = 50, where dose was 45 ml of 95% alcohol) using orthogonal least squares.

4 558 J. G. WAGNER, P. K. WILKINSON and D. A. GANES Apparent volume of distribution of alcohol The apparent volume of distribution of alcohol, in volume per unit body weight (V/W in g/ kg) was calculated from the C o value (estimated in the fittings to equation 2), the dose of alcohol in g and the subject's body weight by using equation 6. (g) V/W (g/kg) = (6) C 0 (mg/dl) W(kg) Data collected following the lowest dose (11.25 g alcohol) in Study I were omitted in calculation of the apparent volume of distribution, since values calculated with these data were significantly higher than those calculated from the other doses as a result of significantly lower Co values, probably as a result of the first pass effect. The Vn/W in g/kg per hr was calculated by multiplying the V m - (mg/dl per hr) by 10 V/W. Intra- and inter-subject variation As indicated in the experimental section, there were eight subjects each of whom received four different doses of alcohol under fasting conditions in Study I and 14 subjects each of whom received three different alcohol treatments in Study II. For the parameters V m > and K m and the ratio V m -/K m, the means and intra-subject variances were obtained from the four or three parameter values of the 22 subjects. Inter-subject variances of each parameter were obtained as the variance of the mean parameter values of the 22 subjects. The distributions of the intra-subject variances were investigated. The intra- and inter-subject variances may be readily calculated from the coefficients of variation (C.V.) and means in Table 1 using equation 7. rc.v. variance =[ x meanj l2 (7) Distribution of parameters V m -, K,, and V m '/Kn, The distributions of the parameters V m -, K m and V m -IK m were studied. Both normal and log-normal distributions of each were considered. Measures of fit of data to equation 2 The program NONLIN (Metzler, 1969) provides the following measures of fit: (a) 2 dev 2 = 2(C - ) 2 where C is the observed alcohol concentration and C is the model-predicted (equation 2) at time t. (b) ^-Squared = (ZC 2-2 dev^yzc 2 (c) Cor = the correlation coefficient for the linear regression of C on C. (d) The standard deviations of the estimated parameters Co, V m > and K m. As a result of trying to conserve table space the measures of fit are not listed, but some comments concerning items (a) to (c) above are given under Results. RESULTS Results of fitting data to equation 2 via numerical integration of equation 1 for each subject are shown in Table 1. This table lists the subjects' body weights and the mean values of each of Q, V m > and K m from the four values of Study I and the three values of Study II. In addition, Table 1 also lists the maximal velocity of metabolism with units g/kg per hr and the volume of distribution as a fraction of body weight, V/W with dimensions I/kg. To conserve journal space, the results of fitting each of the 74 data sets are not given here. The fits of the 74 individual subject data sets of post-absorptive alcohol-concentration-time data to equation 2 were excellent, as indicated by the relatively small standard deviations of the estimated parameters. To conserve space, the values of 2 dev 2, 7?-squared and Cor are not listed. However, a summary of these parameter values follows. The mean 2 dev 2 was 51 with a range of when the concentration had dimensions of mg/dl. The mean 7?-squared was with a range of ; 23 of the 74 data sets had fl-squared values of either or The mean Cor value was with a range of ; 27 of the 74 data sets had Cor values of either or Two reasons for the excellent fits were: (a) the use of a sensitive and specific head-space gas chromatographic assay to measure alcohol in capillary blood samples (Wilkinson et at., 1975); (b) the large number

5 KINETICS OF ALCOHOL ELIMINATION 559 Table 1. parameter values and coefficients of variation calculated from the four parameter values for each subject in Study I and three parameter values for each subject in Study II VJW (g/kg per hr)* v, m' (mg/dl per hr) Km (mg/dl) VJK m (hr- viw-t (lag) W (kg) Study Subject C.V4 C.V. C.V. C.V. C.V. I II C.V 'VJW tv/w = tc.v v m. (V/W) 10" = 100 (dose of alcohol in g = 100 standard deviation/mean. of samples per data set; the average number of data points per set being 15 with a range of Table 2 lists results of Student /-tests for the significance of differences between mean parameter values of fasted vs fed subjects, all given doses of 45 ml of 95% ethanol. The 20 fasting values used are for different subjects from those of the 30 food values in Table 2. For the parameters Co, V m., K m, V, V/W and V m, the differences in means were not significant (P > 0.10 and P > 0.25). However, the difference between the mean peak of 69 mg/dl for fasting Table 2. Results of r-tests for significance of differences between mean parameter values of fasted and fed subjects given 45 ml of 95% alcohol Parameter Co (mg/dl) [mg/(dlhr)] K m (mg/dl) V(\) WW(l/kg) V m (g/hr) Fasting Food Student's (N = 20)(N = 30) Significance (P) >0.25 >0.10 >0.10 >0.25 >0.10 >0.10

6 560 J. G. WAGNER, P. K. WILKINSON and D. A. GANES subjects and the mean peak of 49 ml/dl for subjects fed liquid meals was highly significant (P < 0.001). Similarly the difference between the mean AUC of 1.63 g/(l-h) for fasting subjects and the mean AUC of 1.29 g/((lh) for subjects fed liquid meals was highly significant (0.01 > P > 0.001). Figure 2 shows that the peak blood-ethanol concentration is directly proportional to the dose. The slope of the regression line (equation 3) shown in the figure is 150 and the regression is highly significant (P < 0.001). Figure 3 shows that, unlike the peak concentration, the AUC increases more than proportionately with increasing the dose in fasted subjects. The trend line drawn in the figure is the parabolic fit (equation 4) and the equation of the line can be seen in the legend to the figure. The statistics of the fit are shown in Table 3. Using a quadratic root computer program, the inversely estimated dose, D1W, was obtained for each point in Fig. 3, then the per cent error from the actual dose, D/W, was obtained with equation 8: (D/W - D/W) % error = 100 D/W (8) An analysis of these errors is shown in the _ DOSE OF fllcohol (g/kg) Fig. 2. Plot of peak blood alcohol concentration vs dose of alcohol for fasting subjects (N = 36). The least squares line forced through the origin, and drawn in the figure, has a slope equal to ISO, with a standard deviation of The correlation coefficient for the regression is (P < 0.001) ORRL FflSTING (Eq.Ut.).B.20 3D DOSE OF fllcohol (g/kg) Fig. 3. Area-dose data for fasting subjects (N «44) fitted with the parabola: AUC (Ig/l]hr) (D/W) (DtWf. Statistics for the fit are given in Table 5. lower half of Table 3. Similar results, but using the fit to equation 5, are also listed in Table 3. These results show that dividing the AUC by the body weight then regressing AUC/W vs the g/kg dose provides somewhat less error in the inversely estimated doses. The mean parameter values and the intrasubject coefficients of variation of V m >, K m and V m JKn are listed in Table 1. The inter-subject coefficients of variation of each parameter, which were estimated from the mean parameter values, are also shown in Table 1. The intra-subject variances of each parameter were found to be log-normally distributed and the parameters of these distributions are listed in Table 4. Theoretically, two-thirds of the intrasubject variances of each parameter are contained between the 16% point and the 84% point. The distributions are quite skewed since there are considerable differences between the medians (3rd row of Table 4) and the means shown in the 5th row of the Table; and there are large coefficients of variation. The overall mean parameter values are 18.3 mg/dl per hr for V m., 7.04 mg/dl for K m and 3.71 hr" 1 for V m -/K m. It should be noted that V m IK m is the limiting slope of the hi C vs t at line as the concentration approaches zero. However, if one uses the terminal concentration data and calculates the slope of the least squares In C vs r line that slope will always be less than V m./k m, since V m -/K m is the limiting slope. As a mea-.70

7 KINETICS OF ALCOHOL ELIMINATION 561 Table 3. Results of nonlinear least squares fittng of area-dose data to a parabola forced through the origin (N = 44) AUC AUC/W Parameters* a, or a r (S.E.) 02 or a r (S.E.) Measures of fit S.D. of data Cor M.S.C. Error analysis of inversely estimated t)/w absolute deviation (%) S.D. of above (%) C.V. of above (%) Largest positive deviation (%) Largest negative deviation (%) No. of positive deviations No. of negative deviations % of values within ± 5% of mean % of values within ± 10% of mean Weighting during fitting of data "Sec equation 5. sure of the intra-subject variance/inter-subject variance, S^/S^, it appeared reasonable to use the median S. These ratios were for V m., for K m and for V m M m. The 74 parameter values of each V m -, K m and V m 'IK m were found to be log-normally distributed and the parameters of those distribuions are listed in Table 4. DISCUSSION Metzler and Tong (1981) simulated alcohol concentration-time data and stated: 'The mathematical development and computer simulation indicate that it is not possible to estimate V m and K m of a Michaelis-Mententype pharmacokinetic model with any precision from a single dose experiment.' However, data presented in this article indicate that V m > and K m can be estimated with precision from real single-dose blood alcohol concentrations providing that a sensitive and specific assay is used to measure alcohol and there are an adequate number of samples per data set. In fact, the (0.486) (0.962) Eq (0.626) (1.24) Eq. computer fittings reported here are the best one of us (JGW) has seen in both the linear and nonlinear pharmacokinetic area during his 19-year experience of fitting data with the program NONLIN of Metzler (1969). However, the real alcohol data we evaluated support other statements made by Metzler and Tong (1981). As found from the computer simulations, V m - and K m were highly correlated; our real alcohol data gave a correlation coefficient of for the linear regression of K m on V m - (Fig. 4) for the 74 pairs of values estimated. Metzler and Tong (1981) reported that their distribution of V m - and K m were strongly skewed to the right; we found similar skewness for both parameters and for the ratio V m 'IK m (see log-normal distribution parameters in the top three rows of Table 4). We believe that most of the variation seen in our V m - and K m values was due to intra- and intersubject variation of these pharmacokinetic parameters as a result of hereditary and environmental influences. Other methods of estimating V m - and K m gave essentially the same

8 562 J. G. WAGNER, P. K. WILKINSON and D. A. GANES in n i 1 2O0- ; U.0-5J>- H- ORTHOGONRL o o o Q/ LERST SOUflRES ^ o Vra" (mg/dl/hr) V Fig. 4. Correlation of K m with V m. (N = 66) fitted with the orthogonal least squares line: /t m = V m with r = (P < 0.001) and standard deviation of scatter of 3.08 mg/dl. parameter values as reported in this article, but conservation of journal space prevents reporting such data. In addition, we found that the intra-subject variances of V m -, K m and V m <IK m were also log-normally distributed (Table 4). The usefulness of estimates of V m - and K m to produce plots of amount of alcohol absorbed as a function of time has been illustrated by Wilkinson (1976) and Wagner (1983). In the article by the latter author, estimates of V m -, and K m were made for seven subjects from post-infusion data by the method of fitting described here. An absorption equation using these estimates of V m - and K m was then applied to the data on blood concentration obtained during the 2-hr infusion in order to estimate the constant input rate during the infusions. The estimated rate of infusion as a percentage of the known rate averaged 99.6% with a coefficient of variation of 6.87%. We have also shown (unpublished work) how the CQ values estimated in computer fitting to equation 2 may be used to estimate the dose of alcohol ingested orally. For those subjects given the same dose of alcohol (33.8 g or 45 ml of 95% ethanol), the differences between the mean values of C o, V m., K m, V, V/W and V m for fasting (N = 20) and fed (N = 30) subjects did not differ significantly (Table 2). However, the differences in the mean peak blood concentrations and mean areas under the blood concentration-time curve were highly significant. Peak alcohol concentrations were directly proportional to the dose of alcohol (Fig. 2); the same relationship was reported with a slope of 133 (O'Neil et al., 1983) compared with our slope of 150 (Fig. 2). The area, however, increased more than proportionately with increasing the dose (Fig. 3 and Table 3), as had previously been reported, but with different data, by Rangno et al. (1981) and Wagner (1986). The P.O. data of Rangno et al. (1981) were fitted by equation 4 and gave a x = and a 2 = compared with those coefficients listed under AUC in Table 3. For example, at a dose of 0.6 g/kg of alcohol the equation from the Rangno data gave an estimated AUC of 2.76 while the equation from our data gave an estimated AUC of 2.73 ([g/l]hr) hence the excellent agreement. Vestal et al. (1977) administered 1-hr infusions of 0.57 g/kg of ethanol to 25 young subjects and 25 old subjects. They presented kine- Table 4. Parameters of the log-normal distributions of parameters and their intra-subject variances and ratios of intra/inter-subject variances Variable u Median S.D. s 16% Point ^ n 84% Point C.V. (%) 100 V (<f-\) Median N V m. [mg/(dlhr)] K m (mg/dl) V,.^m (hr- 1 ) Intra-subject variance of V m Intra-subject variance of K m Intra-subject variance of V m J t K m

9 tic arguments which indicated that they could treat their data as if only alcohol dehydrogenase (ADH) had metabolized the alcohol and that the microsomal ethanol-oxidizing system (MEOS) was not involved. Since the highest dose of alcohol in our studies was 0.6 g/kg, which is essentially the same as theirs, we may make a similar assumption that only ADH, a single enzyme, was involved in oxidizing the alcohol in our subjects. Based on the inter-subject coefficients of variation shown in the last row of Table 1 the inter-subject variabilities of the parameters reported are in the order: VIW < VJW < V m. < V m./k m < K m Based on the mean intra-subject coefficients of variation shown in the second last row of Table 1, the intra-subject variabilities of the parameters reported are in the same order. This article clearly shows that kinetically post-absorptive alcohol concentration-time data can be fitted very well to the integrated form of the Michaelis-Menten equation (i.e. equation 2) and that the zero order elimination concept of Widmark (1932, 1933) is technically incorrect. The present article also shows that the intra-subject variances of V m -, K m and V m <IK m as well as the parameters V m -, K m and V m 'IK m are log-normally distributed (Table 4). Acknowledgements This work was supported in part by grant number 1RO1AA A1 from the National Institute on Alcohol Abuse and Alcoholism, Alcohol, Drug Abuse and Mental Health Administration, U.S.A. Financial support for DG was provided by Schering Research, Miami, FL, U.S.A. REFERENCES KINETICS OF ALCOHOL ELIMINATION 563 Coldwell B. B. (ed.) (1957) Report on impaired driving tests. Crime Detection Laboratory, Royal Canadian Mounted Police, Ottawa. Hawkins, R. D. and Kalant, H. (1972) The metabolism of ethanol and its metabolic effects. Pharmacological Reviews 24, Henri, V. (1902) Theorie gdne'rale de 1'action de quelques diastases. Comptes Rendus Hebdomadaires des Stances de I'Academie des Sciences 125, Holford, N. H. G. (1987) Clinical pharmacokinetics of ethanol. Clinical Pharmacokinetics 13, Lamson, M. (1987) MINSQ: MferoMath Scientific Software, 2034 East Fort Union Blvd., Salt Lake City, UT Lin, Y.-J., Weidler, D. J., Garg, D. C. and Wagner, J. G. (1976) Effects of solid food on blood levels of alcohol in man. Research Communications in Chemical Pathology and Pharmacology 13, Lunquist, F. and Wolthers, H. (1958) The kinetics of alcohol elimination in man. Ada Pharmacologica et Toxicologica 14, Metder, C. M. (1969) NONLIN, a computer program for parameter estimation in nonlinear situations. Technical Report 7292/69A7292/005, The Upjohn Company, Kalamazoo, MI, U.S.A. Metzler, C. M. andtong, D. D. M. (1981) Computational problems of compartmental models with Michaelis- Menten-type elimination. Journal of Pharmaceutical Sciences 70, Mkhaelis, L. and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49, O'Neill, B., Wieliams, A. F. and Dubowski, K. M. (1983) Variability in blood alcohol concentrations: Implications for estimating individual results. Journal of Studies on Alcohol 44, Rangno, R. R., Kreeft, J. H. and Sitar, D. S. (1981) Ethanol 'dose-dependent' elimination: Michaelis- Menten vs. classical kinetic analysis. British Journal of Clinical Pharmacology 12, Sedman, A. J. and Wagner, J. G. (1974) Importance of the use of the appropriate pharmacokinetic model to analyze in vivo enzyme constants. Journal of Pharmacokinetics and Biopharmaceutics 2, Sedman, A. J., Wilkinson, P. K., Sakmar, E., Weidler, D. J. and Wagner, J. G. (1976*) Food effects on absorption and metabolism of alcohol. Journal of Studies on Alcohol 37, Sedman, A. J., Wilkinson, P. K. and Wagner, J. G. (1976a) Concentration of ethanol in two segments of the vascular system. Journal of Forensic Sciences 21, Vestal, R. E., McGuire, E. A., Tobin, J. D., Andres, R., Norris, A. H. et al. (1977) Aging and ethanol metabolism. Clinical Pharmacology and Therapeutics 21, Wagner, J. G. (1973) Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics. Journal of Pharmacokinetics and Biopharmaceutics 1, and Wagner, J. G. (1983) The Wagner-Nelson method applied to a multkompartment model with zero order input. Biopharmaceutics and Drug Disposition 4, Wagner, J. G. (1986) Lack of first-pass metabolism of ethanol at blood concentrations in the social drinking range. Life Sciences 39, Wagner, J. G. and Patel, J. A. (1972) Variation in absorption and elimination rates of ethyl alcohol in a single subject. Research Communications in Chemical Pathology and Pharmacology 4, WagneT, J. G., Wilkinson, P. K., Sedman, A. J., Kay, J. R. and Weidler, D. J. (1976) Elimination of alcohol from human blood. Journal of Pharmaceutical Sciences 65, Widmark, E. M. P. (1932) Die theoretischen Crundlagen

10 564 J. G. WAGNER, P. K. WILKINSON and D. A. GANES und die praktische Verwenbarkeit der Gerichdich Medizinischen Alkololbestinvnung, Urban und Schwarzenberg, Berlin. Widmark, E. M. P. (1933) Verteihing und Unwandlung des Atbylalkohols im Organismus des Hundes. Biochemische Zdtschnft 267, Wilkinson, P. K. (1976) Effects of food on blood levels of ethanol. Ph.D. dissertation, The University of Michigan, University Microfilm No Wilkinson, P. K., Sedman, A. J., Sakmar, E., Kay, D. R. and Wagner, J. G. (1978) Pharmacokinetics of ethanol after oral administration in the fasting state. Journal of Pharmacokinetics and Biopharmaceutics 5, Wilkinson, P. K., Sedman, A. J., Sakmar, E., Lin, Y. J. and Wagner, J. G. (1977) Fasting and nonfasting blood ethanol concentrations following repeated oral administration of ethanol to one adult male subject. Journal of Pharmacokinetics and Biopharmactutics 5, Wilkinson, P. K., Wagner, J. G. and Sedman, A. J. (1975) Sensitive head-space gas chromatographic method for the determination of ethanol utilizing capillary blood samples. Analytical Chemistry 47,