CBAC: COMPUTERISED BLOOD ALCOHOL CONCENTRATION - A COMPUTER MODEL AS A CLINICAL AND AN EDUCATIONAL TOOL.
Ann. Biochim. Clin. Qué. 30(2):36-39 (1991)

Bhushan M Kapur, Addiction Research Foundation, 33 Russell St, Toronto (Ont) M5S 2S1, and Dept. of Clin Biochem, Faculty of Medicine, U. of Toronto, Canada.

(Current address: Div.of Clinical Pharmacology and Toxicology, The Hospital for Sick Children, 555 University Ave. M5G 1X8, Toronto, ON. Canada)

This publication is reproduced here with the permission of the publishers.

During a social event often alcoholic beverages are served and require the drinker to estimate their consumption so as not to compromise their driving ability. Most countries have some specified blood alcohol concentration (BAC) (e.g Canada 17.4 mmol/L (80 mg/100mL) above which the drinker is in violation of the law if he undertakes to drive a motorvehicle. Self estimation of BAC has been tried and a recent study [1] found that the subjects fell into three categories: the "underestimators", "overestimators" and "mixed pattern estimators". Underestimators rated themselves fit to drive although their actual BAC was higher than the statutory limit. This is not surprising since regular drinking can lead to tolerance [2] and overestimation of one's abilities. Although "impairment" can be demonstrated at very low BAC with sophisticated methods [3], clinical intoxication is difficult to judge and may not be apparent [4-6]. Urso et. al. [4] found a mean BAC of 63 mmol/L, (290mg/100mL) in emergency room patients who did not show any clinical signs of intoxications. Perper et.al [5] and Kapur [6] have reported similar results.

Alcohol rapidly diffuses throughout the aqueous compartments of the body [7], therefore, it is necessary to calculate total body water (TBW) in order to form a reasonably accurate estimate of BAC on the basis of amount consumed. Watson et. al. [8] have shown that age, sex, height and weight are important determinants in the calculations of total body water. These authors reviewed various studies in literature measuring total body water, with solutes other than ethanol, and derived a set of regression equations (fig 1) for males and females. Their regression equations which relates TBW to sex, age, height and weight were derived from data based on 458 males (aged 17 to 86) and 265 females (aged 17 to 84) [8].

Most of the BAC prediction models [9] are based on a mathematical equations developed by Widmark [10] in 1932. Widmark's equation describes the relationship, under fasting conditions between alcohol ingested (A), the theoretical BAC at time = 0 (C₀) and the body weight (p) as:

where r is the factor defining the fraction of the body mass in which alcohol would be present if it were distributed at concentrations equal to that in blood. Accounting for ethanol metabolism this equation can be rewritten as:

where C_t is the BAC at time t, and ß is the rate of ethanol disappearance from blood. From these equations, r can be determined if the values of the other variables are known. Widmark [9,10] assigned r for males as 0.68 +0.085 and for females as 0.55 +0.055 based on experimental studies he had done. Studies since then have shown the range to vary from 0.50 to 0.94 [9]

Commonly Used Prediction Models

Estimation of blood alcohol concentration (BAC) using the number of drinks consumed is often done for educational, forensic and research purposes. Rather than trying to gauge one's BAC a number of aids have been available [11,12, Fisher Kapur] to do this. Law enforcement officials in some jurisdictions (e.g Ontario) use cards [11] which have graduated scales or tables based on weight and number of drinks for the estimation of BAC. "Slide Rules" of various types have also been available to do these calculations [12].

Most of the formulas in these models use a constant Widmark's factor r varying between 0.50 to 0.68 to correct for body weight. Thus given the body weight of the individual and the number of drinks, BAC can be predicted. Some correct for sex. Factors such as height and age are not accounted for. Size of the drink is often defined in generic terms such as 1 drink = 28.4mL (1 oz) liquor or 1 drink = 42.5mL (1 1/2 oz) liquor. Actual serving volume and the alcohol concentration of the beverage can vary considerably from occasion to occasion and location to location (bar, private parties etc.) thus affecting the amount of alcohol consumed and this variable becomes a potential source of error in any BAC projection. Even when the dosage of alcohol is controlled in terms of gram/Kg body weight, O'Neill et. al [13] have shown great variations in peak BAC, further supporting that a constant r will lead to erroneous results. Thus, in order to get an accutate estimate of BAC, TBW needs to be calculated accurately; age, sex and height in addition to weight should be considered. Not including these would result in incorrect TBW calculations and therefore inaccurate estimation of BAC. Slide rules, cards and tables have to be limited due to their two dimensional nature, so it in not surprising that only a few of variables can be taken into account without increasing the complexity of the mathematical model.

Description of the computer Model.

We have developed a mathematical computer model (CBAC: Computerized Blood Alcohol Calculator) that takes all these variables into account to calculate TBW. To our knowledge this is the first computer model that factors-in variables that effect TBW. As input, personal statistic (weight, height, sex and age (for males only) are supplied by the user. CBAC uses the appropriate regression equation (fig 1) to calculate TBW. Volume and concentration of alcoholic beverage to be consumed is selected from a menu so that the absolute amount of alcohol consumed, in grams, can be used in the estimation of BAC. This model, for the sake of interpretation convenience and simplicity, uses the local legal limits as "marker" of impairment since the general public usually relates to this level easily. The program was developed in the Microsoft DOS environment using Pascal as the programming language.

Limitations of the CBAC Model:

In typical real-life drinking, many variables can effect peak BAC [7,13]. Factors such as rate of drinking, absolute volume of the beverage and its final alcohol concentration, food and other factors that influence stomach emptying may affect absorption of alcohol and the peak BAC [7,13,16]. Alcohol is rapidly absorbed from the duodenum. Presence of food slows the gastric emptying and thus absorption. Type of food seems to make little difference, since the effect has been demonstrated with proteins, carbohydrates and fat [7]. The greater the interval between the meal and alcohol ingestion the less the effect on alcohol absorption. If delay in emptying of the stomach occurs, then the peak BAC is delayed and it is lower [7]. During the development of the model, the computer program was demonstrated to the "lay public" at many shopping plazas in various cities in the province of Ontario during the summer of 1989. After numerous demonstrations of the computer program, it became evident to the author that, when drinking is done over a longer (> 1 hour) period, the effect of food on absorption will be minimal. Typically, on the average, most of the food intake takes place at the beginning of the drinking session and drinking during the later hours is essentially done on an empty stomach. The effect of delay in absorption caused by food in stomach will decrease with increase in time [7,13]. To our knowledge there are no known methods which will account for absorption variables for a specific individual such that it could be used in a mathematical model. This model assumes peak BAC to be at 30 minutes post drinking. Since this programme is also aimed at the "lay public", errors in peak will be on the conservative side i.e the peak shown may actually be slightly higher than in the specific case being studied.The model also assumes that the drinking is done at a steady pace, although sequential addition of drinks could be done, but it would add to the complexity of data entry.

Elimination of alcohol follows nearly a zero order kinetics at high concentrations, but compliance to Michaelis-Menten equation is observed at lower levels. The elimination curve is pseudolinear [14]. Since the primary purpose of this computer model is education in the reduction and control of drinking behaviour, for simplicity, CBAC assumes zero order kinetics and a linear decline in blood levels. A wide range of BAC rates of decline have been reported [15]. There are no known methods that will allow the prediction of the elimination rate of ethanol for a specific individual so the model assumes a default rate of 3.26 mmol/L (15mg/100mL), although it can be changed prior to, and during any demonstration.

Since all calculations in this model are based on TBW, the maximal BAC achievable, given the amount of alcohol consumed, can be predicted. The regression equation is designed to apply to any healthy Western adult population, from lean to obese. The equations do not apply to patients who have clinical conditions where the relationship between TBW and weight are disturbed such as edema, malnutrition and diuretic therapy [9].

Validation of the Model:

Watson et al after having derived the equation to estimate TBW [8] in 1980, further described its usefulnes in the calculation and prediction of BAC [9]. They reviewed studies in literature on 54 women and 85 males. They used the developed regression equations (fig 1), and, in some cases where height measurements were missing, a slightly modified equation was used in their evaluation [9]. These authors showed that the measured C₀ (the theoretical peak at time = 0) and calculated C₀ using TBW were almost the same but when Widmark's equations was used the results were positively skewed. For men the measured mean C₀ was 22.4 +11.3mmol/L, (103 +52 mg/100mL), the calculated was 21.9 +11.0mmol/L, (101 +51mg/100mL), whereas the same data set was calculated using Widmark's equation the mean was 23.9+11.7mmol/L, (110 +54mg/100mL). In women the values were 19.7 +4.8mmol/L, (91 +22mg/100mL); 20.2 +5mmol/L (93 +23 mg/100mL), and 22.6 +5.6mmol/L, (104 +26 mg/100mL) respectively.

In our model, the regression equations developed by Watson et.al. [8] are used to calculate TBW before any BAC projections are made. Further accuracy is acheived by carefully defining the amount of alcohol consumed which we belive to be a significant source of error. Although we do not have any actual experimental data at this moment, studies are under way to confirm Watson et.al [9] findings using our model. Our preliminary ancectodotal data would support Watson et. al's [9] findings.

Using this computer model the variables that effect BAC can be demonstrated.

Variables that affect TBW and BAC

1. Effect of Age on BAC. In the male the TBW has been shown to decrease with age [8]. Thus, the volume of distribution for alcohol, in the older male will be smaller than the younger male of the same height and weight. Table 1 shows the change in BAC at various ages. In this calculations height (177cm (5ft. 10in,), weight (68Kg, (150lbs) and the number of drinks (3 drinks - 127ml (4.5 oz) of whisky) are kept constant. Age is the only variable. For the same amount of alcohol intake, the younger male will have a lower BAC than his older counterpart. All things being equal, the older male can have BAC as much as 16% higher.

2. Effect of height on BAC. Effect of height is not as significant as age, but nevertheless for every 2.5 cm (one inch) difference there is 1% change in BAC if both weight and age are kept constant. Table 2 compares the BAC in individuals of various heights. In these calculations age, weight and number of drinks are kept constant. Although the effect of height may not critical by itself, when combined with another variables, such as age, the change can be very significant. Table 3 shows, a 21% difference between a 183cm (6'0''), 20 year old male and a 173cm (5'8"), 60 year old male individual for the same amount of drinks. This effect is due to the reduction of TBW and therefore the distribution space for alcohol.

T A B L E 2

T A B L E 3

3. Effect of Weight on BAC.

Weight is the most significant variable. As the weight increases so does the TBW and the volume of distribution. If all the other variables are constant then a lower BAC will be observed with increase in weight. Table 4 compares the BAC of individuals from 56 Kg (140 lbs) to 88 Kg (220 lbs) of the same height and age. A difference of 37% between these two extremes can be present.

T A B L E 4

4. Effect of Sex on BAC. Females have a higher total body fat content resulting in a lower TBW [8]. Thus when compared to a male of equal height and weight the female will have a higher BAC for an equivalent amount of alcohol consumed. Fig 2. shows an idealised absorption and elimination profile using 3.26mmol/hr (15mg/hr) as the elimination rate. This curve profile drawn with CBAC also shows the "legal" BAC limits in Canada.

Applications of CBAC model

"Intoxication" and "impairment" are ambiguous terms which mean different things to different people. Although driver of an automobile can be charged with "driving while impaired" at any BAC, BAC levels of > 17.4mmol/L (80mg/100mL) are associated with a criminal offence in Canada. In Canada there is also a provision in law, that if the BAC is between 10.8mmol/L (50mg/100mL) and 17.4mmol/L (80 mg/100mL) the driver can be temporarily suspended from driving his vehicle. In many States of the USA, BAC of > 21.7mmol/L (100 mg/100mL) is associated with a the criminal offence and BAC of > 8.7mmol/L (40 mg/100mL) is "illegal" for the DOT (department of transport) employees. In Europe the legal limits vary from 0 to 17.4mmol/L (0 to 80 mg/100mL). In general, our society tends to associate the "legal" BAC as a marker of "impairment", although potentially impairing effects of alcohol have been demonstrated at levels as low as 3.26mmol/L (15 mg/100mL) [3], a BAC which is well below "legal" limits in many countries.

CBAC is an educational program with a goal to reduce alcohol consumption through education. It is also a teaching tool in the academic environment. This teaching model can be personalised to the users' vital statistics, so that given how much and over what period of time the alcoholic beverage was consumed, it will project BAC. Number, size and types of the alcoholic beverage can be infinitely varied and the effects on BAC can be demonstrated. Effects of the variables influencing TWB and their effect on BAC can also be demonstrated. Rise and fall in BAC is shown graphically and for ease of interpretation with the "legal" limits are shown on across the graph (Fig 1).

An example of an educational exercise: During the demonstrations in shopping plazas of various cities we found that the consumption of 10-12 regular 5% beers at one siting was not uncommon. By using CBAC's graphical display of the an elimination curve, we were able to show to many of these heavy alcohol consumers that, their BAC exceeded the legal limits for many hours after the last drink. This was found to be an important issue to those whose activities require fine motor skills, such as driving a motor vehicle or operating heavy equipment. Using this model changing the type of drink i.e. regular beer (5%) to light beer (4%) and/or changing the pattern of drinking, i.e. slowly, or reducing the number of drinks/hour, a significant effect on the BAC could be demonstrated.

We see applications of this computer model in various clinical and educational activities. Some examples are: patient management in emergency departments to project and monitor patient recovery, teaching of students in university departments of pharmacology, research in alcohol and alcoholism, alcohol treatment programmes, employee assistance programs in industry, alcohol awareness programs, school and driver education programs are but a few of the many. We also see an application of this program within the law enforcement environment as well as the legal community since it is possible to project the number of drinks in the body given the BAC which has been measured.

Acknowledgements: Encouragements and help from Dr. H. Kalant while the CBAC program was being developed is sincerely appreciated. Help from Mr.D.Morris who translated the original CBAC from Turbo Basic to Turbo Pascal is gratefully acknowledged.

REFERENCES

[1] D.J. Bairns, Self-estimates of blood alcohol concentration in drinking-driving context, Drug and Alcohol Dependence, 1967; 19: 79 -90.

[2] Drugs and Drug Abuse: A Reference Text, 2^nd Edition, Eds. Jacobs and Fehr, Addiction Research Foundation, Toronto, 1987; pp 274-288.

[3] H.Moskowitz, M.M. Burns and A.F.Williams, Skills performance at low blood alcohol levels, J. Stud Alco, 1985; 46: 482-485.

[4] T.Urso, J.S.Gavaler and D.H.Van Thiel, Blood ethanol levels is sober alcohol users seen in an emergency room; Life Sci, 1981; 28: 1053-1056.

[5] J.A. Perper, A. Twerski and J.W. Wienand; Tolerance at high blood alcohol concentration: A study of 110 cases and review of the literature; J. Foren. Sci, 1986; 31: 212-221.

[6] B.M. Kapur, Alcohol: Pharmacology, methods of analysis and its presence in the casualty room, In Drinking and Casualties: Accidents, poisonings and violence in an international perspective, Eds: N Giesbrecht, R Gonzalez, M.Grant et. al., Tavistock/Routledge, London/New York, 1989; pp 172-187.

[7] H. Kalant, Absorption, diffusion, distribution and elimination of ethanol. In: Effects of biological membranes: The biology of alcoholism, Eds. Kissin B, Begleiter H, Vol. 1, Biochemistry, Plum Press, New York, 1971; pp 1-62.

[8] P.E. Watson, I.D. Watson and R.D. Batt, Total body water volumes for adult males and females estimated from anthropometric measurements, Am. J. of Clin. Nutr. 1980; 33: 27-39.

[9] P.E. Watson, I.D. Watson and R.D. Batt, Prediction of blood alcohol concentrations in human subjects. Updating the Widmark equation. J Alc Stud. 1981; 42: 547-556.

[10] E.M.P. Widmark, Die theoritischen Grundlagen und die praktische Verwendbarkeit der gerichtlich-medizinischen Alkoholbestimmung. Berlin; Urban & Schwarzenberg; 1932. (Widmark EM. in Principles and applications of medicolegal alcohol determination; Translated form 1932 german edition, Biomedical Publications, Davis, CA. 1981)

[11] Blood Alcohol Chart, The Ontario Provincial Police, Ontario, Canada.

[12] Circular slide rule: a) ALCO-DIAL, The Alco-Dial Co, 1918 Stanley Ave., Detroit, Michigan; b) DRINK/DRIVE CALCULATOR, Datalizer Slide Chart Inc, 1786 W.Armitage Ct. Addison, IL 60101.

Linear slide rule: a) ALCO-CALCULATOR, Rutgers University Center of Alcohol Studies. b) Ampol Know Your Limit Card, -A joint project of Ampol Limited and the Alcohol and Drug Foundation Australia. 1989.

[13] B.O'Neill, A.F. Williams and K.M. Dubowski: Variability in blood alcohol concentrations: Implications for estimating individual results. J Alc Stud. 1983; 44: 222-230.

[14] J.G. Wagner, P.K. Wilkinson, A.J. Sedman et. al., Elimination of alcohol from human blood. J. Pharm. Sci., 1976; 65: 152-154.

[15] M.D. Holzbecher and A.E. Wells, Elimination of ethanol in humans. Can Soc Foren. Sci. J. 1984; 17: 182-196.

[16] A.J. Sedman, P.K. Wilkinson, E. Sakmar et. al., Food effects on absorption and metabolism of alcohol. J Stud Alc 1976; 37: 1197-1214.

BKapur Homepage