Alcohol Calculations in Emergency and Forensic Medicine

Knowing the degree of alcohol intoxication can be imperative in the decision-making process of diagnoses, treatment and discharge decisions in some situations. Blood testing provides a snapshot of intoxication at the time the sample is drawn but not earlier (e.g., at the time of injury) or later, although information of the latter would be useful in epidemiological comparisons about risk and injury. Mathematical analyses based on reported alcohol use or from a single objective chemical test are presented validated and recommended to allow estimates of alcohol intoxication at specifi c times relative to an injury or other event. Review Article Alcohol Calculations in Emergency and Forensic Medicine John Brick* and William Bennett Intoxikon International, Yardley, PA 19067, USA Dates: Received: 25 June, 2017; Accepted: 13 July, 2017; Published: 14 July, 2017 *Corresponding author: John Brick, PHD, MA, FAPA, Intoxikon International, Yardley, PA 19067 USA. E-mail:


Introduction
In emergency medicine, the most common legal drug encountered worldwide is ethanol (alcohol). Alcohol is consumed by a large portion of people in most countries.
The harmful and hazardous consequences of acute alcohol intoxication are an international problem and a signifi cant contributing factor to injuries and death. About 20% of emergency department admissions involve alcohol [1], and overall, alcohol is a direct or indirect cause of approximately half of all intentional and unintentional injuries resulting in death [1,2]. Non-quantitative clinical tools to assess intoxication may include casual observation (e.g., odor of alcoholic beverage, behavioral disturbances), which may lead to screening, brief interventions, referral and treatment (SBIRT).
In some instances, a method to make quantitative estimates of intoxication based upon pre-admission patient history may be useful and often of clinical and medicolegal value. For example, estimating the blood alcohol concentration (BAC) in overdose patients based on reported alcohol intake may be required to assist in a diagnosis or medication treatment plan before a chemical test is available or in estimating when a patient will be sober enough to ethically be released from the ED. This is particularly important because clinical signs of intoxication are not reliably observed at lower BACs [3][4][5], even though impairment and risk for further injury may be signifi cant [6].
In hospitals, chemical testing using clinical (e.g., ADH method) or other methods (e.g., breath testing, gas chromatography), while objective, only provide an objective result at the time the sample is obtained. In medico-legal matters, accurate estimates of intoxication at different points of time are also useful as is a simple method to convert serum alcohol to whole blood alcohol (often the legal standard in alcohol matters is the concentration of alcohol in blood, not serum). Finally, clinical alcohol researchers and others, including medical epidemiologists, report on the consequences of intoxication but their conclusions are limited to the relationship between a preadmission event (injury) and treatment record (including blood alcohol results) obtained hours later. During that time, the BAC may be higher or lower due to changes in absorption and elimination. Estimating intoxication at the time of an injury, rather than at the time of the blood test would provide a more accurate insight into the relationship between intoxication and injuries.
Medical records often include self-report or witnessprovided data regarding drinking history. An admission of drinking or signs of intoxication may precipitate a blood test to quantify the concentration of alcohol in blood. Alternatively, when reliable information regarding total alcohol intake is provided with other patient information, alcohol intoxication can be estimated mathematically. Methods for such estimates have been published to assist legislators in their deliberations regarding drinking-driving laws [7], for use by epidemiologists, researchers [8][9][10][11], and forensic scientists in defi ning what constitutes "a drink" [11][12][13][14][15], but are subject to the limitations described. including the blood. Since many clinical laboratories use serum as the matrix to analyze alcohol and serum contains more water than the whole blood from which it is derived, the concentration of alcohol in whole blood is less than that of the serum in proportion to their respective water contents.

Methodology
Early studies reported the serum: whole blood alcohol ratio to be about 1.1 to 1.2 [16], with an accepted average of 1.18 [17,18]. A hospital serum alcohol can be reasonably and quickly converted to a whole blood equivalent by dividing the serum concentration by 1.18 or multiplying the serum value by the reciprocal (e.g., serum x .85). When compared with whole blood test results in the same subject, we have found this conversion accurate when physiology is relatively normal. The potential limitation of this method is that it does not account for medical conditions of hemodilution or hemoconcentration that might follow medical intervention or medical conditions. For example, aggressive fl uid replenishment will dilute alcohol in blood resulting in a lower than actual BAC, as may conditions such as anemia or severe blood loss. To correct for this, the hematocrit may be used to mathematically calculate the blood water content. That value, when divided by water content of serum, provides a conversion factor for that patient [11]. Because women have a lower average hematocrit than men [19], different conversions may apply. We fi nd that paired serum and blood test results are within about ± 5 milligrams using this method and we are currently working to refi ne this further. These models require information about the drinking period, assumptions about the rates of absorption and elimination, anthropometric characteristics of the subject, specifi c drink input data and scientifi c or other assumptions. A discussion of the strengths and weaknesses of such approaches is discussed elsewhere [11].
Historically, models using single rates of absorption and elimination and variability associated with an assumed Vd for all subjects have been criticized [23]. We now describe a more specifi c and accurate method for estimating the BAC. As= alcohol in the stomach/small intestines Ab= alcohol in the blood Drink input: The drink input constant, K1, is in grams of alcohol ingested per hour based on subjective data or calculated from an objective chemical test by algebraically rearranging Equation 2 to calculate grams of alcohol consumed. This is discussed in detail elsewhere [11].
K1= ((0.79 grams of alcohol per mL) x (29.57 mL/fl uid ounce) x (percent alcohol/100) x (fl uid ounces per drink) x (number of drinks))/total drinking time in hours Absorption of alcohol: Under experimental conditions, a small quantity of alcohol is absorbed through the walls of the stomach but under normal (social) drinking conditions, the overwhelming majority of alcohol enters the circulation through the small intestine. The rate of gastric emptying is a function of many factors, including force and frequency of peristalsis and determined largely by gastric volume. Gastric emptying is proportional to the distension of the stomach, which is directly related to the volume within the stomach and the presence or absence of food. While the rate of emptying may increase with larger volumes, the time to empty is predictably longer because of the larger volume [24]. In practice, small amounts of alcohol reach maximum concentrations rapidly whereas larger amounts require more time and are, to some degree, subject to other factors. The time to maximum BAC does not usually correspond with the time required for total absorption.
The drink constant is K1 (into the stomach) and the absorption constant (from the stomach into the blood) is K2. Where r(abs) is a percent of As per minute and corresponds to grams of alcohol absorbed per gram As per hour. The r(abs) or Ka (in some literature), is approximately .01 to .06/min [25], which corresponds to a percent of the total alcohol available in the stomach (As).
With drinking, the increase of As, which is d(As)/dt in calculus terms, is shown in the following equation. Each of these terms is in units of alcohol grams per hour: This is a fi rst-order differential equation for As. It is linear as far as the alcohol in the stomach is concerned (movement through and out of the intestines is rapid and considered one compartment). Assuming there is no alcohol in the stomach when drinking starts, the solution to this equation is shown in  Where "exp(-K2t)" means "e" to the power of (minus K2 times t), and t is time in hours. Because in the fi rst minutes of drinking K2(As) is very low and metabolism begins almost immediately, mathematically a pre-load dose (14 grams of alcohol) in ten minutes is used to avoid a net sum of zero alcohol entering the blood after passing through the liver. This is the input to the blood compartment (and the start of non-linearity). The output from the blood compartment is a function of distribution and primarily hepatic metabolism.
Distribution: Alcohol from the fi rst compartment is a linear function of t and where  1-n is the selected range of rates (e.g., 10 mg/dL/h, 15 mg/dL/h or 20 mg/dL/h). Since the pioneering work of Widmark (1932), and for many decades, it was believed that alcohol metabolism followed zero-order kinetics [28]. Evidence now suggests that at very low BACs (usually less than 30 mg/dL), Michaelis-Menten fi rst order kinetics apply [22]. Calculations based on measured BACs of less than 30 mg/dL must account for dynamic changes in metabolism at low BACs or avoided. Since BAC estimates below 30 mg/dL are rarely of clinical value, fi rst order kinetics is not included in this model. The results predicted from the model (Equation 12) were compared with blood alcohol concentration estimates from six representative subjects from fi ve studies: Figure 1 [37], Figure   2 [38], Figure 3 [20], Figure 4 [39], Figure 5 [37] and Figure   6 [40]. The absorption rate variable is based on a percentage of As that resulted in peak blood alcohol concentrations about of 30 to 90 minutes. This rate is adjustable (e.g., from .02 to .06%/min) to correspond to the peak BACs and time of the known BAC, and elimination rates of 10, 15 or 20 mg/dL/hr were applied in each case. The time or drinking period varied from 10 minutes for lowest BAC study [39], to 240 minutes for the highest BAC study [40]. Subjects were tested after an overnight fast with a light meal or snack prior to drinking.
One study [37], compared subjects with a "full stomach" with "empty stomach" subjects. In another study [20] a lower last dose was administered at 90 minutes. This variable range of drinking conditions was deemed to be representative of the range of actual drinking conditions against which to compare the model. Figures 1-6 show actual BAC data (solid squares) derived from the studies selected superimposed on the predicted BAC estimates (A, B and C). For all fi gures, Analysis A is based on a high r(abs) with a peak BAC of approximately 30 minutes post drinking and a high r(elim), Analysis C is based on a low r(abs) with a peak BAC at approximately 90 minutes and low r(elim) and Analysis B is based on a widely observed average r(abs) of 45 minutes and average r(elim) of 15 mg/dL/hr. Results are presented as g% in the fi gures. Combining r(abs) with r(elim) as described yields maximum and minimum BACs. The effect   It can be seen that even though the test conditions and alcohol doses varied among studies and subjects, all predicted BACs (A-C) corresponded extremely well with the actual data. These results demonstrate the importance of using a range of assumptions in such analyses and the accuracy of this methodology. Since most drinking occurred with very little or no food in the stomach, the actual BAC data were best predicted by analyses A and B and less by analysis C. Data points outside the predicted range produced by A through C were within 5 mg/ dL (less than .005%) of the projections and infrequent.

Discussion
The results from this study demonstrate that accurate estimates of alcohol intoxication can be made based on available anthropometric data, a range of known pharmacokinetic parameters, a reliable drinking history and objective chemical test results. In clinical practice, estimates of intoxication based on drinking history should not supersede objective testing. Nevertheless, the usefulness of this study is three-fold. First, applying such methodology will be particularly helpful to epidemiologists who study the relative risk for injury associated with a BAC at about the time of injury. Currently, most relative studies correlate injury with the BAC at the time of death and therefore, do not address the issue of relative risk for more frequent non-fatal injuries. Second, allowing emergency medicine physicians to make estimates of intoxication at the time of examination before chemical test results are available may be useful in better diagnosing signs or administering medications. Finally, in forensic medicine, an understanding and appreciation of these methods will be useful when queried about the interpretation of alcohol results in a legal matter where the lab reports a serum value but the legal standard is whole blood alcohol, or where estimating the BAC at the time of an event is of legal interest.