How To Extrapolate Alcohol With Certainty

Fri, 08/05/2011 - 4:51pm
Henry J. Swofford

The courts have recently decided that single numerical values for blood and breath test results without a measure of uncertainty are inadmissible as they preclude objective interpretation.

Alcohol is one of the most widely tested chemicals in forensic laboratories, and the numerical test results carry probative weight as evidence. Many jurisdictions have imposed statutory law defining alcohol intoxication as having a blood alcohol concentration (BAC) of 0.080g/dl or greater. Because of this, forensic toxicologists are frequently faced with the question “What was the BAC of the defendant at the time he/she was operating the vehicle?” The problem with answering this question is that the BAC is typically measured at a time long after the incident occurred and does not reflect the alcohol level at the time in question. Therefore, to answer this, toxicologists must extrapolate the BAC at the time in question. Alcohol extrapolations are typically conducted using empirically derived formulae which account for the manner in which the alcohol is metabolized. Alcohol metabolism consists of three key processes (absorption, distribution, elimination) which occur simultaneously in the human body and each affecting how much and how fast alcohol accumulates in the blood stream.

Alcohol metabolism is well understood, but highly variable amongst the human population.1,2 Forensic toxicologists must have a keen understanding of these variable factors and incorporate them during the extrapolation and interpretation of the BAC results. To accomplish this, forensic toxicologists typically rely on population averages for the rate of absorption, manner of distribution, and rate of elimination. Extrapolated BAC results, then, are typically reported as singular numerical values which are compared to the statutory limit of 0.080g/dl by the courts to determine guilt or innocence. Recently, however, the National Academies of Science (NAS), in their report Strengthening Forensic Science in the United States:A Path Forward, recognized that “methods for measuring the level of blood alcohol in an individual...can do so only within a confidence interval of possible values.”3 By continuing to report BAC results as a single numerical value without accounting for the uncertainty associated with the metabolic process and calculations precludes objective interpretation of, and testimony concerning, the result which interferes with the quest for truth in the courtroom and the jury’s ability to execute justice. In the last few months, courts have recognized this and have decided blood and breath test results without a measure of uncertainty are inadmissible under Evidence Rules (ER) 702 and ER 403.4,5 With regard to ER 702, the court found:

If an expert testifies that a particular blood alcohol content measurement is value A, without stating a confidence level, it is this court’s opinion that the evidence is being represented as an exact value to the trier of fact... [and] that presenting to the trier of fact the result of a blood test as an exact numerical value without stating a confidence level, is not generally acceptable in the scientific community and misrepresents the facts to the trier of fact... This court holds that the result of the blood test in this case is not admissible under ER 702 in the absence of a scientifically determined confidence level because it misrepresents the facts and therefore cannot be helpful to the trier of fact.4

With regard to ER 403, the court found:

It has been this court’s experience since 1983 that juries it has presided over place heavy emphasis on the numerical value of blood alcohol tests. To allow the test value into evidence without stating a confidence level violates ER 403. The probative value of this evidence is substantially outweighed by its prejudicial value. Therefore this court holds that the result of the blood test in this case is not admissible under ER 403 in the absence of a scientifically determined confidence level.4

The question many toxicologists now ask is “How can a measure of uncertainty be included with extrapolated BAC results?” To accomplish this, the term “uncertainty” must first be understood. The term uncertainty is defined as “a parameter associated with the result of a measurement that characterizes the dispersion of values that could reasonably be attributed to the measurand” according to the International Vocabulary of Basic and General Terms in Metrology.6 In terms of BAC results, the uncertainty is the range of possible BAC values that could reasonably be attributed as the actual BAC at the time in question. Empirical research has found physiological ranges which characterize the speeds of alcohol absorption and elimination and various algorithms for determining the distribution of alcohol between the blood and the body tissues and fluids.With respect to absorption, Uemura et al. (2005) found that the physiological range of the absorption rate constant (ka) is from 1.0 to 8.0 with the lower numbers representing slower rates of absorption (i.e. full stomach) and higher numbers representing faster rates of absorption (i.e. empty stomach).7 This method of extrapolating the BAC during the absorptive phase is represented by the modified Widmark formula in Figure 1:

Figure 1: Modified Widmark formula for estimating BAC.

With respect to distribution, the first and traditional method of characterizing the distribution of alcohol was published as average coefficients (0.68 for males and 0.55 for females) in 1932 by Widmark.8 Since 1932, several methods have been published to improve the accuracy of these calculations by relying on measurable anthropological data.1,9,10,11,12 These methods are listed in Figures 2 through 6.

Figure 2: Watson formula for estimating the volume distribution of alcohol in the human body.

Figure 3: Forrest formula for estimating the volume distribution of alcohol in the human body.

Figure 4: Seidl formula for estimating the volume distribution of alcohol in the human body.

Figure 5: Ulrich formula for estimating the volume distribution of alcohol in the human body.

Figure 6: Posey & Mozayani formula for estimating the volume distribution of alcohol in the human body.

With respect to elimination, through a comprehensive evidence based review, Jones (2010) reports the physiological range of the elimination of alcohol from the blood is from 0.010g/dl/hr to 0.035g/dl/hr.13

By relying on averages of these physiological ranges and a single method for determining the distribution of alcohol, the extrapolated BAC which results from these calculations will not reflect the entire range of possible BAC values that could reasonably be attributed as the actual BAC at the time in question, and as such fails to account for the measure of uncertainty in the result. By utilizing the full physiological ranges of values associated with the absorption and elimination of alcohol combined with all major methods characterizing the distribution of alcohol, forensic toxicologists will be able to more accurately extrapolate and interpret BAC results with greater certainty.1,14 Doing this, however, is mathematically challenging due to the complexity of the formulae involved and requires tedium and repeated calculations which require significant time and resources.14 A solution to this, however, is the use of computer software to complete these necessary calculations and model the BAC profile of the individual during the entire drinking scenario.15 Utilizing software to extrapolate BAC with scientific certainty not only improves the accuracy and quality of the results, conveying the dynamics of alcohol metabolism for the judge and jury to consider, but also presents this information in a standardized and easily understandable format.


  1. Posey, D. & Mozayani, A. The Estimation of Blood Alcohol Concentration: Widmark Revisited. Forensic Science, Medicine and Pathology. 3: 33-39, 2007.
  2. Norberg, A., Jones, A.W., Hahn, R.G., and Gabrielsson, J.L. Role of Variability in Explaining Ethanol Pharmacokinetics: Research and Forensic Applications. Clin. Pharmacokinet. 42(1) 1-31, 2003.
  3. Strengthening Forensic Science in the United States: A Path Forward; National Research Council, National Academy Press: Washington, DC, 2009.
  4. State of Washington v. Weimer, No. 7036A- 09D Memorandum Decision on Motion to Suppress, 2010. Available at
  5. State of Washington v. Fausto, No. C076949 Order Suppressing Defendant’s Breath Alcohol Measurement in the Absence of a Measurement for Uncertainty, 2010. Available at
  6. Quantifying Uncertainty in Analytical Measurement; EURACHEM / CITAC Guide CG 4, 2nd Ed., 2000.
  7. Uemura, K., Fujimiya, T., Ohbora, Y., Yashuhara, M., and Yoshida, K. Individual Differences in the Kinetics of Alcohol Absorption and Elimination. A Human Study. Forensic Science, Medicine and Pathology. 1: 24-7, 2005.
  8. Widmark, EMP. Die theoretischen Grundlagen und die praktische Verwendbarkeit der gerichtlich-medizinnischen Alkoholbestimmung, Berlin. Urban Schwarzenberg, 1932.
  9. Watson, P.E., Watson, I.D., and Batt, R.D. Prediction of blood alcohol concentrations in human subjects: updating the Windmark equation. Journal of the Studies on Alcohol. 42: 547-556, 1981.
  10. Forrest, A.R.W. The estimation of Windmark’s factor. Journal of Forensic Sciences. 26: 249-252, 1986.
  11. Seidl, S., Jenson, U., and Alt, A. The calculation of blood ethanol concentrations in males and females. International Journal of Legal Medicine. 114: 74-77, 2000.
  12. Ulrich, L., Cramer, Y., and Zink, P. Relevance of Individual parameters in the circulation of blood levels relative to volume intake. Blutalkohol. 24: 192-198, 1987.
  13. Jones, A.W. Evidence-Based Survey of the Elimination Rates of Ethanol from Blood with Applications in Forensic Casework. Forensic Science International. 200: 1-20, 2010.
  14. Ogden, E. & Swofford, H.J. An Integrated Software Model for Alcohol Absorption and Metabolism. Presented at the 19th International Conference on Alcohol, Drugs, and Traffic Safety (ICADTS), Oslo, Norway, 2010. Available at: Doc&pAction=View&pDocumentId=27373.
  15. BAC Tracker International, Inc. <> accessed January 10, 2011.

Henry J. Swofford is the Director of BAC Tracker International, Inc., a forensic consulting company providing forensic alcohol litigation services internationally to the criminal justice community. BAC Tracker International, Inc., P.O. Box 162383, Atlanta, GA 30321; 1-800-274-9744;;


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