The Contribution of Body Mass and Volume of Distribution to the Estimated Uncertainty Associated with the Widmark Equation

[Uncertainty estimate in calculation of ingested ethanol]

OBJECTIVE

To develop a method of uncertainty estimate in calculation of ingested ethanol by E. Widmark formula and its realization as a computer program.

MATERIAL AND METHODS

The methodological design of the study was an analytical construction of the equation of uncertainty estimates of the mass of ingested ethanol, obtained on the basis of E. Widmark kinetic model. Mathematical analysis operations were performed independently, as well as using WolframAlfa web application. The computer program code was compiled in the C# programming language using the free version of Microsoft Visual Studio application.

RESULTS

The equation of uncertainty estimate of the mass of ingested ethanol, obtained on the basis of E. Widmark kinetic equation, with standard deviation of the sought value as its measure has been derived. The Alcohol Calculator V 5.0 application was created in the C# programming language. This program implements a complex of computational procedures related to the use of developed uncertainty equation, and allows to determine the confidence error intervals for estimates of ingested ethanol for any probability of error.

CONCLUSION

The obtained equation of uncertainty estimates of the mass of ingested ethanol and the computer application implementing it are recommended for forensic medical evaluation of the kinetics of orally administered ethanol.

Forensic alcohol calculations in transgender individuals undergoing gender-affirming hormonal treatment

There are an increasing number of individuals undergoing gender‐affirming hormonal treatment (GAHT) to treat gender dysphoria. Current forensic alcohol calculations require knowledge of the sex of the individual, but this may disadvantage trans people as research has demonstrated that there are physiological changes in individuals who are undergoing GAHT. Using previously published studies on total body water (TBW) in cis individuals, and the known changes in lean body mass and hematocrit in trans individuals, it is possible to estimate TBW in trans individuals and compare them to those cis equation estimations. When using these revised rubrics, we determined that for trans women the use of the cis male anthropometric TBW equation only gives a small underestimation of TBW (0.9%) compared to the underestimation of TBW using the cis female TBW equation (−17.7%). For trans men, the use of the cis female TBW equation gives the largest disadvantage, underestimating TBW by −10.8% compared to the cis male TBW equation, that overestimates TBW by 6.6%. For this reason, we recommend that if the sex at birth of an individual is not known or disclosed, any forensic alcohol calculations in a forensic alcohol reports are made assuming that the gender declared by the individual is their sex at birth. Further research to develop validated anthropometric TBW equations are urgently needed as to not disadvantage trans people when forensic alcohol calculations are carried out.

Revised equations allowing the estimation of the uncertainty associated with the Total Body Water version of the Widmark equation

Widmark calculations are the most commonly used alcohol calculations to estimate a) the amount of alcohol consumed based on blood alcohol concentration (BAC) and b) BACs at a set time after consumption of a known amount of alcohol. These calculations are vital in forensic casework. Previous work has demonstrated that using general error propagation-based equations the variability associated with alcohol calculations can be estimated, but these equations have only been determined for the volume of distribution version of the Widmark equation. However, recent investigations have shown that the total body water (TBW) version of the Widmark equation is more reliable than the version that utilizes the apparent volume of distribution of ethanol. To date, there is no general error propagation equation to determine the variability associated the TBW version of the Widmark equation. Using previously published studies of 185 individuals in which alcohol elimination rate (β) and ethanol's volume of distribution were determined, we have shown that there is a negative correlation (-0.247) between the alcohol elimination rate (β) and TBW. Using these data, we were able to produce equations allowing the estimation of the variability of the results calculated using the TBW version of the Widmark equation. This will allow forensic practitioners to give the best determination of the variability associated with Widmark calculations currently possible.

Just say no to postmortem drug dose calculations

For years, a number of professional groups have warned forensic and clinical toxicologists against calculating an administered dose of a drug based on postmortem blood drug concentrations. But to date, there has been limited information as to how unreliable these dose calculations may actually be. Using amitriptyline as a model drug, this study used empirically determined pharmacokinetic variables for amitriptyline from clinical studies coupled with clinical overdoses (where the individual survived), and death case studies (ascribed to amitriptyline toxicity) in which the dose of amitriptyline was known. Using these data, standard pharmacokinetic equations, and general error propagation, it was possible to estimate the accuracy of calculated doses of amitriptyline, compared with the doses that were consumed. As was expected in postmortem cases, depending on the pharmacokinetic equation used, the accuracy (mean +128% to +2347%) and precision (SD ± 383% to 3698%) were too large to allow reliable estimations of the dose of amitriptyline consumed prior to death based on postmortem blood drug concentrations. This work again reinforces that dose calculations from postmortem blood drug concentrations are unreliable.

Total body water is the preferred method to use in forensic blood-alcohol calculations rather than ethanol's volume of distribution

During the prosecution and defence of drink-driving cases, forensic practitioners are often required to engage in various blood-alcohol calculations, such as whether or not the statutory limit was exceeded (e.g. 80mg/100mL, 0.08g/100mL or 0.80g/L). For this purpose, most forensic scientists utilize the Widmark equation, or some modification thereof, to calculate a person's blood alcohol concentration (BAC) based on information about the amount of ethanol consumed and the pattern of drinking. This equation comes in two main forms; one of which incorporates the apparent volume of distribution of ethanol (V) and the other a person's total body water (TBW). In this study, we utilised two independent data sets, one involving the determination of V for ethanol in 173 men and 63 women, and the other TBW determined for 582 men and 884 women. Those subjects included in the TBW group represented various racial groups (Caucasians, African Americans, Hispanics, Asians and Puerto Ricans), with body mass index (BMI) ranging from 17 to 80kg/m². Both versions of the Widmark equation were evaluated in relation to their accuracy and precision in predicting TBW and/or V using the two most common anthropometric equations; those of Watson et al. and Forrest. Both anthropometric equations exhibited good accuracy (<4.3%) for the prediction of both TBW and V. However, the root mean square error was lower TBW was used for prediction (9.09-12.84%) rather than V (11.72-15.08%). Overall, this study has demonstrated (a) that blood-alcohol calculations are more reliable using TBW rather than V (b) that both equations (Watson et al. and Forrest) are applicable to ethnic groups other than Caucasians and (c) the Forrest equation predicts TBW in men and women with BMI from 17 to 35kg/m² and that the Watson et al. equation works for those with more extreme BMI; females (17-80kg/m²) and males (17-67kg/m²).