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

The Widmark equation is used forensically for the determination of the amount of ethanol (alcohol) that may have been consumed and also to determine the blood alcohol concentration (BAC) of an individual at a specific time. It is important to be able to estimate the uncertainty associated with Widmark equations. To date, there has been no detailed determination of contribution to the final uncertainty of Widmark calculations of the volume of distribution of ethanol (V_d), using anthropometric equations, or the contribution of an individual’s body mass. Using published data, published literature, and freedom of information data, we determined that the variability (%CV) associated with V_d was ~10% (Watson et al. and Forrest anthropometric equations) and that the %CV associated with estimated body mass was ~15% compared to ~3% when body mass was directly measured. These data allow an estimation of the overall uncertainty of Widmark calculations using general error propagation. The estimated total uncertainty for BAC calculations increased from ~11% (volume consumed) and ~22% (BAC) to ~19% (volume consumed) and ~37% (BAC) when using measured body mass compared to estimated body mass. These results demonstrate that forensic practitioners should be mindful of the increase in estimated uncertainty in calculated Widmark equation results when estimated body mass is used rather than measured body mass. These data further improve the knowledge around the uncertainty of results calculated with the Widmark equation.