Interpretation and presentation of alcohol results
Retrograde extrapolation or back-calculation of alcohol concentration
Many jurisdictions express an offence under DUI as having, or exceeding, a specified alcohol concentration ‘at the time of driving’. Some time is likely to have elapsed between the time that a person is stopped for suspicion of DUI and the time at which either evidential breath alcohol testing is carried out or samples are taken for laboratory testing to determine blood alcohol.
During this time, the level of alcohol in a person’s system will change owing to distribution, metabolism and excretion processes. Thus the level at the time of evidential testing or sampling will not be the same as it was at the time the driver was questioned initially. There is then a need to provide some retrograde estimate of a subject’s blood- or breath-alcohol concentration at the time the DUI offence occurred. Several terms are applied to this estimate, including retrograde extrapolation, back calculation, estimating back, back-extrapolation or relating back. All refer to the process of applying basic principles of pharmacokinetics to arrive at an estimate of a person’s blood or breath alcohol result at a prior time based on a measured concentration at a later time. An example might serve to illustrate its application (see Fig. 1).
Back-calculation estimations generally assume two extremes of likely alcohol elimination rates based on published data for alcohol elimination in impaired drivers (Jones and Andersson 1996) which are used to estimate the upper and lower likely limits of the alcohol concentration at a particular time prior to testing or sampling together with a ‘most likely’ elimination value. Back-calculation estimations, as illustrated by Figure 1, rely on the following assumptions:
• the subject’s BrAc concentration (BrAC) or BAC is on the linear elimination portion of the concentration–time curve at the time of arrest
• the elimination rate remains linear and constant throughout the time from arrest to breath-alcohol analysis
• the subject’s true elimination rate for the time in question is captured between the extreme limits employed in the calculation (i.e. 0.009<β <0.029)
• the measurements of the subject’s BrAC or BAC provide acceptably accurate and precise estimates of the subject’s true BrAC or BAC, respectively.
The acceptability of this type of calculation is often challenged legally, but it is admissible for forensic purposes as long as the expert provides the extrapolated estimates and the assumptions used in the calculation and the uncertainties involved.
Figure 2 is a graphical representation of the data shown in Figure 1. The broad range for the extrapolated results is seen clearly.
Figure 1 An example of retrograde extrapolation (back-calculation).
Figure 2 Retrograde extrapolation example.
