“The things we hate about ourselves aren't more real than things we like about ourselves.” Ellen Goodman


Friday, July 21, 2017

Back extrapolation of blood alcohol concentrations - a forensic exercise


A case was presented of an alleged rape of an woman intoxicated with alcohol. The question was how to back extrapolate from a measure blood sample taken a number of hours after the alleged rape to the time of the alleged rape. The case is reproduced here for discussion:


A 33 year old Chinese bar hostess (45kg, slim built), drank heavily from about 7pm on eve of public holiday. Began to feel sick, and drowsy at about 10pm. Vomited after last drink at about 11pm.

Some well meaning friends brought her to hotel room where she passed out.

At about 1am, the accused found her unconscious and took advantage of her.

She roused at about 1pm next day. Was able to collect her thoughts, inferred what had happened, called friends, and reported to police at about 4pm when blood sample for alcohol was obtained. Sample was 0.4mg/mL.

The simplest method is to assume that alcohol elimination follows zero order kinetics over the concentration range that are relevent here. The generally accepted 95% confidence interval for the beta-slope of elimination is 0.09 - 0.29 mg/mL per hour. Since the alleged rape occured 15 hours prior to the blood sample, the expected blood alcohol concentration (BAC) concentration at the time of the alleged rape will be approximately 0.4mg/mL + (15 hours x the beta slope). Therefore, depending on whether you apply the lower or higher boundaries of the 95% confidence interval, you will obtain BAC of either 0.4 + (15 x 0.09) or 0.4 + (15 x 0.29). The 95% confidence interval for the expected BAC at the time of the alleged rape would therefore be 1.75mg/mL to 4.75mg/mL. These are concentrations consistent with a fairly extreme level of intoxication and impairment of judgement.

The above is using a simple back-extrapolation method based on zero order alcohol kinetics. To try a graphical method of back extrapolation using a mixed zero to first order model, you can  go here

To view the correlation between BAC and cognitive degradation, please go here.