Estimation of blood alcohol concentration (BAC)

A case was presented of a young man who engaged in a bout of binge drinking.

"A.M., 22 year old Indian student of a private college, received news that his childhood sweetheart wanted to end their relationship.

​

In a fit of depression, he bought a bottle of vodka, retreated to his hostel room, and sometime between 8pm to midnight he ingested about two thirds of a bottle (1L) of vodka. His room-mate who was out had spoken to him over the phone at 1130pm and had found him incoherent. When he arrived back to the hostel at 0045am, he found A.M. unconscious, and called for an ambulance."

The question is whether we can estimate the blood alcohol level when he was found. What do we know, and what assumptions can we make?

In this case, we may assume he consumed about 640mLs of vodka. The equivalent in terms of cans of beer can be found here, and is approximately 16.5 cans of beer. If we can make assumptions about his volume of distribution (body weight, BMI), and about the bioavailability (0.8), we can begin to estimate the possible maximum BAC, as well as the BAC at any time we are interested in, if consumption and absorption were relative rapid.

The interactive graph here allows you to visualize the BAC-time profile following binge drinking. 

The two models (mixed order, and zero order) estimates that at the time he was found, BAC might have been about 3.4 mg/mL and 2.7 mg/mL, respectively. Both these estimates are above the legal limit for driving and consistent with severe degree of intoxication (see Chart). From the plots we can also estimate when he was likely to rouse, and recover from the intoxication.