## Thursday, August 6, 2015

### Conclusions Drawn From Schweisheimer's Blood Alcohol Measurements

The 3-compartment model predictions for blood alcohol content gives a fairly good explanation for Schweisheimer's 1913 observations. The dependence of the peak time on the transport constant λ explains the decreased peak time with increasing alcohol usage. The magnitude of the peak blood alcohol just depends on the initial values of D0 and B0. When someone chugs a drink B0 = 0 and we get the largest value for the peak alcohol, Bmax = D0/e. The exponential base, e, in the divisor would have to be included in Widmark's rho factor, ρW, which corrects the BAC value for the ratio of the mass of alcohol to the body mass. The conclusion is that the divisor in Widmark's formula is just proportional to the body water content and the expected blood alcohol vs time is given by the formula,

Notice that only the mass of alcohol in the digestive tract, D0, is multiplied by t in the expression in parenthesis. So sipping a drink over time increases B0 and reduces one's peak BAC which is somewhat intuitive.

People participating in drinking parties should show some social responsibility and not allow individuals to poison themselves. Fraternity pledging rituals often involve drinking and from time to time we hear about a pledge dying of alcohol poisoning. The same could be said about people passing out during Spring Break.

One needs to be careful about definitions. The e in the divisor could be moved to modify the numerator and the exponent would become 1-λt. The formula for BAC above needs to be checked out more thoroughly and it might be useful to have an app for one's cell phone which would compute the percentage blood alcohol content vs time or predict the peak BAC so one could avoid getting fined for a DUI violation. One should check to see what formula an app uses for best results.

Supplemental (Aug 6): Widmark's formula appears to have been modified in the English Wikipedia. A simple relation defining the Widmark rho factor would be the proportionality factor connecting the amount of alcohol consumed with the product of the peak BAC and body mass. If we define alpha as the conversion factor between B and BAC we can show that the formula for BAC vs time is,

Supplemental (Aug 7): In the previous supplement it was assumed that the chugging procedure was used and so the amount of alcohol consumed equals to D0. To be consistent we would need to set B0 = 0. With steady drinking the peak BAC can fluctuate since some of the alcohol enters the blood while drinking and so B0 does not zero. In addition D0 does not equal the amount of alcohol consumed at the end of the drinking period and so doesn't cancel out in the conversion factor. The net result is the Widmark factor, ρW, is not well defined for the steady drinking case and consequently one cannot make accurate predictions of the BAC according to the 3-compartment model.