Tuesday, August 4, 2015
Comparison of the Blood Alcohol Model with Observations
I found some blood alcohol content data in measurements made by Schweisheimer in 1913 to test the 3-cell Blood Alcohol Model on. The data was rather sparse so I separately combined the results for Abstainers, Moderates and three of the Heavy Drinkers to obtain a nominal least squares fit for each group. One can use the formula for the chugged drink curve to do the fit since it approximately the same shape as the steady drinker curve. One does not know the total amount of alcohol in the blood but one can assume that it is proportional to the blood alcohol content and use X and Y as instead of G and H. One does not know when the drinkers started drinking so a B0 constant has to be included in Y. If λ and μ are known one can solve for X and Y using ordinary least squares. One can then search a grid of λμ-values to find the minimum variance for each set of data. Here are the results for the fits for the Abstainers, Moderates and Heavy Drinkers.
The values for the absorption factor, λ, and the elimination factor, μ, are approximately equal in each case and increases with the amount of drinking. The sum of D0 and B0 are approximately independent of the amount of drinking. Each test subject drank one liter of wine whose alcohol content was 10.35 percent.
The abstainers showed the highest peak blood alcohol content. They were also the slowest to recover. The length of time for which the blood alcohol content was 0.10 decreased with the amount of drinking.
Widmark's formula relates the blood alcohol content to the amount of alcohol consumed and the body's water content.