Saturday, September 5, 2015
Fit of Widmark's 1914 BAC Data Assuming Constant Removal Rate
Using a few tricks I was able to get a fit for the blood alcohol content data published by Widmark in 1914 for a 4-compartment model. The flow was modeled by the following analogous electrical circuit with I0 representing the removal rate.
There wasn't very much data to work with and at first my fits looked a little strange but I decided to estimate the time at which the BAC was zero and adjusted those for the best least squares fit of the general solution of the assumed model. One criterion for the fit was that the downward slope be approximately linear. Another problem was that the best fit again appears to be degenerate suggesting that the two time constants are equal.
The peak value still appears to be a little off but the fit would probably benefit from more accurate data over a longer span of time. Only positive values for the BAC fit make any physical sense. The fitted curve can act a little weird to the left and right of the region shown but the assumed removal rate isn't valid in these regions either.