Saturday, August 29, 2015

Some Concerns About the Diffusion Model for the Widmark Fit

  I was concerned about the large deviation of the peak value of Widmark's data from the diffusion model curve for the best fit of the alcohol concentrations so I did a plot that included the three standard deviation error bounds the data and it just passes this statistical test.

The data used for the plot were the mean values shown in Table III of Widmark's 1914 paper. As is, one cannot reject the model based on just this experiment. One could try a more complicated diffusion model with a 5 compartment model including an eliminated compartment. The assumption is that the alcohol in the digestive tract flows into the blood before it flows into the remaining body tissues and the liver where it is eliminated.

The more complicated scheme may affect the peak value slightly since there will be a slightly greater concentration of alcohol in the blood than in the liver. Trying to find an equivalent circuit with fewer components will result in loss of information about the quantities of alcohol in each compartment and may confuse the situation somewhat.

To test more complicated models like the one above to see if they will product a slightly higher peak one could put together a number of electronic circuits and measure the voltage drop across capacitor CB. An alternative would be to simulate the response of a model using an electronic analog computer.

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