## Wednesday, August 12, 2015

### Expected Correlation Between Effective Fluid Volume and Body Mass

We can use the Widmark factor to estimate the expected correlation of the effective fluid volume with the body mass.* This is probably best done with actual data since the peak blood alcohol content and consequently Widmark's factor may depend on the t = 0 values of D and B. A calculation for the abstainers will illustrate this.

Using Widmark's formula we find that ρWMb = 57.05 liters. Vfl = 1/α so using the previous result for α we can compute a Vfl and get the result found in the last blog. We can combine the ρW/e into a single constant β = 0.258 liter/kg for men. The result for women will be β = 0.221 liter/kg.

*edit (Aug 12): meant the proportionality factor instead of the correlation coefficient.

edit (Aug 13): Made some minor changes to the calculation. One can compare the correlation of Widmark's "volume" and the effective fluid volume with mass and see if there is less dispersion for the latter. Eating is likely to affect the effective fluid volume. The saying is one shouldn't drink on an empty stomach. This is something that should be taken into account while doing a study. It is not included in this simple model of the blood alcohol content.