The pharmacokinetics of alcohol (ethanol) is a complex business. The communication of alcohol content of drinks, alcohol in breath and blood alcohol concentrations is quite confusing. It is also variable around the world.

Pieters, Wedel and Schaafsma (Alcohol and Alcoholism, Vol. 25. No. 1. pp. 17-24, 1990) published a three compartment model (stomach, intestine, and blood). The model equations are as follows:

y_1'(t)=-k_1\frac{y_1(t)}{(1+a y_1(t)^2)}

y_2'(t)=k_1\frac{y_1(t)}{(1+a y_1(t)^2)}-k_2 y_2(t)

y_3'(t)=k_2y_2(t)-\frac{V_m y_3(t)}{(K_m+y_3(t))}

Parameter estimates were derived from empirical observations in men and women subjects.

The following video uses this model and provides insights into the relationship between ingestion and alcohol concentration:


  • Ethanol, C_2H_5OH, has an approximate molecular weight of 46 (24+6+16) g/mol.
  • Alcohol content is usually represented as % by volume, e.g. 5% = 0.05 mL ethanol/mL drink
  • In Australia, a standard drink is defined as 10 g of ethanol.
  • The volume of ethanol equivalent to a standard drink can be determined using the specific gravity of ethanol (density of ethanol to density of water at standard temperatures). This is usual taken to be 0.789. A standard drink is approximately 12.5 mL
  • The threshold for driving under the influence in Australia is “0.05”=0.05 g/100 mL=0.05 g/dL=0.5 g/L~11 mmol/L
  • The red horizontal line in the graphic is the  threshold for driving under the influence in Australia.


  • let cursor hover over lines or points in graphic above
  • this is another illustration of exporting tooltips from Mathematica to html.
  • Two y-axes are used. The left y-axis is g% (g/dL) and right y-axis is mmol/L
  • Some modification of the html was required to remove added characters in the tooltip text.
  • Better size, coloring (esp, data elements) could have been used.
Categories: Mathematica, Uncategorized
  1. November 18, 2011 at 3:09 pm

    See the embedded CDF for this post at:

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