Retrograde Extrapolations

Retrograde extrap­o­la­tions are a some­what con­tro­ver­sial cal­cu­la­tion per­formed in foren­sic alco­hol cases (DUI cases). The goal is to pre­dict what someone’s alco­hol con­cen­tra­tion would be ear­lier in time, given a known con­cen­tra­tion later in time.

The rea­son it is con­tro­ver­sial is that is heav­ily relies on assump­tions, many of which are not in evi­dence. The per­son per­form­ing the cal­cu­la­tions must rely on pop­u­la­tion based aver­ages. Some fac­tors that might not be known, but have an effect on the cal­cu­la­tions are:

Volume of dis­tri­b­u­tion: This is the frac­tion of someone’s body that is com­prised of water, as opposed to fat and bone. Alcohol dis­trib­utes itself through­out the water in the body. The more water in someone’s body, the less their alco­hol con­cen­tra­tion will be given the same amount of alco­hol dosed.

Volume of dis­tri­b­u­tion is com­posed of two dif­fer­ent fac­tors (Widmark con­stant and sub­ject weight). Widmark is a sci­en­tist who per­formed a series of exper­i­ments to deter­mine a con­stant that could be used to con­vert someone’s weight, into the vol­ume of dis­tri­b­u­tion avail­able for alco­hol to dis­trib­ute into. Widmark found two dif­fer­ent con­stants, based on gen­der. The dif­fer­ence pri­mar­ily being in his test sub­jects, women had a higher per­cent body fat than the men. This over gen­er­al­iza­tion is prob­a­bly not true today, with the grow­ing prob­lem with obesity.

In order for the cal­cu­la­tions to be valid, it relies on the sub­ject being fully absorbed. That is to say that there is no alco­hol in the stom­ach of the per­son both at the time of the known alco­hol con­cen­tra­tion, AND back to the ear­lier time of inter­est. The prob­lem here is that absorp­tion rates vary con­sid­er­ably for each indi­vid­ual and cer­tain fac­tors (stress, drink com­po­si­tion, food con­sumed, bio­log­i­cal vari­abil­ity) can influ­ence that absorp­tion time. There is also no gen­eral absorp­tion time among experts. In Arizona some of the more “state biased” experts tes­tify fully absorp­tion within a half hour (with no eat­ing or drink­ing his­tory in evi­dence), many use one hour, and a grow­ing num­ber of experts (both gov­ern­ment and inde­pen­dent experts) believe two hours (with no eat­ing or drink­ing his­tory) is an appro­pri­ate number.

Studies have shown peo­ple not being fully absorbed around 4 hours. So there is a lot of idio­syn­cratic variability.

And finally there is no way to know the elim­i­na­tion rate of the indi­vid­ual. Elimination rate is how rapidly some­one “elim­i­nates” (metab­o­lizes) the absorbed alco­hol. One again experts have to use either aver­ages, or ranges of val­ues for this cal­cu­la­tion. Generally in Arizona the “median” elim­i­na­tion rate used is 0.015 g EtOH/ 100 mL blood/ hour. An appro­pri­ate range that cov­ers the major­ity of social drinkers is 0.01 – 0.03 %BAC/hour. Some really good expe­ri­enced heavy drinkers can be ever faster than that, and some peo­ple with very poor “tol­er­ance” for alco­hol, might have a much slower elim­i­na­tion rate.

The end result is an approx­i­ma­tion based on aver­ages, which may or may not be an accu­rate rep­re­sen­ta­tion of the par­tic­u­lar sub­jects ear­lier alco­hol con­cen­tra­tion. On top of that, it also relies on the “known” alco­hol con­cen­tra­tion to be accu­rate to begin with.

Some states don’t even allow for this type of evi­dence, oth­ers allow it. The state of Arizona is one that does.

What does this mean to the aver­age social drinker? Not much. These aren’t the types of cal­cu­la­tions one wants to do at a bar while meet­ings with friends or out on a date. But if you are look­ing for some­thing to give you a rough ball­park esti­mate of your BAC, that is easy to use on your iPhone or iPod Touch, try Alculator.