By Deandra Grant, J.D., M.S. (Pharmaceutical Science), ACS-CHAL Forensic Lawyer-Scientist
You were pulled over at 11:00 PM. Your blood was drawn at 12:15 AM. The lab reports your blood alcohol concentration (BAC) at 0.09. The legal limit is 0.08.
But in Texas the prosecution’s question is not what your BAC was at 12:15 AM. It is what your BAC was at 11:00 PM, i.e. when you were actually driving. To answer that question, the prosecution (via a State’s expert witness) will attempt to use a mathematical technique called retrograde extrapolation: working backward from a known BAC result to estimate an earlier BAC at the time of the alleged offense.
Retrograde extrapolation sounds scientific. Prosecutors present it as reliable mathematics. But the pharmacokinetic reality is far more complicated than the calculation suggests, and the assumptions underlying it are frequently wrong. I published an article on this topic in Counterpoint: The Journal of Science and the Law in 2016 which was updated and re-published in 2022, and the science has not changed. If anything, the literature has become more critical of the technique’s reliability.
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How Retrograde Extrapolation Works (In Theory)
The basic premise is straightforward. Once alcohol absorption is complete and the body is in the elimination phase, blood alcohol declines at a roughly linear rate. The standard calculation uses Widmark’s equation, which estimates the BAC at an earlier time by adding back the amount of alcohol that would have been eliminated between the two time points:
BAC at time of driving = BAC at time of testing + (elimination rate × time elapsed)
For example, if the tested BAC is 0.09, the elimination rate is assumed to be 0.015 per hour, and 1.25 hours have elapsed, the prosecutor’s expert will calculate: 0.09 + (0.015 × 1.25) = 0.109 at the time of driving.
This looks precise. It is not.
The Pharmacokinetic Problems
1. The Absorption Phase Problem
Retrograde extrapolation assumes the subject has completed absorption and is in the elimination (post-peak) phase at the time of testing. But absorption is not instantaneous. Depending on the type and quantity of alcohol consumed, food in the stomach, gastric emptying rate, and individual physiology, absorption can continue for 30 to 90 minutes or longer after the last drink. Add surgical procedures like gastric bypass surgery and the huge rise in the usage of GLP drugs (ex. Ozempic) and even more complicated issues are thrown into the mix.
If the person was still absorbing alcohol at the time of driving, their BAC was rising, not falling. In this scenario, the BAC at the time of driving was lower than the BAC at the time of testing which is the opposite of what the prosecution’s extrapolation assumes. Applying an elimination rate to a subject who is still absorbing produces a grossly inflated estimate.
This is not a theoretical concern. Many DWI arrests occur within 30–60 minutes of the person’s last drink which is well within the absorption window.
2. Individual Elimination Rate Variability
The prosecutor’s expert will typically use an elimination rate of 0.015 g/dL/hour, which is commonly cited as the “average.” The actual range documented in the scientific literature is approximately 0.010 to 0.025 g/dL/hour which is a 2.5-fold difference. Some studies have reported rates as low as 0.006 and as high as 0.040 in outlier cases.
Factors affecting individual elimination rates include body weight and composition, liver health and enzyme activity, chronic alcohol use (which induces CYP2E1 and increases elimination rate), genetics (variations in alcohol dehydrogenase and aldehyde dehydrogenase enzymes, particularly common in certain populations), recent food intake, and medications that affect hepatic metabolism.
Using an “average” elimination rate for a specific individual is pharmacokinetically indefensible. It is like using the average shoe size to fit a specific person’s foot. The range is too wide for a single value to be meaningful.
3. The Widmark Factor Assumptions
Widmark’s equation also requires a “r factor” representing the volume of distribution which is essentially how alcohol distributes through the body based on body composition. The standard values used (0.68 for males, 0.55 for females) are population averages derived from studies conducted nearly a century ago. Individual values vary based on age, body fat percentage, hydration status, and other factors. Using population averages for an individual adds another layer of imprecision.
4. The Single-Point Problem
A single BAC measurement tells you nothing about the shape of the blood alcohol curve. You know where the person was on the curve at the moment of testing, but you do not know whether they were ascending, at the peak, or descending. You do not know when absorption ended. You do not know when elimination began. You cannot derive the slope of the elimination phase from a single data point. A second measurement at a known time interval would provide information about the direction and rate of change; a single measurement does not.
5. Non-Linear Elimination at Higher BACs
At higher blood alcohol concentrations, elimination may follow Michaelis-Menten kinetics rather than the zero-order (linear) kinetics assumed by Widmark’s equation. When the liver’s alcohol dehydrogenase enzyme is saturated, the elimination rate can change. This is a known pharmacokinetic phenomenon that the standard linear extrapolation model does not account for.
Case Results
What the Courts Have Said
Texas courts have addressed retrograde extrapolation. In Mata v. State (2001), the Texas Court of Criminal Appeals held that retrograde extrapolation testimony is admissible but only if the expert’s opinion takes into account:
- The length of time between the alleged offense and the test
- The number of drinks consumed
- The time of the first and last drinks
- The person’s weight and gender
- Whether food was consumed and what type
- The person’s typical drinking pattern
If the prosecution’s expert cannot account for these factors with specificity (and in most cases, this information is unknown or only partially known) the extrapolation lacks the foundation required by Mata.
Defense Strategy
When the prosecution relies on retrograde extrapolation in your DWI case, the defense must challenge every assumption:
- Was the person still absorbing? If the last drink was consumed within 60–90 minutes of driving, absorption may not have been complete, and the BAC at the time of driving may have been lower than at the time of testing.
- What elimination rate was used? Demand the specific rate and the basis for selecting it. If the expert used an “average” rather than an individually determined rate, challenge the scientific validity of applying population data to an individual.
- Was food consumed? Food dramatically slows absorption. A person who ate a full meal before drinking may still be absorbing alcohol hours after their last drink.
- How many data points exist? A single BAC measurement cannot establish the direction or rate of change. Without at least two time-separated measurements, the extrapolation is speculation, not science.
- Does the expert have pharmacokinetic training? Retrograde extrapolation is a pharmacokinetic calculation. An expert who lacks formal training in pharmacokinetics is applying a tool they may not fully understand.
At Deandra Grant Law, Deandra Grant’s Master’s Degree in Pharmaceutical Science includes extensive coursework in pharmacokinetics which is the science of how the body absorbs, distributes, metabolizes, and eliminates drugs and alcohol. When we challenge retrograde extrapolation, we are not simply questioning the math. We are questioning whether the pharmacokinetic model is appropriate for the individual case. Call (214) 225-7117 or visit texasdwisite.com.
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