An Introduction to Retrograde Extrapolation
Part 2: The Retrograde Extrapolation Calculation
Counterpoint Volume 6: Issue 3 - Article 1 (June 2022)
An article in the Foundational Skills II-4 Module
Deandra M. Grant, JD, GC, MS
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Article information:2600 words (approximately 8-10 minutes)
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In Part 1 of this series, we examined the concept of the retrograde extrapolation. In this follow-up article we will examine the retrograde calculation itself, look at its limitations, and see how it is often used in court proceedings. Is it accurate? Is it sufficiently reliable?
The Widmark Equation
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Dr. Erik Widmark is the grandfather of blood alcohol analysis and the formulator of the Widmark Ratio. This mathematical calculation forms the basis for the retrograde extrapolation calculation that the State’s expert will perform in court in front of the jury.
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It is important to remember that Widmark's work dealt exclusively with calculating blood alcohol concentration—not breath. His calculation can be expressed as follows:
Widmark's Equation:
Where:
Solving for BAC:
What this formula means:
Widmark calculated what is referred to as the Widmark Ratio or "rho" factor. The rho factor refers to the relationship of the concentration of ethanol in the body to ethanol in the blood. It is based on the concept that alcohol seeks water and distributes throughout the body based on water content. As such, gender and weight are important factors. The following are the Widmark values assigned for r:
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Female = 0.55 (+/- 0.055)
Male = 0.68 (+/- 0.085) |
Various modern studies have attempted to validate Widmark's research and found a fairly significant range for both men and women with regards to the r ratio. Widmark's original research focused on a fairly small group of men (20) and women (10) in 1930's Sweden. It would not be a stretch to imagine that those test subjects (1930's Swedes, all in their early 20's) would differ greatly from modern-day Americans with our higher body fat percentages. The most significant re-evaluation of Widmark's work was by ARW Forrest. In order to get a more precise value, he used body mass index (BMI) to calculate r. BMI is calculated as follows:
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Body mass index = weight in kilograms/height in meters squared
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For charts reflecting r values calculated using BMI, see "Simplified Estimation of Widmark 'r' Values by the Method of Forrest," Barbour, AD, Science & Justice 2001; 41: 53-54.
This article is available at http://home.lightspeed.net/~abarbour/jfss.htm.
This article is available at http://home.lightspeed.net/~abarbour/jfss.htm.
Forrest "r" value for males
Forrest's r value for females
Another important factor in the Widmark equation is referred to as Beta. The Beta factor refers to the rate of elimination of alcohol from the body. Widmark settled on an average rate of 0.015 g/dL per hour, though, as previously discussed, not every person follows this average rate.
Minimum Data Needed for Retrograde Extrapolation:
At the very minimum, a person attempting to perform a retrograde extrapolation calculation needs the following information:
Arguably, the calculation should also take into account:
At the very minimum, a person attempting to perform a retrograde extrapolation calculation needs the following information:
- Gender
- Weight
- Food in the stomach or empty stomach
- Time food was eaten
- Time of last drink
- Time of first drink
Arguably, the calculation should also take into account:
- Body mass index
- Type of alcoholic beverage consumed
- Type of food eaten
- Trauma or stress that could have delayed absorption.
Practice Tip: |
Using Widmark in Your Own Cases
Let's take some typical situations you may encounter in your own cases and evaluate them for purposes of retrograde extrapolation.
Hypothetical #1:
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Your client is pulled over for speeding at 1 AM. He provides a breath sample of 0.12 g/dL at 2 AM. The following information is given to the police officer:
The officer also knows that: (1) your client is male; and (2) he weighs 180 lbs (from booking information).
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Question:
Does the State’s expert have enough information to perform a back extrapolation calculation?
Does the State’s expert have enough information to perform a back extrapolation calculation?
Answer:
Yes. The expert knows your client's gender, weight, time of first drink, time of last drink, type and size of drink and has some idea of possible food in the stomach. This is enough information for them to calculate a possible range at the time of driving.
Yes. The expert knows your client's gender, weight, time of first drink, time of last drink, type and size of drink and has some idea of possible food in the stomach. This is enough information for them to calculate a possible range at the time of driving.
Remember that this does not mean the result is accurate. The calculation still consists of averages.
Hypothetical #2:
Your client is pulled over for speeding at 1 AM. His breath test result is 0.12 g/dL at 2AM. The following information is given to the police officer:
- He had his first drink "at 7 or 8."
- He drank "a few beers."
- He had his last drink "a little while ago."
The officer also knows that: (1) your client is male; and (2) he weighs 180 lbs (from booking information).
Question:
Does the State’s expert have enough information to perform a back extrapolation calculation?
Does the State’s expert have enough information to perform a back extrapolation calculation?
Answer:
No. There is not sufficient information regarding the time of the first and last drink and there is no information regarding food in the stomach. I would object to any attempt to perform back extrapolation on this information and argue that it should be excluded.
No. There is not sufficient information regarding the time of the first and last drink and there is no information regarding food in the stomach. I would object to any attempt to perform back extrapolation on this information and argue that it should be excluded.
Embracing Retrograde Evidence
Admissibility
Every state has its own caselaw regarding the admissibility of retrograde extrapolation testimony. Justice Keasler's analysis in Mata includes a summary of the pertinent scientific literature as well as the areas in which scientists disagree. If you have not read the opinion, I encourage you to do so. The Court ruled that retrograde extrapolation evidence can be admissible in certain cases.
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We believe that the science of retrograde extrapolation can be reliable in a given case. The expert's ability to apply the science and explain it with clarity to the court is a paramount consideration. In addition, the expert must demonstrate some understanding of the difficulties associated with a retrograde extrapolation. He must demonstrate an awareness of the subtleties of the science and the risks inherent in any extrapolation. Finally, he must be able to clearly and consistently apply the science.
The court evaluating the reliability of a retrograde extrapolation should also consider: (a) the length of time between the offense and the test(s) administered; (b) the number of tests given and the length of time between each test; and (c) whether, and if so, to what extent, any individual characteristics of the defendant were known to the expert in providing his extrapolation. These characteristics and behaviors might include, but are not limited to, the person's weight and gender, the person's typical drinking pattern and tolerance for alcohol, how much the person had to drink on the day or night in question, what the person drank, the duration of the drinking spree, the time of the last drink, and how much and what the person had to eat either before, during, or after the drinking. [Mata at page 916.] |
Each Case Requires Separate Analysis
From a tactical standpoint, each test case requires an analysis of whether or not retrograde extrapolation evidence will help or harm your client. State’s experts will testify to a range of possible alcohol concentrations based on a mathematical calculation. Depending on the particular facts of your case, the range may include an alcohol concentration below the legal limit of 0.08. If this is the case, then the expert should admit during cross-examination that he/she cannot tell the jury that your client's BAC or BrAC was over 0.08 g/dL at the time the client was actually driving. In fact, it is just as likely that your client was below 0.08 g/dL as above it.
As a result, you may choose not to contest the State's offer of this testimony as part of your trial strategy. Moreover, you may actually elicit the testimony yourself if the State fails to do so. I have asked State’s experts to perform retrograde calculations in low breath test cases where the State's attorney specifically did not ask about it because the prosecutor knew the testimony would include a low-end concentration level below 0.08 g/dL.
Practice Tip: |
Excluding and Challenging Retrograde Evidence
Request an Evidentiary Hearing to Exclude Retrograde Extrapolation
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Each state has its procedures regarding objections to the admissibility of scientific evidence. In most instances, you will need to ask for a hearing BEFORE the State’s expert gives an opinion. Some judges like to hold hearings at the start of a trial in order to make their rulings in advance and to keep the trial flowing. Others will remove the jury when you make your request and hold the hearing in the middle of testimony. Either way, you will need to be prepared to voir dire the State’s expert on the factors used to perform the retrograde extrapolation equation and then specify why you do not believe the State's expert has enough data to calculate a retrograde extrapolation range.
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A Sample Cross-Examination Challenging the Validity of Retrograde Extrapolation Evidence:
If testimony regarding retrograde extrapolation is admitted and it is not helpful to your defense, your best line of attack is pointing out the "dubious" nature of the practice. Here are some sample questions, assuming you have already had the witness recognize Doctors Dubowski and Jones as authorities. These questions are geared toward the articles previously discussed in this chapter. If the State’s expert denies something included in one of the articles, be prepared for it so that you can give them an opportunity to review that particular section and possibly re-think the answer.
For excerpts of trial transcripts that discuss the issue of retrograde extrapolation, please see Ch. 6. of the Texas DWI Manual by Deandra M. Grant & Kimberly Griffin Tucker
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Q: This calculation you just did for the jury, isn't it true that you had already performed the calculation for the DA prior to trial?
Q: So when she just gave you that hypothetical information and you punched some numbers into your calculator, you both already knew the answer to her question? Q: What is the exact calculation you are making? Q: Have you heard of a scientist by the name of Widmark? Q: Can you tell the jury who Dr. Widmark was? Q: Are you using Dr. Widmark's formula to compute the numbers in this case? Q: You would agree that performing a back extrapolation requires you to use several "averages," correct? Q: You would agree that you have no way of knowing whether my client actually falls into the category of "average" for any of the factors you are using in your equation? Q: You agree that the scientific community frowns on the use of back extrapolation testimony due to the large number of uncertainties involved? Q: In fact, your teachers, Dr. Dubowski and Dr. Jones, the two most well-known and well-published experts in this field who you recognize as authorities in this area, disagree with the use of back extrapolation? Q: You are aware that Dr. Jones has referred to the practice as "dubious"? Q: What elimination rate are you using? Q: Isn't it true that the scientific literature reports a wide range of elimination rates found in test subjects and that 0.015 [or 0.020 or whatever the witness used] is merely a commonly used AVERAGE? Q: As you sit here today, can you tell this jury what my client's elimination rate was on the night he was arrested? Q: So if it was not 0.015 [or whatever rate was used], then your calculation would be off, wouldn't it? Q: Another important variable in retrograde extrapolation is the rate of absorption? Q: You agree that the calculation itself is meaningless if the person is still absorbing alcohol? Q: In order to perform this calculation, you made the assumption that all of the alcohol in my client's stomach had been fully absorbed and that he was in what is commonly referred to as the elimination phase? Q: You agree that the scientific literature also reports a wide range of absorption rates? Q: In fact, your teachers, Dr. Dubowski and Dr. Jones, as well as many others, have experimented and written extensively on all of the many variables that can impact absorption rates, correct? Q: Do you agree with Dr. Jones that the rate of absorption of alcohol can be impacted by the type of alcohol a person drinks? (i.e., beer vs. whiskey) Q: Time of day? (For this factor and the ones that follow, see Garriott's 5th edition at page 57.) Q: Trauma? Q: Cigarette smoking? Q: Carbonated drinks? Q: Prescription medications? Q: Low blood sugar? Q: Those are lots of variables, aren't they? Q: Food in the stomach? Q: Do you know how much food was in my client's stomach that evening? Q: You're really just making assumptions with regard to whether or not food might have slowed down the alcohol absorption process? Q: Body fat vs. muscle mass is another variable that needs to be taken into consideration, wouldn't you agree? Q: Dr. Widmark used young Swedish male subjects in the 1930s for his study, correct? Q: In fact, researchers after Widmark have recommended using body mass index numbers to more accurately reflect a population that perhaps is not quite the same physically as the 1930s Swedes that Dr. Widmark tested, correct? Q: After all, people today tend to carry more body fat, don't they? Q: When taking into account all of the uncertainty involved in attempting to back extrapolate, the calculated range you just gave the jury of what my client's alcohol concentration MIGHT HAVE BEEN when he was driving amounts to nothing more than a guess, right? [witness might say it's an educated guess but emphasize that it's still a guess]. |
Conclusion
Retrograde extrapolation evidence is often used in DUI prosecutions and it is important for DUI defense attorneys to understand what it is and its limitations. As is the case whenever “scientific” evidence is offered by the State, the prepared defense attorney is the effective attorney.
Bonus material
Click here to download a printable version of these two articles:
| retrograde_2022.pdf |
Send me your questions or comments:
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For further study:
- Dubowski, K. M., Absorption, Distribution and Elimination of Alcohol: Highway Safety Aspects, J. Stud. Alcohol, Supp. No. 10 (July 1985).
- Fenna, D., et al. Ethanol Metabolism in Various Racial Groups, C.M.A. Journal, Vol. 105, September 1971.
- Forrest, A.R.W., The Estimation of Widmark’s Factor, Journal of the Forensic Science Society, 1986; 249- 252.
- Garriott’s Medico-Legal Aspects of Alcohol, 5th Edition, Lawyers & Judges Publishing Co., 2008.
- Grant, D.M. and Tucker, K.G., Texas DWI Manual, James Publishing Company, 2015.
- Jones, A.W., Forensic Science Aspects of Alcohol Metabolism, For Sci Prog Vol 5, 1991.
