The Problems with Retrograde Extrapolation of Blood Alcohol Levels

The Law Offices of Brent M. Christensen is pleased to present this insightful treatise relevant to DUI cases.

If a driver’s blood-alcohol concentration (BAC) is below the legal limit when the driver gives a breath or blood sample, this fact will not stop the prosecution from trying to obtain a DWI conviction. At trial, the state may attempt to use retrograde extrapolation to convince the jury that the BAC exceeded the legal limit earlier when the police stopped the driver on the highway. But retrograde extrapolation is an unreliable tool.
According to the concept of retrograde extrapolation, a blood-alcohol concentration derived from the analysis of a subject’s breath or blood sample at a particular test time¹ can be extrapolated back to the supposedly higher BAC existing at an earlier incident time. This is accomplished by adding to the BAC at test time the product of the hourly rate of alcohol elimination from blood (commonly termed the β value, as per Widmark²) and the number of hours elapsed between incident and test times. This process is expressed mathematically by Equation 1 (eq 1).

Equation 1

BAC_{Test Time} + Elapsed Hours x β = BAC_{Incident Time}­
The application of this equation can be demonstrated via the following example. An individual is characterized by a test BAC of 0.07 percent at 6:00 a.m., and assume that his hourly rate of alcohol elimination is 0.015 percent/hour (hr) — an average β³ often used by those who employ retrograde extrapolation — then his BAC at 3:30 a.m., 2.5 hours earlier, would be estimated to be 0.10 percent. This BAC would be obtained by using eq 1 to perform the calculation shown in Equation 2. The result initially obtained and not shown, namely 0.1075 percent, would be truncated to 0.10 percent, as indicated, in accord with the established law enforcement practice of truncating BACs to two decimal places by eliminating all decimal places beyond the second without rounding.⁴

Equation 2

0.07% + 2.5 hr x ^0.015%⁄_{1 hr} = 0.10%
The apparent simplicity of retrograde extrapolation renders it an attractive tool among proponents of this methodology. The examples profiled in the next section, stemming from newspaper coverage of various DWI cases, reflect this reality. The re-examination of these examples in a forthcoming section, however, within the context of the arguments offered in this article concerning the drawbacks of retrograde extrapolation, provides an alternative and scientifically reliable perspective on the conclusions stemming from law enforcement personnel that are offered in each of the examples.

Documented Cases Involving Retrograde Extrapolation

Brooklyn (New York) District Attorney Charles Hynes made the following statement in 2000 concerning a DWI case: “Reaching a drunken state between the time of the car stop and … testing for alcohol when no additional alcohol is consumed is a metabolic impossibility.”⁵ Implicit in that statement is the assumption by Hynes that BAC cannot increase between the time of the car stop (the incident time) and the time of the test. Rather, it appears that, according to him, the BAC must decrease, so that the BAC at the time of the car stop must necessarily be higher than at the time of testing.
In 2002, law enforcement authorities charged nationally recognized public television journalist and author Bill Moyers with DWI in Vermont. A breath test administered at the Shaftsbury Police Barracks where officers took Moyers after he failed a roadside breath test indicated a nontruncated BAC of 0.079 percent.⁶ Although this test result was below the legal limit of 0.08 percent in Vermont, Lt. Steve Poirot, the barracks commander, said that the BAC for Moyers was adjusted upward “to take into account alcohol that would have left Moyers’ system between the arrest and the test [conducted at the barracks].”
Law enforcement officers found that a driver involved in a Brooklyn, N.Y., accident in 2005 that resulted in a fatality had a BAC of 0.06 percent approximately 2.5 hours after the accident occurred. The report of this fatality indicated that, although the arrested driver had a BAC below New York’s legal limit of 0.08 percent at Brooklyn’s Lutheran Medical Center when he was tested, “Brooklyn prosecutors believe that [the driver’s BAC] was much higher at the time of the accident.”⁷
In 2009, journalist Michael Daly⁸ described a case involving a fatality in which authorities found that the arrested driver, suspected of DWI and tested more than seven hours after the accident occurred, had no BAC, despite indications that he had been ingesting alcohol prior to the accident. According to Daly, “Experts say that even in those circumstances there would still be enough of a trace [of alcohol] for ‘retrograde extrapolation.’ The rate of dissipation is used to work backward from the test results, deducing what the level must have been at the time of the accident, [in accord with the application of eq 1].”
These four incidents are a mere sampling of the “retrograde extrapolation” mindset that typically exists in law enforcement concerning many DWI cases. Given that this issue is likely to continue to surface, revisiting the topic and addressing its inherent flaws are warranted.

The Flawed Basis of Retrograde Extrapolation

The schematic diagram appearing in Figure 1 represents an ideal blood-alcohol or breath-alcohol curve (hereinafter termed “BAC profile” or “BrAC profile”) adapted from the classic research of Widmark.⁹ The various phases of alcohol metabolism are shown in the figure. It must be stressed, however, that actual BAC or BrAC profiles can deviate significantly from the profile in Figure 1,¹⁰ as is emphasized below. In fact, the delineations depicted in Figure 1 are not always as clear-cut as they appear to be, so that, for example, the plateau and diffusion-equilibration phases in an authentic profile are not necessarily distinguishable. Nevertheless, this figure serves as a useful instructional aid that facilitates the understanding of the flawed basis of retrograde extrapolation.
Within this context, therefore, the focus is on the elimination phase — also termed the postabsorptive state¹¹ — following the equilibration of alcohol in the body. In this regard, Dubowski¹² has indicated that the “peak” region of a BAC/BrAC profile, which would encompass the “plateau” in Figure 1, “often marks … the changeover between the rising and falling [BACs or BrACs], reflecting the absorption … and elimination … phases … [respectively].” As indicated in Figure 1, the elimination phase in the ideal situation is linear, and it must necessarily be so if eq 1 is to apply. That is, the mathematical requirement for the application of eq 1 to a calculation involving a retrograde extrapolation in a given case is that a straight line denotes the graphical representation of the elimination phase associated with that case.
In reality, the shape of the BAC/BrAC profile of a subject charged with DWI is typically unknown, so that where the subject’s BAC — or BrAC in a breath-alcohol analysis, as per note 10 — lies on the subject’s particular profile at test time is also unknown. Consequently, the fundamental assumption, that a given test subject is in the postabsorptive state at test time and that the subject’s BAC/BrAC profile in that state exhibits linearity, has no basis in fact. In this regard, Dubowski¹³ has referred to the “infeasibility of retrograde extrapolation” and has offered three key reasons in support of his position: “(1) lack of knowledge, usually, about the timing of the alcohol concentration peak and absorption-postabsorption status; (2) ignorance about the mathematical characteristics (e.g., linear, pseudolinear, exponential) and the mean rate of change of the individual’s blood- or breath-alcohol elimination [profile]; and (3) unpredictable irregularities of the [profile], especially short fluctuations from the best-fit trend line of the blood- or breath-alcohol [profile].”
More recently, Jones¹⁴ characterized retrograde extrapolation as “a dubious practice, owing to the many variables and unknowns involved.” He added that, “In a typical impaired driving trial, only a single measurement¹⁵ of BAC or BrAC is usually available, making it very difficult to engage in retrograde calculations with sufficient certainty for a criminal prosecution.” Jones’ position, coupled with Dubowski’s, as described above, reinforces the argument put forth earlier by Martin et al.¹⁶ that “back extrapolation of venous blood alcohol levels, based on a single known concentration, can lead to estimates bordering on wild guesses.”  In a recent case, DuPage DUI attorney Brent Christensen successfully challenged the Cook County State's Attorneys attempt to use retrograde extrapolation in a DUI case in which Christensen's client passed two of three field sobriety tests and submitted a breath test with a result of .079.

Exemplification of Flawed Retrograde Extrapolations

The BAC/BrAC profile of a DWI arrestee, based on that individual’s drinking pattern in the case involved, is unknown when law enforcement personnel makes the relevant concentration measurement for that arrestee as indicated above.¹⁷ Therefore, the only reliable assessment of a BAC/BrAC profile, within the context of retrograde extrapolation, must necessarily reflect published research. In this regard, and based on the documented BrAC profiles presented by Watkins and Adler¹⁸ — who studied nine subjects (six males, three females) using two separate protocols, alcohol consumption after a large meal and after an approximate six-hour fast — Fitzgerald and Labianca¹⁹ have demonstrated that a prediction of a prior BrAC derived from a reported BrAC using retrograde extrapolation is unreliable.
One example, among many, derived from the work of these authors that supports this conclusion involves the BrAC profile of a “full stomach” female subject (Figure 40M of the Fitzgerald/Labianca work²⁰) that indicates an estimated nontruncated test BrAC value of 0.065 g/210 L 2.7 hours after drinking. The predicted BrAC, two hours earlier (i.e., at 0.7 hour, or 42 minutes, after drinking), would be a nontruncated 0.095 g/210 L. This prediction is obtained from the application of eq 1 and the use²¹ of a β value of 0.015 g/210 L/hr that would be equivalent to 0.015 percent/hour if a BAC calculation were involved (0.065 g/210 L + 2 hr x 0.015 g/210 L/hr = 0.095 g/210 L). The actual, “two-hour-earlier” BrAC estimated from the Figure 40M profile is a nontruncated 0.065 g/210 L. Note that this is the same BrAC derived from the profile at 2.7 hours after drinking, as noted above.
That there is no change in BrAC during the two-hour period under consideration is a consequence of the fact that the 0.7-hour BrAC occurs before the peak BrAC is achieved, so that the absorption phase is apparently still in place. The 2.7-hour BrAC occurs at a point in the profile beyond the peak where the BrAC has been changing slowly, apparently due to the presence of food in the subject’s stomach. So the predicted BrAC at 0.7 hour after drinking, which truncates to 0.09 g/210 L, is obviously higher than the actual BrAC, which truncates to 0.06 g/210 L.
The analysis of Fitzgerald and Labianca²² is consistent with Dubowski’s conclusion²³ that retrograde extrapolation is “infeasible.” A relevant example in this regard from Dubowski’s work²⁴ — one of many the interested reader can personally explore using the BrAC profiles presented in that work — involves Figure 2D, one of the six BrAC profiles reported by Dubowski involving alcohol consumption after a four-hour fast. He used BrAC values that employ the concentration unit, milligrams (mg) of alcohol per 230 liters (L) of breath (mg/230 L). This unit can be converted into the equivalent unit of “g/230 L” by dividing the former unit by 1000, since 1000 mg equals 1 g. Dubowski’s use of this concentration unit is based on a blood-alcohol to breath-alcohol ratio (BBR)²⁵ of 2300:1, essentially the mean, or average, postabsorptive BBR reported by Dubowski.²⁶ To convert any of Dubowski’s g/230 L BrAC values into corresponding g/210 L BrAC values — the latter based on the standard 2100:1 BBR²⁷ — the former BrAC values would simply be multiplied by the fraction, 2100/2300, to generate the latter BrAC values.
Given the preceding stipulation, one can estimate from Dubowski’s Figure 2D, referred to above, a nontruncated BrAC of 0.1068 g/210 L, measured 2.5 hours after the commencement of alcohol consumption and prior to the occurrence of the peak BrAC and, therefore, during the absorption phase. If one wanted to retrograde extrapolate this BrAC to the supposedly existing BrAC 1.5 hours earlier, a point in time still characterized by the absorption phase, one would apply eq 1 to obtain a predicted, nontruncated BrAC of 0.1293 g/210 L (0.1068 g/210 L + 1.5 hr x 0.015 g/210 L/hr = 0.1293 g/210L). The actual BrAC 1.5 hours earlier, however, as estimated from Dubowski’s Figure 2D, is a nontruncated 0.0639 g/210 L. In effect, then, the predicted, truncated BrAC of 0.12 g/210 L is significantly higher than the actual, truncated BrAC of 0.06 g/210 L.
Dubowski²⁸ also emphasizes the “fluctuations phenomenon” that characterizes his reported BrAC profiles. That is, according to him, “It is evident from these rather typical [BrAC profiles] that breath-alcohol analysis results, even under highly controlled conditions, can and do rapidly oscillate in short time periods above or below any given concentration.” In fact, one of the profiles (Figure 2F) exhibits “positive and negative spiking as great as 0.030 g/230 L in less than 10 [minutes].” This concentration is equivalent to 0.027 g/210 L — obtained via multiplication of 0.030 g/230 L by 2100/2300, as noted previously — which, in turn, truncates to 0.02 g/210L. Such “spiking” is particularly revealing when considered within the context of an example involving, for instance, a BrAC of 0.07 g/210 L at a particular time such as 8:00 p.m. Thus, 10 minutes earlier, at 7:50 p.m., the BrAC could have been 0.09 g/210 L; 10 minutes later, at 8:10 p.m., it could have been 0.05 g/210 L; and at 8:20 p.m., it could have returned to 0.07 g/210 L. Obviously, such fluctuations — which also characterize the work of Watkins and Adler²⁹ that was relied upon by Fitzgerald and Labianca,³⁰ as described previously — constitute a potentially disturbing feature of any attempt to use retrograde extrapolation based on a reported BAC or BrAC derived from forensic breath-alcohol analysis.
Moreover, Dubowski³¹ stresses that the “fluctuations phenomena” described above are not restricted to breath-alcohol analysis. In fact, he observed similar patterns in BAC profiles, as demonstrated by “the very close correlation of numerous separately measured simultaneous [BACs] and [BrACs] in the course of the experiments that yielded the [BrAC profiles]” he reported.³²

Re-examination of Previously Described Documented Cases

In view of the problems concerning retrograde extrapolation, a brief review of the four documented cases presented previously is warranted. Consider first the comment by Brooklyn District Attorney Charles Hynes in 2000 characterizing an increase in BAC between incident and testing times as a “metabolic impossibility.”³³ The subject in this case could very well have been in the absorptive state of alcohol metabolism at incident time, so that by test time the BAC could have risen from an inconsequential level to a level reflecting intoxication.
Consistent with this argument is the work of Jones et al.,³⁴ who found the rise in BAC to average 0.10 percent per hour on an empty stomach (0.10 g/210 L, based on a 2100:1 BBR)³⁵ and the work of Simpson,³⁶ who, relying on Dubowski’s data,³⁷ determined an average rise in BAC of about 0.15 percent per hour (0.15 g/210 L). Rates of alcohol absorption on a full stomach, on the other hand, tend to be lower, but are, nevertheless, significant. In this regard, Labianca’s analysis³⁸ of the data of Jones and Neri,³⁹ derived from their study of subjects who ingested mixed drinks with a meal, revealed an absorption rate averaging about 0.05 percent per hour.
Also noteworthy concerning an individual’s absorption status is Dubowski’s relevant commentary.⁴⁰ He emphasized that “it is not possible to establish whether an individual is in the absorption or elimination [postabsorptive] phase … from the results of two consecutive blood- or breath-alcohol measurements, however timed.”⁴¹ In terms of specific time frames, Baselt⁴² has reported that, for fasting subjects, the time-to-peak BAC typically ranges from 0.5 to 2.0 hours, with an average of 0.75 to 1.35 hours, depending on alcohol dose and time of last meal. For nonfasting subjects, on the other hand, the range is 1.0 to 6.0 hours, and the average is 1.06 to 2.12 hours. Furthermore, Dubowski⁴³ has said that, in addition to the factor of food consumption, the rate of alcohol absorption is dependent on other factors. These factors include the type and concentration of alcoholic beverage ingested, and a “multitude of other physical, biological, psychological, and time factors that combine with the individual’s sex, bodyweight and body water, and related habitus characteristics as well as offsetting metabolic disposition to determine the ultimate peak blood-alcohol concentration [or BrAC] and other characteristics of the time course of the blood-alcohol concentration [or BrAC].”
The second and third cases previously profiled, like the first case, could realistically have involved lower incident time BACs than law enforcement personnel claimed. In the Bill Moyers case,⁴⁴ the reported, nontruncated BAC of 0.079 percent could very well have been significantly lower at the time of the arrest, and not higher, as barracks commander Lt. Poirot argued. Between the time of the arrest and the time of the breath test at the police barracks, Moyers could have been in the absorptive state of alcohol metabolism, so that his BAC would have been rising.
In the third case⁴⁵ involving a reported BAC of 0.06 percent 2.5 hours after the accident occurred, there is no way to verify prosecutorial claims that the driver’s BAC was substantially higher at the time of the accident. Once again, the assumption was made that the driver was in the postabsorptive state at test time, that he was still postabsorptive 2.5 hours earlier, and that his particular BAC profile was linear in the postabsorptive state, so that a retrograde extrapolation to a higher BAC could have been conducted. On the other hand, the driver could have been absorbing alcohol 2.5 hours earlier, and his BAC at that time could have been lower than 0.06 percent. Consequently, once again, the uncertainty stemming from lack of knowledge of the driver’s BAC profile renders any conclusion regarding a prior BAC untenable.
The fourth and final case, as described by journalist Daly,⁴⁶ is troubling because he says that, according to “experts,” even a “trace” of alcohol in the blood would be sufficient to facilitate a retrograde extrapolation. There are two key issues to consider concerning this argument. First, what is meant by a “trace” of alcohol? Dubowski⁴⁷ has stated, in this regard, that “putative BAC results of less than [0.01 percent] should not be reported numerically, but simply designated as negative for alcohol.” Second, even if the BAC exceeds this lower limit threshold of 0.01 percent, lack of knowledge concerning the driver’s BAC profile necessarily casts serious doubt on any attempted retrograde extrapolation of a low BAC to a higher incident time BAC.

Conclusion

The underlying uncertainty characterizing retrograde extrapolation renders this process an unreliable tool in the DWI arena. The conclusions of Dubowki are unequivocally applicable: “[n]o forensically valid forward or backward extrapolation of blood- or breath-alcohol concentrations is ordinarily possible in a given subject and occasion solely on the basis of time and individual analysis results … [and, furthermore,] extrapolation of a later alcohol test result to the time of the alleged offense is always of uncertain validity and, therefore, forensically unacceptable.”