EVIDENCE LIBRARY
Can a Widmark Calculation Imply More Than 100% Alcohol Absorption? An Eight-Man Model Comparison
A model-derived ‘105% absorption’ is not a physical test result. See the 8-man serum ethanol study and why model-based BAC estimates require caution.
Short answer: Yes. A pharmacokinetic calculation can produce an apparent ethanol-absorption fraction above 100%, even though the body cannot absorb more ethanol than was administered. In a controlled study of eight healthy men, Zekan and colleagues reported a mean Widmark-derived fraction of 1.05 for an unsweetened ethanol drink. That figure is a model estimate, not a physical measurement of 105% absorption. A more detailed model fitted the same serum concentration series using a differently defined absorption parameter near 0.51. Neither fraction was independently measured, and neither model was validated for calculating an individual defendant’s historical blood alcohol concentration.
The primary research is Zekan and colleagues, Pharmacokinetic Analysis of Ethanol in a Human Study: New Modification of Mathematic Model, Toxics (2023), doi:10.3390/toxics11090793. Its strongest forensic lesson is about model dependence, biological assumptions, and uncertainty—not a newly established alcohol-absorption correction factor.
Why can an alcohol-absorption estimate exceed 100%?
An absorption fraction is physically bounded between zero and one: a fraction of 1 means the entire administered quantity, and a fraction greater than 1 cannot represent actual absorption of additional material from that dose. A model can nevertheless output 1.05 if it infers the fraction indirectly from a concentration curve using assumptions that do not perfectly represent the observed process. The result should trigger scrutiny of the calculation, not an allegation that the person consumed an extra 5%.
In the studied version of the Widmark model, an initial concentration is extrapolated backward from serum measurements at 60, 90, and 120 minutes. The model assumes a fixed distribution volume of 0.7 liters per kilogram, immediate entry into one well-mixed compartment, and a linear elimination rate. The inferred intercept, assumed distribution volume, and known administered dose are then combined to estimate the absorbed fraction. None of those steps directly counts molecules transported from the intestine to the circulation.
Critically, the alcohol in this experiment was swallowed, absorbed over time, distributed among body tissues, and metabolized. Instant absorption is a simplifying assumption, not an observation. If the extrapolated intercept or assumed distribution volume does not match the participant’s physiological kinetics, an impossible-looking fraction is a mathematical warning about the model’s interpretation.
What experiment generated the 1.05 Widmark result?
The investigators enrolled eight healthy male volunteers aged 24–25 years, with reported weights between 82 and 112 kilograms. Every participant attended three experimental drinking sessions separated by at least three days. The beverage order was randomized, and participants were blinded to the sweetening condition. The eight people—not the 24 possible drinking sessions—are the independent human participants; repeated observations do not turn them into 24 unrelated subjects.
Each session involved the same intended ethanol dose, 0.3 grams per kilogram of body weight, delivered in approximately 300 milliliters of whisky mixed with tea and consumed within two minutes. Conditions were unsweetened control, sucrose-sweetened tea, and steviol-glycoside-sweetened tea. The study specified a three-hour interval since the last meal. These tightly defined experimental conditions are not interchangeable with drinking over a prolonged evening, food taken during consumption, different body compositions, or drinking after a motor-vehicle collision.
The researchers collected venous blood before consumption and at 15, 30, 60, 90, 120, and 180 minutes afterward. They obtained multiple time points from each person, allowing both the conventional and modified models to be fitted to an observed concentration trajectory. That is materially more informative than attempting to estimate an entire drinking history from a single later specimen, although the design remains small and controlled.
Were these direct forensic whole-blood alcohol measurements?
No. Venous blood was drawn, but the analytical sample was serum. The original Methods describe clot-activator serum-separator tubes, an hour for clotting, centrifugation, transfer of serum, and measurement with an automated alcohol dehydrogenase enzymatic spectrophotometric method on a Beckman Coulter AU680 platform. The paper does not document a separate forensic headspace gas-chromatographic whole-blood assay with a complete validation and uncertainty budget.
This matrix distinction matters. A direct laboratory determination of ethanol in serum is not the same reported quantity as ethanol measured in unseparated whole blood, and it is not a breath-analyzer reading. Equally, a serum concentration observed at a specific collection time is not the concentration imagined at another time by a pharmacokinetic model. Treating all three as interchangeable conceals important analytical and inferential steps.
For the separate analytical question, see this site’s live guide to blood-alcohol chromatography and confirmatory methods. The Zekan study assessed mathematical modeling of serum measurements rather than establishing comparative performance between serum enzymatic analysis and forensic whole-blood GC testing.
What did the researchers actually measure after the three drinks?
The study reported mean serum ethanol concentrations at 15 minutes and the maximum sampled concentration over 180 minutes. These are measured-concentration summaries, distinct from an instantaneous modeled concentration at time zero. The three conditions had comparable group-level values and did not show statistically significant differences on the reported tests.
| Drink condition | 15-minute serum ethanol, mean (95% CI), g/L | Maximum sampled serum ethanol, mean (95% CI), g/L |
|---|---|---|
| Unsweetened control | 0.32 (0.22–0.42) | 0.42 (0.38–0.47) |
| Sucrose sweetened | 0.33 (0.21–0.46) | 0.37 (0.25–0.49) |
| Steviol glycoside sweetened | 0.32 (0.30–0.38) | 0.41 (0.33–0.49) |
| Three-condition test | p = 0.9153 | p = 0.8597 |
Interpretation: These p-values do not support an established difference between the sweeteners in this sample. They do not prove the formulations physiologically identical; with only eight participants and variable concentrations, a small or context-dependent effect may be undetected. The study does not supply evidence for a universal rule that replacing sugar with stevia raises, lowers, or leaves unchanged every person’s blood alcohol concentration.
The authors also reported an area-under-the-curve analysis. However, the published Table 3 prints exactly the same numerical entries in its area-under-the-curve row as in its 15-minute concentration row, despite different physical units. Consequently, those printed AUC numbers should not be reproduced as an independently verified cumulative-exposure calculation. A reliable forensic reconstruction would need a checked concentration-time series and a transparent integration procedure, not an unexplained copied table entry.
How was the classic Widmark estimate computed?
For the conventional approach, the paper fits a straight line to three observed serum concentrations at 60, 90, and 120 minutes. The line’s negative slope supplies an elimination parameter, and its backward intercept supplies an inferred initial concentration. With distribution volume set to 0.7 L/kg, the model calculates an apparent absorbed fraction by multiplying that extrapolated intercept by the assumed distribution volume and dividing by the administered ethanol dose.
Its mean apparent fractions were 1.05 for control, 0.93 for sucrose, and 1.00 for steviol glycoside, with the three-group comparison p = 0.5845. The control point estimate above one is a direct illustration of the method’s inability to guarantee a physically interpretable absorption fraction under these assumptions. Confidence intervals span additional uncertainty; the results are not exact measurements of systemic bioavailability.
Estimated elimination parameters were approximately 0.0023–0.0025 g/L/min across conditions, with no demonstrated sweetener effect (p = 0.8267). A rate estimated from only a few later serum values in eight young men is not a measured elimination rate for a litigant who was never studied. Retrograde calculations also depend on where the person lies on the absorption-versus-elimination trajectory; moving backward through an absorptive interval with a fixed declining line can seriously misrepresent the earlier curve.
How did the modified Norberg model differ?
The modified model describes ethanol in a gastrointestinal compartment, a liver compartment, and central and peripheral distribution compartments. Rather than requiring all absorbed ethanol to appear instantly in one volume, it introduces an estimated intestinal-to-portal absorption rate and a hepatic Michaelis–Menten elimination process. Movement between compartments and several physiological constants are represented explicitly.
The authors used nonlinear mixed-effects estimation in Monolix. Some parameters were fitted; others, including the compartment volumes, assumed blood flow, Michaelis–Menten constant, and distribution relationships, were fixed from selected reference values. Calling a model physiologically structured does not mean every physiological property was actually measured in the eight participants.
The resulting population-model parameters included a first-order absorption rate constant kA = 0.081 min−1 (standard error 0.0077) and an estimated portal-absorption fraction f2 = 0.51 (standard error 0.016). Within-condition mean f2 estimates were 0.520 control, 0.507 sucrose, and 0.492 steviol glycoside; their comparison was p = 0.360. Group-specific kA results likewise did not differ significantly (p = 0.731).
These are values fitted by a different mathematical definition. The modified model’s f2 represents a modeled fraction transferred from the gastrointestinal compartment into the portal circulation under its equations, whereas the Widmark f1 is a one-compartment quantity inferred from systemic concentration and an intercept. The two parameters should not be subtracted as if independent chemical assays measured the same physiological event. Their disagreement establishes model dependence; it does not measure the true unabsorbed fraction in this experiment.
Which results are measurements and which are model outputs?
| Quantity | Source and status | What it cannot establish |
|---|---|---|
| Serum ethanol at scheduled collections | Laboratory enzymatic ethanol analysis of serum separated from venous blood | Direct forensic whole-blood GC result, breath reading, historical event-time BAC, or impairment |
| Administered dose | Controlled study preparation, 0.3 g/kg oral ethanol | How much ethanol reached a particular tissue or survived first-pass metabolism |
| Widmark f1 and β | Computed from late sampled serum data plus fixed volume and linear assumptions | Direct gut-absorption measurement or known elimination constant for another individual |
| Modified-model f2, kA, vMAX | Nonlinear fitted parameters incorporating fixed physiological assumptions | Independent observation of actual portal transport, liver extraction, or a person’s true absorbed dose |
| Model-fit statistics | Reported fit to this experimental dataset | Out-of-sample validation, courtroom error rate, or person-specific prediction accuracy |
| Driving or cognitive impairment | Not experimentally measured in this study | Individual task deficits, culpability, crash mechanism, or event causation |
The overarching evidentiary chain is administered dose → specimen collection → serum chemical result → fitted parameter → inference. Each arrow requires separate support. The presence of a numerical parameter with several decimal places does not collapse those stages into one measurement.
Did the more complex model fit the data better?
By the authors’ reported Akaike information criterion comparison, the modified model had an AIC of −1607.86, compared with −215.55 for the conventional model under their analysis. The publication also presents observed-versus-predicted plots favoring the modified structure, while acknowledging residual imprecision, especially at higher concentrations.
That is evidence of a better reported fit within these experimental observations, not automatic evidence of superior predictions in independent drinkers, uncontrolled drinking histories, trauma patients, women, older populations, or a defendant whose last alcohol intake and relevant metabolic state are disputed. A model with additional mechanisms can fit a small dataset more closely while remaining sensitive to parameter assumptions.
In particular, the authors did not independently determine each volunteer’s total body water, adiposity, or actual distribution volumes. They also did not directly measure how much ethanol passed from gut into portal blood, how much was extracted in the liver, or the individual’s true first-pass fraction. Those omissions prevent an independent physiological validation of the fitted 0.51 fraction.
Why do the sweetener findings matter—and what do they not prove?
The comparison is clinically interesting because sucrose and a low-calorie steviol sweetener could plausibly alter the speed of delivery from the stomach and thus the time course of systemic exposure. This particular study, however, found no statistically significant difference across the three preparations for its directly observed 15-minute and maximum serum concentrations or its reported absorption-model parameters.
The three drinking conditions were not a randomized trial of different ethanol doses: each subject received a fixed 0.3-g/kg dose every session. They were not a meal-effect trial with measured gastric emptying, and the model was not fitted using independent stomach or intestinal measurements. A possible sweetness or food mechanism discussed by the authors is a hypothesis rather than proof that the sweeteners changed gastric transit in these volunteers.
Study restrictions matter: the participants were all young adult men, the time since food was standardized at only three hours, the ethanol solution had a specific concentration and volume, and samples were available for only 180 minutes. A numerical non-significant finding under this protocol does not establish that all other combinations of sex, food, ethanol dose, drinking rate, or sweetener produce equal alcohol curves.
What should a forensic expert disclose before using either model?
At minimum, a reliable forensic explanation should distinguish the underlying measured specimen and method from the simulated concentration, identify which parameters came from the case and which were assumed from population data, and disclose sensitivity to drinking time, dose, food, body-water estimates, absorption state, and elimination behavior. It should specify whether the event occurred before, near, or after the actual ethanol peak—something a single later concentration often cannot demonstrate.
It should also show the computational steps and units, verify that the modeled parameters are physically interpretable, and discuss the range of plausible outcomes instead of selecting a single favorable parameter. If a model produces an apparent fraction above one, calling it an estimated or apparent fraction is materially more accurate than claiming that the person’s body absorbed 105% of a dose.
Case-specific interpretation must separately address specimen identity and collection history. See this site’s published explanations of toxicology specimen collection and handling and pharmacokinetics in forensic toxicology. These topics do not cure unsupported assumptions in a retrospective drinking model, but they clarify where the evidence originates.
What does this study permit an expert to conclude?
It permits a focused conclusion: in eight young male volunteers receiving controlled oral ethanol doses, a classic single-compartment retrospective calculation and a physiology-structured nonlinear model yielded different parameters from the same series of enzymatic serum ethanol observations. One Widmark point estimate exceeded a literal absorption fraction of one. The three sweetener formulations did not differ significantly on the cited primary results. The modified model was reported to fit these data better, but the parameters were not independently confirmed by direct absorption measurements.
It does not establish an alternative numerical rule that should simply replace Widmark for every DUI case. Nor does it determine any individual’s consumption history, whole-blood BAC at an unmeasured time, neurobehavioral impairment, intent, or accident causation. The proper scientific use is to examine model assumptions and uncertainty rather than to exchange one unsupported precise prediction for another.
Primary source: Zekan P, Ljubičić N, Blagaić V, Dolanc I, Jonjić A, Čoklo M, Boban Blagaić A. “Pharmacokinetic Analysis of Ethanol in a Human Study: New Modification of Mathematic Model.” Toxics. 2023;11(9):793. doi:10.3390/toxics11090793.
Frequently asked questions
Does an apparent ethanol-absorption value of 1.05 prove someone consumed more alcohol than reported?
No. A value of 1.05 is an estimate derived from a model and assumed distribution volume. Actual absorption cannot exceed the amount administered. The number calls the model’s assumptions and input data into question, not the participant’s honesty.
Did the investigators measure a true blood alcohol concentration?
They drew venous blood and chemically measured ethanol in separated serum using an enzymatic assay. Their measurements are not independently validated forensic whole-blood GC BAC values. Any matrix conversion or extrapolation would be a separate inference.
Is the modified-model estimate of 0.51 proof that only 51% of the ethanol was absorbed?
No. It is a fitted parameter representing movement into the model’s portal compartment under assumed kinetics and volumes. The study did not independently measure intestinal absorption or hepatic first-pass elimination, and the two models define their fractions differently.
Did sucrose or steviol glycoside significantly alter maximum serum ethanol in this experiment?
No significant difference was demonstrated among the three conditions for sampled peak serum ethanol (p = 0.8597). Small sample size and study-specific conditions limit the broader interpretation; this result is not proof that sweeteners can never affect alcohol exposure.
Can a lower Akaike information criterion validate an individual’s retrograde BAC reconstruction?
No. The reported comparison favors the modified model’s fit to this dataset. It does not provide independently validated error bounds, prospective case predictions, or a person-specific criterion for deciding historical BAC from an unrelated specimen.
Was any driving, cognition, or impairment outcome evaluated?
No. The experiment measured serum ethanol over time and compared models. It administered no road-driving test, field sobriety battery, simulator assessment, or case-specific causation analysis.
What is the most important limitation for courtroom use?
The experiment contains only eight young male participants, relies on a serum enzymatic method and several fixed physiological assumptions, and has no direct measurement of the modeled gut-absorption fractions. It illustrates uncertainty but does not establish a universal correction factor or determine an individual’s unobserved alcohol level.