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BAC Retro-Extrapolation

Run the BAC Retro-Extrapolation MicroSim Fullscreen

About This MicroSim

Blood alcohol concentration (BAC) is often measured hours after a relevant event such as driving. Because alcohol leaves the body at a roughly steady rate during the elimination phase, a toxicologist can work backward — a process called retro-extrapolation — to estimate what the BAC was at the earlier event time.

This MicroSim does both halves of that job. The left panel computes peak BAC with the Widmark formula; the right panel graphs BAC over time and lets you drag an event-time marker to read the retro-extrapolated value.

How to Use It

  1. Set sex, weight, and number of drinks — the panel shows each step of the Widmark calculation and the peak BAC.
  2. Set the blood-draw time (hours after the last drink) and the elimination rate β.
  3. Drag the gray marker on the graph to the event time (e.g., time of driving).
  4. Press Calculate to reveal the retro-extrapolation arithmetic and the BAC at the event time — colored red if it is over the 0.08% legal limit.
  5. Toggle Show absorption phase to add the pre-peak rising curve.

What You Can Learn

  • Calculate peak BAC from body weight, sex, and drinks using the Widmark formula.
  • Retro-extrapolate a measured BAC backward to an earlier time.
  • Explain why a BAC under the limit at the blood draw can still mean the person was over the limit while driving.

You can embed this MicroSim on your own web page with this iframe:

<iframe src="https://dmccreary.github.io/forensic-science/sims/bac-retro-extrapolation/main.html"
        width="100%" height="517" scrolling="no"></iframe>

Lesson Plan

Audience: High-school forensic science (grades 9–12) Time: 15–20 minutes Bloom level: Apply (L3) — calculate and retro-extrapolate.

Worked example. Male, 80 kg, 4 drinks. Compute A = 56 g, peak ≈ 0.103%. Set draw = 3 h, event = 1 h, β = 0.015. Have students compute BAC at event by hand before pressing Calculate.

Guided questions:

  • The measured BAC at the draw is below 0.08%. Could the driver still have been over the limit two hours earlier? Show the arithmetic.
  • How does a larger body weight change the peak BAC?
  • Why is retro-extrapolation only valid during the elimination phase, not during absorption?

Extension. Discuss the legal assumptions and uncertainties (unknown drinking pattern, individual variation in β) that make retro-extrapolation contested in court.

References

Specification

This MicroSim was generated from a specification in Chapter 9: Forensic Toxicology and Chemical Analysis.

Design note: the model uses 14 g of ethanol per US standard drink and the classic Widmark r-values (0.68 male, 0.55 female). Numbers are illustrative for teaching the method, not for casework. The event-time marker is positioned by dragging it on the graph rather than with a separate slider.