🧪 Lethal Dose (LD50) Extrapolation Simulator

LD50 — The Median Lethal Dose

LD50 is the dose lethal to half a population.

• OECD 425: Defined by (toxicity test guideline)
• mg/kg: Units (body weight basis)
• 50%: Population killed (of test subjects)
• 1927: First proposed (by J.W. Trevan)

Origin of the LD50 concept

J.W. Trevan coined LD50 in 1927.

Standardized toxicology testing

Animal studies estimate the dose killing half of subjects.

Why a statistical midpoint

Individual variation makes one universal lethal dose impossible.

The Dose-Response Curve

Mortality climbs from zero to total along an S-curve.

• Sigmoid: Curve shape (logistic dose-response)
• Near LD50: Steepest region (small dose shifts matter most)
• ~0%: Low-dose plateau (sub-threshold exposure)
• ~100%: High-dose plateau (supra-lethal exposure)

Shape of the curve

Low doses kill almost no test subjects.

The steepest point

Mortality rises fastest right at the LD50 dose.

Reading the axes

X-axis is dose; y-axis is percent mortality.

Scaling LD50 to Body Weight

LD50 in mg/kg converts directly using body mass.

• mg/kg: Basis (per kilogram body weight)
• 60–90 kg: Typical adult (reference range)
• Linear: Scaling method (simple mg/kg model)
• No PK: Limitation (ignores metabolism differences)

Why scale by weight

Heavier bodies dilute a fixed dose over more tissue.

The linear assumption

Total dose is assumed proportional to body mass.

Where scaling breaks down

Fat, age, and metabolism all alter true sensitivity.

Extrapolating the Lethal Dose

Multiply LD50 by body weight for a milligram estimate.

• LD50 × kg: Formula (total mg estimate)
• Nicotine: Example substance (~50 mg/kg oral rat)
• 3,500 mg: 70 kg example (at LD50 50 mg/kg)
• Forensic estimate: Use (not a clinical prediction)

The extrapolation formula

Dose in mg equals LD50 times body weight in kg.

Animal-to-human caveats

Rodent LD50 rarely transfers precisely to human physiology.

Forensic use case

Investigators estimate exposure from LD50 and victim weight.

Population Variability in Response

Individual susceptibility spreads real risk around the estimate.

• ±20%: Variability band (typical individual spread)
• Lower dose: Sensitive subgroup (children, illness, age)
• Higher dose: Resistant subgroup (tolerance, body composition)
• None: Certainty (LD50 is not a guarantee)

Why individuals differ

Genetics, health, and tolerance shift personal susceptibility.

The variability band

A shaded zone shows the range of likely outcomes.

Forensic interpretation

Toxicologists report ranges, never single certain outcomes.