Question

The LD \(_{50}\) (see problem 68 ) of cocaine in rats is \(17.5 \mathrm{mg} / \mathrm{kg}\). What would be the approximate lethal dose for an \(80-\mathrm{kg}\) person?

Short answer

Lethal Dose for an 80-kg person = 1400 mg

Step-by-step solution

Understanding LD50

The LD50 value represents the dose of a substance that is lethal to 50% of a test population. Here, the LD50 of cocaine is 17.5 mg per kg of body weight in rats.

Calculate the Human Lethal Dose

Use the provided LD50 value and the weight of the person to calculate the lethal dose. Multiply the LD50 value by the human's body weight: Lethal Dose (mg) = LD50 (mg/kg) × Body Weight (kg).

Perform the Calculation

Substitute the given values into the formula: Lethal Dose (mg) = 17.5 mg/kg × 80 kg.

Key concepts

Toxicology

Toxicology is the branch of science that studies the harmful effects of substances on living organisms. It delves into the nature and mechanism of toxic effects, as well as the detection and treatment of poisoning. This area of science is critical in assessing the risks and safety of chemicals and drugs, ensuring public health and environmental protection.

Toxicologists analyze various substances, including pharmaceuticals, industrial chemicals, and environmental pollutants, to determine their potential for harm. By understanding the adverse effects and the conditions under which they occur, toxicologists help in developing safe dosage guidelines and exposure limits for humans and wildlife.

Dose-Response Relationship

The dose-response relationship is a fundamental concept in toxicology that describes how the magnitude of a biological response is proportional to the amount of a substance administrated. The response could be a therapeutic effect or an adverse effect, including toxicity.

Typically represented through a dose-response curve, this relationship helps scientists and doctors understand the efficacy and the potential toxicity of a substance at various doses. Safe dosing regimens can be established by identifying the dose that triggers a significant yet non-harmful response. It is crucial to differentiate between the different phases of the curve, such as the threshold, where effects begin to manifest, and the plateau, where increasing the dose further does not significantly increase the response.

Lethal Dose

A lethal dose, typically expressed as LD50, refers to the quantity of a substance that is sufficient to kill 50% of a test population. This measure is widely used in toxicology to express the acute toxicity of a substance. The LD50 value is usually determined through controlled experiments on animal models.

The lower the LD50 value, the more toxic the substance. This quantitative measure helps in estimating the potential risks of exposure to various compounds. However, it is crucial to understand that the LD50 is a statistical approximation and that individual organisms may respond differently due to a range of factors, including genetics, age, health, and concurrent exposure to other substances.

Body Weight Adjustment

Adjusting the dosage of a substance according to body weight is an essential consideration in both human and veterinary medicine. This practice ensures that an individual receives a dose that is proportional to their body weight, maximizing the efficacy while minimizing the risk of adverse reactions.

In the context of toxicology, and particularly when extrapolating animal data to humans, as in the case of calculating an LD50 for a human from rat data, body weight adjustment is critical. It is based on the assumption that the effects of the substance scale with the mass of the organism. The straightforward calculation involves multiplying the per-kilogram dose by the individual's body weight. While this method provides a rough estimate, it is important to consider differences in metabolism, absorption, and distribution between species when interpreting the results.