# Week 31 – Calculating Toxicity

For this lesson, we need to develop a basic understanding of how toxins can be compared.  We know that bites from snakes and spiders can sometimes be deadly.  But why only sometimes?  We know eating some berries can be deadly, but not all berries are toxic…or are they?  Can anything be toxic if encountered in large enough amounts?

To talk about toxicity, we need to understand the meaning of LD50 (the lethal dose at which 50% of a population of organisms die after exposure to a given amount of a substance).  LD50 is often expressed in mg/kg, which means the number of milligrams (mg) of a substance per kilogram (kg) of organism body mass.  Before we work through an example, take a look at the Lethal Doses Handout.  The first entry is for aspirin (acetysalicylic acid)  Aspirin has an LD50 of 200 mg/kg when fed orally to a rat.

Important Concept: Rats are commonly used for toxicity studies as the way rats metabolize chemicals is similar enough to humans for rats to be a good model organism for predicting toxicity in humans.  A typical lab rat has a mass of up to 0.5 kg, while a typical human may have a mass of 70 kg (equivalent to 154 pounds, 1 kg = 2.2  pounds, or lbs).  You can imagine an experiment where a scientists feeds aspirin in increasing amounts to various groups of rats.  All of the rats have a mass of 0.5 kg.  The first group of rats eats 1 mg of aspirin and the rats all live.  The next group eats 3 mg of aspirin and the rats all live.  Eventually, a group of rats eats 100 mg of aspirin and half of the rats die.  The scientist just found the LD50 of aspirin: 100 mg of aspirin / 0.5 kg of rat body mass = 200 mg/kg.

To figure out how to apply the LD50 of 200 mg/kg to a human with a mass of 70 kg, we need to multiply the LD50 by 70 kg:

200 mg/kg x 70 kg = 14,000 mg aspirin

Aspirin tablets often come in 81 mg doses.  To figure out how many 81 mg aspirin tablets a person would need to eat to have a 50% chance of dying (assuming a mass of 70 kg), we need to divide 14,000 mg by 81 mg/tablet:

14,000 mg x 1 tablet / 81 mg = 172.8 tablets, (about 173 tablets)

To answer the question of how much is too much when it comes to aspirin, taking more than the recommended dose per day is too much.  Anyone contemplating taking 173 tablets of aspirin needs to get help first!