Mixture toxicology formulas | DoseDescriptor.com

Mixture toxicology formulas

In mixture toxicology the combined effect of chemicals in a mixture can be calculated based on formulas for 1) dose addition (aka concentration addition), 2) Independent action and 3) Generalised concentration addition.

The formulas for dose additon and independent action are:

Dose addition

X = (f_A/x_A+ f_B/x_B+ ….)^-1

Where X is the combined dose of the mixture at which a specific effect occurs. f_Ais the fraction of chemical A in the mixture and so-forth for chemical B etc.; x_A is the dose at which chemical A exerts this specific effect on its own. For a range of effect levels, X values are calculated and a prediction curve is established.

Independent action

E = 1 – ((1-e_A)(1-e_B)(…..))

E is the effect of the mixture at a specific dose. eA is the effect of chemical A at that specific dose and so-forth for chemical B etc.. For several dose points effects (E) are calculated, and a prediction curve is established.

Important note

These formulas can only be use din cases where there is no synergy between the components in the mixture

Fun fact: mixture effects are called 'cocktail effekter' in Danish - Likely, at one point, someone thought cocktail effects would be easier to remember than simply the more boring word 'mixture' - perhaps mixture effects where no alchol groups are involved could be called mocktail effects......

Further knowledge on mixure toxicology

Chemical mixtures occur in many settings in the working environment, as most products are actually mixtures of different substances. We use mathematical models based on the additive principle to calculate the toxicological effects of mixtures. I.e. the calculation involves the addition of the toxicity of the single components according to their concentration in the mixture. However, one highly important prerequisite for this is that synergy does not occur. In other words, when adding the effect of the single chemicals together we can say that 1+1=2 and not 1+1= 100 in effect level.

Thus, in order to be able to apply the mathematical models we need to determine the extent to which synergy occurs at human-relevant doses. To do this, we try to disprove the hypothesis that synergy does not occur at human-relevant doses.