Druckrey-Küpfmüller equation

The Druckrey-Küpfmüller equation is in the toxicology used mathematical relationship between the dose of a toxic substance and the duration of administration, or exposure , this poison.

It is a dose-effect relationship that takes into account the principle of the summation effect , for example with carcinogenic substances. For example, the toxicity of many substances such as organophosphates and neonicotinoids can be described by the Druckrey-Küpfmüller equation, since there are irreversible bonds to specific receptors .

The equation is:

${\displaystyle d\times t^{n}=konstant}$

where d is the dose and t is the duration of exposure.

history

The equation is named after the pharmacologist Hermann Druckrey and the engineer Karl Küpfmüller . The work was created in 1948 in a detention center of the Allies .

See also

• Haber's rule

literature

• HA Tennekes: The significance of the Druckrey-Küpfmüller equation for risk assessment - the toxicity of neonicotinoid insecticides to arthropods is reinforced by exposure time. In: Toxicology. Volume 276, Number 1, September 2010, pp. 1-4, PMID 20803795 .
• HA Tennekes, F. Sánchez-Bayo: The molecular basis of simple relationships between exposure concentration and toxic effects with time. In: Toxicology. Volume 309, July 2013, pp. 39-51, doi : 10.1016 / j.tox.2013.04.007 , PMID 23603429 .

Individual evidence

1. ↑ Henk Tennekes, Josef Hoppichler: Chemicals: amount and time make the poison . In Oekoskop - the specialist journal of doctors for environmental protection 4/15, 2015, pp. 19–22.
2. ^ Hermann Druckrey, Karl Küpfmüller: Quantitative analysis of the development of cancer . In: Journal for Nature Research . 1948, Volume 3b, pp. 254-266.
3. ^ V. Wunderlich: [On the origins of the Druckrey-Küpfmüller Papers (1948–1949): dose-effect relations in carcinogenic substances]. In: Medical History Journal. Volume 40, Numbers 3-4, 2005, pp. 369-397, PMID 16382692 .