Growth dilution

During certain periods within a growing season, organisms may develop and increase in somatic biomass. Specific storage compartments within the organism too may increase during periods of high food availability. When the biomass growth rate or storage is larger than the uptake of NMs, concentrations in the organisms may decrease, even as exposure to the NMs continues. Generally, this is temporary, but so-called growth dilution may result in counterintuitive results when monitoring accumulation patterns. It should be noted that the converse is also possible, when energy stores in which NMs may be stored become depleted.

Occurs in


Fate descriptors



Growth dilution rate constant

"Growth dilution" consists of the uptake and elimination equations with the inclusion of kg which is the growth dilution rate.

1. Uptake phase

\(C_{org} = C_{env}\ast k_{1}\ast SF\ast t\ast C_{env}\ast \frac{k_{1}}{k_{2}+k_{g}}\ast (1-e^{-(k_{2}+k_{g})\ast t})\ast (1-SF)\)

2. Elimination phase

\(C_{org} = C_{env}\ast k_{1}\ast SF\ast t_{m}+ C_{env}\ast \frac{k_{1}}{k_{2}+k_{g}}\ast(1-(e^{-(k_{2}+k_{g})\ast t})\ast e^{-(k_{2}+k_{_{g}} )\ast(t-t_{m})})\ast (1-SF)\)


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VIsit the NanoFASE library to see summaries.

NanoFASE Report D9.2 Loureiro et al. Parameter sets on uptake and toxicokinetics of selected pristine NMs in aquatic and terrestrial organisms

Ardestani MM, van Straalen NM, van Gestel CAM (2014) Uptake and elimination kinetics of metals in soil invertebrates: a review. Environ. Poll 193, 277-295. DOI: 10.1016/j.envpol.2014.06.026

van den Brink NW et al. 2019. Tools and rules for modelling uptake and bioaccumulation of nanomaterials in invertebrate organisms. Environ Sci Nano 6, 1985-2001. DOI: 10.1039/C8EN01122B




Nico van den Brink

Wageningen University



Kees van Gestel

Department of Ecological Science
Faculty of Science, Vrije Universiteit