Toxicokinetics of metals in terrestrial invertebrates: making things straight with the one-compartment principle.

PLoS ONE. 2014;9(9):e108740 DOI 10.1371/journal.pone.0108740

 

Journal Homepage

Journal Title: PLoS ONE

ISSN: 1932-6203 (Online)

Publisher: Public Library of Science (PLoS)

LCC Subject Category: Medicine | Science

Country of publisher: United States

Language of fulltext: English

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AUTHORS

Boris Skip
Agnieszka J Bednarska
Ryszard Laskowski

EDITORIAL INFORMATION

Peer review

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Time From Submission to Publication: 24 weeks

 

Abstract | Full Text

In this analysis, we first performed a critical review of one-compartment models used to describe metal toxicokinetics in invertebrates and found mathematical or conceptual errors in almost all published studies. In some publications, the models used do not represent the exact solution of the underlying one-compartment differential equations; others use unrealistic assumptions about constant background metal concentration and/or zero metal concentration in uncontaminated medium. Herein we present exact solutions of two differential-equation models, one describing simple two-stage toxicokinetics (metal toxicokinetic follows the experimental phases: the uptake phase and the decontamination phase) and another that can be applied for more complex three-stage patterns (toxicokinetic pattern does not follow two phases determined by an experimenter). Using two case studies for carabids exposed via food, based on previously published data, we discuss and compare our models to those originally used to analyze the data. Our conclusion is that when metal toxicokinetic follows a one-compartment model, the exact solution of a set of differential equations should be used. The proposed models allow assimilation and elimination rates to change between toxicokinetic stages, and the three-stage model is flexible enough to fit patterns that are more complex than the classic two-stage model can handle.