We modelled the effects of mixtures of compounds
on the survival of organisms using biology-based methods, which
relate effects of compounds on the hazard rate of organisms to their
internal concentrations. This model, therefore, involves a
toxico-kinetic module, which is here taken to be a one-compartment
model for simplicity's sake. We started to write a review on physiology-based
toxico-kinetic models. The interaction of compounds is taken to be
proportional to the product of their internal concentrations. This way
of modelling interactions originates from Taylor's theorem of the
approximation of ``smooth'' functions by polynomials, and is
standardly applied in the analysis of variance (ANOVA). The parameters
of the model can be obtained from data using the Maximum Likelihood
(ML) methods. We wrote code to apply the model as part of the DEBtool
software package, that can be downloaded from the electronic DEB laboratory. This
code also provides estimates for the variance-covariance matrix of the
parameter values. The model turns out to have nice statistical
properties. The code allows a variety of algorithms for the
calculation of the ML estimates (scoring, simplex, genetic
algorithms), varying from fast to robust. The use of these procedures,
however, does require some experience.

We applied the model, using DEBtool, to data on the binary mixture
of metal (Cu, Cd, Pd & Zn) on the survival of the springtail
Folsomia candida, and found that the irreversible-binding
variant of the model fitted the data best, and that the fit was very
good indeed. We concluded that none of these metals showed
interactions, except the mixture Cu & Pb, which showed slightly a
antagonistic interaction. The spreadsheet that
resulted from the EU-project Mixtox gave inconsistent results about the
interaction of these metals.

Results for RP4

The OECD (Branschweig 1996) recommended the development of
exposure-time explicit methods. This extension of the biology-based
methods does exactly that, and it is still the only method that does
so for lethal and sublethal effects in a single framework.
We developed theory for the derivation of the toxicity for compounds
as function of their chemical properties of compounds. This theory has
close links with other theory that we developed for the co-variation
of parameter values across species. This paper discusses the
interrelationships between the two pieces of theories, which can be
very useful for filling gaps in our knowledge on behalf of risk
assessment applications.
We also did research on the effects of variation of parameter values
among individuals, focusing on the statistical consequences for such a
variation on the No
Effect Concentration (NEC). We showed that NEC-estimates are
really robust for such changes, and, therefore, the NEC is a natural
successor of the still widely used No-Observed Effect
Concentration. The OECD and the ISO recommended out-phasing on this
misleading concept. Download poster