In virgile-baudrot/CETACC: What the Package Does (One Line, Title Case)

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Toxicokinetics model

Ingestion part

The dynamic of the internal concentration of the contaminant, also known as the toxicokinetics, may be describe by this simple equation:

[ \frac{dC_{j,in}}{dt} = TrIng_{j,tot} - k_{j, out} C_{j,in} ]

[ \frac{dC_{a,in}}{dt} = TrIng_{a, tot} - k_{a, out} C_{a,in} ]

where: - $C_{j, in}$ and $C_{a,in}$ are respectivelly the internal concentration for juveniles and adults - $TrIng_{j, tot}$ and $TrIng_{a, tot}$ are the trophical ingestion of contaminant for juveniles and adults respectivelly (see later for details) - $k_{j,out}$ and $k_{a, out}$ the excretion rate of the contaminant for juveniles and adults respectivelly

Note that since $TrIng_{a, tot}$ is constant, we have:

[ C_{i,in} = \frac{TrIng_{i, tot}}{k_{out}}\left( 1 - e^{- k_{i,out} t} \right) ]

About $TrIng_{\dot, tot}$

A juvenile is only exposed to the contaminant through the maternal feeding (milk). Note that a new-born has likely been exposed through maternal gestation, that is, at time $t=0$ (or birth date) $C_{j,in}(t=birth) = C_{j,init}>0$.

[ TrIng_{j, tot} = \eta_{j} \times I_{maternal} \times C_{maternal} ]

And, for $n$ prey species, and adult is exposed to the contaminant through food items:

[ TrIng_{a, tot} = \eta_{a} \sum_{i=1}^{n} \times I_{i} \times C_{i} ]

In both equations, we have: - $\eta_{j}$ and $\eta_{a}$ the assimilation rate in juveniles and adults, - $I_i$: the ingestion rate of item $i$ (e.g., $kg.day^{-1}$), - $C_i$: the concentration in item $i$ (e.g., $mg.kg^{-1}$).

Ingestion rate:

[ I_i = \phi_i \times B_i ]

• $\phi_i$ is the proportion of item $i$ in the diet.
• $B_i$ is the Biomass of item $i$ in the diet (e.g., mean biomass of whole or part of ingested individuals of species $i$).

virgile-baudrot/CETACC documentation built on May 14, 2019, 12:11 p.m.