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Individual based Chemokinetic Models

The chemokinetic model used by OLAF is a compartment model. The modeler has to divide the body of a modeled individual into as many compartments as he or she wishes and define the pathways for the pollutant between the body compartments and the ecosystem compartments defined previously. Usually, each body compartment represents a specific organ or a specific tissue type. An extremely small example is depicted in Figure 3.3.

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Figure 3.3: Simple model for the distribution of a pollutant in an animal.  

A model of such a simplicity, is, of course, only useful for didactical reasons. In toxicology, models of this type are also called physiologically based pharmacokinetic models (PBPK). The interconnection between ecosystem compartments and chemokinetic compartments can be seen in Example 1. Here, the grass and the cow compartment are, strictly speaking, parts of the ecosystem, while the interplay between the milk compartment and the cow compartment models the pollutant flow inside the body of a (typical) cow.


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Note that chemokinetic compartment models model the mass flow of the pollutant alone, leaving the mass flow of proteins, lipids etc. aside. As such, a compartment model is not necessarily inherently simplistic, but it has obvious limits. More detailed models, based on energy balance instead of mass balance exist (cmp, e. g., [12]), but they are inevitably nonlinear in the mass of the pollutant in different body tissues. Moreover, the right-hand side of most of these models is discontinuous in the energy integrator, a feature which makes these models susceptible to numerical difficulties.

Several different types of individuals can also be modeled by specifying the defining compartments for each of them. A typical example would be a structure as defined in Figure 3.6 (p. gif), in which three types of animals are considered: females, adolescents, and males. Here, the topological structure of each of the different animal classes is the same, since the simple model from Figure 3.3 is simply copied three times. The differences between the individuals considered are therefore hidden in the proportionality constants tex2html_wrap_inline3029. However, the actual topology of the subgraphs defined might differ, too.

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Figure 3.6: Simple model for the distribution of a pollutant in several types of animals.  

For instance, it might make sense to use a more detailed model for the adolescent compartment group to get more information about how the pollutant affects those members of the population considered which are, for some reasons, probably more affected than others.


next up previous contents
Next: Age-Classes Up: Ecology and Chemokinetics Previous: Ecosystems and Food Webs

Joerg Fliege
Wed Dec 22 12:25:31 CET 1999