Population Analysis of Toxicological Combination Effects

M. Baaz, T. Cardilin, T. Lundh, M. Jirstrand. In Proceedings of The 21st International Symposium on Pollutant Responses In Marine Organisms, PRIMO21, May 22-25 2022, Gothenburg, Sweden.



Nonlinear mixed effects (NLME) modeling is currently the state-of-the-art mathematical framework for analyzing population data in medicine. We aim to illustrate how NLME modeling and the Tumor Static Exposure (TSE) concept can be beneficial for analyzing the effects of combined pollutants in marine life.


TSE is defined as all drug exposure that results in tumor stasis and therefore separates the space of all exposures into a region of tumor growth and a region of tumor shrinkage. TSE is derived from the equations of the NLME model and when two drugs are investigated the TSE for the median individual can be illustrated in a diagram with each axis representing the exposure of one of the drugs.

We apply a similar approach to a toxicological model that describes the combined toxicological effects of two pollutants on marine animals. The model is based on a set of ordinary differential equations and from these, we derive a curve, similar to TSE, which describes all exposure combinations that result in a critical toxicological event. We use simulated data to calibrate the model and illustrate how predictions of toxicity can be made on a population level.


Since all possible combinations of pollutants cannot be tested experimentally the modified version of the TSE-curve can be useful to explore how different combinations affect marine life populations. Thus, it could be used to rank which pollutants are most important to reduce in the oceans.

The NLME framework provides a powerful method for analyzing time-series data and could increase the statistical power when analyzing data from animal studies. In addition, it allows for simulation-based analysis, which could help reduce the number of animal experiments.

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