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Modeling and simulation for toxicity assessment

1. Department of Mathematics and Statistics, Grant MacEwan University, Edmonton, Alberta, T5P2P7, Canada
2. Department of Mathematical and statistical Sciences, University of Alberta, Edmonton, Alberta, T6G2G1, Canada
3. Alberta Health, Edmonton, Alberta, T5J1S6, Canada
4. Department of Laboratory Medicine and Pathology, University of Alberta, Edmonton, Alberta, T6G2B7, Canada
5. Alberta Centre for Toxicology, University of Calgary, Calgary, Alberta, T2N4N1, Canada
6. ACEA Biosciences Inc, San Diego, California, 92121, USA

The effect of various toxicants on growth/death and morphology of human cells is investigated using the xCELLigence Real-Time Cell Analysis High Troughput in vitro assay. The cell index is measured as a proxy for the number of cells, and for each test substance in each cell line, time-dependent concentration response curves (TCRCs) are generated. In this paper we propose a mathematical model to study the effect of toxicants with various initial concentrations on the cell index. This model is based on the logistic equation and linear kinetics. We consider a three dimensional system of differential equations with variables corresponding to the cell index, the intracellular concentration of toxicant, and the extracellular concentration of toxicant. To efficiently estimate the model's parameters, we design an Expectation Maximization algorithm. The model is validated by showing that it accurately represents the information provided by the TCRCs recorded after the experiments. Using stability analysis and numerical simulations, we determine the lowest concentration of toxin that can kill the cells. This information can be used to better design experimental studies for cytotoxicity profiling assessment.

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