Modeling and simulation for toxicity assessment
Cristina Anton Jian Deng Yau Shu Wong Yile Zhang Weiping Zhang Stephan Gabos Dorothy Yu Huang Can Jin
Mathematical Biosciences & Engineering 2017, 14(3): 581-606 doi: 10.3934/mbe.2017034

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.

keywords: Mathematical model cytotoxicity parameter estimation persistence
Stochastic dynamics and survival analysis of a cell population model with random perturbations
Cristina Anton Alan Yong
Mathematical Biosciences & Engineering 2018, 15(5): 1077-1098 doi: 10.3934/mbe.2018048

We consider a model based on the logistic equation and linear kinetics to study the effect of toxicants with various initial concentrations on a cell population. To account for parameter uncertainties, in our model the coefficients of the linear and the quadratic terms of the logistic equation are affected by noise. We show that the stochastic model has a unique positive solution and we find conditions for extinction and persistence of the cell population. In case of persistence we find the stationary distribution. The analytical results are confirmed by Monte Carlo simulations.

keywords: Stochastic logistic equation stationary distribution ergodic property extinction stochastic permanence

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