Modeling and simulation for toxicity assessment
Open Access
- 1 January 2017
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Biosciences and Engineering
- Vol. 14 (3), 581-606
- https://doi.org/10.3934/mbe.2017034
Abstract
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
This publication has 24 references indexed in Scilit:
- Global sensitivity analysis used to interpret biological experimental resultsJournal of Mathematical Biology, 2014
- A model for the impact of contaminants on fish population dynamicsJournal of Theoretical Biology, 2013
- Sensitivity analysis for volcanic source modeling quality assessment and model selectionComputers & Geosciences, 2012
- Early determination of toxicant concentration in water supply using MHEWater Research, 2010
- A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxinNonlinear Analysis: Real World Applications, 2009
- The survival analysis for a population in a polluted environmentNonlinear Analysis: Real World Applications, 2009
- Dynamic Modelling and Prediction of Cytotoxicity on Microelectronic cell Sensor ArrayThe Canadian Journal of Chemical Engineering, 2006
- Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture modelsComputational Statistics & Data Analysis, 2003
- A new method for the nonlinear transformation of means and covariances in filters and estimatorsIEEE Transactions on Automatic Control, 2000
- Effects of toxicants on populations: A qualitative approach II. first order kineticsJournal of Mathematical Biology, 1983