Uncertainty and confidence in applying mathematical models and in vitro data in toxicological safety assessments

Over the past decade, there has been substantial research effort into the development and utilisation of systems biology models for a range of applications. At the same time, there has been increasing pressure to end the over-reliance on animal experiments within toxicology and to consider the information from non-animal alternatives when making decisions about human safety. A key challenge is to understand how the different proposed elements of a pathways-based toxicological risk assessment (e.g. chemical characterisation, human exposure information, in vitro toxicity testing data on compounds and metabolites from potentially diverse test systems, dose response modelling, population-based modelling and risk contexts) can be integrated to enable robust safety decisions.

Our objectives are to answer how mathematical models could fit into a risk assessment alongside relevant in vitro data sources and to give toxicological risk assessors more confidence in using mathematical models. To achieve this, we must understand what the key input parameters of the models are and how existing in vivo and in vitro assays can be used to validate and parameterise the models. Using data sets (e.g. ToxCast, EPA) and models, which are publicly available or provided by Unilever, and working closely with expert toxicologists and risk assessors at Unilever, we will demonstrate the potential of existing uncertainty analysis techniques to evaluate the confidence in a toxicological risk assessment decision using non-animal data. This will take the form of prototype risk assessments based on in vitro data interpreted through a systems biology model and compared to human exposure concentrations estimated using a physiologically-based pharmacokinetic model. The approach therefore requires the linking of models at different scales and the determination of the contributions of experimental and model uncertainty to assess the confidence in the resultant risk assessment.


Gosling J (2019). The importance of mathematical modelling in chemical risk assessment and the associated quantification of uncertainty. Computational Toxicology 10:44-50. doi: 10.1016/j.comtox.2018.12.004

Chu HH et al. (2016). Continuous Effector CD8(+) T Cell Production in a Controlled Persistent Infection Is Sustained by a Proliferative Intermediate Population. Immunity 45(1):159-71. doi: 10.1016/j.immuni.2016.06.013


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Strategic grant



Principal investigator

Dr John Gosling


University of Leeds

Grant reference number


Award date

May 2013 - May 2015

Grant amount

£81,195 (Co-funded by EPSRC)