with Undergraduate students

2020: Sensitivity Analysis and Optimization of a Mathematical Model of Bromochloromethane

Through the Spring 2019 semester and the 2019-2020 academic year, I worked with two SNHU undergraduates on a mathematical modeling project involving sensitivity analysis and optimization.  

The undergraduates were:

Project Description: 

Using work from Jepson and McDougal (1997) with updated parameters from Cuello, et al (2012), we looked at a physiologically based pharmacokinetic (PBPK) dermal model of bromochloromethane (BCM) in rats.  Although BCM is currently unregulated, it is similar to a regulated trihalomethane, bromodichloromethane, so there is interest in the behaviors of this compound.  In this study, we looked at the effects of the addition of parameters to the model in terms of both optimization procedure and global sensitivity analysis of the parameters (specifically using Morris' Method).  

W. S. Cuello, T. A. T. Janes, J. M. Jessee, M. A. Venecek, M. E. Sawyer, C. R. Eklund, and M. V. Evans, Physiologically based pharmacokinetic (PBPK) modeling of metabolic pathways of bromochloromethane in rats, Journal of Toxicology, 2012.
G. W. Jepson and J. N. McDougal, Physiologically based modeling of nonsteady state dermal absorption of halogenated methanes from an aqueous solution, Toxicology and Applied Pharmacology, 144.2 (1997), 315-324.

Published Paper:

Our paper describing this work was published in November 2021 in the Missouri Journal of Mathematical Sciences.  

Sawyer, M.E., McElwain, J,. and Kenney, J.W. (2021). Applications of global sensitivity analysis to the optimization of a dermal PBPK model of bromochloromethane.  Missouri Journal of Mathematical Sciences.  33 (2), 137-150. DOI: 10.35834/2021/3302137  


Physiologically based pharmacokinetic (PBPK) models can be used to develop frameworks for risk assessment and predictive toxicology testing routines. However, the predictive power of these models is only as good as the confidence in the parameters within the model itself. Sensitivity analysis, or the study of the effect of propagated error on the predictive power of the model, can be used to determine which model parameters are most likely to affect change in the model. This is important when considering optimization routines, as optimizing non-sensitive parameters may lead to biologically incorrect parameter estimates. This study explores the sensitivity of physiological, metabolic, and chemical-specific parameters for a published dermal exposure PBPK model of bromochloromethane.


Aspects of project has been taken to several conferences, including an invited presentation at the PIC Math session at 2019 MAA Mathfest.  Portions of this project were supported by the PIC Math program, a program of the Mathematical Association of America (MAA). Support for this MAA program is provided by the National Science Foundation (NSF grant DMS-1722275) and the National Security Agency (NSA).