Information below is on my own research;
for description of research with students (individuals, courses, and Research Experiences for Undergraduates), please see the Student Research Page. 

Current Research Summary

My mathematical research centers around physiologically-based pharmacokinetic (PBPK) modeling.  PBPK models use physical properties (e.g., blood flow and organ weights) and chemical properties (e.g., chemical structure and solubility) to predict dose-response curves for exposure to a variety of compounds.  In particular, I have focused on an inhalation exposure model of water disinfection byproducts, as well as dermal exposure models of lindane and oral exposure models of vitamin D.  With any good model comes sensitivity analysis to determine which parameters are identifiable and estimable; I am also exploring subfields of global sensitivity analysis as they apply to PBPK modeling.  Details about specific projects are below.

I maintain a strong interest in conducting research with students: a recent research project involved two students (John Kenney and Jessica McElwain) based off work done by their predecessors in individuals and course-based research (see the Student Research Page).  An article stemming from this project was published in 2021 in the Missouri Journal of Mathematical Sciences.  

Note: Most research is currently published under my previous name, Megan E. Sawyer.  

Published Research

Note: Some publications are listed under my previous name, Megan E. Sawyer.

Sawyer, C.W., Tuey, S. M., West III, R. E., Nolin, T. D., & Joy, M. S. (2022). Physiologically based pharmacokinetic modeling of vitamin D3 and metabolites in vitamin D insufficient patients. Drug Metabolism and Disposition, 50(9) 1161-1169.  DOI:10.1124/dmd.121.000609.

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

Dow, T., Gilbert, A., Sawyer, M.E., York, K. (2017). Inspiring interdisciplinary collaboration experiences. Experiential Learning & Teaching in Higher Education, 1(2), 71-89

Sawyer, M.E., Tran, H.T., and Evans, M.V. (2017). A physiologically based pharmacokinetic model of vitamin D. Journal of Applied Toxicology, 37, 1448-1454. DOI:10.1002/jat.3489

Sawyer, M.E., Evans, M.V., Wilson, C.A., Beesley, L.J., Leon, L.S., Eklund, C.R., Croom, E.L., Pegram, R.A. (2016). Development of a human physiologically based pharmacokinetic (PBPK) model for dermal permeability for lindane. Toxicology Letters, 245,106-109. DOI:10.1016/j.toxlet.2016.01.008

Cuello, W.S., Janes, T.A.T, Jessee, J.M., Venecek, M.A., Sawyer, M.E. , Eklund, C.R., Evans, M.V., (2012). Physiologically based pharmacokinetic (PBPK) modeling of metabolic pathways of bromochloromethane in ratsJournal of Toxicology, vol. 2012, Article ID 629781. DOI:10.1155/2012/629781

Prints of all articles are available upon request. 

Research under Review

Sawyer, C.W and Buckmire, R.  (In review). The Automathography: A Humanistic Autobiographical Writing Assignment for Mathematics Courses.

Project Details

PBPK Modeling of Vitamin D

Figure: Sawyer, et al., (2017), J. Appl. Toxicol

Although there are many studies that discuss the benefits of vitamin D on physiological functioning, there are few studies that focus on the physiological response of low-dose daily supplementation of vitamin D under sunlight restricted conditions.  This portion of my research explores the use of a PBPK model to predict the serum concentration of vitamin D and its metabolites, and has a novel adaption to incorporate for vitamin D binding by lipids and addition proteins.  Through allowing the effective adipose-plasma partition coefficient to vary with circulating concentrations of vitamin D, it may be possible to more accurately model seasonal variations of vitamin D. 

In addition, I am working with Dr. Melanie Joy at the University of Colorado, Skaggs School of Pharmacy and Pharmaceutical Sciences to explore the effects of vitamin D on individuals with chronic kidney disease.  A paper exploring healthy populations has been published in Drug Metabolism and Disposition.

Dermal Modeling

The stratum corneum acts as a barrier to most compounds entering the skin through surface exposure.  Using published data under finite dose conditions, this portion of my research is investigating the use of a four compartment model to represent in vitro dermal exposure for the purposes of calculating diffusion and permeability.  My research question asks if knowing various measurable properties of the chemical (e.g., lipophilicity, molecular weight, volatility, and solubility) helps to define the permeability and diffusion parameters.  In addition, I am interested in exploring if there are different pathways of movement through the stratum corneum resulting in differing dermal permeation coefficients.    

Exploration of Local and GLobal Sensitivity Analysis

Sensitivity analysis is the study of the effect of propagated error on the predictive power of the model.  Throughout the course of modeling, many parameters may be estimated or loosely measured; by calculating the amount of variability the parameter variations can introduce to the model, the experimentalist can more accurately make decisions about optimization sets or which parameters to focus more attention on.  I am interested in the applications of local and global sensitivity analysis to PBPK and other compartmental models, and in particular, I am considering Morris' Method and extended Fourier Amplitude Sensitivity Test (eFAST) to refine parameter optimization sets in my algorithms.  

Figure: Sawyer, et al., (2021) Missouri J. Math. Sci.