Research

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

I currently split my research focus between mathematical toxicology and the scholarship of teaching and learning (SOTL) in mathematics.  My SOTL work is primarily geared toward finding ways to improve retention of students in mathematics courses through developing a sense of belonging as well as to improve experiences within the course itself. This could be through assignment choice or through use of specific technology (such as WeBWorK) in the classroom.

My mathematical toxicology 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 am focusing on inhibition in an inhalation model of trichloroethylene (TCE) and chloroform in rats.  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.

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

Note: Most research is currently published under my previous name.  

Curriculum Vitae (updated January 2024)

Published Research

Sawyer, C.W. & Buckmire, R.  (2024). The Automathography: A humanistic autobiographical writing assignment for mathematics courses.  Journal of Humanistic Mathematics, 14(1), 54-73.  DOI: 10.5642/jhummath.KHJA2262.

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 bromochloromethane.  Missouri 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., & 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 rats.  Journal of Toxicology, vol. 2012, Article ID 629781. DOI:10.1155/2012/629781

Prints of all articles are available upon request. 

SOTL Research

Students who feel understood and supported in the classroom typical retain at an institution - one of my SOTL question addresses how to make incoming and mathematically-young students feel comfortable in a classroom in which the topic may not be comfortable.  One way to address this is with the use of the Automathography, a semester-long mathematical autobiography which allows students to express their past, present, and future hopes with mathematics in a structured format.  My work with Dr. Ron Buckmire at Occidental College was recently published (2024) in Journal of Humanistic Mathematics.  

A secondary focus is on the use of technology in the classroom or as part of the course experience.  I am in the early stages of a project with Dr. Annie Bergman at Fort Lewis College to explore student perceptions of the open-source online homework system WeBWorK and the impact of this instructional tool on their current and future course experiences.  

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 was published in 2022 in Drug Metabolism and Disposition, and we are currently working on an adaption of the model to fit data for chronic kidney disease.

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.