Pharmacokinetic Models for Active Learning of Differential Equations

Abstract

We present adaptable activities for models of drug movement in the human body – pharmacokinetics – that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models, progressing in complexity to a system of differential equations. We investigate the effects of parameter values that distinguish various health levels, and dosing that may have toxic effects. Our assignments include modeling in a student-centered, active, and increasingly inquiry-oriented setting through which the mathematics and biology inform and reinforce each other. We include supplemental information regarding inquiry methods, student learning outcomes, a student’s commentary about our activities, and support through mathematical communities such as POGIL and SIMIODE.

Keywords:

• Differential equations
• mathematical modeling
• SIMIODE
• pharmacokinetics
• drug models
• real-world context
• active learning
• inquiry-based learning
• POGIL

ACKNOWLEDGEMENTS

The authors are grateful to the undergraduates whose interactions and work contributed to this work. We thank Dr. S. Adrian, Associate Professor of Education at Southwestern University for helping us use “person-first” language, respectfully referring to the person before the medical condition. We acknowledge the supportive mathematicians in SIMIODE and in POGIL-MATH.

Additional information

Funding

We gratefully acknowledge the aid to our collaboration afforded by two grants at Southwestern University: the W. M. Keck Foundation Grant, and the Inquiry Initiative funded by the Howard-Hughes Medical Institute.