An Interactive Jupyter Notebook for Teaching the Foundational Mathematical Basis of Compartmental Pharmacokinetics

Abstract

Pharmacokinetics is often taught as two different lessons, the foundational mathematical basis and the clinical application. Due to the lack of hands-on exercises, pharmacokinetics can be difficult to teach and students report struggling with the topic. Therefore, I have developed an interactive Jupyter notebook that demonstrates the mathematical basis behind one- and two-compartment pharmacokinetic models. This notebook uses a combination of “markup” cells, which display relevant equations and text, and “code” cells, which hold Python code that executes, models, and graphs the various pharmacokinetic equations. Students benefit from exposure to this aspect of computer science because the code remains visible. With the code pre-written, students are able to see the implementations of programming in drug pharmacokinetic modeling without having to construct the code themselves. This notebook includes both the differential and algebraic versions of one- and two- compartment models. The code also generates interactive graphs where students can use sliders for each parameter (half-life, inter-compartmental distribution rates, and dose of drug) to explore the effects of the equations parameters on the output of drug concentration over time. The conversion between macro constants and micro constants is also demonstrated and explained. All software used is freely available, so students can download the notebook onto their personal computers. No computer science experience is needed to execute this tool. However, instructors can easily adapt the notebook to their particular needs, adding or removing cells as desired. I successfully used this notebook in my undergraduate upper-division biology elective, “Foundations of Pharmacology”, and in a guest lectured Master's level course on the practical application of pharmacokinetics. Overall, this tool will be useful for teaching the mathematical basis of basic pharmacokinetics while allowing students to gain useful exposure to computer data science.