Koch, Gretchen A. 2011. Mathematical Modelling of Natural Phenomena Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling . Preprint of article to appear in Mathematical Modelling of Natural Phenomena. 6(6): 227-244.
Abstract: Pharmacokinetics is an excellent way to introduce biomathematical modeling at the sophomore level. Students have the opportunity to develop a mathematical model of a biological phenomenon to which they all can relate. Exploring pharmacokinetics takes students through the necessary stages of mathematical modeling: determining the goals of the model, deciphering between the biological aspects to include in the model, defining the assumptions of the model, and finally, building, analyzing, using, and refining the model to answer questions and test hypotheses. Readily accessible data allows students to use the model to test hypotheses that are meaningful to them on an individual level. Students make interdisciplinary connections between this model and their previous personal, mathematical, and other classroom experiences. By beginning with a simple model involving the half-life of a drug, students take advantage of their mathematical abilities to explore the biology. They can then use the new knowledge gained from analyzing the simple model to create more complicated models, thus gaining mathematical and modeling maturity through improving the biological accuracy of the model. Through this experiences, students actually get to do applied mathematics, and they take ownership of the model.
This paper introduces various drug administration schemes and leaves the reader with some interesting exercises.
Here is something interesting, “The Food and Drug Administration requires that all manufacturers publish the half-life of medications. This information can be found by typing in the drug’s name at http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm and selecting the “Label Information” link.”
Keywords: pharmacokinetics, dynamical systems, biomathematics, model, single injection, multiple injection, two compartment, compartment
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