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Modeling Scenario

1-086-MedicinalPill-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: medicine spillover compartment bloodstream GIT-Track

58 total view(s), 18 download(s)

Abstract

Resource Image Administration of a medicinal pill in single and multiple doses is modeled.

Citation

Researchers should cite this work as follows:

Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Technology
Approach
Skills
Key Scientific Process Skills
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level

Description

A medicinal pill, e.g., decongestant or antihistamine, is swallowed by a patient and enters the Gastro-Intestinal Tract (GI-Tract), whereupon it dissolves and then diffuses into the Bloodstream. Finally, the medicine leaves the body through Kidney and Liver removal.

We consider two instances:

(a) Just one pill with $P$ mg of the medicine is administered.

(b) A regimen of pills, one per hour, each with $P$ mg of the medicine is administered.

Activities

  1. For both (a) and (b) model the amount of medicine in both the GI-tract and the Bloodstream over time in hours. Be sure to make your assumptions clear and relevant.
  2. In both cases, describe the amount of medicine in each compartment (GI-Tract and Bloodstream) with a plot based one some numbers you think are reasonable from your understanding of taking medicine, e.g., a doctor says, ``Take one every four hours.''
  3. Describe the long term behavior of the amount of medicine in each compartment (GI-Tract and Bloodstream).
  4. Reflect on the reasonableness of your model results.

Article Files

Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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