Assigned Jan 27th
Due Feb 3rd Beginning of Class
Caffeination
For this lab, we will investigate and model the accumulation of caffeine in the human body. From
Wikipedia:
Caffeine is the world's most widely consumed psychoactive substance, but unlike many other
psychoactive substances it is legal and unregulated in nearly all jurisdictions. In North
America, 90% of adults consume caffeine daily.[5] The U.S. Food and Drug Administration
lists caffeine as a "Multiple Purpose Generally Recognized as Safe Food Substance."
We are interested in the differences between moderate and excessive amounts of caffeine usage in
the human body.
Write up each step of your model
Research
To create your model, you need to research some facts about caffeine. At a minimum, you should
find
- Average number of cups of coffee per day.
- Amount of caffine in cup of coffee.
- Absorption rate of caffeine into bloodstream.
- Half-life of caffeine in system, breakdown due to metabolism.
Document each reference found with a proper citation.
Models
You will be creating four models for this lab.
- moderate intake, one compartment
- excessive intake, one compartment
- moderate intake, two compartment
- excessive intake, two compartment
The one compartment model assumes instantaneous absorption of caffeine, while the two compartment
model should use the absorption rate of caffeine into the bloodstream that you found through your
research.
Run each of your models to simulate one week of caffeine intake. Include the code you write as
an appendix to your paper.
Diagram
Draw two diagrams of the relationships present within the one compartment model and the two
compartment model. Be sure to include which differential equations affect the simulation
in various ways, so someone can follow the flow of caffeine into and out of the system
Analysis
Describe the caffeine levels present over time in each of the two types of coffee drinkers.
You should show graphs, describe each axis and the information contained.
Is equilibrium reached in either situation? If so, what is this equilibrium?
What are the major differences (if any) between the results of the one vs. two compartment models?
Sensitivity
Discuss the sensitivity of your models to the parameters you found through research. Back up your
statements with numerical results based on altering the parameters of the original models.
Some researchers
are recommending 7 grams of dark chocolate per day to prevent heart disease.
Decide how to incorporate this into your models, and rerun. How does this
change the results of your models?
What else did we ignore in our models? Suggest one way we could enrich the model to improve
the accuracy of our results.