CSCI 385 - Lab 5
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. 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. Go beyond wikipedia to find your sources.

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 from the stomach that you found through your research.

Run each of your models to simulate one week of caffeine intake.

Diagram

Include diagrams to explain 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. In your graphs, describe each axis and the information conveyed in the graph.

Is an average 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?