Multiple Drug Doses

This project is based on a project by Brian Winkle. https://www.simiode.org/resources/2981/supportingdocs

You are to design an intravenous drug administration plan for a 24 hour span for a hospital patient. The patient has a port or shunt to her vein so medicine can be administered without further "sticking." This medicine is to be administered in such a way that the amount of the drug in her blood stream must be between 2 and 4 mg throughout the 24 hour period. To go over 4 mg is to risk adverse effects and to go under 2 mg is to possibly not benefit from the drug. The drug is absorbed into the tissues where it does its work at the rate of 50% of the amount present in the bloodstream per hour.

There are two options for administration of the drug:

1. bolus or plug injection of a set amount of the drug at fixed time intervals, or
2. continuous drip administration of the drug over set time intervals.

In either case:

Because of possible shock effect, the drug can be administered in any amount for no more than 1/2 hour of each hour long time interval.

(A bolus (from Latin bolus, ball) is the administration of a discrete amount of medication, drug or other compound in order to raise its concentration in blood to an effective level.)

Exercise 1: Sketch, by hand, several possible graphs of the amount of drug administered as a function of time for each of the options listed above.

• Make sure to label both axes with units and numerical values.
• We don't yet know exactly how we want these graphs to look: rather this exercise is to help us build the model.

Exercise 2: Sketch several possible graphs that show what you expect to happen to the amount of drug in the bloodstream as a function of time.

• These graphs probably correspond to the graphs you provided in exercise 1.
• Again, make sure to include units and numerical values.
• Again, we don't really know what these graphs look like.
• This exercise is so that we can evaluate our model and its solution once we have it.

Exercise 3: Identify the players and the action:

• What is the quantity we are interested in? This may seem like a silly question, but you'd be surprised how much this simple question can help to develop a model.
• What is changing? With respect to what? In this class something will always be changing: otherwise we wouldn't need derivatives.
• There are two actions is this scenario. What are they?

Exercise 4: By the end of the project, we will have functions that show the amount of drug in the blood stream. They should, of course, satisfy all the criteria listed in the scenario statement. Still, there may well be many solutions. What criterion would you use to compare different solutions? List at least 3.