Thinking Quantitatively Project 8: Dosage Modeling

When a drug is administered the amount of the drug in the subject’s blood stream quickly spikes up, then slowly decreases as the body naturally absorbs and excretes it.

1. Make a sketch of the graph of the amount of a drug in the bloodstream over time. Don’t worry about specific numbers; we are interested in the pattern of increase and decrease.

2. Suppose that a patient is given doses of 100 milligrams of an antibiotic every 12 hours, and that the body removes the medication at the rate of 80% every twelve hours. Make a spreadsheet/sequence that describes the amount of the antibiotic in the bloodstream at 12-hour intervals over a seven day period.

3. Graph the amount of antibiotic over this time period.

4. Does it look like what you expected?

5. It is clearly desirable to have the peaks and valleys of the graph not be too extreme; that is, we may not want the subject swinging between very high and very low amounts of the medication. One way to smooth the graph out a bit is to apply smaller doses at shorter intervals. Modify your spreadsheet/sequence to reflect 50 mg doses every six hours,

6. and then 25 mg every three hours.