# Math 106--Calculus II: Project 3, Fall 1999

## Yet another wonder drug.....

### by Gavin LaRose (glarose@umich.edu), Nebraska Wesleyan University, October 1999

idea and data from Janet Berry, U. of Redlands, and MAA ILAPs book

### Medres, Inc.

Office 728 Ratherold Hall
325 Eep Street
Lonlinc, SK 04685

15 November 1999

Sophisticated Technical Contractors (STC), Inc.
Lonlinc, SK 04685

Dear STC:

We are, here at Medres, concerned with the research and development behind all manner of medical advances. In this capacity we are a leader in the field, and this level of excellence has lead to our being asked to analyze a slightly different problem in the medical field---which, as it lies outside of our particular field, we are subcontracting to you.

This involves the examination of the effect of a child ``accidentally'' ingesting an overdose of some relatively standard medication. For the sake of this problem, we would like to consider the child to have ingested 11 100mg tablets of a drug some two hours before his or her admission to the hospital. The child may be assumed to have about 2 liters of blood, and to be in serious trouble if the concentration of the drug in his or her blood reaches 100mg/l---and fatal trouble if it reaches 200mg/l. In addition, the drug is absorbed with a half life of 5 hours and eliminated from the system with a half life of 6 hours.

The drug enters the child's system through his or her gastrointestinal system, where the rate of change in the amount of drug present as it is absorbed into the bloodstream is proportional to the amount there. The blood is cleaned through regular body functioning, of course, with the result that the amount of drug in the blood increases at a rate proportional to the amount present in the gastrointestinal tract and decreases proportional to the amount already in the bloodstream.

We are of course interested in determining what the prognosis for the adorable child is, with the possible additional questions of whether his/her prognosis would be improved by immediately evacuating his/her stomach on arrival at the hospital or if he/she had ingested rather fewer of the pills. Alternately, even if the stomach evacuation is not possible it may still be possible to filter the child's blood, thereby increasing the drug removal rate by a factor of six, and we would be interested in knowing if this is a viable way of attacking the problem as well.

We look forward to receiving your final report on this problem on or before the 6th of December. We have arranged with a local expert in all things mathematical, the well-regarded Dr. P. Gavin LaRose, to serve as a contact with you should you find that you have questions in its completion. Please note that you must contact him by the 22nd of November with your initial appraisal of the problem and the manner in which it should be resolved. Failure to meet either of these deadlines will be cause for a significant penalty in your payment.

Yours sincerely,
Cever Etkoop, M.D.
President, Medres, Inc.

ce:glr

Gavin's Calc II Project 3, Fall 1999