Medicinal Math: Ensuring a Properly Calculated Dose and Concentration

Abstract

Pharmacology is the scientific study of seeing what drugs do and how the body responds to them. Initial dose evaluations, the gastric system and blood concentration calculations, and metabolic product elimination are major areas investigated. This research looks at whether or not certain pediatric equations developed throughout the last 200 years are reliable for specific medications. It's meant to see if these equations are valid in calculating the recommended dosing for the ages between infant and 20. The medications being focused on are acetaminophen, amoxicillin, cephalexin, morphine and phenytoin. Fried's Rule, Young's Rule, Clark's Rule, Dilling's Rule, and the BSA (body surface area) method are the five formulas that were tested. This testing was done using Wolfram Mathematica. In addition, this project focuses on how differential equations describe the five drugs' absorption into and elimination from the body. The equation for absorption represents the weight of the medication in the stomach that's waiting to be absorbed into the blood stream. The other equation shows the amount still in the blood that hasn't left the body. These equations are then combined to show the concentration in plasma vs time. The graphs to model this data were made in Mathematica as well. This work is usually done by scientists to evaluate how much of an initial drug dose should be given and to figure out an appropriate treatment regimen. The results showed that Fried's Rule, Young's Rule, and Clark's Rule were the least reliable as they underdosed significantly for most of the medications. Dilling's Rule was only accurate for late teens, and the BSA Method gave mixed results for every age and all the medications. When the medication concentrations in plasma reach zero in the body, the results for cephalexin and morphine were consistent with other findings but inconsistent for acetaminophen and amoxicillin.