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# Faculty Distinguished Lecture Explores the Use of Mathematical Modeling in Medicine Dosing

Professor of Mathematics Cammey Cole Manning presented her research titled “Mathematical Modeling of Antibiotics: Should the Dose be the Same for Everyone?” at Meredith’s 2018 Faculty Distinguished Lecture, held on October 9 in Jones Auditorium.

During the 57th installment of the lecture series, Manning explored how mathematical modeling could be used in determining the dosing of antibiotics. In particular, she looked at whether the same dose of the antibiotic
ertapenem should be given to everyone.

She opened her talk with a visual showing things might appear the same, but in reality, they differ in many ways, explaining the
importance of truly defining a problem before
developing the solution model. Manning had
three students demonstrate filling jars of
various sizes with the same number of M&M’s, showing that the M&M’s will fill each jar differently.

“Defining the size of the jar is a really important part of the process. For problems such as this one, it is important to know the size of the jar we are talking about, what type of M&M’s we are using, and what is meant by filling the jar. This is all part of defining the problem and making assumptions.”

A type of mathematical model, known as a physiologically-based pharmacokinetic (PBPK) model, was used to answer the question of whether everyone should receive the same dose of antibiotics.

Manning studied the distribution of the antibiotic, ertapenem, in men and women with varying body mass indexes (BMI), following a typical dose, which was based on a normal weight, normal height male.

“Clearly, not all people are ‘normal weight, normal height males,’ just as not all jars are quart size and not all M&M’s are plain,” said Manning.

Manning found that individuals with higher BMI have a lower free concentration of the drug in the blood. The free concentration is the portion of the drug that is available to fight the infection. She also found that all females, regardless of BMI, store larger amounts of the drug in fat than males.

In addition, she found that given the normal dose of the antibiotic, males have a greater potential for the drug to be less effective because of lower levels of free concentration in the blood, but they are less likely to develop resistant bacteria because of having higher minimum free concentrations in the blood.

In comparison, females have a greater probability of undesired side effects because of substantially higher peak concentrations of ertapenem in the blood as well as higher amounts in the fat.

“Individuals with higher BMI have a greater
minimum free concentration of the drug in the blood and have less chance of developing resistant bacteria,” said Manning. “For individuals with a lower BMI, the drug has a shorter half-life and a lower minimum free concentration; thus, these individuals have a higher probability of undesired side effects and potential for development of resistant bacteria.”

Using the results of the mathematical model, Manning’s goal is to develop different dosing regimens in terms of amounts and number of times per day for individuals of different sex, weight, and height.

Cammey Cole Manning is a professor of mathematics and head of Meredith’s Department of Mathematics and Computer Science. She has been actively involved in several professional organizations where she serves as a mentor and helps plan professional development programs and workshops. Manning earned her B.S. at Duke University and completed her Ph.D. at North Carolina State University.

Melyssa Allen

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