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When you were sitting in a mathematics class, did you ever wonder if math really affects your life? In fact, mathematics plays an integral part in your daily life – often in surprising ways. To take one specific example, mathematical modeling and statistical analysis are critical in the health care and pharmaceutical fields.

From time to time, all of us are sick and need to take medication. In this era of antibiotic resistance, getting the correct dosage is particularly important – but how are dosage levels determined to ensure you get the amount you really need?

Mathematicians work on a specific type of models called Physiologically-Based Pharmacokinetic (PBPK) models that help determine appropriate dosing. These models investigate the uptake, distribution, and elimination of a drug in the body.

PBPK modeling incorporates known physiological parameters such as body weight, body height, organ volumes, and blood flow rates in particular tissues. These models can take into account information about the excretion, via urine and feces, of the drug as well as the metabolism of the drug.

The antibiotic ertapenem is used to treat a wide range of infections and is usually administered intravenously to individuals who are hospitalized because of an infection. The advantage of this drug is that it only has to be administered once a day. But because of the way it is absorbed, the amount of fat in the body can influence how the drug binds, how quickly the drug passes through the body, and thus how effective the drug is.

Work is now being done to see if body height and weight, which determine the body mass index (BMI) for an individual, should play a role in the antibiotic dosage because BMI can affect the absorption and excretion of a drug. This work (more mathematics!) could lead to even more effective dosing of the drug, which could significantly impact your health.

The next time you reach for a medication, remember the significant role that mathematics plays in your health.

Cammey Cole Manning, Ph.D., is a professor of mathematics at Meredith College. She has been actively involved in the Society for Industrial and Applied Mathematics (SIAM) and the Association for Women in Mathematics (AWM). Additionally, she has been involved for over a decade with programs, particularly those for undergraduate and graduate students, at the Statistical and Applied Mathematical Sciences Institute (SAMSI). She continues to be active in research, most recently coauthoring “A Physiologically-Based Pharmacokinetic Model for the Antibiotic Ertapenem” in the Mathematical Biosciences and Engineering journal.

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Melyssa Allen

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