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EXPERT OPINION: Meds and math, with Rachel Roe-Dale

What’s the mixology behind drug cocktails? More and more, physicians are collabo- rating with mathematicians to refine the science of chemotherapy in cancer, AIDS, and other illnesses where med- ications are often given in certain com- binations or sequences. There’s plenty of clinical evidence that giving drugs in different combinations and orders can affect the success of treatments, but how and why are not easy to pin down. Not a lot of physicians have all the math training to do detailed modeling of the variables. And of course mathematicians don’t usually have biology labs for test- ing their models. So it’s great when they can collaborate—as they’re increasingly doing in clinical trials and major re- search hospitals affiliated with univer - sities. Getting a handle on the statistics through mathematical modeling can greatly improve the predictability of multiple-medication dosing options.

What are you learning about cancer drugs? I started modeling biological and medical phenomena in grad school, specifically working with the order and timing of certain cancer drugs. We began by as- suming a simple or ideal state in which tumor cells all stay the same so you’d never need to change the medication, and we developed our basic equation to reflect the drug’s effect against the cells. Then we incorporated new variables, and relationships among the variables, to account for some of the differences in real-life cancers. My study focused on two factors: a particular genetic mecha- nism for withstanding the drugs and also where the cells were in their life cycle. We can quantify the kill fraction of a drug (what percentage of cancer cells it succeeds in killing), and we can define tumor-cell proliferation rates (the expo- nential process of cells doubling over time), so we can simulate the delivery of

a medication, the fraction of cells killed by it, and the continuing growth of those cells not killed. But we’ve also learned that drugs can have dif- ferent effects on cells in different phases of life, as they’re preparing to reproduce, actively dividing, resting, or transitioning between phases. So we expanded our model to account for drug timing and cell-phase timing. With differ- ential equations we managed to model the effectiveness of two drugs given either se- quentially—for example, as AAABBB—or in alternating doses—as ABABAB. And our models showed that when cell life- cycles are factored in, the order of the drugs does matter. So this kind of math- ematical modeling can help researchers and clinicians figure out how to target cancer cells when they’re most vulnera- ble to each drug in a combined therapy.

Can patients make use of such information? There’s a huge amount of data out there that you can access directly to get an idea of a drug’s success rates in clinical trials, or just to familiarize yourself with the terminology so you can be more in- formed when you discuss medication options with your doctor. Two good on- line resources are PubMed (pubmed .com) and the National Institutes of Health (

Is there student interest in this field? As a pre-health-professions advisor at Skidmore, I often point to medication modeling as a great example of why and how math is so important for pre-med students. Plus it has become a hot ca- reer field in itself and is now being used for streamlining the way drug trials are designed and set up. Math really gives you a different set of tools for critical

thinking—a crucial skill for students— and in this case for evaluating drug testing and other research results—a useful skill for anybody.

Rachel Roe-Dale earned a doctorate from RPI and joined Skidmore’s faculty in 2005. She teaches calculus, algebra, sta- tistics, and other applied-mathematics courses.

14 SCOPE FALL 2012


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