# Math in Medicine

One of our constant themes is the innovative ways that tools and ideas from math and physics can lead to new insights in the life sciences. Take, for example, a recent study produced by a group that included a professor of mathematics, an oncologist who works in pharmaceutical research and has a Ph.D. in mathematics, an electrical engineer and applied mathematician who is doing a postdoc at Harvard Medical School, and physicians in a medical center research lab.

The idea was to create a mathematical model of a medical syndrome – in this case neutropenia, the low counts of the white blood cells called neutrophils that can develop following chemotherapy. Those blood counts, apparently, do not always predict which patients are most at risk from a life-threatening bacterial infection and which will be able to fight off such an infection.

Though we may imagine that mathematical models tend to provide a simplified, abstract version of reality, in this case the model revealed the hidden subtleties of the syndrome. It showed that the immune system of a patient with neutropenia can be seen as a bistable system – a mathematical term for one in which small disruptions can rapidly send the system spiraling out of equilibrium. In this bistable system, tiny differences that wouldn’t normally affect immune function can take on overwhelming importance. So, for instance, variations in the abilities of the neutrophils to kill bacteria or an increase in the permeability of barrier tissues to those bacteria (another side effect of chemo) could spell the difference between life and death.

Indeed, the mathematical model predicted bistability, and experiments corroborated this prediction. In other words, it showed that several types of variability between patients could be crucial.  Although the model needs to be tested further in a clinical setting, the medical researchers already believe it can explain some mysteries that simple blood counts haven’t been able to solve. Even better, if trials confirm that neutrophil quality is an important factor in fighting infection when the immune system is compromised, the insight could be applied fairly soon to diagnostic and treatment protocols.

Image: Thinkstock

For more on mathematical models, see today’s online article on a group that used simulations to figure out how a handful of proteins in the Drosophila ova membrane manage to create a molecular gradient that sets the pattern for the rest of embryonic development.

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