Math Appreciation Month has finally come to a close. And I thought I would end with some math that could save your life. This is serious — and I think really interesting — stuff.
If you’re seen a recent “best college degrees” list, you probably wondered two things: Why the heck is Applied Mathematics on the list, and what is it? First off, applied mathematics is not about crunching numbers. Instead, these folks use higher level mathematics — from abstract algebra to differential equations to statistics — to solve a myriad of problems in a myriad of industries. And that, my friends, is why it’s on the list. In industries like energy, cell phone technology and medicine, math modeling and statistical analysis have been applied to solve really big problems.
Math modeling is one branch of this field that has become a very big deal. Let’s say a city planner wants to know how many snow plows to buy so that the city isn’t paralyzed by a winter storm. Modeling this problem using mathematics is one way to address this problem. The way I look at it, math modeling helps us understand things we can’t see — because they’re part of situations that haven’t occurred or are too far away or are too tiny and hidden.
That too tiny and hidden part that is what math modelers are honing in on with medicine. In this field — sometimes called bioinformatics or computational biology — mathematicians help medical professionals address problems that are under the skin. Here are two examples:
Fighting Cancer: Researchers at University of Miami (UM) and University of Heidelberg in Germany have created a math model that will help oncologists predict how a tumor will grow, and even if and how it will metastasize. There have been other math models that look at tumors, but this one is different. Instead of looking at each cell or all of the cells has a big group, this model creates a kind of patchwork quilt of areas of the tumor to examine. As a result, the doctor can create a tailored plan for treating the disease that is very specific for each patient. The promise is that with specialized (rather than generalized) treatment plans will offer patients a better chance at survival.
Treating Acetaminophen Overdoses: When a patient comes into the emergency room having overdosed on acetaminophen, the ER staff is faced with a really complex decision. Often these patients are hallucinating, unconscious or comatose. And since it’s relatively easy to overdose on the drug (it takes only five times the daily safe dosage, and acetaminophen is in many different over-the-counter and prescription medications), it’s sometimes impossible to determine when and how much of the drug was ingested. There is an antidote, but at a certain point, the doctor needs to skip that step and put the patient on the liver transplant list immediately. The trick is accurately identifying that point. University of Utah mathematician, Fred Adler, developed a set of differential equations that can better pinpoint the critical information needed to make these decisions.
In both of these cases, the math is pretty darned complicated, depending on a branch of calculus called differential equations. This approach is a step up from statistical analysis, which compares patient data to data collected from other patients. In other words, it assumes that tumors grow in the same way in all patients — which we know isn’t true. These dynamical math approaches allow doctors to offer treatments that are customized for each patient, based only on the information collected from the patient.
And the best part is that the doctors don’t have to know the math. If future studies bear out these new discoveries, a simple app can be designed for smart phones or tablets, allowing physicians to make diagnoses and treatment plans bedside.
I suspect these applications will continue to grow, as the medical community turns to mathematicians for insight into what we can’t see. That’s great news, because these advances can save lives.
I hope you’ve enjoyed what we’ve put together here for Math Appreciation Month. If you have questions, please ask them below. I’m always open to ides for future blog posts, so please share them!