As an applied mathematician working in the medical sciences, Anastasios Matzavinos’s job essentially is turning flesh, blood, and molecules into numbers, algorithms, and models.
“The medical sciences give us a lot of data that need to be analyzed,” Matzavinos said. “What I do as a mathematician is develop the tools to make sense of the data.”
He explores methods of sifting through data to find important patterns, and he builds models that can manipulate the data to make predictions. These kinds of computational tools are becoming increasingly important as the size of datasets increases. Without these tools, Matzavinos says, “you’re just staring at data.”
An example of how useful computational tools can be is a project Matzavinos worked on involving breast reconstruction following mastectomy. One of the trickier aspects of the procedure turns out to be one that can be addressed computationally.
The surgery is generally done by taking a tissue flap from the abdominal area and using it to build a new breast. It’s crucial that the tissue be well supplied with blood in its new location. To do that, the surgeon takes some arteries from the abdominal area along with the tissue flap. But this is delicate. Take too few arteries or arteries that are too small, and the new breast will necrotize due to lack of blood. But taking too many arteries could lead to vascular problems in the abdomen where the tissue was harvested.
“The surgeon approached me and another applied mathematician and asked if we could construct a computational model for this,” Matzavinos said. “If we know the parameters of blood flow in this tissue and we know the diameter of the arteries, can we produce a model that predicts whether a tissue flap of a given size will be oxygenated enough?”
The answer was yes. Matzavinos and his colleague published just such a model in the Proceedings of the National Academy of Sciences, and they plan to continue testing it. Ultimately they hope it will become a tool that takes guesswork out of the procedure.
“This was an optimization problem,” Matzavinos explained. “You need to have a computational description of the process in order to actually to perform the optimization. The first step is to construct a model that mimics the actual process so you can go in and tweak the parameters you want. That’s an example of predictive modeling.”
There are also cases in which the model isn’t so much predictive as it is analytical. The model sifts through data and looks for an underlying structure or mechanism that drives a phenomenon. An example of that is work Matzavinos did with Ohio State biologist Jeff Kuret on the tau protein, which is thought to play a role in Alzheimer’s disease.
In Alzheimer’s disease, the tau protein inside neurons polymerizes abnormally, forming tangles that deform the cells and disrupt their function. But it wasn’t known how these polymers nucleate, meaning how monomers come together to form the polymer. If researchers could understand the nucleation process, it might be possible to disrupt it.
Observing nucleation under a microscope isn’t possible. The only data the researchers had to go on were observations of the polymers themselves. Those data could only narrow down the nucleation process to four possible scenarios.
“What we did was write down differential equations describing the kinetics of the system,” Matzavinos said. “We were able to see that of the four possible mechanisms, three didn't fit the data — only one did. So we were the first ones who discovered that the rate-limiting step in the nucleation process is tau dimer formation.”
Thanks in large part, that is, to the power of a mathematical model.
Matzavinos earned his Ph.D. from University of Dundee in Scotland in 2004, and completed three years of postdoctoral work at the University of Minnesota. He was a visiting professor at Ohio State University’s Mathematical Biosciences Institute and most recently an assistant professor at Iowa State University.
He’s very much looking forward to settling into his new home at Brown.
“Brown is a great place, especially the applied math division,” Matzavinos said. “I know some of the people here and it was my dream to collaborate with them. There are so many good ideas bouncing around here.”