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Taking Mathematics to Heart

John Wesley Cain, 34, started graduate school with a mathematician's aversion to biology. He took a course in his first semester at Duke University with David Schaeffer, an applied mathematician who was just beginning to study models of cardiac rhythms. In the class, Cain had to choose from a list of projects and ended up working on mathematical models of cardiac action potential. "I think that was secretly his favorite project," Cain says.

Cain himself took quickly to the work. "I thought the mathematics was cool. I thought the applications were cool." Eventually, Schaeffer became Cain's Ph.D. adviser. Now, Cain is an assistant professor at in the Department of Mathematics and Applied Mathematics at Virginia Commonwealth University in Richmond. There, he works in applied mathematics with an emphasis on cardiac electrophysiology.

"The mathematics is very rich and ... there is just absolutely no end to the types of questions you can pose about dynamics in cardiac tissue." -- John Wesley Cain

Much of the work he does is in interdisciplinary teams. In fact, he is a co-principal investigator on a training grant in computational cardiology that focuses on teamwork. "The idea is to try to get clinicians, basic science researchers, mathematicians, computer scientists -- you name it -- to actually talk to each other," Cain says. The culmination of that grant will be the World Congress on Mathematical Modeling and Computational Simulation of Cardiovascular and Cardiopulmonary Dynamics at the College of William and Mary from 31 May to 3 June.

This summer, Cain will move to a new position as an associate professor at the University of Richmond, which, he says, is more geared toward undergraduate education. "I have a lot of projects that I have been really itching to get some of their undergraduates involved [with]," he says. He will continue his collaborations with VCU, in part for its medical center and team of cardiologists.

Cain spoke with Science Careers earlier this spring. Below is a partial transcript of the conversation, edited for clarity and brevity.

Q: Tell me what mathematical cardiology is. What does that mean in terms of research?

J.W.C.: You can take a natural phenomenon, such as a heart attack or anything that you would like to understand the mechanisms for ... [and] you can ... run mathematical and computer-based simulations ... to gain intuition, as opposed to actually having to maybe excise a heart from a rabbit or a sheep or something like that to run an experiment. I ... try to gain intuition so that I can then report to the biomedical engineers and then tell them, "These might be the sorts of experiments that you might want to run."

Q: Can you give me an example of a particular cardiac event that you have worked on and how that would translate?

J.W.C.: Sure. Sometimes, for example, regions of damaged tissue can anchor abnormal wave patterns in the heart, and those sorts of things can be simulated. ... So the idea would be: ... take an example of a substrate for anchoring some particular type of arrhythmia. Try to describe that set-up using a system of equations that could be solved using a computer. And then try to see if we can actually reproduce the phenomenon at least qualitatively and hopefully quantitatively with some computer assistance. Because then we can experiment with different types of damaged regions of tissues to see which ones might anchor abnormal rhythms a little bit better than others and then try to simulate or design an experiment for telling a clinician how you might want to use techniques that they use to terminate the arrhythmia.

[Clinicians] have their own range of techniques, of course. They usually use things like radio frequency ablation ... to try to fix the heart when they detect this type of abnormal rhythm. Our idea would be to just try to simulate such rhythms on a computer and then try to figure out, well, how would we correct those sorts of rhythms?

Q: Do you work directly with clinicians or bioengineers in understanding the processes and working on the models?

J.W.C.: We do. The groups tend to be very interdisciplinary. ... Cardiologists are the ones who really keep us honest and they tell us exactly what ... they see when they look at a damaged heart and ... then would need to go in and ablate or do something of that sort. The biomedical engineers are very useful folks to talk to because they are very nice in bridging language gaps. ... I am trained as a mathematician and sometimes it's nice to have somebody who can speak ... from an engineering standpoint and talk about quantitative things, and also understand some of the more technical physiology that's going on.

Physics folks tend to be good at running experiments, just like the biomedical engineers. And then the mathematicians like myself would be more geared towards analyzing mathematical models and computational models that are designed to try to explain different types of rhythm [and] explain mechanisms for generating arrhythmias. So there is a big spectrum of scientists who are involved in these sorts of projects, and it actually makes for very fun and lively discussion groups.

Q: Let's talk a little bit more about your experience. You were originally trained as a mathematician?

J.W.C.: All of my training was in mathematics. Biology, of all the basic sciences, was the one that I had the least interest in when I first started graduate school.

Q: So how did you get exposed to it and how did you end up taking this direction?

J.W.C.: Right when I was getting ready to start graduate school, I thought briefly about maybe trying to take an excursion out of academia and getting a job in the tech sector. But that was around the year 2000 when the tech sector was in the process of going belly up, so I decided, well, I will try the graduate school route. And in my first semester I took a math course, an applied mathematics course in ordinary differential equations. And during that course, we all had to choose a project to work on, and one of the projects that we were able to choose from was mathematical models of cardiac action potentials in a single cell.

As it happened, the professor had just gotten involved in that, and I think that was secretly his favorite project. By happy coincidence, he asked if I would be willing to work on that as an independent study with him the following semester. And I said "Sure, okay." I thought the mathematics was cool. I thought the applications were cool. We continued it as an independent study the following semester and then we decided to continue into the following summer. And by the end of the summer, I was ... ready to pop the question of, "will you be my academic advisor? Will you advise my dissertation?" It seemed like a great match.

The mathematics is very rich and the physiology -- there is just absolutely no end to the types of questions you can pose about dynamics in cardiac tissue. So it's kind of a happy story where I believe several nice coincidences happened to just put me on the right track.

Q: Have you picked up biology and cardiology along the way or did you go back and take some courses to catch up on that?

J.W.C.: I did have to learn a fair amount of electrophysiology to make sure that I wasn't doing anything too outlandish, because the idea isn't just to come up with some sort of mathematical model that is purely phenomenological to the point that all it's designed to do is to try to reproduce different graphs. If you design your model, you can make a model do anything you like. That doesn't necessarily mean that it's grounded in reality.

So we would typically have roundtable discussions where cardiologists, biomedical engineers, physicists and mathematicians would sit around the table and discuss the physiology. This is how I learned it: from roundtable discussions with a research group where the cardiologists and biomedical engineers were the ones who would really keep us honest and made sure that what we were doing was grounded in physiologically reasonable assumptions.

I tried taking a course one time but after a couple of lectures decided to abort that because the roundtable discussions were a lot more fruitful. I found that it was a lot easier to learn some of the physiology background just by directly asking a cardiologist or a biomedical engineer.

Q: How do you go about making a mathematical model that is biologically relevant? Is it understanding the physiology? Is it trying to get the clinicians to understand the math?

J.W.C.: I would say all of the above. It's not necessarily essential that the clinicians understand the math. It's trying to figure out how to ask the right questions of the clinicians to make sure that your model stays honest.

Usually you want to use the mathematics to try to gain insight as to what you should be looking for, and the more complex the model, ... the less amenable to mathematical analysis it's going to be. So you really have to try to convey to the clinicians what a mathematician's limitations would be so that they can craft their questions in such a way that it helps design an experiment. And that's a really delicate tight-wire act to try to walk.

Q: What would you tell undergraduate mathematics students who aren't quite sure where they are going to take their interest in math if they wanted to pursue a biomedical field?

J.W.C.: Biology used to be the science that was not traditionally the one that mathematicians would gravitate toward. There was a nice article that appeared several years back in the Notices of the AMS, "Why Is Mathematical Biology So Hard?" And in that, [Mike Reed] points out that in biology, there is no Newton's Second Law. There is no F = ma that you can resort to. Physics has traditionally been one of the fertile grounds for using mathematical modeling. ... But I would say that as computing has improved over the last several decades, biological modeling has become a very hot area. And a lot of the mathematical techniques are independent of the underlying applications.

So I try to tell students, even if biology is not necessarily your favorite science, it really can grow on you and the techniques you are going to use will be very similar to the techniques you would use to attack certain problems in physics or chemistry or economics. A lot of those techniques are independent of the underlying application and ... a lot of the most exciting questions are biologically motivated.

Q: Is there anything else that you'd like to tell me in terms of getting into the field or collaborative work?

J.W.C.: Other than just to drive home this point: that I really encourage any student who is interested in getting into this sort of career, you have to be willing to meet with people in fields ... very different from yours, and you have to listen. It took work at first. The electrophysiology literature has a lot of long words that I didn't understand and a lot of difficult things that pushed the limits of what I had remembered from basic chemistry. There was some start up involved but, boy, the rewards sure did make up for that. It's fun to talk to people from a variety of scientific fields. I encourage anybody who is interested in getting into this, don't hesitate to immerse yourself in any sort of quantitative training that you can and immerse yourself in any other sorts of science. ... It is a very, very fun field to be in.

Additional Reading

Mathematical cardiology and related fields typically fall under applied mathematics at universities. For example, Duke University, where Cain did his Ph.D., has a program in mathematical biology; graduate students in that program are supported in part by a grantfrom the National Science Foundation. There are math biology departments at several universities throughout the country.

In Cain's article, "Taking Math to Heart: Mathematical Challenges in Cardiac Electrophysiology,"published in April in Notices of the AMS, he recommends Mathematical Physiology (J. P. Keener and J. Sneyd, Springer-Verlag, New York, 1998) as a good introduction to mathematical cardiology.

In addition to the articles linked to in the above article, the American Mathematical Society has also published "Getting Started in Mathematical Biology." in Notices of the AMS,

The Society for Mathematical Biology maintains links to some resources on its Web page.

See also the Science collection, "Mathematics in Biology," published in February 2004.

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