Just read about this rather amazing biography: https://today.duke.edu/2017/10/hau-tieng-wu-vital-signs. From a medical doctor, Hau-tieng Wu pursued a Ph.D. in math, and is now a math professor at Duke. Quite an interesting transition, that is quite rare, possibly less than 100 such cases in the world. Most mathematicians know little about medicine, and most medical doctors know little about math. It is rare to have someone know both fields.
Listen to your heartbeat with a stethoscope and you’ll hear a rhythmic lub-dub, lub-dub that repeats roughly 60 to 100 times a minute, 100,000 times a day.
But the normal rhythm of a healthy heart isn’t as steady as you might think, says Hau-tieng Wu, M.D., Ph.D., an associate professor of mathematics and statistical science who joined the Duke University faculty this year.
Rather than beating like a metronome, heart rhythm varies depending on whether you’re asleep or awake, sitting or jogging, calm or driving in rush hour. Breathing rate, brain activity and other physiological signals vary in much the same way, Wu says.
He should know. Before becoming a professor, Wu trained as a medical doctor in Taiwan. In his fifth year of medical school he was doing clinical rotations in the hospital when he was struck by the complex fluctuations in heart rhythm during anesthesia and surgery.
Where some saw noisy patterns — such as the spikes and dips on an electrocardiogram, or ECG — Wu saw hidden information and mathematical problems. “I realized there are so many interesting medical data that aren’t fully analyzed,” Wu said.
When a patient is in the hospital, sensors continuously monitor their heart rate and rhythm, breathing, oxygen saturation, blood pressure, brain activity and other vital signs.
The signals are sent to computers, which analyze and display the results and sound an alarm if anything veers outside normal ranges.
An ECG, for example, translates the heart’s electrical activity into a squiggly line of peaks and valleys whose frequency, size and shape can change from one moment to the next.
Wu is using techniques from differential geometry and harmonic analysis to detect patterns hidden in these oscillating signals and quantify how they change over time.
His methods have been applied to issues in cardiology, obstetrics, anesthesiology, sleep research and intensive care.