When Dustin Liang was diagnosed with T-cell acute lymphoblastic leukemia in June, the cancer consumed his life. But despite a monthlong hospital stay, aggressive chemotherapy treatments, and ongoing headaches, fatigue, loss of appetite, and nausea, the 17-year-old high school senior enrolled in MITx’s class 18.01.1x (Calculus 1A: Differentiation).
MITx, part of MIT Open Learning, offers hundreds of high-quality massive open online courses adapted from the MIT classroom for learners worldwide. The Calculus 1A: Differentiation course was designed and created by the Department of Mathematics and offered through the MITx program. Liang took the free course this summer in between treatment sessions and medical tests so that he could meet the four-year math requirement to graduate from a Massachusetts high school — an arrangement he made with his school.
In class, Liang learned how to differentiate functions and how to make linear and quadratic approximations. He then applied this knowledge to estimate his blood cell counts. “I was in a hospital bed when I saw the doctor draw a graph of my neutrophils on a whiteboard, and I thought you could apply a quadratic approximation to it to estimate my blood cell counts at a certain time in the future,” Liang recalls. “I talked to the doctors about it, and they said it was a good idea but that they currently didn’t have the technology to do that.”
When doctors conduct blood tests on a patient, they look at multiple cell counts. Three of those are especially important for cancer patients: hemoglobin, which is the protein in red blood cells responsible for the delivery of oxygen to tissues; platelets, tiny blood cells that help the body form clots to stop bleeding; and neutrophils, a type of white blood cell that helps the body fight infections.
“Heavy chemo kills all of the cells, regardless of whether they’re good or bad,” says Thomas Liang MS ’97, who is Dustin Liang’s father. “We asked the doctor a few times about the nadir [the lowest value of the neutrophil count after drug administration], but the doctors couldn't predict when Dustin would get to it. The anxiety was pretty high.”
While Liang was in the intensive care unit, his doctors ordered blood tests hourly to get a clearer picture of his blood cell counts. Being able to predict blood cell counts allows doctors to more accurately manage the next treatment procedure, and it allows patients and their caregivers to be more cautious and prepare for the next treatment.
Predicting neutrophil counts with math
After being hospitalized for weeks, Liang couldn’t wait to go home. He had his eyes locked on his absolute neutrophil count, which needed to reach 1,000 per microliter of blood in order for Liang to get discharged.
In Calculus 1A, Liang was learning how to predict the near future value of a function using linear or quadratic approximation methods. After seeing a doctor’s chart of his neutrophils, Liang hypothesized that he could use quadratic approximation to predict his neutrophil count.
“Given a series of points of the blood cell counts, a function can be modeled,” Liang explains. “So, predicting a future point not far away is mathematically feasible.”
Determined to test his idea, Liang called his mentor, Jiawen Sun, who works in a London security exchange firm as a trading analyst simulating and modeling stock market behavior. Sun helped Liang create a graph to estimate Liang’s neutrophil count at a certain time. When Liang compared the graph to his blood test results, he found that the math worked.
“I was able to predict the blood cell counts. It was a little off, but close enough,” Liang says. “There are some challenges in simulating the function of blood cells. However, the human blood cell counts turned out to be converging easier than the stock market to simulate.”
Now, Liang is working on a more accurate model for the neutrophil count based on input he received from doctors at Dana-Farber Cancer Institute. He hopes to use data from other cancer patients to test his model; however, much more work will be needed to determine if this kind of model can be used on other patients.
“If this works, it will alleviate some of the anxiety of cancer patients, and make their lives a little bit easier,” Liang says. “For doctors, they will be able to come up with more accurate procedures for treating cancer.”
Searching for better treatment options
Liang completed Calculus 1A: Differentiation in September, receiving a grade of 100 percent on his final exam. “My other chemo had started, and I was feeling pretty bad when my dad told me the grade,” he recalls. “I’m proud I managed to accomplish something while I was undergoing chemo.”
Liang, who continues to undergo chemotherapy treatment, enrolled in class 18.01.2x (Calculus 1B: Integration) through MITx this fall semester. He is also taking an English class at his high school. After graduating from high school next year, Liang wants to study pre-med and become a cancer researcher.
“I was always pretty interested in the science field. Then I got cancer, and I got even more interested in it,” he says. “I want to research it, find ways to help people get rid of their cancer, and better patients’ treatment.”
For Thomas Liang, his son’s survival is the first priority. “I want him to be a successful survivor,” he says. “Dustin is a brilliant kid and a chess prodigy. He thinks fast. He’s very sensitive. He doesn’t talk a lot, but is very popular among his friends. He's a kindhearted kid. I am proud of his aspirations to be a doctor.”