In a view looking into a radiation therapy machine, a female patient is shown with only her arms visible, raised behind her head, as an attendant stands by.
A cancer patient undergoing radiation therapy.

Even before she learned to multiply and divide, Nara Yoon, PhD, assistant professor of mathematics and computer science, was flexing her mathematical skills by playing Omok (five-in-a-row), Chinese chess and 15 puzzles.

Games that were inherently mathematical just came naturally to her.

In school, she developed what she calls a profound interest in mathematics, which led her to choose it as one of her majors in college and in her graduate studies, undertaken at Ewha Womans University in South Korea, and then for her PhD, which she earned in applied mathematics at Case Western Reserve University in Ohio.

Dr. Yoon’s first move after earning her doctorate is telling about her philosophy on the higher purpose of math: She took a position as a mathematician in the Jacob Scott Laboratory at the Cleveland Clinic, which uses mathematical and experimental models to develop an understanding of how resistance to cancer therapies develops, with the goal of increasing the efficacy of targeted therapies and radiation.

“To me, mathematics transcends mere numbers and textbook logic; it is an integral part of our world,” Dr. Yoon said. “At Case Western, I was exposed to numerous professors engaged in diverse mathematical applications. Among these, the health-related field intrigued me the most, given its close connection to our everyday lives.”

Dr. Yoon’s most recent exploration of how math can be an instrumental element of healthcare is “Radio-immune response modelling for spatially fractionated radiotherapy,” published in 2023 in Physics in Medicine & Biology and co-authored with colleagues from the Cleveland Clinic and Case Western Reserve University.

Unlocking Secrets of the Bystander Effect

Radiotherapy eliminates cancer cells through targeted radiation exposure. Though it is one of the most widely used cancer treatments, some aspects of it are not completely understood due to its physical, chemical and biological complexity—in particular the “bystander effect,” whereby cells affected by irradiation convey beneficial effects to other cells not directly targeted for irradiation. Dr. Yoon says this phenomenon is thought to be linked to enhanced immunity after cancer and radiation exposure.

Dr. Yoon and her research team decided to study this effect by developing a mathematical model that explores the population dynamics of viable tumor cells, T cell lymphocytes (cells that protect the body from infection and may help fight cancer), immune triggering cells (cells with an anti-tumor response), and doomed cells (damaged cells doomed to die), and elucidates their interactions with one another. Her contributions to the study include analyzing the established model, focusing on prognosis patterns, treatment possibilities and promising treatment plans.

“The model allows for the simulation of two scenarios: an easily activated immune system responding to cancer, limiting tumor size even without radiation—immune limited—and a suppressed immune system lacking sufficient power to combat the cancer—immune escape,” Dr. Yoon said. “Unlike the ‘immune-limited’ scenario, effectively treating ‘immune-escape’ cancer requires a sophisticated radiation strategy.”

These understandings are particularly important in treatment of cancer that is initiated when a tumor’s size is in a curable range. “When treatment begins at an opportune time, careful consideration is needed for designing radiation, such as Spatially Fractionated Radiotherapy (SFRT),” Dr. Yoon explained. “This aims to maximize the bystander effect, while minimizing the radiation amount, thereby reducing damage to immune cells compared to cancer cells.”

The model demonstrated that the highly varied dose distribution in SFRT can make a drastic difference in tumor-cell killing compared to the uniform radiation dose distribution, not only enhancing but also moderating the killing of cells depending on immune response triggered by various factors. In other words, SFRT can be customized to more precisely treat tumors based on the immune characteristics of the cells near it.

Implications for Cancer Care

“In the course of our research, we uncovered valuable insights into the impact of immune response on cancer prognosis through analysis based on our newly developed tumor model,” Dr. Yoon said. “In identifying the two distinct modes of tumor status—immune limited and immune escape—we were able to further delve into promising approaches for treating cancer.” Using patient-specific data and a data-based parameter estimation method, she said this study can be applied in the clinic for the design of individualized treatment plans.

Their research also offers that “understanding the role and response of the immune system during and after radiotherapy is of critical importance as we move further into the era of immunotherapy.” In developing mathematical models that intend to explain phenomena occurring during cancer treatment, we gain a deeper understanding of complexities at the cellular level—which is vital to developing clinical studies and identifying new treatments.


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