The Brain's Hidden Plumbing and the Math Behind It - Profile Derya Bakiler

When A. Derya Bakiler arrived at the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin as a Ph.D. student, she already knew exactly what had led her here. She had watched a short introductory video about the Institute years earlier while still completing her master's degree at Bilkent University in Ankara, Turkey. In it, Professor Omar Ghattas described the Institute's mission in a way that stopped her in her tracks. "He was saying something like, 'at the Oden Institute, we come up with the mathematical models that describe complex systems, and then develop the necessary numerical methods to solve these equations,'" she recalled. "I realized that the Oden Institute would be the place I would want to be if I wanted to go further with this line of research."

What makes that moment striking is how close she came to never being in a position to recognize it at all.

In the third year of her undergraduate degree in mechanical engineering at Bilkent, Derya was convinced she had chosen the wrong field. The first two years had been dense with statics, materials, thermofluids, calculus, and differential equations. A mandatory internship at a tractor factory had been interesting in its own way, but she couldn’t picture herself doing this specific line of work.. "I was quite depressed and felt lonely academically," she said. "I was even thinking about changing my major."

That semester, a new professor named Ali Javili joined the department. He was offering a graduate-level course on the molecular simulation of materials, and the department head suggested Bakiler speak with him. She enrolled. The course introduced her to continuum mechanics and, through it, to computational mechanics, a field she had never known existed. "I realized it was perfect for me, because I always enjoyed coding, and understanding the underlying physics of systems and materials," she said.

Equally important was Javili himself. "He was such an effective instructor that I never felt overwhelmed or discouraged, even though I pretty much had no idea what I was doing in the beginning." She liked the topic and the mentorship so much that she stayed on after her undergraduate degree for a three-year master's, continuing to work on modeling instabilities in soft materials.

Soft material instabilities might sound abstract, but Derya's entry point into the problem was anything but. Consider the human brain. Its characteristic folds and creases, known as sulci, form because the brain's white and gray matter have different stiffnesses and grow at different rates. The skull constrains that growth, so the brain "buckles" to fit, much like a ruler under compression. Because brain tissue is extraordinarily soft, modeling these large deformations requires specialized mathematical tools. That problem drew Derya in, and the computational techniques she developed to study it would bring her to Austin.

Her current research as a doctoral student in the Computational Science, Engineering and Mathematics (CSEM) program where she works with the Computational Mechanics Group, takes those tools in a new direction. She is now working on modeling the glymphatic system, the brain's waste disposal network, only discovered about fifteen years ago. The system works by allowing cerebrospinal fluid to flow through pathways in the skull and along pipes surrounding arteries and veins, mixing with the fluid inside the brain tissue, gathering metabolic waste on the way, and carrying it back out. When the system malfunctions, proteins like amyloid beta and tau can accumulate into plaques, the same plaques used as biomarkers for Alzheimer's disease.

"We don’t know yet if the plaques are the cause or effect of Alzheimer's," Derya explained. "That is the critical knowledge gap we are trying to address.” Her goal is to build a computational model of the glymphatic system calibrated to real patient data that can simulate how plaque formation progresses in a specific individual's brain, work that would otherwise require repeated invasive procedures directly on a patient's brain. “Having a calibrated model allows you to test millions of different scenarios on a patient's clearance system, which would be impossible to do experimentally," she said. "Furthermore, the model itself tells you so much about the underlying mechanics of the system that was previously unknown.

The transition from her earlier work on soft material instabilities to glymphatic modeling was more natural than it might appear. "Fundamentally, we use the same approach," she said. Both fields start from mathematical equations governing a physical system and apply numerical methods to solve them. What is new, and what she is still learning, is the experimental side: coordinating with collaborators who perform the magnetic resonance imaging (MRI), understanding what data the computational model needs, and communicating what is and is not useful on her end. "I am still learning about the brain and MRI technologies, and I doubt I will be done anytime soon."

Derya works under the supervision of Shaolie Hossain, senior research fellow in the Computational Mechanics Group and principal investigator of the project, and Professor Tom Hughes, lead of the Computational Mechanics Group and her academic advisor. "I have learned so much from both of my advisors," she said. "They are always there to help, especially when I'm working through problems, which helps me stay motivated." 

Hossain describes what makes Derya's approach distinctive. "What stands out about Derya is her ability to move fluidly between advanced mathematics, computational methods, and image processing, all while keeping the clinical question at the center of her work," she said. "Derya's core contribution has been in inverse problems, working backward from MRI data to determine the physical parameters that govern how amyloid is transported through this system and deposited in the brain, a key hallmark of Alzheimer's disease. This modeling gives us a mechanistic, brain-wide view of how these waste proteins build up, offering insights that could reshape our understanding of neurodegenerative diseases broadly."

Hughes echoes that assessment. “Derya is a talented and focused researcher, and CSEM student,” he said. “She has demonstrated perspicacity and determination in her glymphatic system research and has already obtained very important results. I predict she will make significant contributions to the understanding of neurodegenerative disease.” 

The environment at the Oden Institute has reshaped how she approaches problems. Before arriving, she had little experience working across disciplines. Now she collaborates with imaging specialists, biologists, and clinicians.. "I approach problems differently," she said, "I now know experts in their own fields, and have an idea of how to work with them." One recent moment crystallized this shift: shortly after attending a workshop on the glymphatic system, she had a realization that two systems she had long regarded as separate were in fact connected. "If we could find and model that connection, we would be solving one of the biggest questions in the field," she said. "That is really exciting for me."

An accomplished pianist, Derya has played since she was five years old, and she sees a direct line between practicing an instrument and conducting research. "Having to sit down, practice the same passages, learning new techniques, and having slow, incremental progress that requires time, effort, and patience is similar to how I see research," she said. "Playing the piano puts me in the right mindset." She also pursues watercolors and crochet, and volunteers as an instructor through the Texas Prison Education Initiative, teaching college-level mathematics to inmates at the Coleman Women's Correctional Facility in Lockhart. "I always leave with a newfound love of teaching and learning, and inspired by strong, smart women."

She is quick to note that she took what she calls "the scenic route," completing a full master's degree in Turkey before applying to Ph.D. programs, arriving in Austin with more research experience, more published work, and a clearer sense of what she wanted to do. "I realize that may not work for everybody but it worked out really well for me." The trajectory has not gone unnoticed. Bakiler recently received the Outstanding Graduate Research Fellowship from the UT Graduate School, which will fund her continued research at the Oden Institute. 

The long-term vision for her research is ambitious. Within five years, Derya hopes to have a pipeline that takes a patient's brain MRI as input and produces long-term plaque formation predictions as output, eventually without relying on invasive experimental procedures. In the ten-year view, she sees patient-specific computational models like hers becoming a genuine part of clinical practice, shifting medicine toward prevention rather than treatment. "I truly believe that digital twins will be the next big revolution in healthcare," she said, "and will change how we approach many diseases that we currently do not have a cure for, like Alzheimer's disease."