The brain is often described as a network of firing neurons. But what if its true computational power lies not just in its signals – but in its shape?
At Texas A&M University, two researchers are challenging conventional neuroscience by pursuing a bold idea: that there is a mathematical description of the brain’s geometry that uniquely houses its electrical activity, giving rise to its extraordinary processing power.
While recent studies have begun to recognize that the brain’s shape may hold important clues to how it works, the methods for truly understanding and describing that shape remain a frontier. Researchers seek to bridge this gap that could transform how we think about cognition and inspire the design of intelligent systems, such as soft robots, where behavior is embedded directly in the system’s physical structure.
Blending expertise from mechanical engineering, computer science and visualization, Texas A&M faculty Drs. Vinayak Krishnamurthy and Ergun Akleman are leading a project funded through the Defense Advanced Research Projects Agency’s (DARPA) INSPIRE program. Short for Investigating how Neurological Systems Process Information in Reality, INSPIRE is part of DARPA’s Advanced Research Concepts (ARC) initiative, which seeks new models for how brains process information, beyond digital representations and neuron-based models.
The project explores how the brain’s intricate physical structure, the folds, layers and shapes of its cortex, may drive how it functions and communicates. Backed by $233,415 in federal funding, the team is building a new computational framework rooted in geometry, not code.
The researchers will analyze imaging data, such as fMRI scans, to extract what they call the “skeletal” structure of the brain. This underlying framework guides how brain regions grow and take shape. From there, they will:
- Create a new way to break down and study the shape and structure of the brain using a graph-based method that helps map out how different parts are connected and interact.
- Develop algorithms that utilize the skeletal structure to reverse engineer the intricate geometry of functional brain segments.
- Conduct comparative analyses to determine correlations between the geometry of the brain (as characterized by the extracted skeletal structures) with the neural connections (i.e., wiring patterns) in the nervous system.
Partitive geometry is central to the work, a geometric modeling paradigm pioneered by Krishnamurthy and Akleman. Inspired by the discovery of scutoids, 3D shapes found in tightly packed biological tissues, partitive geometry provides a way to represent how biological forms, like the brain, evolve under spatial constraints.
Krishnamurthy explains that the brain’s complex folded structure may emerge from three simple conditions: resistance to collision and self-intersection, an internal skeleton that guides its growth, and the underlying growth model that governs how this skeletal structure expands and morphs over time.
By formalizing these into computational models, the research team aims to discover rules behind how the brain’s shape is formed and how that shape influences thought.
By integrating advanced geometry with neuroscience, this project places Texas A&M at the forefront of interdisciplinary research, uniting engineering, visualization and computing to take on one of science’s most complex challenges. The work can potentially influence both brain science and the design of future AI systems that mirror the brain’s structural intelligence.
In answering bold scientific questions, Aggie researchers are pushing boundaries, advancing knowledge and shaping the future.
Krishnamurthy is an associate professor and J. Mike Walker '66 Career Development Professor in the J. Mike Walker ‘66 Department of Mechanical Engineering. His work focuses on geometric and topological computing, human-AI collaboration and tangible interaction. He received an NSF CAREER award and was named one of ASME’s 2024 Rising Stars of Mechanical Engineering.
Akleman, a professor in the College of Performance, Visualization and Fine Arts and the Department of Computer Science and Engineering, brings decades of experience in geometric modeling, computer graphics, and architectural design. His interdisciplinary background strengthens the team’s ability to bridge mathematical theory with biological and visual analysis.