# Understanding Mechanism of Functional Dynamics Through An Explainable Neural Network Landscape with Geometric Control

> **NIH NIH R21** · UNIV OF NORTH CAROLINA CHAPEL HILL · 2024 · $416,750

## Abstract

Project Summary/Abstract
One of the fundamental scientific problems in neuroscience is to have a good understanding of how cognition and
behavior emerge from brain function. Tremendous strides have been made over the past decade to elucidate the biological
mechanism that creates remarkable oscillatory patterns of functional fluctuations. From a data science perspective,
functional neural activities manifest geometric patterns, as evidenced by the evolving network topology of functional
connectivities (FC) even in the resting state. Since the co-activation of spontaneous functional fluctuations is often
encoded in a symmetric and positive-definite (SPD) matrix, it is more reasonable to put the spotlight on the geometric
patterns of evolving functional connectomes on the Riemannian manifold of SPD matrices, instead of using Euclidean
operations. In this regard, we will develop a novel computational model to understand the control mechanism underlying
functional dynamics through the lens of cutting-edge manifold, control theory, and machine learning technologies. The
overarching goal of our project is to establish a new underpinning of the relationship between analytic measurement of
control mechanisms and cognitive functions, which allows us to understand the mechanism of how the human brain works
and discover new imaging biomarkers with great mathematics guarantee. To do so, we define a trajectory of the complex
neural system to be the temporal path on the Riemannian manifold that steers the human brain traverses through diverse
cognitive states. In this regard, we will first develop a deep end-to-end model to uncover the characteristic equation of
dynamical systems from the time series of FC matrices in Aim 1. The backbone of our deep model is a data-driven
linearization process that projects high-dimensional manifold instances to a subspace such that the nonlinear dynamic
mechanism of evolving SPD matrices on the manifold can be dissected using a well-studied linear model on the latent
vector space. Furthermore, we integrate the notion of optimal control into the deep model, which allows us to (i) uncover
the multi-frequency oscillatory functional network modes for brain state transitions and (ii) measure the controllability for
not only the whole brain but also each brain region. We will address the following scientific questions in Aim 2 using the
existing unprecedented amount of human connectomes: (i) What is the relationship between brain controllability and
visual working memory? (ii) In what control mechanism does each brain region contribute to the altered functional
dynamics associated with auditory verbal hallucinations (AVH)? (iii) What is the statistical power associated with the
identification of disease-specific connectomes using the newly established system-level understanding of functional
dynamics? Successfully executing this project will shed new light on elucidating the working mechanism that links brain
function and cognition,...

## Key facts

- **NIH application ID:** 10889390
- **Project number:** 1R21AG084375-01A1
- **Recipient organization:** UNIV OF NORTH CAROLINA CHAPEL HILL
- **Principal Investigator:** Guorong Wu
- **Activity code:** R21 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2024
- **Award amount:** $416,750
- **Award type:** 1
- **Project period:** 2024-09-24 → 2026-08-31

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/10889390

## Citation

> US National Institutes of Health, RePORTER application 10889390, Understanding Mechanism of Functional Dynamics Through An Explainable Neural Network Landscape with Geometric Control (1R21AG084375-01A1). Retrieved via AI Analytics 2026-05-27 from https://api.ai-analytics.org/grant/nih/10889390. Licensed CC0.

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