Abstract

Traumatic brain injury (TBI) has been the focus of multidisciplinary research for decades due to its significant impact and high incidence rate. Computational models, simulations of TBI, and in vivo human brain imaging methods such as magnetic resonance elastography (MRE) and tagged magnetic resonance imaging (tagged MRI) are powerful tools to understand the mechanisms of TBI, from the loading and kinematics to strain fields experienced by brain tissue to its complex pathology. Remaining challenges include: 1) assumptions and approximations in models and simulations; 2) limited model evaluations; 3) low-amplitude (linear-regime) deformations in experiments; 4) the effect of noise on experimental strain calculations; and 5) the high dimensionality of brain deformation fields, making them computationally expensive to simulate and analyze. These difficulties compromise our understanding of TBI, raise questions concerning the biofidelity of simulations, and limit the generalizability of in vivo experiments to real-world TBI scenarios. Two main objectives are pursued in this thesis: 1) developing a quantitative comparison framework that can provide objective scores for the degree of similarity (or discrepancy) across measured and simulated human brain deformation; and 2) discovering the governing equations of human brain and reducing the dimensionality of brain deformation by revealing the dominant coherent patterns. To achieve the first aim, we introduced a framework that integrates nonlinear registration with image-based reconstruction of the finite element mesh and developed new correlation metrics that enable local and global comparisons across multiple simulations and experiments. The second aim was accomplished by designing a novel data-driven algorithm, time-augmented, space-contracted dynamic mode decomposition (TASC-DMD), and combining it with sparse identification of nonlinear dynamics (SINDy) to discover reduced-order models (ROMs) and governing equations describing the dynamics of 45 in vivo human brain tagged MRI subjects. Additionally, we showed that TASC-DMD is a universal dimensionality reduction technique that outperforms other popular DMD methods in modeling spatiotemporal data and capturing the correct underlying physics from quantum mechanics to fluid flows.

Committee Chair

Philip Bayly

Committee Members

Ahmed Alshareef; Fanwei Kong; Matthew Bersi; Ruth Okamoto

Degree

Doctor of Philosophy (PhD)

Author's Department

Mechanical Engineering & Materials Science

Author's School

McKelvey School of Engineering

Document Type

Dissertation

Date of Award

8-18-2025

Language

English (en)

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Available for download on Sunday, August 15, 2027

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