Abstract
Gliomas are highly infiltrative brain tumors whose evolution is commonly modeled using reaction--diffusion partial differential equations. Estimating patient-specific tumor growth characteristics from clinical imaging remains challenging because only sparse observations of tumor morphology are typically available, and conventional numerical methods often incur significant computational cost towards solving this problem. Physics-Informed Neural Networks (PINNs) have emerged as a mesh-free framework for solving differential equations and performing parameter estimation by embedding the governing physics directly into neural network training. Despite their promise, their application to clinically relevant tumor growth modeling remains limited by sparse imaging observations, optimization difficulties, and heterogeneous tissue properties. This dissertation investigates the use of PINNs for both inverse and forward modeling of glioma growth governed by the Fisher-KPP reaction-diffusion model. The first contribution develops an anatomically informed PINN framework for estimating patient-specific diffusion and proliferation parameters from single-timepoint MRI-derived tumor morphology. The proposed methodology incorporates lesion-filled brain anatomy together with patient-specific brain tissue segmentations and systematically investigates optimization strategies, including multi-phase optimization, multi-resolution training, adaptive loss balancing, and sampling strategies, for robust parameter estimation. Evaluation on synthetic and clinical datasets demonstrates that biologically meaningful growth parameters can be recovered from sparse imaging observations under appropriate optimization conditions while also identifying morphology-dependent limitations of the underlying reaction--diffusion model. The second contribution investigates Extended Physics-Informed Neural Networks (XPINNs) for modeling tumor growth in heterogeneous brain tissue through domain decomposition. Tissue-specific subnetworks and interface continuity constraints are developed to represent heterogeneous diffusion across white and gray matter. Experimental results demonstrate the potential of XPINNs for heterogeneous biophysical modeling while highlighting the optimization challenges that remain for anatomically realistic tumor growth simulations. Together, these studies advance the application of physics-informed machine learning for personalized mechanistic modeling of glioma growth and provide practical insights into both the capabilities and current limitations of PINN-based computational oncology.
Committee Chair
Aristeidis Sotiras
Committee Members
Aimilia Gastounioti; Daniel Marcus; Hongyu An; Joseph O’Sullivan
Degree
Doctor of Philosophy (PhD)
Author's Department
Electrical & Systems Engineering
Document Type
Dissertation
Date of Award
8-17-2026
Language
English (en)
DOI
https://doi.org/10.7936/7w79-6890
Recommended Citation
Ghosh, Soumyendu Sekhar, "Physics-Informed Deep Learning for Computational Image Analysis and Personalized Medicine in Neuro-Oncology" (2026). McKelvey School of Engineering Graduate Student Theses & Dissertations. 1419.
The definitive version is available at https://doi.org/10.7936/7w79-6890