Collaborative Research: FDT-BioTech: Mathematical Foundations of Adaptable Digital Twins for Glioblastoma

This project will develop the mathematical foundations for trustworthy digital twins of brain disorders. A digital twin is a patient-specific computational model that is updated with that patient's own data, makes predictions, and reports the uncertainty associated with each prediction. Building a digital twin for brain disorders is challenging for several reasons. First, clinically important processes (e.g., cell infiltration in the normal brain) are often not directly observable because of the constraints of imaging technologies. Second, the mechanistic model used to describe a disorder may be incomplete, and third both the data and the underlying science continue to evolve, so the model needs to adapt to new knowledge and new imaging modalities. The project will confront these difficulties using glioblastoma, an aggressive brain cancer whose cells infiltrate tissue beyond the tumor region visible on standard MRI imaging, as a demanding test case. The methodology developed here will be general enough to extend directly to other infiltrative tumors and neurodegenerative diseases such as Alzheimer’s disease. The digital twins could also contribute toward the evaluation of new medical technologies. The framework and trained models developed here will be released openly, and the project will train students from high school through graduate school at the interface of applied mathematics, computer science, and biomedicine. Building a trustworthy digital twin for brain disorders requires solving four tightly coupled mathematical problems: identifying the right mechanistic model from indirect imaging data, calibrating patient-specific parameters, quantifying uncertainty in predictions, and adapting the pipeline as scientific knowledge and imaging modalities evolve. The unifying backbone is the Bilevel Local Operator (BiLO) framework, which poses the partial differential equation (PDE) inverse problem as a bilevel optimization problem in which the PDE constraint is enforced strongly, enabling accurate calibration and uncertainty quantification via Bayesian inference. The framework will address all four problems: iterative joint learning of the PDE and imaging models, which also recovers interpretable analytical forms of unknown mechanistic terms; in silico simulation of clinical interventions with calibrated uncertainty intervals; transfer learning for rapid adaptation to new patients, PDE models, and imaging modalities; and grid-based neural field representations with bilevel-specific acceleration for three-dimensional deployment at clinical resolution. Verification, validation, and uncertainty quantification are integrated throughout and grounded in data from glioblastoma patients. This project is jointly supported by the National Institutes of Health through the Office of Data Science Strategy. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.