Building Digital Twins of Personalized Models for Alzheimer’s Disease Prevention and Treatment
PI: Zi-Kui Liu (Materials Science and Engineering)
Plan for funding tuition for graduate students, or the remainder of the researcher’s salary for postdoc and research faculty: Other funded projects of the researcher’s salary for postdoc and research faculty
Principal Investigators
Zi-Kui Liu, Department of Materials Science and Engineering
Qing Yang, Department of Radiology and Department of Neurosurgery
Both will serve as mentors for an ICDS Junior Researcher.
Level of effort: 25% of the ICDS Junior Researcher’s effort
Plan for the remainder of the researcher’s salary: Other funded projects.
Project Description
According to classical statistical mechanics, a system can be described as a statistical ensemble of independent configurations, characterized by partition functions. In contrast, quantum mechanics— particularly through density functional theory (DFT)—describes a system at absolute zero as occupying a unique ground-state configuration, with its minimum energy determined by a specific electron density.
Zentropy theory, developed by Liu’s group, extends these frameworks by asserting that a system’s entropy comprises both the quantum entropy of individual configurations and the configurational entropy arising from their statistical distribution. As a result, the partition function for each configuration must be evaluated using its free energy rather than its total energy. Zentropy theory has shown excellent agreement with experimental data in magnetic materials, successfully capturing phenomena such as magnetic phase transitions, critical behavior, and negative thermal expansion in INVAR alloys—without relying on phenomenological models or fitting parameters.
For complex systems like the brain, ground-state configurations are currently beyond the reach of DFT. The proposed project hypothesizes that zentropy theory can be applied to model the evolution of such systems, as they are governed by both quantum and statistical mechanics. A central challenge lies in defining the number of configurations and accurately evaluating the total energy and entropy of each, enabling the prediction of macroscopic behavior through derivatives of the system’s free energy as described by fundamental thermodynamics.
To address this, the proposed project aims to develop a Zentropy-Enhanced Neural Network (ZENN) that learns the configurations, total energy, and entropy of brain states using data related to Alzheimer’s disease (AD). This data will be sourced from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), from Co-PI Yang’s group at the College of Medicine, and from other open literature publications.
Preliminary results indicate that ZENN outperforms classical deep neural networks (DNNs) in multiclass classification and modeling energy landscapes with singularities, particularly in extrapolation and higherorder derivative estimation. These capabilities are crucial for developing a ZENN-based digital twin (DT) for AD, especially when working with heterogeneous and longitudinal datasets.
As a proof of concept, the project has three primary objectives:
1. Develop a ZENN digital twin for personalized AD modeling using ADNI and Yang’s group data.
2. Submit a scientific manuscript for peer-reviewed publication.
3. Generate preliminary data to support a future NIH proposal.
This project aligns closely with the mission of the Institute for Computational and Data Sciences (ICDS) in advancing digital twin technologies and developing innovative, science-driven AI architectures.
Liu has been actively engaged with ICDS and its predecessor organizations since joining Penn State in 1999 and remains committed to contributing to its initiatives.