2025 Theses Doctoral

Nonparametric Functional Modeling of Dynamic Positron Emission Tomography Data

Shi, Baoyi

Positron emission tomography (PET) is a nuclear imaging technology used to quantify and visualize in vivo biochemical processes, such as estimating the density of a target protein across brain regions in studies of mental illnesses and neurological disorders. PET data are typically analyzed using kinetic modeling approaches, which approximate the target process based on assumptions about its kinetic behavior over time. However, traditional kinetic modeling approaches face significant challenges. They rely on strong parametric assumptions that, while sometimes reasonable, often oversimplify the true underlying process. Violations of these assumptions can lead to unstable model estimation, lack of interpretability of estimates, and ultimately, erroneous conclusions. Additionally, traditional kinetic modeling approaches require frequent arterial blood sampling during PET scans. This invasive procedure causes discomfort, carries risks of adverse reactions, and limits the feasibility of PET in many clinical and research settings.

To address these limitations, this dissertation proposes a series of methodological innovations grounded in the principles of functional data analysis. First, it extends traditional kinetic modeling by developing a substantially less invasive approach that requires arterial blood sampling at only a single time point, using functional principal component analysis. This approach significantly reduces arterial blood sampling while still producing unbiased estimates that closely align with those obtained through complete blood sampling. Second, it introduces nonparametric approaches based on functional mixed models to characterize the target process, relaxing the strong parametric assumptions of traditional kinetic modeling approaches.

By adopting a nonparametric framework, these approaches avoid model misspecification, offer greater flexibility and precision in capturing complex biochemical dynamics, and yield deeper insights into subtle in vivo biochemical processes. Third, it develops permutation testing strategies within functional mixed models to support robust statistical inferences under complex data structures. The proposed approaches are demonstrated using data from a dynamic PET imaging study of the human brain.

Collectively, these methodological advancements provide more robust, efficient, and flexible tools for PET data analysis, reducing reliance on invasive procedures and enabling a more comprehensive characterization of biochemical processes in vivo. Beyond methodological innovation, these contributions also have substantial translational potential. The proposed methods can facilitate earlier disease detection, improve diagnostic precision and patient stratification, and provide minimally invasive tools for rigorous target validation and treatment monitoring in drug development. More broadly, this dissertation advances PET imaging as a powerful, clinically feasible, data-driven framework with wide-ranging applications in early disease detection, personalized medicine, and both drug development and therapeutic innovation.