Latent Gaussian Process Modeling for Dynamic PET Data: A Hierarchical Extension of the Simplified Reference Tissue Model

Dynamic positron emission tomography (PET) provides a powerful tool for studying in vivo neurochemical processes, including transient neurotransmitter release. However, widely used models such as the simplified reference tissue model (SRTM) assume time-invariant kinetic parameters, limiting their ability to capture dynamic changes in binding. Existing extensions introduce time-varying effects through parametric response functions or basis expansions, but are often constrained by restrictive functional assumptions, computational complexity, or limited uncertainty quantification. We propose a latent Gaussian process extension of SRTM (LGPE-SRTM), in which the apparent efflux parameter is modeled as a smooth, time-varying function within a hierarchical framework. By applying a first-order implicit discretization of the governing differential equation, the model admits a representation that is linear in all kinetic parameters in the mean structure, while nonlinearity is confined to a parameter-dependent covariance. This yields a conditionally linear mixed-effects model with structured covariance, enabling efficient likelihood-based inference. The proposed approach integrates mechanistic modeling, nonparametric flexibility, and hierarchical inference in a unified and computationally scalable framework. By representing functional effects on a shared temporal domain, all core computations reduce to operations on low-dimensional matrices whose size is independent of the number of subjects. This enables robust population-level inference on timevarying neurotransmitter dynamics without imposing restrictive parametric forms. The method is demonstrated on both simulated and empirical PET data, where it accurately recovers transient effects, provides well-calibrated uncertainty, and distinguishes constant from time-varying dynamics.