Bayesian Posterior Distribution Estimation of Kinetic Parameters in Dynamic Brain PET Using Generative Deep Learning Models.

Positron Emission Tomography (PET) is a valuable imaging method for studying molecular-level processes in the body, such as hyperphosphorylated tau (p-tau) protein aggregates, a hallmark of several neurodegenerative diseases including Alzheimer's disease. P-tau density and cerebral perfusion can be quantified from dynamic PET images using tracer kinetic modeling techniques. However, noise in PET images leads to uncertainty in the estimated kinetic parameters, which can be quantified by estimating the posterior distribution of kinetic parameters using Bayesian inference (BI). Markov Chain Monte Carlo (MCMC) techniques are commonly used for posterior estimation but with significant computational needs. This work proposes an Improved Denoising Diffusion Probabilistic Model (iDDPM)-based method to estimate the posterior distribution of kinetic parameters in dynamic PET, leveraging the high computational efficiency of deep learning. The performance of the proposed method was evaluated on a [18F]MK6240 study and compared to a Conditional Variational Autoencoder with dual decoder (CVAE-DD)-based method and a Wasserstein GAN with gradient penalty (WGAN-GP)-based method. Posterior distributions inferred from Metropolis-Hasting MCMC were used as reference. Our approach consistently outperformed the CVAE-DD and WGAN-GP methods and offered significant reduction in computation time than the MCMC method (over 230 times faster), inferring accurate ( $\lt {0}.{67}\,\%$ mean error) and precise ( $\lt {7}.{23}\,\%$ standard deviation error) posterior distributions.