Abstract
623
Objectives Kinetic models are typically fit to dynamic imaging data using weighted least squares (WLS) and related maximum likelihood-type fitting algorithms. This work investigates Bayesian approaches to fitting and analyzing 2-tissue compartment models, and compares them to Separable Parameter Space modeling techniques which permit complete visualization of the nonlinear objective function.
Methods In the Bayesian approach, the multidimensional posterior distribution of kinetic parameters is determined using Markov Chain Monte Carlo sampling. The posteriors, which comprise sets of samples of the values of parameters, can be marginalized to provide 1D and 2D visualizations of particular parameters of interest. In addition to providing point-estimates of the unknown parameters, the covariance (correlations) between parameters can be visualized by means of 2D graphing. This allows intuitive interpretation of the mathematical modeling, and enables visual identification of cases with high to severe correlations that prevent obtaining a reliable estimate. The posteriors can also be marginalized directly to compute posterior distributions of macroparameters (e.g. net influx, volume of distribution), providing graphical characterizations of statistical uncertainty indicative of the reliability of such estimates.
Results Analyses of posterior distributions for dynamic FDG PET data in 10 patients with primary brain tumors reveal strong and visually striking correlations between K1 and k3 parameters. Comparisons with nonlinear minimizations using Separable Parameter Space Compartment Modeling demonstrate differences in the WLS solution and Bayesian point estimates.
Conclusions Bayesian approaches to fitting and analyzing compartment modeling in dynamic PET provide informative visualization of parameter variance and covariance, as well as alternative statistically-meaningful point estimates of parameter values. Such visualizations provide new insight into the robustness and uncertainty inherent to compartment model fits.
Research Support R01CA135556