Variance Estimation for Myocardial Blood Flow by Dynamic PET

The estimation of myocardial blood flow (MBF) by 13 N-ammonia or 82 Rb dynamic PET typically relies on an empirically determined generalized Renkin-Crone equation to relate the kinetic parameter K1 to MBF. Because the Renkin-Crone equation defines MBF as an implicit function of K1, the MBF variance cannot be determined using standard error propagation techniques. To overcome this limitation, we derived novel analytical approximations that provide first- and second-order estimates of MBF variance in terms of the mean and variance of K1 and the Renkin-Crone parameters. The accuracy of the analytical expressions was validated by comparison with Monte Carlo simulations, and MBF variance was evaluated in clinical 82 Rb dynamic PET scans. For both 82 Rb and 13 N-ammonia, good agreement was observed between both (first- and second-order) analytical variance expressions and Monte Carlo simulations, with moderately better agreement for second-order estimates. The contribution of the Renkin-Crone relation to overall MBF uncertainty was found to be as high as 68% for 82 Rb and 35% for 13 N-ammonia. For clinical 82 Rb PET data, the conventional practice of neglecting the statistical uncertainty in the Renkin-Crone parameters resulted in underestimation of the coefficient of variation of global MBF and coronary flow reserve by 14-49%. Knowledge of MBF variance is essential for assessing the precision and reliability of MBF estimates. The form and statistical uncertainty in the empirical Renkin-Crone relation can make substantial contributions to the variance of MBF. The novel analytical variance expressions derived in this work enable direct estimation of MBF variance which includes this previously neglected contribution.