Abstract
323
Objectives Myocardial blood flow (MBF) can be estimated by dynamic PET using various radiotracers. In several cases (eg, Rb-82, C-11 acetate) an empirical fit to the generalized Renkin-Crone (GRC) equation must be used to relate the fitted kinetic parameter K1 to MBF. It is common practice to neglect the uncertainty in the GRC equation and to express the MBF variance in terms of the estimated K1 variance alone. In this work we derived a analytical expression for MBF variance that includes both the K1 variance and the uncertainty in the empirical GRC relation, and show that the latter contributes significantly to the MBF variance.
Methods The MBF variance (varMBF) is comprised of the K1 variance (varK1) and the variance in GRC (varGRC). Because the GRC equation cannot be analytically inverted for MBF as a function of K1, varGRC is commonly neglected. To overcome this limitation, we derived an expression for varMBF using the implicit function theorem and chain rule. An empirical GRC relation was derived from data reported by Lortie et al (EJNMMI 34:1765,2007). The new variance expression was evaluated by fitting 31 clinical rest/dipyridamole stress Rb-82 PET scans to a 1-compartment kinetic model using conventional ROI-based arterial input functions. We compared the standard errors (SE) of global and regional MBF and coronary flow reserve (CFR) from varK1 alone and from our expression for varMBF=varK1+varGRC.
Results Mean global MBF, CFR and standard errors are shown in the table. For MBF, mean SE(K1,GRC) was 57-76% higher than the conventional SE(K1) (p<0.001); for CFR, mean SE(K1,GRC) was 67% higher than SE(K1) (p<0.001). Similar results were observed for regional MBF and CFR.
Conclusions We conclude that the common practice of neglecting the uncertainty in the empirical GRC relations used to relate K1 to MBF leads to a significant underestimation of MBF and CFR uncertainty. The new variance expression derived in this work may be useful in evaluating different kinetic modeling approaches. These results have important implications for clinical use of MBF and CFR to distinguish normal and diseased states