Analytical propagation of errors in dynamic SPECT: estimators, degrading factors, bias and noise

Dynamic SPECT is a relatively new technique that may potentially benefit ma ny imaging applications. Though similar to dynamic PET, the accuracy and pr ecision of dynamic SPECT parameter estimates are degraded by factors that d iffer from those encountered in PET. In this work we formulate a methodolog y for analytically studying the propagation of errors from dynamic projecti on data to kinetic parameter estimates. This methodology is used to study t he relationships between reconstruction estimators, image degrading factors , bias and statistical noise for the application of dynamic cardiac imaging with Tc-99m-teburoxime. Dynamic data were simulated for a torso phantom, a nd the effects of attenuation, detector response and scatter were successiv ely included to produce several data sets. The data were reconstructed to o btain both weighted and unweighted least squares solutions, and the kinetic rate parameters for a two-compartment model were estimated. The expected v alues and standard deviations describing the statistical distribution of pa rameters that would be estimated from noisy data were calculated analytical ly. The results of this analysis present several interesting implications f or dynamic SPECT. Statistically weighted estimators performed only marginal ly better than unweighted ones, implying that more computationally efficien t unweighted estimators may be appropriate. This also suggests that it may be beneficial to focus future research efforts upon regularization methods with beneficial bias-variance trade-offs. Other aspects of the study descri be the fundamental limits of the bias-variance trade-off regarding physical degrading factors and their compensation. The results characterize the eff ects of attenuation, detector response and scatter, and they are intended t o guide future research into dynamic SPECT reconstruction and compensation methods.