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

Dynamic SPECT is a relatively new technique that may potentially benefit many imaging applications. Though similar to dynamic PET, the accuracy and precision of dynamic SPECT parameter estimates are degraded by factors that differ from those encountered in PET. In this work we formulate a methodology for analytically studying the propagation of errors from dynamic projection data to kinetic parameter estimates. This methodology is used to study the relationships between reconstruction estimators, image degrading factors, bias and statistical noise for the application of dynamic cardiac imaging with 99mTc-teboroxime. Dynamic data were simulated for a torso phantom, and the effects of attenuation, detector response and scatter were successively included to produce several data sets. The data were reconstructed to obtain both weighted and unweighted least squares solutions, and the kinetic rate parameters for a two-compartment model were estimated. The expected values and standard deviations describing the statistical distribution of parameters that would be estimated from noisy data were calculated analytically. The results of this analysis present several interesting implications for dynamic SPECT. Statistically weighted estimators performed only marginally better than unweighted ones, implying that more computationally efficient 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 describe the fundamental limits of the bias variance trade-off regarding physical degrading factors and their compensation. The results characterize the effects of attenuation, detector response and scatter, and they are intended to guide future research into dynamic SPECT reconstruction and compensation methods.