Effects of noisy weights on Rb-82 MBF estimation

Objectives Weighted least-squares regression is used in the estimation of myocardial blood flow (MBF) with Rb-82 dynamic PET. The regression weights are an effective method to account for nonconstant variance over the time-activity data. In this study we evaluated five weighting methods and used Monte Carlo simulations to assess the effects of noise in the weights on bias and variance of MBF and coronary flow reserve (CFR).

Methods A 1-tissue-compartment model was simulated using a measured Rb-82 image-based arterial input function, typical clinical values of rest MBF, and both normal and abnormal stress MBF. Gaussian-like noise (5-20%) was added to simulated time-activity curves (TAC) with variance proportional to activity concentration and inversely proportional to time-frame duration (TF). Regression weights were assessed based on 5 common variance models (VM): [1] uniform; [2] inverse TF; [3] inverse TF and decay correction (DC); [4] inverse TF and tissue TAC; [5] inverse TF and DC and tissue TAC. For each noise level and variance model 1000 realizations were simulated; K1 estimates were mapped to MBF using a Renkin-Crone model; bias and relative standard deviation (SD) of K1, MBF and CFR were computed.

Results K1 bias was positive (0-4%) for VM1-3 and negative (1-10%) for VM4-5. MBF bias was positive (0-5%) for VM1-3 and negative (2-15%) for VM4-5. Absolute CFR bias was < 3% for VM1-5 at all but the highest noise level (abnormal CFR, VM1: 6%) and (normal CFR, VM4-5: -6%). SD was similar for all VM (K1 SD 3-12%), (MBF SD 5-20%), (CFR SD 6-28%); except at the highest noise level, for which VM2 was lowest, 3-9% lower than VM5.

Conclusions VM4 and VM5 use noisy TACs to estimate data variance. These yield noisy weights which produced increased negative bias in K1, MBF and CFR, and significantly higher SD at high noise levels. Weights from VM1-3 are noise-free and produced smaller bias and SD than VM4-5. We conlude that even when the variance model matches noise present in the data (VM5), noisy weights may result in greater MBF and CFR bias and SD than mismatched but noise-free weights.