Linear least squares method for MBF estimation from 0-15 water PET: error analysis

Linear least squares (LLS) method for estimating MBF and generating of MBF parametric image was developed. In this study, computer simulation was performed to investigate the statistical properties of LLS method using simulated input function and tissue time activity curves contaminated by various level of Poisson noise. Noiseless tissue time-activity curves were generated with the single compartment model using an average LV input function obtained from the canine experiments. PTF. p, and Va values were fixed at 0.55 g/ml, 0.91 ml/g, and 0.2 ml/ml, respectively. MBFp value varied between 0.5∼0.4 ml/min/g. Pseudo random noise was added to each frame of tissue time-activity curve to simulate the noisy measurements. To simulate Poisson noise, the measurement error variance was taken to be proportional to the radioactivity concentration and inversely proportional to the scan length. The scaling factor that determines the level of noise varied between 0.25∼3.0. 10,000 realizations were produced for all the simulations at each noise level. MBFp and other parameters were estimated using nonlinear least squares (NLS) and LLS methods, and coefficient of variation (CV), error, and bias in the estimation of MBFp were calculated. As the true MBF decreased and noise level increased, CV, error, and bias in the estimation of MBFp were increased. LLS showed lower CV, error, and bias than NLS in almost conditions. Reduction of CV and error by the LLS method was approximately 35% and 25%, but the bias reduction was dependent on the true MBF level. LLS method for the estimation of MBF and related parameters improved statistical reliability in the parameter estimation compared to the conventional NLS method and would be useful for the generation of parametric images