Performance evaluation of the non-linear and linear estimation methods for determining kinetic parameters in dynamic FDG-PET study

Dynamic positron emission tomography (PET) is a promising diagnostic tool to quantitatively predict biological and physiological changes in vivo through estimation of kinetic parameters. In this work, several popular linear and non-linear estimation methods for determining kinetic parameters using PET imaging with Fluorine-18 fluorodeoxyglucose ([¹⁸F]FDG) are compared and evaluated. The simulation studies are presented. The linear estimation methods include linear least squares (LLS), generalized linear least squares (GLLS) and total least squares (TLS), while the non-linear estimation methods include non-linear least squares (NLS), weighted nonlinear least squares using noisy tissue time activity data (WNLS-N), weighted non-linear least squares using noise-free tissue time activity data (WNLS-NF) and iteratively re-weighted non-linear least squares (IRWNLS). There are several findings: 1. Compared with non-linear estimation methods, GLLS performs well when noise level is low, but worse especially in determining k₃ and k₄ when noise level is high. What's more, GLLS does not show obvious advantage in running time. 2. The choice of weights plays an important role in nonlinear estimation methods. Weighting using noisy data should be avoided. WNLS-NF and IRWNLS perform best. Since the noise-free data can not be obtained in clinical and IRWNLS is time-consuming, NLS is most recommended. 3. Non-linear estimation methods are prone to produce lower-biased, higher-precision parameter estimates, however, also more easily affected by noise. Linear estimation methods are prone to be more biased, however, much more computational efficient and noise robust.