Adaptive Weighted Nonlinear Least Squares Method for Fluorodeoxyglucose Positron Emission Tomography Quantification

Abstract

This study developed an adaptive weighted nonlinear least squares (AWNLS) method for solving the problem of high variability in the estimates of the microrate constants of fluorodeoxyglucose (FDG) kinetics caused by measurement noise. In the AWNLS method for adaptive quantitative analysis, the cost function is adjusted according to the characteristics of the tissue time-activity curve (TTAC). Specifically, the average of the early part of the TTAC was used to modify the cost function when fitting the FDG model to the TTAC. A computer simulation study applying different sets of parameter values and noise conditions was conducted. The accuracy and reliability of the parameter estimates obtained using AWNLS were compared with those of nonlinear least squares (NLS), weighted nonlinear least squares (WNLS), linear least squares (LLS), and generalized linear least squares (GLLS). The errors in k1–k3 obtained using NLS indicate this method’s poor precision in the presence of high noise levels. NLS and WNLS were sensitive to the initial values. Moreover, the results of k4 estimated using LLS and GLLS were inaccurate because of large bias. By contrast, the microrate constants (k1–k4), the FDG metabolic rate (K), and the volume of distribution (k1/k2) obtained using AWNLS were stable and accurate regardless of the noise level and initial values. The AWNLS method could estimate the FDG metabolic rate (K) and the microrate constants (k 1–k 4) of the FDG model accurately at various noise levels, irrespective of the initial values.