Abstract
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Objectives In PET kinetics modeling, a compartment model can be described in differential equations with kinetic parameters. Although the estimation of the rate constants requires nonlinear curve fitting techniques, conventional methods are quite vulnerable to high-level noise. In this study, we assessed the feasibility of a particle swarm optimization (PSO) method for indirect and direct kinetic parameter estimation, which is insensitive to initial values and robust to local minima.
Methods To enhance the estimation accuracy and calculation speed, we propose a modified PSO algorithm which is partially linearized for a two-tissue compartment model equation and requires the nonlinear estimation of only two parameters. We evaluated the PSO algorithm in terms of bias and variation in parameters by analyzing time-activity curves (TACs) with 1,000 realizations of Gaussian noise at two different noise levels (0.5 and 1) added. We also simulated a dynamic PET image of a phantom containing five regions. The image was then projected to sinogram space and corrupted with Poisson noise. Finally, we applied PSO and the conventional Levenberg-Marquardt algorithm (LMA) to the reconstructed PET images from the noisy sinogram (indirect estimation) and incorporated the PSO into the reconstruction process (direct reconstruction).
Results The PSO showed much lower bias and variance for the four parameters (K1-k4) from the noisy TACs and required less computation time (approximately 50%) than LMA. In indirect estimation for simulated phantom data, root-mean-square-errors (RMSEs) of LMA for K1, k2, k3 and k4 maps were 0.11, 0.51, 0.11 and 0.65 and RMSEs of PSO were 0.037, 0.23, 0.058 and 0.030, respectively. The PSO-based direct reconstruction yielded lower RMSEs of 0.033, 0.23, 0.058 and 0.030. In addition, the direct reconstruction showed much better convergence properties than MLEM for dynamic frames.
Conclusions The results of this study suggest that PSO allows robust estimation of kinetic parameters in noisy environments and appears more promising in a direct kinetic parameter reconstruction framework.