Deep neural network-based trust region optimization for estimating the kinetic parameters of hepatocellular carcinoma from dynamic 18F-FDG PET/CT scans

18 F-fluorodeoxyglucose ( 18 F-FDG) positron emission tomography/computed tomography (PET/CT)-based pharmacokinetic analyses can be used to quantitatively characterize hepatocellular carcinoma (HCC), and algorithmic advances have improved the pharmacokinetic parameter estimation process. Trust region optimization (TRO) enables robust estimation, but whether TRO functions in pharmacokinetic analysis remains unclear. TRO, which is represented by trust region Bayesian optimization (TURBO), is preliminarily introduced in this study, and a deep neural network (DNN)-based TRO (DTRO) algorithm is proposed for pharmacokinetic parameter estimation to characterize HCC. Twenty-eight HCC lesions on 24 patients were subjected to five-minute dynamic and one-minute static PET/CT scans. The performances of the pharmacokinetic parameters \((K_{1} ,k_{2} ,k_{3} ,k_{4} ,f_{a} ,v_{b} )\) estimated by TURBO, DTRO and the conventional nonlinear least-squares (NLLS) method in terms of differentiating HCCs from background liver tissues were compared with those of a two-input, three-compartment model. After undergoing incremental learning, the performance of the proposed algorithm was evaluated via the lower root mean square error (RMSE), R 2 values and a receiver operating characteristic (ROC) curve analysis. DTRO achieved the lowest mean RMSEs (HCC: 1.147; liver: 1.009) and highest mean R2 values (HCC: 0.930; liver: 0.912), outperforming NLLS (HCC: 1.245, 0.923; liver: 1.042, 0.906) and TURBO (HCC: 1.200, 0.928; liver: 1.025, 0.909). Moreover, DTRO significantly distinguished HCCs from background liver tissues with all six parameters, whereas TURBO did so with four parameters \((K_{1} ,k_{2} ,f_{a} ,v_{b} )\) and NLLS did so with four parameters \((k_{2} ,k_{4} ,f_{a} ,v_{b} )\) (all P<0.05). The ROC analysis results obtained for \(K_{1}\) and \(k_{3}\) ​ (AUCs: 0.926 and 0.930, respectively) demonstrated that DTRO outperformed both NLLS (AUCs: 0.887 and 0.805) and TURBO (AUCs: 0.897 and 0.821). TRO has proven feasible for pharmacokinetic estimation tasks, with the proposed DTRO algorithm achieving superior performance and offering a reliable foundation for conducting HCC analyses.