Dual-phase multiobjective Bayesian optimization method for estimating hepatocellular carcinoma dynamics parameters from PET/CT scans

Optimization algorithms provide robust analytical frameworks for assessing hepatocellular carcinoma (HCC) pharmacokinetics based on dynamic positron emission tomography/computed tomography (PET/CT) scans. The aim of this study was to assess the role of estimating HCC pharmacokinetics from PET/ CT scans via the Bayesian optimization (BO) method and the dual-phase (DP) and multiobjective (MO) strategies into BO (DPMO-BO) method. Five-minute dynamic and one-minute static PET/CT imaging data derived from 27 HCC tumors were used to estimate kinetic parameters (K1,k2,k3,k4,fa,vb,Ki) via a double-input three-compartment model. The role of pharmacokinetic parameters in distinguishing HCC was compared among the Bayesian method (BM), BO method, and DPMO-BO method. The fitting deviation between the predictions of the model and the actual observations was assessed via the root mean square error (RMSE). The results demonstrated that the BM significantly distinguished HCC from background liver tissues with k2 , k3 , fa , and vb (all P<0.05), whereas the BO method achieved this degree of differentiation for fa and vb (both P<0.001). The DPMO-BO method resulted in significant differences in all of these parameters (K1,k2,k3,k4,fa,vb,Ki) (all P<0.05). DPMO-BO yielded greater area under the receiver operating characteristic (ROC) curve (AUC) values for Ki (AUC =0.709) than did BO (AUC =0.595, P<0.001). Additionally, reduced RMSEs for HCC and normal liver tissues were observed with DPMO-BO (1.226 and 1.051, respectively) relative to those values obtained with the BM (1.324 and 1.118, respectively) and BO (1.308 and 1.143, respectively). The BO method can be used to assess HCC pharmacokinetics, whereas the DPMO-BO method further enhances diagnostic performance by achieving improved fitting accuracy.