PET/CT Characterization of Treatment Resistance

There are two groups, or cohorts, in this study. Participants are assigned to Cohort A if they have advanced prostate cancer and are scheduled to start a second-generation AR-targeted therapy (such as enzalutamide, abiraterone, darolutamide, or apalutamide) or PSMA directed radiotherapy (e.g. Lu177-PSMA radio-ligand therapy. Participants are assigned to Cohort B if they have advanced prostate cancer, are already on a second-generation AR-targeted therapy, and have shown an increase in their PSA (prostate-specific antigen) levels. There are two medical imaging scans that will be done for research purposes in this study. One is called 18F-fluorodeoxyglucose positron emission tomography (FDG PET) and the other is prostate-specific membrane antigen positron emission tomography (PSMA PET). These scans are done simultaneously with computed tomography (CT) scanning. Participants will be scheduled to have 6 scans, 3 FDG PET/CT scans and 3 PSMA PET/CT scans.