PET/CT Characterization of Treatment Resistance

Inclusion Criteria: * Histologically proven adenocarcinoma of the prostate. * At least 1 radiographic metastases as seen on conventional CT imaging or bone scan * Progressive prostate cancer as evident by at least two separate increase in PSA over nadir, and absolute PSA value at least 2 ng/ml (INTRINSIC RESISTANCE COHORT, ARSI patients ONLY) * Patients must be candidate for a second-generation androgen receptor (AR) inhibitor (e.g. enzalutamide, abiraterone, darolutamide, apalutamide), or Lu177-PSMA radioligand therapy (INTRINSIC RESISTANCE COHORT ONLY) * Men of age \>18 years. * Patients must be able to comply with all study procedures, including having both the ability and willingness to lie flat for ≥ 30 minutes during imaging * Patients must be informed of the exploratory nature of the study and its potential risks, and must sign IRB-approved consent form indicating such understanding. * Life-expectancy at least 12 months * Patients currently receiving a second-generation androgen receptor (AR) inhibitor (e.g. enzalutamide, abiraterone, darolutamide, apalutamide) and must have had 1) PSA decline on treatment and 2) now have PSA increase over nadir while still on treatment (patients must be registered within 12 weeks of first documented PSA increase) (ACQUIRED RESISTANCE COHORT ONLY) Exclusion Criteria: * Must not have uncontrolled diabetes (fasting blood sugar \> 200 mg/dL or inability to safely hold diabetes medication or fast 6 hours prior to FDG PET scan) * Prior treatment with second-generation AR inhibitor for prostate cancer in the metastatic disease setting (prior second-generation AR inhibitor in the neoadjuvant or adjuvant setting is permitted unless patient developed progression while on treatment) (INTRINSIC RESISTANCE COHORT, AR-INHIBITOR GROUP ONLY) * Pain or clinical symptoms from metastatic prostate cancer requiring opioid analgesics * Known neuro-endocrine prostate cancer * Prior radioisotope therapy for castration-resistant prostate cancer * To avoid the possibility of unintended coercion, vulnerable populations such as incarcerated subjects, subjects unable to provide their own informed consent and non-English speaking patients will not be considered