This study will use different types of medical imaging to assess how lesions from advanced prostate cancer become resistant to second-generation AR-targeted therapy, and how the different types of imaging compare in that assessment. Participants in this study have advanced prostate cancer and are either scheduled to start a second-generation androgen receptor (AR) targeted therapy (such as enzalutamide, abiraterone, or apalutamide) or are already being treated with one. Participants can expect to be in the study for at least 9 months, and up to 2 years.

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.

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

Men of all races and ethnic groups are eligible for this trial. Women are excluded given that prostate cancer is a male disease.