Mechanisms of Metabolic and Hormone Action on Plaque Formation in Brain and Carotid Vessels in Patients With Prostate Adenocarcinoma

Inclusion Criteria: * Signed informed consent * Histologically confirmed adenocarcinoma of the prostate * Non-castrate disease with a serum testosterone level \>= 50 ng/dL (1.73 nmol/L) at baseline * No evidence of distant metastatic disease on baseline computed tomography-chest, abdomen and pelvis (CT-CAP) and bone scans * Patients will be stratified by the presence or absence of pre-existing cardiovascular disease defined as at least one of the following: * Prior myocardial infarction \>= 30 days before enrollment * Prior revascularization procedure \>= 30 days before consent, including: * Coronary artery stent placement or balloon angioplasty * Coronary artery bypass graft surgery * Stent placement or balloon angioplasty to a carotid, iliac, femoral, or popliteal artery * Carotid endarterectomy surgery * Vascular bypass surgery of the iliac, femoral, or popliteal artery * Results from angiogram or CT angiogram of coronary, carotic, iliac, femoral, or popliteal arteries that documents at least one vascular stenosis \>= 50% at any time point before enrollment * Carotid ultrasound results that shows stenosis \>= 50% at any time point before enrollment * Ankle-brachial pressure index \< 0.9 at any time point before enrollment * Intent to initiate continuous androgen deprivation therapy (ADT) for at least 12 months Exclusion Criteria: * No prior treatment with ADT at time of study entry. (Prior neoadjuvant/adjuvant ADT is allowed only if the last injection of a depot formulation wore off at least 12 months prior to enrollment) * Previous or concurrent hormonal or systemic therapy for prostate cancer including: anti-androgens, estrogens, megestrol acetate, ketoconazole, abiraterone, enzalutamide, or chemotherapy. (Prior or planned neoadjuvant bicalutamide for prevention of tumor flare is allowed) * Plans to start or continue treatment with an investigational product after enrollment * Poorly controlled type 1 or type 2 diabetes mellitus, based on hemoglobin A1c, as judged by the investigator * Prior or planned surgical castration * Poorly controlled hypertension at time of study entry, as judged by the investigator * Myocardial infarction or stroke \< 30 days prior to enrollment * Coronary, carotid, or peripheral artery revascularization \< 30 days prior to enrollment * Planned or scheduled cardiac surgery or percutaneous coronary intervention (PCI) procedure that is known at the time of enrollment * Mental incapacity or language barrier precluding adequate understanding or cooperation * Inability to tolerate magnetic resonance imaging (MRI) imaging, or both Lupron and Degarelix * Any other clinically significant disorder which may affect the subject's health or the outcome of the trial as judged by the investigator * Estimated glomerular filtration rate (eGFR) \< 45 * History of allergy to gadolinium contrast agent