Whole Body Fluorine F 18 Sodium Fluoride PET/CT Scan and Whole Body MRI in Finding Bone Metastases in Patients With Prostate Cancer

Inclusion Criteria: * Any ethnic group * Pathologically proven prostate cancer with high risk for bone metastases * Rising prostate-specific antigen (PSA) despite androgen deprivation therapy (ADT), PSA \> 10 ng/mL * Ability to understand and the willingness to sign a written combined Health Insurance Portability and Accountability Act (HIPAA) and informed consent document * Patients Eastern Cooperative Oncology Group (ECOG) performance is =\< 1 Exclusion Criteria: * Patients may not receive any other investigational therapeutic agents from within 7 days prior to study drug administration through 7 days following study drug administration * Patients with known contraindications to MR imaging such as presence of MRI incompatible devices such as pacemakers and certain aneurysm clips, severe claustrophobia, or any other condition which would preclude proximity to a strong magnetic field; this exclusion is a standard of practice * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; patients in this category are excluded to reduce medical risk to their safety and to avoid confounding variables in regard to the possibility of adverse events * Patient is unable to tolerate or has a lifer threatening allergy to the radiopharmaceutical used for bone scan or 18F-fluoride PET