This phase II trial studies how well fluorine F 18 sodium fluoride positron emission tomography (PET)/computed tomography (CT) and whole body and axial magnetic resonance imaging (MRI) work in finding metastases in patients with recurrent prostate cancer. New imaging techniques, such as fluorine F 18 sodium fluoride PET/CT and whole body and axial MRI, may be more effective than standard CT and bone scan in finding metastatic prostate cancer.

PRIMARY OBJECTIVES:

I. To determine the proportion of patients with biochemically-recurrent prostate cancer (PC) in whom imaging with whole body (WB)/axial MRI and F-18 NaF (fluorine F 18 sodium fluoride) PET/CT results in detection of metastatic disease not visualized on CT scan and bone scan.

SECONDARY OBJECTIVES:

I. To estimate the percent of eligible patients with negative, indeterminate and positive CT scan/bone scan and targeted X-rays if done.

II. To determine the proportion of patients with biochemically-recurrent PC in whom recurrence in the prostate bed can be visualized using MRI in the absence of detection using CT scan.

III. To correlate the presence of metastatic disease detected using WB/axial MRI and/or F-18 NaF PET/CT with the predicted 6-year probability of progression-free survival based on the Memorial Sloan Kettering Cancer Center salvage radiation therapy (RT) PC nomogram, and with prostate-specific antigen (PSA) level at baseline.

IV. To compare the role of axial MRI of the spine to WB/axial MRI with respect to their ability to identify sites of disease. Similarly, to evaluate the relative contribution of F-18 NaF PET and WB/axial MRI.

OUTLINE:

Patients first undergo CT scan and bone scan. Patients with negative results from the CT and bone scans then undergo WB MRI scan using diffusion-weighted MRI, axial MRI scan using 3-Tesla MRI, and fluorine F 18 sodium fluoride PET/CT scan.

After completion of study, patients are followed up at 4-6 months and periodically until week 52.

Inclusion Criteria:

• History of prior radical prostatectomy for prostate cancer
• Two PSA values >= 0.2 ng/mL at least 4 weeks after prostatectomy
• Patients who have started radiographic evaluation and underwent CT scan and/or bone scan prior to registration to the study will be able to participate under a late registration provision, provided that the more modern scans (WB/axial MRI and F-18 NaF PET/CT) can be completed within 8 weeks after CT scan and bone scan

Exclusion Criteria:

• Patients with known metastatic disease
• PSA recurrence not verified by elevated PSA as discussed in the eligibility section
• Patients who initiated androgen deprivation therapy or other systemic therapy (chemotherapy, immunotherapy, targeted therapy) for PSA recurrence; nutritional supplements used for treatment of PSA recurrence will be allowed