Metastatic Prostate Neuroendocrine Carcinoma

This phase II trial studies how well lutetium Lu 177 dotatate works in treating patients with prostate cancer with neuroendocrine differentiation that has spread to other places in the body (metastatic). Neuroendocrine differentiation refers to cells that have traits of both hormone-producing endocrine cells and nerve cells. These cells release hormones into the blood in response to a signal from the nervous system. Hormones are biological substances that circulate through the bloodstream to control the activity of other organs or cells in the body. Lutetium Lu 177-dotatate is a radioactive drug. It binds to a protein called somatostatin receptor, which is found on some neuroendocrine tumor cells. Lutetium Lu 177-dotatate builds up in these cells and gives off radiation that may kill them. It is a type of radioconjugate and a type of somatostatin analog. Treatment with Lutetium Lu 177 dotatate may shrink the tumor in a way that can be measured in patients with metastatic prostate cancer with neuroendocrine differentiation.

This research study is studying a positron emission tomography (PET) agent called 18F-fluciclovine to evaluate how well 18F-fluciclovine-PET scans determine the extent of advanced prostate cancer that either has low prostate-specific membrane antigen (PSMA) expression or has neuroendocrine features. The name of the study interventions are: * 18F-fluciclovine-PET/CT scan * Two research blood collections