Study of 177Lu-PSMA-0057 in Metastatic Prostate Cancer

Inclusion Criteria: * Male, age\>18 years old; * The expected life must be\>9 months (determined by the researcher); * Eastern Cooperative Oncology Group(ECOG) score 0-2 points; * Suffering from prostate adenocarcinoma confirmed by histological or cytological examination (current or previous prostate and/or metastatic site biopsy); * Patients with high PSMA uptake (standardized uptake value (SUV) max ≥ salivary gland or proximal small intestine, or SUVmax ≥ 12) at the lesion site displayed on 68Ga-PSMA-0057 positron emission tomography / computer tomography(PET/CT) scan, and without FDG positive but PSMA negative lesions; * There are diagnostic documents confirming metastatic prostate cancer; * The patient must have ≥ 1 detectable metastatic lesion in the bone and/or soft tissue/visceral area, which is present on baseline CT, MRI, or bone scan imaging obtained ≤ 28 days prior to the start of study treatment; * Lymphatic and skeletal metastases or visceral metastases that cannot be removed through surgery; * After ADT treatment, the disease continues to progress; * The patient must have recovered to ≤ 2 levels from all clinically significant toxicity associated with previous treatments (i.e. chemotherapy, radiotherapy, immunotherapy, etc.); * The functions of important organs meet the following requirements: 1. Bone marrow reserve: White blood cell (WBC) count ≥ 2.5 × 10 \^ 9/L or absolute neutrophil count (ANC) ≥ 1.5 x 10 \^ 9/L; Platelet count ≥ 100 x 10 \^ 9/L; Hemoglobin ≥ 90g/L. 2. Liver: Total bilirubin ≤ 2 times the upper limit of normal value (ULN) (excluding subjects confirmed to have Gilbert's disease, no more than 10 times the ULN is sufficient); AST and ALT: ≤ 2 times ULN for those without liver metastasis or ≤ 3 times ULN for those with liver metastasis. 3. Kidney: Serum/plasma creatinine ≤ 1.5 times ULN or creatinine clearance rate ≥ 50 mL/min. * Albumin\>25 g/L; * Agree to use appropriate methods of contraception during the study period and within 1 month after the end of administration; * Signed informed consent form. Exclusion Criteria: * Received radioisotope diagnosis or treatment (such as 89Sr, 153Sm, 186Re, 188Re, 223Ra) before enrollment, or received PSMA targeted radioligand therapy; * Received systemic anti prostate cancer treatment such as chemotherapy, PARP inhibitors, immunotherapy or biotherapy (including monoclonal antibodies) within 28 days prior to enrollment; * Received any other study drug diagnosis/treatment within 28 days prior to enrollment, unless it is an observational (non intervention) clinical study or an intervention clinical study follow-up; * Other accompanying cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy; * Known to be allergic to any research treatment or its excipients, or to drugs of similar chemical categories; * Unable to lie flat, remain stationary, or tolerate PET/CT imaging; * Severe urinary incontinence, hydronephrosis, severe urinary dysfunction, or the need for indwelling a catheter for any reason; * There are contraindications to furosemide, including known allergies or intolerance to furosemide or sulfonamide drugs; * Patients with central nervous system (CNS) metastasis accompanied by neurological instability or symptoms or receiving corticosteroids to maintain neurological integrity. If epidural diseases, spinal canal diseases, and previously affected areas of the spinal cord have been treated, stabilized, and have no neurological damage, they are eligible to participate in the study. For patients with a history of CNS metastasis to the brain parenchyma (or CNS metastasis), baseline and subsequent radiological imaging must include brain evaluation (preferably magnetic resonance imaging (MRI) or enhanced CT); Note: Patients with a history of CNS metastasis who have previously received treatment, have stable neurological function, are asymptomatic, and have not received corticosteroid treatment are allowed to be included in the group. * Diagnosed as other malignant tumors that are expected to change life expectancy or may interfere with disease assessment. However, patients with a past history of malignant tumors, who have been fully treated and have no disease for more than 3 years are eligible to participate in the study, and patients with fully treated non melanoma skin cancer and superficial bladder cancer are also eligible to participate in the study; * The presence of clinically significant active heart disease is defined as any of the following: Within 6 months before signing the ICF, New York Heart Association(NYHA) grade 3/4 congestive heart failure, unless improved after treatment, and if the echocardiogram shows ejection fraction(EF) \>45%, the symptoms improve to\<grade 3; Previous or current diagnosis of ECG abnormalities indicates significant safety risks for study participants, such as accompanying clinically significant arrhythmias such as persistent ventricular tachycardia, complete left bundle branch block, and high degree atrioventricular (AV) block (such as double bundle branch block, Mobitz II type, and third degree atrioventricular block); A family history of familial long QT syndrome or known family history of torsade de pointe ventricular tachycardia; Cardiac abnormalities or cardiac repolarization abnormalities, including any of the following: a history of myocardial infarction (MI), angina pectoris, or coronary artery bypass grafting (CABG) within 6 months prior to signing the ICF. * Complicated with any serious and/or uncontrollable diseases or other diseases that may affect the subject's participation in this study as determined by the investigator, as follows: Uncontrolled diseases (such as hypertension patients' blood pressure ≥ 150/100 mmHg or diabetes patients' fasting blood glucose ≥ 8mmol/L or 2h after meal blood glucose ≥ 11mmol/L); Life threatening autoimmune and ischemic diseases; Suffering from any other disease that may increase the risk of toxic reactions (such as nephrotic syndrome, uremia, acute or severe cholinergic syndrome, etc.); Clinically severe gastrointestinal dysfunction, including active ulcerative colitis, intestinal obstruction, intestinal bleeding, diarrhea, Crohn's disease, or the need for intravenous nutrition treatment; * The disease progresses rapidly and the expected survival period is less than or equal to 3 months; * Known to have bilateral hip joint prostheses; * Positive individuals with Immunodeficiency virus antibodies(HIV-Ab) or treponema pallidum antibody(TPAb) during the screening period (examination); * Complicated serious (determined by the main investigator) medical diseases, including but not limited to uncontrolled infections, known active hepatitis B or C, or other major comorbidities that the investigator believes may harm research participation or cooperation; * A history of physical or mental illness/condition that may interfere with the purpose and evaluation of the study; * Symptomatic spinal cord compression, or clinical or radiological findings indicating imminent spinal cord compression; * Any situation that hinders the position of raising the arm; * According to the judgment of the researchers, there are other factors that may lead to the subject being forced to terminate the study midway, such as non-compliance with the protocol, suffering from other serious illnesses (including mental illness) that require concurrent treatment, clinically significant laboratory test values that are severely abnormal, family or social factors that may affect the safety of the subject or the collection of experimental data.