Radioactive bullet targets Hard-to-Treat prostate cancer

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Willingly participate in this clinical trial, demonstrate a clear understanding of the research procedures, and be capable of signing the informed consent form in person. * Be at least 18 years of age at the time of signing the informed consent form. * Histologically or cytologically confirmed prostate cancer (excluding neuroendocrine or small cell features). * A positive result on the 18F-PSMA-137 PET/CT scan is required. * The serum testosterone levels of the subjects must be maintained at a castrate level (\< 50 ng/dL or \< 1.7 nmol/L). Despite maintaining castrate-level serum testosterone, disease progression was confirmed based on at least one of the following criteria: Progression in PSA was defined as an increase in serum PSA measured twice, one week apart, with the initial value being ≥ 2.0 ng/mL. Soft tissue progression as defined by RECIST v1.1. Bone progression: two new lesions (PCWG3). * Subjects who have previously failed treatment with at least one novel androgen receptor pathway inhibitor (e.g., enzalutamide, apalutamide, and/or abiraterone) and taxane-based therapies are eligible. Prior exposure to purpurane drugs should not exceed two regimens, defined as at least two cycles of treatment with purpurane agents. If the investigator determines that a subject is unsuitable for receiving or re-initiating paclitaxel-based therapy due to reasons such as poor physical condition or intolerance to prior paclitaxel regimens, or if the subject declines further paclitaxel treatment, they may still be enrolled in the study. * Imaging examinations conducted during the screening period of the subjects (within 4 weeks prior to administration) confirmed the presence of one or more metastatic lesions. * Subjects must demonstrate adequate organ function as follows: Bone marrow reserve: Absolute neutrophil count ≥1.5×10\^9/L, platelet count ≥100×10\^9/L, hemoglobin level ≥90g/L. No relevant supportive treatments, including blood product transfusions or granulocyte colony-stimulating factor (G-CSF), should have been administered within 14 days prior to the screening period examination. Liver function: Total bilirubin ≤1.5× upper limit of normal (ULN), alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤3×ULN. In cases of liver metastasis, ALT and AST levels ≤5×ULN are acceptable. Kidney function: Serum creatinine ≤1.5×ULN or creatinine clearance rate (CrCl) ≥60 mL/min (calculated using the Cockcroft-Gault formula). Serum albumin must be ≥3g/dL. * The ECOG PS score must range from 0 to 2. * Expected survival should exceed six months. * Participants must use condoms during sexual intercourse throughout the study period and for 18 weeks following the administration of the last dose of the investigational product to prevent conception and avoid transferring the study drug to their partners via semen. Furthermore, participants are required to refrain from donating sperm during this specified timeframe. Exclusion Criteria: * Within six months prior to the first study treatment, subjects had received systemic or local radioisotope therapy. Subjects who have undergone any prior treatment targeting PSMA are ineligible for participation in the study. * Within 28 days before the first study treatment or within five half-lives of the agent (whichever is shorter), subjects received systemic anti-tumor treatments, including chemotherapy, immunotherapy, small molecule inhibitors, or cell therapy. Within 28 days before the first study treatment, subjects received external beam radiotherapy, with the exception of palliative radiotherapy. Within two weeks before the first study treatment, subjects had received traditional Chinese medicine therapies with anti-tumor indications. * Subjects who have experienced Grade 4 myelosuppression following prior anti-tumor therapy, or Grade 3 myelosuppression requiring more than six weeks for recovery, or who have received external radiotherapy targeting extensive bone marrow (\> 25%) in the past are ineligible. Within 28 days prior to the first study treatment, subjects must not have received blood transfusion therapy. - * The subjects' prior anti-tumor treatment toxicity had not resolved to CTCAE grade ≤1 (NCI CTCAE v5.0), with the exception of alopecia (all grades permitted) and peripheral neuropathy (requiring recovery to grade ≤2). * Within 28 days prior to the first study treatment, subjects must not have participated in other interventional clinical trials or be within five half-lives of the investigational drug, whichever is shorter. * Subjects with a documented history of hypersensitivity reactions to 18F-PSMA-137 and/or 177Lu-PSMA-137 drugs, their excipients, or chemically similar agents are excluded. * Subjects with untreated active brain metastases or meningeal metastases are ineligible. However, subjects with previously treated active brain metastases (e.g., surgery, radiotherapy, gamma knife) who do not require steroid or anticonvulsant therapy, exhibit no symptoms, and demonstrate stable neurological function for at least 28 days may participate. * Subjects with symptomatic spinal cord compression or imaging evidence suggesting imminent spinal cord compression are eligible (subjects who have undergone treatment for spinal cord compression, including surgery and/or radiotherapy, and are currently stable without neurological deficits, may participate in the study); * Bone scans conducted during the screening period reveal findings suggestive of supra-bone imaging abnormalities; * Subjects with claustrophobia or other conditions, such as an inability to lie flat or remain still, that preclude tolerance of imaging examination procedures; * Subjects with poor venous conditions, as assessed, making frequent collection of pharmacokinetic (PK) blood samples impractical (applicable only to subjects participating in the PK study). * The concurrent presence of severe and/or uncontrollable diseases or conditions (as determined by the central researcher), which may compromise subjects' participation in the study, will be excluded. This includes but is not limited to: New York Heart Association (NYHA) Class 3 or 4 congestive heart failure, long QT syndrome or a confirmed family history of long QT syndrome, severe infections requiring intravenous administration of antibiotics, antifungals, or antivirals according to clinical guidelines, active hepatitis B (positive for HBsAg and/or HBcAb with HBV-DNA \> 500 IU/mL or \> 2000 copies/mL), or hepatitis C (positive for anti-HCV with HCV-RNA above the lower limit of detection). * Other malignant tumors diagnosed as potentially affecting life expectancy or interfering with disease evaluation will be considered. Subjects with a history of other malignant tumors prior to enrollment, who have received adequate treatment and have remained disease-free and treatment-free for more than three years, are eligible to participate in the study. Additionally, patients with fully treated non-melanoma skin cancer and superficial bladder cancer are also eligible for participation. * Participants with uncontrollable bladder outlet obstruction or urinary incontinence are excluded. Note: Subjects with bladder outlet obstruction or urinary incontinence that can be managed through the best available standard treatment (e.g., absorbent pads, catheterization, etc.) are eligible for inclusion in the study. * History of any physical or mental health condition deemed by the investigator to potentially compromise the safety or adherence to the drug treatment in this study.