Predictive Factors for Response to Lutetium-177 PSMA Radioligand Therapy in Patients With Metastatic Castration-Resistant Prostate Cancer

The goal of this observational study is to learn which factors can predict how well lutetium-177 PSMA therapy works in people with metastatic castration-resistant prostate cancer (mCRPC). This therapy is a radioactive medicine (Pluvicto) given into a vein. The main questions it aims to answer are: * Can scan results, radiation dose measurements, and blood test results predict which participants will have their prostate-specific antigen (PSA) level drop by half or more? * Can the same results predict how long participants live without their cancer getting worse? All participants receive Pluvicto as part of their regular medical care. Taking part in the study does not change their treatment. Participants will: * Receive up to 6 Pluvicto treatments, about every 6 weeks, as part of regular care * Have a PSMA PET/CT scan (an imaging test that shows where the cancer is) before treatment and after the last treatment, as part of regular care * Have 3 SPECT/CT scans after each treatment (at 3 to 4 hours, 24 hours, and 5 days) to measure how much radiation reached the tumors and organs, as part of regular care * Give 1 extra blood sample (10 ml) after each treatment to measure tumor DNA in the blood. It is taken from the same needle stick as routine blood tests. * Fill in a quality of life questionnaire (SF-36) before treatment and after every second treatment, during their hospital stay * Have check-ups every 4 to 6 months after treatment ends Researchers will also use existing medical records of people who started Pluvicto at the hospital before the study began.