Study of Re-treatment With [177Lu]Lu-PSMA in Men With Metastatic Castration Resistance Prostate Cancer

Inclusion Criteria: * Males ≥ 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 assessed within 7 days of study treatment initiation * Histologically or cytologically confirmed adenocarcinoma of prostate (Patients with small cell carcinoma of the prostate may be included) * Metastatic disease documented by at least one lesion on bone scan or abdominal/pelvic/chest computed tomography (CT) or magnetic resonance imaging (MRI) scan assessed by investigator. Patients without bone metastasis must have measurable lesions in extra-pelvic lymph nodes or in soft-tissues as defined by RECIST 1.1 criteria * Confirmed progression mCRPC despite ongoing androgen deprivation with serum testosterone \< 50ng/dl (1.7nM) within 3 months prior to screening. Progression is defined by the presence of at least one of the following criteria : * PSA progression using local laboratory values as defined by a minimum of 2 consecutive rising PSA levels with an interval of ≥1 week between each assessment where the PSA value at screening should be ≥1 ng/mL * Radiographic disease progression in bone based on PCWG3 criteria defined as the appearance of 2 or more new bone lesions on bone scan, with or without PSA progression * Radiographic disease progression in extra-pelvic lymph nodes based or soft-tissues on RECIST1.1 criteria with or without PSA progression * PSMA positive metastatic lesions on \[68Ga\]-PSMA-PET/CT without PSMA negative lesion (The presence of PSMA-positive lesions is defined as \[68Ga\]-PSMA-11 uptake greater than that of liver parenchyma in one or more metastatic lesions of any size in any organ system. The presence of PSMA-negative lesions is defined as PSMA uptake equal to or lower than that of liver parenchyma in any lymph node with a short axis of at least 2.5 cm, in any metastatic solid-organ lesions with a short axis of at least 1.0 cm, or in any metastatic bone lesion with a soft-tissue component of at least 1.0 cm in the short axis. Patients with any PSMA negative metastatic lesion meeting these criteria are ineligible). * Participants must have been previously treated with at least 4 consecutive cycles of \[177Lu\]Lu-PSMA with no evidence of progression during this first course of treatment (including radiological, clinical but also PSA progression). * Participants must have been previously treated with at least one ARSI - Androgen Receptor Signaling Inhibitors - (including enzalutamide, apalutamide, abiraterone or darolutamide) initiated for mCSPC, nmCRPC or mCRPC. (ARSI may be also administered together with \[177Lu\]Lu-PSMA-617 provided that the patient has not received an identical ARSI in the past and that this ARSI was initiated at least 15 days before the first cycle of \[177Lu\]Lu-PSMA-617 and less than 2 months ago. The ARSI administrated in association with LuPSMA should not be considered as a prior therapy. A previous ARSI treatment is mandatory for patient eligibility) * Patients must have been previously treated with at least one taxane based chemotherapy (with docetaxel or cabazitaxel) (The number of previously administrated lines of taxane-based therapy is not limited ; patients can have received a taxane-based chemotherapy before or after the first sequence of \[177Lu\]Lu-PSMA) * Patients must have been progressed at least 120 days after the last injection of the first course of \[177Lu\]Lu-PSMA therapy. (Patients with a radiological or clinical progressive disease during the first 120 days after the last cycle of the first course of \[177Lu\]Lu-PSMA are not eligible. PSA progression is defined by a ≥ 25% increase in PSA and an absolute increase of 2 ng/mL or more from the NADIR and confirmed by a second consecutive value obtained 3 or more weeks later. Patients treated with chemotherapy, ARSI or PARP inhibitors between the first 117LuPSMA course and screening are also eligible). * Be abstinent from heterosexual intercourse OR must agree to use contraception unless confirmed to be azoospermic (vasectomized or secondary medical cause) until 98 days (14 weeks) post-treatment. * Adequate organ functions : * Bone marrow reserve : * ANC ≥ 1.5 X 109/L * Platelets ≥ 100 X 109/L * Hemoglobin ≥ 10 g/dL * Hepatic : * Total bilirubin ≤ 2 x ULN. For patients with known Gilbert's syndrome ≤ 3 x ULN. * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤3 x ULN * Renal : * Clearance ≥40 ml/mn * Patients must have signed informed consent prior to participating in any study related procedures * Willing and able to comply with the protocol, including follow-up visits and examinations * Patients have to be affiliated to the French social security system, or equivalent Exclusion Criteria: * History of a \[177Lu\]Lu-PSMA serious adverse event (SAE) or CTCAE Grade 3 or 4 AE during the initial course of \[177Lu\]Lu-PSMA that led to the discontinuation of treatment * More than one course of \[177Lu\]Lu-PSMA therapy * Less than 120 days from the last dose administrated in the initial course of \[177Lu\]Lu-PSMA treatment and the radiological or clinical disease progression, or the initiation of a subsequent therapy. * Any history of treatment with radium-223 dichloride or other systemic radiotherapy (including strontium-89, samarium-153, actinium-PSMA...) * Transfusion of red blood cells within 30 days prior to the first injection of the re-treatment of \[177Lu\]Lu-PSMA-617 * Current central nervous system (CNS) metastases * Hypersensitivity to the active substance (Lutetium \[177Lu\] vipivotide tetraxetan or Gallium \[68Ga\] gozetotide) or to any of the excipients * Prior \> hemibody external radiotherapy * Imminent or established spinal cord compression based on clinical findings and / or MRI that has not yet been treated * Other malignancy treated within the last 3 years (except non-melanoma skin cancer or low-grade superficial bladder cancer) * Chronic conditions associated with non-malignant abnormal bone growth (e.g., confirmed Paget's disease of bone) * Ongoing participation in any other clinical trial who may interfere with the present study in the judgment of the investigator * Concurrent serious (as determined by the Principal Investigator) medical conditions, including, but not limited to, uncontrolled infection, known active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the investigator would impair study participation or cooperation. * Active clinically significant cardiac disease * History of somatic or psychiatric disease/condition that may interfere with the objectives and assessments of the study * Patients under tutorship or guardianship