Therapeutic Strategies in Patients With Non-squamous Non-small Cell Lung Cancer With Brain Metastases

Inclusion Criteria: 1. Patients with histologically or cytologically proven non-epidermoid, non-small cell lung cancer, non-EGFR (Epidermal Growth Factor Receptor)-mutated (or mutation test impracticable). 2. Patients with brain metastasis/metastases without neurosurgical indication. 3. Asymptomatic patients (without treatment or with stable steroids or antiepileptic treatments for ≥ 5 days prior to obtaining the baseline MRI of the brain, and ≥ 5 days prior to first dose of study treatment (Cycle 1, Day 1). 4. At least one lesion measurable according to the RECIST (Response Evaluation Criteria in Solid Tumors) criteria. 5. ECOG (Eastern Cooperative Oncology Group) Performance Status 0 - 1 6. No previous chemotherapy for this cancer, apart from adjunctive chemotherapy more than 18 months ago. 7. Prior surgery is authorized in case of documented recurrence or progression. 8. Adequate biological functions (hematologic, platelets, hemoglobin, hepatic function, alkaline phosphatases, ASAT (Aspartate transaminase) and ALAT (Alanine Aminotransferase); creatinine clearance). 9. For women: Effective contraception for women of childbearing age during treatment and for 6 months following treatment. For men: They must be surgically sterile or accept the use of effective contraception until 6 months after the treatment period. 10. Patients of more than 18 years of age. 11. Estimated survival of at least 12 weeks. 12. Consent signed by the patient Exclusion Criteria: 1. Patients presenting with a brain lesion eligible for curative treatment (neurosurgical). 2. Symptomatic brain metastasis/metastases in spite of symptomatic treatment. 3. Epidermoid carcinoma. 4. Con indication of Bevacizumab is furthermore 5. Patients presenting with a brain lesion eligible for curative treatment (neurosurgery or radiosurgery). 6. Symptomatic brain metastasis/metastases in spite of symptomatic treatment. 7. Epidermoid carcinoma. 8. Cons indication of Bevacizumab 9. Inability to take the folic acid or vitamin B12 vitamin supplementation or the dexamethasone premedication (or any equivalent corticosteroid), or any inability to comply with the study procedures. 10. History of cancer, with the exception of cervical cancer in situ, skin cancer other than melanoma, adequately treated low-grade prostatic cancer (Gleason score \<6), unless this cancer was diagnosed and treated more than 5 years ago without any signs of recurrence. 11. Patients presenting with a systemic disorder which, in the investigator's opinion, compromises their participation in the study for reasons related to treatment safety or compliance. 12. Patients incapable of discontinuing their aspirin treatment when the dose is \> 1300 mg/day or their non-steroidal anti-inflammatory treatment two days before the day, on the day and two days the day of administration of pemetrexed (Alimta). 13. Patients presenting with a 3rd sector (pleural effusion, ascites) which is clinically detectable and uncontrollable by simple measures of the evacuatory puncture type or other treatment before inclusion in the study. 14. Patients presenting with neuropathy of grade \> 2 according to the criteria of CTC (Common toxicity Criteria) v3.0. 15. Patients whose foreseeable compliance or geographical distance renders monitoring difficult. 16. Pregnant or breast-feeding women. 17. Significant weight loss (≥ 10%) during the 6 weeks preceding inclusion in the study. 18. Vaccination against yellow fever within 30 days preceding inclusion in the study. 19. Cons-indication to taking steroids 20. Persons deprived of their liberty as a result of a judicial or administrative decision 21. Concomitant participation in another trial